PUBLIC REASON

Journal of Political and Moral Philosophy Public Reason is a peer-reviewed journal of political and moral philosophy. Public Reason publishes articles, book reviews, as well as discussion notes from all the fields of political philosophy and ethics, including political theory, applied ethics, and legal philosophy. Texts from other areas of philosophy may be published, if they are relevant for issues in moral and political philosophy. The journal encourages the debate around rationality in politics and ethics in the larger context of the discussion concerning rationality as a philosophical problem. Public Reason is committed to a pluralistic approach, promoting interdisciplinary and original perspectives as long as the ideals of critical thinking and clarity are respected. The journal is intended for the international philosophical community, as well as for a broader public interested in political and moral philosophy. Public Reason publishes two issues per year, in June and December. Public Reason is an open-access e-journal, but it is also available in print. Public Reason is an open-access journal, which does not charge authors a processing fee – neither directly nor indirectly (where applicable) through the author’s institution of affiliation. Hence, publication-related decisions are not made on financial considerations Public Reason is available online at http://publicreason.ro ISSN 2065-7285

EISSN 2065-8958

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Editors

Editors in Chief

Romulus Brancoveanu, University of Bucharest Sorin Baiasu, Keele University

Associate Editor

Thomas Pogge, Yale University

Editorial Team

Assistant Editors

Mircea Tobosaru, University of Bucharest

Carmen-Viviana Ciachir, University of Bucharest Editorial Board

Ovidiu Caraiani, University Politehnica of Bucharest Luigi Caranti, University of Catania

Radu Dudau, University of Bucharest

Mircea Dumitru, University of Bucharest

Adrian - Paul Iliescu, University of Bucharest Ferda Keskin, Istanbul Bilgi University

Laurentiu Gheorghe, University of Bucharest Alina Romascu, Université de Corse Pasquale Paoli Constantin Stoenescu, University of Bucharest Ion Vezeanu, University of Grenoble

Advisory Board

Radu J. Bogdan, Tulane University

Paula Casal, University of Reading

Fred D’Agostino, University of Queensland Rainer Forst, Goethe University, Frankfurt am Main Gerald Gaus, University of Arizona

Axel Gosseries Ramalho, Catholic University of Louvain Alan Hamlin, University of Manchester

John Horton, Keele University

Janos Kis, Central European University, Budapest Jean-Christophe Merle, University of Tübingen Adrian Miroiu, SNSPA Bucharest

Adrian W. Moore, University of Oxford

Philippe Van Parijs, Catholic University of Louvain Mark Timmons, University of Arizona

PUBLIC REASON Journal of Political and Moral Philosophy Vol. 13, No. 2, 2021 & Vol. 14, No. 1, 2022

ARTICLES SARAH PATTERSON

Descartes on Modality and the Eternal Truths 3

Jonathan Head

Divine Simplicity and Freedom in Descartes - Comments on Sarah Patterson’s ”Descartes on Modality and the Eternal Truths” 18

Jennifer Bunker Infinity and Beyond? Learning How to be Finite 23

Pablo Montosa Molinero Learning How to be Finite 38

Sorin Baiasu The Possibility of Kantian Armchair Knowledge 44

Zachary Vereb Kantian Reflections on Conceptual Limits 68

Michael Morris Nonsense and the General Form of the Sentence 76

Oliver Thomas Spinney Truth-Functional Logic and the Form of a Tractarian Proposition 92

Adrian W. Moore Replies 97

Public Reason 14 (1): 3-17

Descartes on Modality and the Eternal Truths

Sarah Patterson

Birkbeck University of London

Abstract. Descartes maintained that God freely created all eternal truths. Yet, while it is impossible for necessary truths to have been otherwise, if they are a matter of God’s free choice, then it seems that they could have been otherwise. Adrian W. Moore (2020) offers a solution to this conflict that, he claims, Descartes “could and should” have adopted. This article argues that Descartes’s position is in a sense closer to Moore’s solution than Moore permits, yet proposes an arguably more accurate account via the Cartesian relationship between omnipotence, indifference, and the dependence of the eternal truths on God. Omnipotence and indifference do not express that God might have created the necessary truths in another way, but rather that God’s decrees are in no way determined by anything other than God. Thus, alternative possibilities are not relevant to this account, since there were none before God’s creative act.

Keywords: Descartes, God, eternal truths, Creation Doctrine, modality, indifference, omnipotence, essence, arithmetic, Aquinas, Adrian W. Moore.

Descartes is notorious for his doctrine that God freely created the eternal truths, including the truths of arithmetic. One of the texts in which he voices this Creation Doctrine is a letter to Arnauld of 1648:

I do not think we should ever say of anything that it cannot be brought about by God. For since every basis of truth and goodness [omnis ratio veri & boni] depends on his omnipotence, I would not dare to say that God cannot bring it about that there is a mountain without a valley or that one and two are not three. I merely say that he has given me such a mind that I cannot conceive a mountain without a valley, or a sum of one and two which is not three; such things involve a contradiction in my conception. (Letter to Arnauld, 29 July 1648, AT V 223-4, CSMK 358-9*)[1]

Here Descartes very nearly says that God can bring it about that one plus two is not three. As Moore notes (2020, 103, n 10), Descartes does not quite say this; he says that he dare not deny it. But in an earlier letter, he is more forthright:

[I]t was free and indifferent for God to make it not true that the three angles of a triangle were equal to two right angles, or in general that contradictories cannot be true together... the power of God cannot have any limits…[This] consideration shows us that God cannot have been determined to make it true that contradictories cannot be true together, and therefore that he could have done the opposite. (Letter to Mesland, 2 May 1644, CSMK 235*, AT IV 118)

If Descartes is prepared to say that God could have made it not true that the angles of a triangle sum to two right angles, presumably he is also prepared to say that God could have made it not true that one plus two is three. However, Descartes also describes such truths as necessary:

[I]t is because [God] willed that the three angles of a triangle should necessarily equal two right angles that this is true and cannot be otherwise; and so on in other cases. (Sixth Replies, CSM II 291, AT VII 432)

But there seems to be a conflict here. If it is necessary that one and two sum to three, then it is impossible that it should be otherwise; there is no other possibility for the sum of one and two. But if one and two summing to three is a matter of God’s free choice, then it seems that it could be otherwise – that there are other possibilities that God could have brought about. Indeed, this seems to be just what Descartes is saying in the passages from the letters to Arnauld and to Mesland. So how should we interpret Descartes’s view?

1. MOORE’S INTERPRETATION OF DESCARTES

Adrian Moore’s paper ‘What Descartes Ought to Have Thought About Modality’ offers an ingenious interpretation of Descartes’s view, defended with typical elegance. The interpretation is guided by what Moore regards as Descartes’s core conception of the possible, namely ”whatever does not conflict with our human concepts” (2020, 102, quoting Descartes’s Second Replies). As Moore points out, if it conflicts with our human concepts that there should be a sum of one and two that is not three, then it also conflicts with our human concepts that God should make a sum of one and two that is not three (2020, 103). Now, Descartes can allow that the mere fact that some proposition conflicts with our concepts is no bar to God’s making it true; there is no conflict with our concepts in affirming that (2020, 105). But when it comes to God’s making it true that one and two do not sum to three, that does conflict with our concepts, so Descartes should not regard it as possible (2020, 105). Hence, if Descartes thinks that the Creation Doctrine makes it possible for one plus two to be other than three, he is thinking contrary to his own definition of possibility. Since that definition implies that a sum of one and two that is not three is an absolute impossibility that not even God can bring about, Moore argues, passages such as those in the letters to Arnauld and Mesland should be set aside as lapses (2020, 103-4).

What leads Descartes astray, according to Moore? One of the factors Moore points to is Descartes’s reluctance to set limits on God’s power, something evident in both the letters quoted earlier. Here Moore says that Descartes ”could and should” have followed the example of Aquinas, who holds that it is no limitation on God’s power to be unable to do the impossible (2020, 106). Aquinas writes:

[T]hat which implies being and non-being at the same time is repugnant to the idea of an absolutely possible thing...such cannot come under the divine omnipotence, not because of any defect in the power of God, but because it has not the nature of a feasible or possible thing. …Hence it is better to say that such things cannot be done, than that God cannot do them. (Aquinas, Summa Theologica I.25.3)

Aquinas says that whatever implies contradiction does not have the nature of a possible thing. When it comes to the impossible, there is nothing, so to speak, to do; so it is no limitation on the power of God to be unable to do it. To say that God cannot do the impossible is not to restrict the possibilities that God can realise, to exclude some possibilities from the scope of his power, because there are no possibilities to be excluded.

Moore interprets the Creation Doctrine itself along similar lines. The doctrine is that God freely created the eternal truths; the truth and necessity of any necessary truth depends on God’s free choice (2020, 107). But, Moore points out, this dependence need not be interpreted in terms of the exclusion of possibilities. In saying that one plus two is three because God made it so, we need not say that in making it so, God excluded other possibilities; and we should not say that, because there are no other possibilities (2020, 107). The doctrine ought rather to be interpreted in terms of explanatory priority: one plus two’s being three is explained by God’s decree, but does not explain it (2020, 108). That is how the eternal truths depend on God’s choice, and it is compatible with their being necessary truths.

I’m sympathetic to Moore’s wish to reconcile the Creation Doctrine with the necessity of the eternal truths, and I agree that thinking of the Creation Doctrine in terms of dependence, rather than the exclusion of possibilities, is a fruitful way of doing this. That is an important point. However, on my reading of him, Descartes already sees the Creation Doctrine in terms of dependence, and he already, like Aquinas, denies that God’s omnipotence requires that he be able to bring about the impossible. Indeed, Descartes writes in a letter to More that it is no defect of power in God to be unable to do the impossible:

[W]e do not take it as a mark of impotence when someone cannot do something which we do not understand to be possible...we do not...perceive it to be possible for what is done to be undone – on the contrary, we perceive it to be altogether impossible, and so it is no defect of power in God not to do it. (Letter to More, 5 February 1649, CSMK 363, AT V 273)

As I see it, Descartes’s views of God’s omnipotence and the eternal truths are closer to the views Moore recommends to him than Moore allows. However, I also see Descartes as holding those views for reasons that are different, I think, from those that Moore attributes to him. For Moore’s Descartes, what is and is not possible depends on human concepts: ”it is necessary that one plus two is three” means, ”in other words”, that ”our human concepts conflict with one plus two’s being anything other than three” (2020, 107). As I read Descartes, what is and is not possible depends not on human concepts, but on the essences freely created by God. So Descartes as I interpret him is in one way close to and in another way distant from Descartes as Moore interprets him: close insofar as he thinks what Moore says he ought to think, but distant insofar as he thinks it for different reasons. The interpretation I offer is motivated by the connection Descartes sees between God’s omnipotence, God’s indifference, and the dependence of the eternal truths on God, a connection I explore in the next section. This interpretation will, I hope, offer a way of accommodating the problematic passages in the letters to Arnauld and Mesland, rather than regarding them as lapses.

2. THE DEPENDENCE OF THE ETERNAL TRUTHS ON GOD

The Creation Doctrine makes its first appearance in three letters to Mersenne of 1630. In the first letter, it is couched in terms of dependence. Descartes writes:

The mathematical truths which you call eternal have been laid down by God and depend on him entirely no less than the rest of his creatures. Indeed to say that these truths are independent of God is to talk of him as if he were Jupiter or Saturn and to subject him to the Styx and the Fates. (Letter to Mersenne, 15 April 1630, CSMK 23, AT I 145; emphasis added)

So mathematical truths are just as dependent on God as his other creations, and to deny this dependence is to speak of God in a way that is unworthy of him. But how does Descartes understand this dependence of the eternal truths on God? As Moore says, it is a question of priority. In the second letter, Descartes writes:

I say once more that [the eternal truths] are true or possible only because God knows them as true or possible. They are not known as true by God in any way which would imply that they are true independently of him. If men really understood the sense of their words they could never say without blasphemy that the truth of anything is prior to the knowledge that God has of it. In God willing and knowing are a single thing in such a way that by the very fact of willing something he knows it and it is only for this reason that such a thing is true. (Letter to Mersenne, 15 April 1630, CSMK 24*, AT I 149)

For Descartes, to say that God knows that one plus two is three because it is true is to insult God by denying the dependence of this truth on him. Rather, we must say that it is true because God knows it – or, rather, God both knows and wills it by a single act.

So far, God’s power has not been mentioned; so how is this implicated in the Creation Doctrine? A passage in the Sixth Replies sheds light on this. According to the Creation Doctrine, God freely created the eternal truths. But what kind of freedom is involved? Descartes explains:

As for the freedom of the will, the way in which it exists in God is quite different from the way in which it exists in us. It is self-contradictory to suppose that the will of God was not indifferent from eternity with respect to everything that has happened or will ever happen […]. (CSM II 291*, AT VII 431).

And he adds that ”the supreme indifference to be found in God is the supreme indication of his omnipotence” (CSM II 292, AT VII 432). This marks a key connection between indifference and power; indifference is a sign of omnipotence. What is the nature of this indifference? The passage above continues:

[F]or it is impossible to imagine that anything is thought of in the divine intellect as good or true, or worthy of belief or action or omission, prior to the decision of the divine will to make it so. I am not speaking here of temporal priority; I mean that there is not even any priority of order, or nature, or of ”rationally determined reason” [ratione ratiocinata] as they call it […] (CSM II 291, AT VII 432)

God’s will is indifferent, then, because it is not constrained by any prior ideas in his intellect. Descartes claims that God does not think of anything as true or good prior to his willing it to be so. And he goes on to link this claim to the Creation Doctrine: God did not will that the angles of a triangle should be equal to two right angles because he recognised that it could not be otherwise; rather, it is because he willed that the angles of a triangle should necessarily equal two right angles that ”this is true and cannot be otherwise” (CSM II 291, AT VII 432).

We can now see why God’s indifference is the indication of his omnipotence. If God understood it to be true that one plus two is three prior to his willing it to be so, he would be constrained to will in accordance with this truth; his will would not be indifferent, but constrained. But his omnipotence would also be compromised, because this truth would be true independent of his willing it to be so; its truth would not be dependent on his decree. The same idea appears in the letters in which the Creation Doctrine first emerges. In the second letter to Mersenne, Descartes complains that ”most people do not regard God as a being who is infinite and beyond our grasp, the sole author on whom all things depend” (CSMK 24-5, AT I 150; emphasis added). If God is the sole author on whom all things depend, and the eternal truths are things, then God is the author of the eternal truths; their truth depends on him alone as creator. Conversely, if it were true that one plus two is three prior to God’s willing it to be so, God would not be the author of this truth. Descartes underlines this by adding that if people truly understood that ”God is a cause whose power surpasses the bounds of human understanding”, they would see that ”since the necessity of these truths does not exceed our knowledge, these truths are therefore something less than, and subject to, the incomprehensible power of God” (CSMK 25, AT I 150). To claim that it is true that one plus two is three prior to God’s willing it to be so is to limit God’s power by claiming that there are truths fixed independently of the exercise of that power, truths of which he is not the author.

On the view we see here, then, God’s freedom in creating the eternal truths, and the omnipotence that this indicates, is understood in terms of his being the indifferent author of those truths. They exist–that is, they are true–because he willed and understood them to be true (so he is their author), and nothing determined him to will and understand them to be true (so he is their indifferent author).[2] If God’s indifference is understood in terms of the absence of any determining factors, it does not imply the existence of alternative possibilities.[3] Moreover, Descartes’s conception of God’s indifference is incompatible with the existence of alternative possibilities for the eternal truths. The next section illustrates this point by comparing Descartes’s view with more orthodox conceptions of the eternal truths.

3. An unorthdox view

One of the hallmarks of Descartes’s view is his claim that in God, the act of willing and the act of understanding are the same.

In God willing and knowing are a single thing in such a way that by the very fact of willing something he knows it and it is only for this reason that such a thing is true. (Letter to Mersenne, 6 May 1630, CSMK 24, AT I 149)

[T]here is always a single identical and perfectly simple act by means of which [God] simultaneously understands, wills and accomplishes everything. (Principles of Philosophy I.23, CSM I 201, AT VIIIA 14)

[N]or should we conceive any precedence or priority between his intellect and his will; for the idea we have of God teaches us that there is in him only a single activity, entirely simple and entirely pure. (Letter to Mesland, 2 May 1644, CSMK 235, AT IV 119)

This contrasts with the more orthodox view that distinguishes between God’s intellect and his will. On the orthodox view, there is some similarity between the creative acts of God and human acts of creation. The human artist’s knowledge and understanding–matters of the intellect–enable her to grasp the creative possibilities; acts of will enable her to put her ideas into effect. This division between intellect and will appears in Aquinas’s description of how God acts:

[E]ffects pre-exist in Him after the mode of intellect, and therefore proceed from Him after the same mode. Consequently, they proceed from Him after the mode of will, for His inclination to put in act what His intellect has conceived appertains to the will. (Summa Theologica I.19.4)

This picture of God as conceiving through intellect and effecting through will dovetails with Aquinas’s account of God’s omnipotence. Aquinas says that a thing is said to be ”absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey” (Summa Theologica I.25.3). The idea of a human donkey is the idea of something that does and does not have the essence of a human; it implies being and not-being at the same time, so it is ”repugnant to the idea of an absolutely possible thing”, as Aquinas puts it in the passage quoted earlier. Since it is not a possible thing, there is no idea of it that could be the object of an act of will. Hence, it does not come within the scope of God’s power; not (as Aquinas puts it) ”through lack of power, but through lack of possibility, such things being intrinsically impossible” (On the Power of God, 1.3).

Descartes’s view is different. As he sees it, to say that some things are intrinsically possible or impossible is to say that they are possible or impossible independently of God. The picture of God understanding essences through his intellect and effecting through his will must be rejected, because it means that God is limited to selecting among the alternatives compatible with the essences understood through the intellect. That is incompatible with God’s indifference, because it means that God’s will is limited by prior understanding.[4] It is also incompatible with his status as sole author on whom all things depend. If we think of God as choosing from a menu of possibilities grasped by the intellect, as it were, then his choice is restricted by the author of the menu; he is not the sole author on whom all things depend. If God is sole author, he writes the menu; he creates possibilities and necessities themselves. As Descartes puts it in the Principles of Philosophy, ”God alone is the true cause of everything which is or can be” (PP I.24, CSM I 201, AT VIIIA 14; emphasis added).[5] Thus, possibilities and necessities, including the eternal truths, must be the products of God’s will as well as being the objects of his intellect. So ”his understanding and willing does not happen, as in our case, by operations that are in a certain sense distinct one from another” (PP I.23, CSM I 201, AT VIIIA 14). Rather, God creates truths by a single act that is both understanding and willing.

4. The problematic letters

How can this understanding of Descartes’s unorthodox account help us with the problematic passages in the letters to Arnauld and Mesland? It might seem that we are back to square one. If God creates truths by an act of willing, and that act is free, then surely God could have done otherwise; he could have made it not true that one plus two is three. And Descartes seems to say as much in the letter to Mesland:

[I]t was free and indifferent for God to make it not true that the three angles of a triangle were equal to two right angles, or in general that contradictories cannot be true together... the power of God cannot have any limits…[This] consideration shows us that God cannot have been determined to make it true that contradictories cannot be true together, and therefore that he could have done the opposite […]. (Letter to Mesland, 2 May 1644, CSMK 235, AT IV 118).

If God could have done otherwise, we want to say, surely it is possible that the angles of a triangle should not sum to two right angles, or that one and two should not sum to three. Hence, this is one of the passages that Moore describes as a lapse on Descartes’s part.

However, if we interpret ”he could have done the opposite” as an allusion to God’s indifference–as meaning that his power was not determined by any prior understanding–then it need not invoke any alternative possibilities. And there is good reason not to interpret it as invoking alternative possibilities, because God did not create alternative possibilities. Later in the same letter, Descartes writes that our minds are

[…] so created as to be able to conceive as possible the things which God has wished to be in fact possible, but not to be able to conceive as possible things which God could have made possible, but which he has nevertheless wished to make impossible. (Letter to Mesland, 2 May 1644, CSMK 235, AT IV 118)

Here too, Descartes alludes to things that God could have made possible. But we should not interpret this as alluding to a realm of alternative possibilities, including the possibility of one and two not summing to three. God has not created any such alternative possibilities. Rather, we should interpret it as an allusion to the fact that nothing determined God to create as he did.

Let’s return to the Arnauld letter, which Moore also identifies as a lapse. Descartes writes:

[S]ince every basis of truth and goodness depends on his omnipotence, I would not dare to say that God cannot bring it about that there is a mountain without a valley or that one and two are not three. (Letter to Arnauld, 29 July 1648, AT V 223-4, CSMK 358-9*)

Descartes holds that it is impossible for there to be a mountain without a valley (or an uphill without a downhill) or for one and two not to sum to three; and he holds that this is so because of God’s decree. But nothing determined God to make that decree; rather, the basis of truth depends on God’s omnipotence. So Descartes’s ”I would not dare to say” can be read, not as a scholastic scruple, but as an unwillingess to say something that could suggest that God was not indifferent (and so omnipotent) in making those decrees.[6] Such an interpretation does not imply that the existence of an alternative possibility for the sum of one and two.

5. Necessity, possibility and human concepts

I concur with Moore in understanding the dependence of the eternal truths on God in a way that does not imply the existence of alternative possibilities. But I think that our reasons for eschewing such possibilities are different. Moore says that there are no other possibilities for the sum of one and two because ”it is necessary that one plus two is three–in other words,…our human concepts conflict with one plus two’s being anything other than three” (2020, 107). He adds that the necessity of one plus two’s being three ”holds because of how God has made our human concepts’”(2020, 107). Similarly, Moore writes that according to Descartes’s core conception of possibility:

When we say that God could not make one plus two anything other than three, we do not describe any limitation on the part of God then. We make an anthropocentric claim. We advert to our own human concepts. We say that these concepts would be contradicted by God’s making one plus two anything other than three. (2020, 106)

This suggests that, as Moore reads Descartes, there is no more to the necessity of one plus two’s being three than its relation to our human concepts. It is because our concepts would be contradicted by one plus two’s being anything other than three that there are no other possibilities, and so we should not understand God’s creation of this necessary truth in terms of the exclusion of other possibilities.

On the interpretation I have been sketching, the necessity of the eternal truths is not tied to human concepts in this way. A remark in the Sixth Replies provides textual support for the view that Descartes does not tie the necessity of these truths to human concepts. He writes, ”we should not suppose that the eternal truths depend on the human intellect or other existing things; they depend on God alone, who, as the supreme legislator, has ordained them from eternity” (CSM II 294, AT VII 436). But though this text is suggestive, it could be reconciled with Moore’s reading if God ordains the eternal truths by making human concepts a certain way. Stronger textual support for my reading comes from a passage in the Fifth Meditation. Claiming that existence is inseparable from God, just as the fact that its angles sum to two right angles is inseparable from the essence of a triangle (CSM II 46, AT VII 66), Descartes writes:

It is not that my thought makes it so, or imposes necessity on any thing; on the contrary, it is the necessity of the thing itself, namely the existence of God, that determines my thinking in this respect. (CSM II 46, AT VII 67).

This passage strongly suggests that the necessity of a triangle’s angles summing to two right angles depends not on our thought or our concepts but on the essence of the triangle itself, which Descartes regards as created by God.

But what of the passage in the Second Replies that guides Moore’s interpretation? Doesn’t that show that Descartes grounds necessity and possibility in human concepts? The passage in question forms part of Descartes’s response to an objection to his Fifth Meditation argument for the existence of God. The objection is that existence can be affirmed of God only if God’s nature is possible. Descartes responds,

But please notice how weak this qualification is. If by ”possible” you mean what everyone commonly means, namely ”whatever does not conflict with our human concepts”, then it is manifest that the nature of God, as I have described it, is possible in this sense […]. (CSM II 107, AT II 150)

As Moore notes (2020, 102, fn. 5), Descartes does not commit himself to this understanding of ”possible”, but describes it as the commonly understood meaning. Moore adds, though, that that context shows that Descartes ”has no stake in understanding the possible in any other way” (ibid.). I draw a different moral from what Descartes says about other ways of understanding possibility. He writes:

Alternatively, you may well be imagining some other kind of possibility that relates to the object; but unless this matches the first kind of possibility, it can never be known [cognosci] by the human intellect […]. (CSM II 107, AT II 150)

Significantly, Descartes does not repudiate this putative ”other kind of possibility that relates to the object”. Instead, he makes an epistemological point: that we know or recognise possibility through compatibility with our concepts. But that epistemological point is compatible with the view that the possibility we recognise has an underlying metaphysical foundation. Compatibility with our concepts captures the extension of ”possible”, as it were, but that need not mean that it captures what makes something possible.[7] The Creation Doctrine fills in the rest of the story; it tells us that possibilities and necessities are created by God. On the view I am attributing to Descartes, the reason we should not understand God’s free creation of the eternal truths in terms of other possibilities is that God did not create any such possibilities, and there are no possibilities unless God creates them.

6. CAN THE ETERNAL TRUTHS CHANGE?

If God was not determined to make it not true that contradictories cannot be true together, does that mean that he might now make them true together? Leibniz certainly thought that the Creation Doctrine has that consequence:

[T]he belief that God was the free author…of truth and of the essence of things…opens the door to the most exaggerated Pyrrhonism: for it leads to the assertion that this proposition, three and three make six, is only true where and during the time when it pleases God; that it is perhaps false in some parts of the universe; and that perhaps it will be so among men in the coming year. (Theodicy §180, quoting Bayle approvingly)

Descartes addresses this worry in the first of the 1630 letters to Mersenne, through the following imaginary dialogue:

It will be said that if God had established these truths he can change them as a king changes his laws. To this the answer is: Yes he can, if his will can change. ”But I understand them to be eternal and unchangeable”. - I make the same judgement about God. ”But his will is free”. – Yes, but his power is beyond our grasp. (Letter to Mersenne, 15 April 1630, CSMK 23, AT I 145)

Here Descartes says that God can change the eternal truths, if his will with respect to them can change. But the clear implication is that his will cannot change with respect to them; the truths, like God, are eternal and unchangeable. Why can his will not change, if it is free? Descartes responds that God’s power is beyond our grasp. God has the power to bind himself, by establishing the eternal truths through his free decree.[8] Descartes explains this in response to Gassendi:

[J]ust as the poets suppose that the Fates were originally established by Jupiter, but that after they were established he bound himself to abide by them, so I do not think that the essences of things, and the mathematical truths which we can know concerning them, are independent of God. Nevertheless I do think that they are immutable and eternal, since the will and decree of God willed and decreed that it should be so. (Fifth Replies, CSM II 261, AT VII 380)

LaCroix (1984, 50) makes a helpful distinction between God’s undetermined power and God’s self-determined power. God establishes the eternal truths through his undetermined power; that is, he is not determined by any prior understanding in creating them. But having established them, he is determined by them; they are immutably and eternally true, and cannot change.

Moore raises the worry that if we treat the letter to Arnauld as expressing Descartes’s considered view, then supreme power extends to making contradictions true, and this means that Descartes cannot escape from scepticism (2020, 113). The worry is that if the ”deceiver of supreme power” mentioned early in the Second Meditation has the power to make contradictions true, Descartes cannot say that ”he will never bring it about that I am nothing so long as I think that I am something” (CSM II 17, AT VII 25). Like Moore, I do not think Descartes needs to worry that God might change the eternal truths; and as I have been suggesting, if we read the Arnauld letter as alluding to God’s undetermined power, his supreme indifference in creating the eternal truths, supreme power need not be the power to falsify eternal truths or make contradictions true. Apart from this, though, I think that the worry about the Second Meditation is misplaced, because the role of the deceiver in the project of the Meditations does not turn on the extent of its power. Detailed defence of this claim would take us too far afield, so I shall elaborate briefly (and contentiously).

Two powerful beings are invoked in the First Meditation, an ”omnipotent God who made me the kind of creature that I am” (CSM II 14, AT VII 21) and ”some malicious demon of the utmost power and cunning” (CSM II 15, AT VII 22). The latter is the being mentioned in the passage in the Second Meditation, so I shall discuss him first. Now, the malicious demon is not introduced in the First Meditation as a reason for doubt. Instead, the pretence of deceit by such a demon is presented as a device to counteract habitual assent to familiar opinions, opinions that have already been shown to be doubtful for other reasons (CSM II 15, AT VII 22).[9] Moreover, the demon’s deceit is presented as specifically targeting beliefs based on reliance on the senses, beliefs in the existence of ”the sky, the air, the earth, colours, shapes, sounds and all external things” (ibid.), rather than beliefs about numbers.[10] Given Descartes’s broader aims, there is good reason for this. The Meditations is a text that is intended to change readers’ minds by introducing them to new metaphysical principles, ones ”that destroy the principles of Aristotle”, as he put it in a letter of 1641 (CSMK 173, AT III 298).[11] In Descartes’s view, this change of mind involves the revision of a complex of erroneous opinions grounded in childhood reliance on the senses.[12] The First Meditation doubt plays a crucial role in this; Descartes himself says that ”its greatest benefit lies in freeing us from all our preconceived opinions, and providing the easiest route by which the mind may be led away from the senses” (Synopsis, CSM II 9, AT VII 12). It is significant, then, that the pretence of deceit by a demon targets both the senses and such preconceived opinions as the belief that we are ”so bound up with a body and with senses that [we] cannot exist without them” (CSM II 16, AT VII 25). If the demon is employed simply as a device to enforce doubt, it need not wield supreme power, and is not hostage to questions about Descartes’s conception of divine power as it figures in the Creation Doctrine.

Let me turn to Descartes’s invocation of ”an omnipotent God” who may have created me so that ”I go wrong every time I add two and three or count the sides of a square” (CSM II 14, AT VII 21). Unlike the demon, this being is explicitly introduced in order to provide a reason for doubt; so doesn’t the scope of that doubt depend on what Descartes means by ”supreme power” in the context of the Creation Doctrine? I think the answer is ”No”. Descartes himself says that this doubt can motivated without recourse to the notion of a being of supreme power. Initially, he motivates the doubt by invoking the figure of an omnipotent God ”who made me kind of creature that I am” and who might have ”created me such that I am deceived all the time” (CSM II 14, AT VII 21). But he goes on to provide a reason for doubt addressed to those ”who would prefer to deny the existence of so powerful a God rather than believe that everything else is uncertain” (ibid.). Those who reject so powerful a creator must posit some less powerful cause for their existence, such as ”chance or fate or a continuous chain of events” (ibid.). And Descartes argues that ”the less powerful they make my original cause, the more likely it is that I am so imperfect as to be deceived all the time” (ibid.). This yields a dilemma: if we originate in an omnipotent creator, that creator has the power to give us a deceitful nature; if we originate in a less powerful cause, our natures are also likely to be so imperfect as to lead us astray. The source of Descartes’s sceptical worry, then, lies in the possibility that we have natures that are so imperfect that we are deceived all the time.13 The possibility of a being of supreme power is not required in order to motivate this worry, and so it is unaffected by questions about what exactly such power amounts to in the context of the Creation Doctrine. What is relevant to Descartes’s worry about our natures as knowers is God’s role as creator of those natures, not God’s power over what it is we know. For these reasons, then, I think that the interpretation of the Creation Doctrine is irrelevant to the dialectical role of the powerful beings invoked in the Meditations.

7. HOW DOES GOD CREATE ETERNAL TRUTHS?

When Descartes unveiled the doctrine that God created the eternal truths in the 1630 letters, Mersenne evidently asked what necessitated God to create them. Predictably, Descartes responds that nothing necessitated him to create them:

[H]e was free to make it not true that all the radii of the circle are equal–just as free as he was not to create the world. And it is certain that these truths are no more necessarily attached to his essence than are other created things. (Letter to Mersenne, 27 May 1630, CSMK 25, AT I 152)

Here we see again God’s indifference; nothing determines God to create as he does. But Mersenne’s question reflects the worry: if God is not necessitated to will the eternal truths, what makes them necessary? This worry is expressed in this passage from Suárez:

Those enunciations are not true because they are known by God [i.e. are in the divine intellect], but rather they are thus known because they are true; otherwise no reason could be given why God would necessarily know them to be true. For if their truth came forth from God Himself, that would take place by means of God’s will; hence it would not come forth of necessity, but voluntarily. (Suárez, Metaphysical Disputations 31.12.40)

The worry is that if the truth of the eternal truths depends on God’s will, then they cannot be necessary. As we have seen, Descartes rejects this claim. For him, the eternal truths are necessary not because God is determined by them, but because God wills and understands them to be necessary, and thereby creates them as such. What then is it to create eternal truths? It might seem pointless to ask, since it would certainly be no surprise if we were unable to comprehend this. But Descartes’s remarks suggest that he does have a story about what God does to create eternal truths. In explaining to Mersenne that God is the total and efficient cause of the eternal truths, he writes that God is

[…] the author of the essence of created things no less than of their existence; and this essence is nothing other than the eternal truths. (CSMK 25, AT I 152; emphasis added)

This suggests that God creates the eternal truths by creating essences, or what Descartes elsewhere calls ”true and immutable natures” (Fifth Meditation, CSM II 44, AT VII 64). So rather than essences pre-existing in God’s intellect, as they do for Aquinas, God brings them into being by a creative act that combines both willing and understanding. However, this view is compatible with Descartes’s holding that the eternal truths exist in God’s intellect, an interpretation for which Rozemond (2008) makes a strong case.[14] Seen in this way, then, Descartes’s view of the ontology of the eternal truths looks quite traditional; it is his view of their origin that is unorthodox. But despite the unorthodox character of the Creation Doctrine, if we interpret Descartes’s more provocative statements about God’s powers with respect to these truths in terms of God’s indifference, we may be able to see how the eternal truths can depend on God’s will and yet be necessary.

s.patterson@bbk.ac.uk

REFERENCES

AT: Oeuvres de Descartes. 1904. Edited by Charles Adam and Paul Tannery. Paris: Vrin.

CSM: The Philosophical Writings of Descartes, Volumes I and II. 1984-5. Edited and translated by John Cottingham, Robert Stoothoff and Dugald Murdoch. Cambridge: Cambridge University Press.

CSMK: The Philosophical Writings of Descartes, Volume III. 1991. Edited and translated by John Cottingham, Robert Stoothoff, Dugald Murdoch and Anthony Kenny. Cambridge: Cambridge University Press.

Aquinas, Thomas. 1952. On the Power of God (Quaestiones disputatae de potentia Dei). Translated by the English Dominican Fathers. Westminster, Maryland: Newman Press.

Aquinas, Thomas. 1947. Summa Theologica. Translated by the Fathers of the English

Dominican Province. Cincinnati: Benzinger Bros.

Aquinas, Thomas. 1955-7. Summa Contra Gentiles. Translated by Anton C. Pegis. New York: Hanover House.

Arnauld, Antoine. 1990. On True and False Ideas: New Objections to Descartes’ Meditations and Descartes’ Replies. Translated and edited by Elmar J. Kremer. Lewiston, New York: The Edwin Mellen Press.

Carriero, John. 2009. Between Two Worlds: A Reading of Descartes’s Meditations. Princeton: Princeton University Press.

Garber, Daniel. 1986. Semel in vita: The Scientific Background to Descartes’s Meditations. In Essays on Descartes’s Meditations, edited by Amelie Oksenberg Rorty. Berkeley: University of California Press.

Hatfield, Gary. 1986. The Senses and the Fleshless Eye: The Meditations as Cognitive Exercises. In Essays on Descartes’s Meditations, edited by Amelie Oksenberg Rorty. Berkeley: University of California Press.

Kaufman, Dan. 2002. Descartes’s Creation Doctrine and Modality. Australasian Journal of Philosophy, 80 (1): 24-4.

LaCroix, Richard R. 1984. Descartes on God’s Ability to do the Logically Impossible. Reprinted in René Descartes: Critical Assessments, Vol. III, edited by Georges J. D. Moyal. London: Routledge, 1991.

Leibniz, Gottfried Wilhelm. 1951. Theodicy. Translated by E. M. Huggard, edited by Austin Farrer. London: Routledge.

Moore, A. W. 2020. What Descartes Ought to Have Thought about Modality. In The Logical Alien: Conant and His Critics, edited by Sofia Miguens. Cambridge, Massachusetts: Harvard University Press.

Patterson, Sarah. 2012. Doubt and Human Nature in Descartes’s Meditations. Royal Institute of Philosophy Supplement, 70: 189-217.

Rozemond, Marleen. 2008. Descartes’s Ontology of the Eternal Truths. In Contemporary Perspectives on Early Modern Philosophy: Essays in Honour of Vere Chappell, edited by Paul Hoffman, David Owen and Gideon Yaffe. Peterborough, ON: Broadview Press.

Suárez, Francis. 1983. On the Essence of Finite Being as Such, on the Existence of that Essence and Their Distinction. Translated and edited by Norman J. Wells. Milwaukee: Marquette University Press.

1] Quotations are marked with an asterisk when the translation in CSM or CSMK has been altered.

2] An important qualification needs to be registered here. I take it that it is compatible with Descartes’s view for God’s act of willing and understanding to flow from his nature. Indeed, it may require it, since Burman reports him as saying that God’s decrees cannot be separated from him and that they are completely necessary as well as completely indifferent (CSMK 348, AT V 166). So God’s act may be determined in the sense of flowing from his nature, but it is not determined by his understanding of truths holding independently of his decrees, since there are none. In what follows, I suppress this qualification.

3] This interpretation of God’s freedom is championed in Kaufman (2002), a paper to which I am much indebted.

4] Aquinas writes that ”if God’s will is determined to will something through the knowledge of His intellect, this determination of the divine will will not be due to something extraneous”, because God’s intellect and will both belong to his essence (Summa contra Gentiles, I.82.8). For Descartes, by contrast, the determination of God’s will by prior truths grasped by his intellect is incompatible with his indifference.

5] This passage is quoted by Kaufman (2002, 36).

6] This reading is defended at length in LaCroix (1984), to which I am much indebted. See pp. 50-52.

7] Compare: Descartes says that he uses the term ”thought” to include everything that is in us in such a way that we are immediately conscious of it (Second Replies, CSM II 113, AT VII 160). That tells us the extension of the word; it tells us how to pick thoughts out. But that is compatible with thoughts’ having an underlying nature that is distinct from being conscious, such as involving ideas (and so being directed on objects). This is suggested by the definition of ”idea” (ibid. and Third Meditation, CSM II 25, AT VII 36-7). Of course, this example is even more controversial than the modal one.

8] As noted by LaCroix (1984, 42) and Kaufman (2002, 38).

9] Descartes writes, ”my habitual opinions keep coming back, and, despite my wishes, they capture my belief... In view of this, I think it will be a good plan to turn my will in completely the opposite direction and deceive myself, by pretending for a time that these former opinions are utterly false and imaginary” (CSM II 15, AT VII 22). The pretence of deception by a malicious demon is introduced as a way to execute this plan.

10] This focus reappears when the pretence is reasserted at the start of the Second Meditation: ”I will suppose then, that everything I see is spurious. I will believe that my memory tells me lies, and that none of the things it reports ever happened. I have no senses. Body, shape, extension, movement and place are chimeras” (CSM II 16, AT VII 24).

11] In this now famous passage, Descartes writes to Mersenne that the six Meditations contain all the foundations of his physics, and that he hopes that readers ”will gradually get used to my principles, and recognise their truth” before they notice their anti-Aristotelian character (Letter to Mersenne, January 1641, CSMK 173, AT III 298).

12] This interpretation is developed more fully in Patterson (2012). For other interpretations stressing the role of doubt as a tool for cognitive reform in the Meditations, see Carriero (2009), Garber (1986) and Hatfield (1986).

13] It is for this reason that Carriero, who provides further textual evidence for this interpretation, refers to the doubt as the ”imperfect-nature doubt” (2009, 56).

14] Rozemond concludes that ”the view that the eternal truths have objective being in God’s mind seems to fit nicely into Descartes’s various remarks about their status”(2008, 53). She adds that the view accommodates their status as eternal, accommodates Descartes’s distinction between God’s creation of these truths and his imprinting them on our human minds, and enables him to avoid the claim that they have a real existence distinct from God (ibid.).

© 2022 by Public Reason

Public Reason 14 (1): 18-22

Divine Simplicity and Freedom in Descartes – Comments on Sarah Patterson’s ”Descartes on Modality and the Eternal Truths”

Jonathan Head

Keele University

Abstract. This paper offers a brief response to Patterson’s paper, ”Descartes on Modality and the Eternal Truths”, which itself is at least in part a response to Moore’s paper, ‘What Descartes ought to have thought about morality”. After reviewing some relevant points from both Patterson’s and Moore’s papers regarding the question of the divine creation of necessary truths, I focus on the possible consequences of Descartes’ understanding of divine simplicity for this interpretive debate. I argue that, by bearing Descartes’ commitment to a strong form of divine simplicity in mind, we can see how he can both be committed to a voluntaristic account of the creation of divine truths and yet indicate that God could not have created things in another way.

Keywords: Descartes, God, necessity, modality, omnipotence, divine simplicity.

Before I consider Dr. Patterson’s illuminating and interesting paper, I want to begin introducing the questions we are concerned with here by discussing Prof. Moore’s paper concerning a possible tension in Descartes’ treatment of God and modality. On the one hand, Moore notes (2020, 101-2), we have statements in favour of a strong voluntarism, that God created the necessary truths solely by an act of divine will, alongside a claim that the inconceivability of a conceptual impossibility does not entail that God could not have created things that way. On the other, we find the claim that possibility is linked to conceivability and that we can rule out something as impossible for God to bring about on the basis of its inconceivability for us. As it is inconceivable for us that the necessary truths could have been otherwise, we can claim that God could not have created the necessary truths otherwise. On the surface, then, we have a straightforward contradiction, with Descartes stating both that God could and could not have created the necessary truths otherwise.

Moore’s answer to this tension in his paper is to claim that the voluntarism expressed in the correspondence and elsewhere is an unfortunate lapse. Descartes should not have stated that necessary truths could have been otherwise, given his official position regarding the nature of possibility and claims regarding what we can clearly and distinctly perceive, and he was potentially led astray by his desire to not impiously limit God’s omnipotence (Moore 2020, 102-3). Moore argues that the Thomist position that God is not limited by being unable to create the impossible is open to Descartes. While we can say that there are things God could not create, this is merely a claim in reference to what we can coherently conceptualise, and not one regarding a limitation on God’s power (2020, 106-7). The necessary truths are necessary because they depend on God, in the sense that the way that they are can be solely explained on the basis of a decree of God’s will (2020, 107 et passim). There are many subtle and interesting points made in Moore’s paper, but I will focus my comments here on the excellent paper by Patterson, though some of what I have to say is relevant to both papers.

Patterson’s intention is to incorporate Descartes’ gestures towards voluntarism within his official position. The argument here suggests a negative construal of Descartes’ account of divine indifference: “God’s indifference is understood in terms of the absence of any determining factors”. (7)[1] God is indifferent and omnipotent because his decrees are not pre-determined in any way, not because he could have acted otherwise in creating the necessary truths that he did create. There are no alternate possibilities implied by the account, because there are no possibilities prior to God’s creative action to be ruled out. As such, there is nothing that is intrinsically possible or impossible, apart from God’s decrees (9). In this way, we can claim that God creates the necessary truths solely through his will (in the sense that they depend on his will and are not pre-determined) and that God could not have made the necessary truths otherwise.

A question we could put to this argument is how we are to read Descartes’ reference to God being able to ‘do the opposite’ with regard to the creation of eternal truths. Patterson argues that any reference by Descartes to God being able to ‘do the opposite’ should be taken as alluding to the divine will not being pre-determined, rather than committing his account to the possibility of God acting otherwise. In addition, we also find the suggestion that Descartes’ claim that he “would not dare to say that God cannot bring it about that there is a mountain without a valley” should be read carefully within its context, which reveals that Descartes is unwilling to rule something out without adverting to what we can clearly and distinctly conceive (rather than claiming that he is unwilling to state that God could not have acted otherwise in creating the eternal truths) (11-12).

There is also a concern that Descartes’ voluntarism leads to sceptical consequences, which is particularly worrisome when he bases his system on clear and distinct perceptions of what must be the case. Patterson explains that though the eternal truths are freely adopted by God, he is now bound to maintain them due to his unchanging will (on this basis, we can make a useful distinction between the divine undetermined and self-determined power), and thus the sceptical worries regarding changing certainties are avoided (13-15). Finally, Patterson addresses the question of what makes the necessary truths necessary on a Cartesian account. The answer is that these necessary truths are embodied in immutable natures, maintained by God’s unchanging will. Thus, the eternal truths can both be necessary and depend entirely on God’s indifferent will (18-19). The tension is resolved: the eternal truths were freely created by God as an action solely dependent on the divine will, yet at the same time things could not have been otherwise in that regard.

Patterson’s paper raises many interesting questions. One possible topic for discussion could be the notion of ”indifference” that Descartes is operating with here. As Kaufman has argued (2003b, 401), there are hints that Descartes sees the kind of indifference enjoyed by God as involving the freedom to do otherwise. As I noted earlier, Patterson’s paper involves a solely negative construal of divine indifference, based around a lack of constraint. However, is it possible to claim that God has indifference if he is not ruling out various possibilities? Does Descartes hold a merely negative account of divine indifference? I think it would be fair to say that indifference of the will was most usually thought of at the time as involving the freedom to do otherwise and so the burden of interpretive proof is perhaps leaning against Patterson here. We could also focus on the distinction drawn by Patterson between divine undetermined and self-determined power (13). Would Descartes wish to say that God’s power is ever used in an entirely undetermined way? Such a claim would seem to make God’s use of his power unacceptably arbitrary (amongst other things, potentially undermining the importance of other aspects of the divine, such as his perfect goodness).

Another question that I wonder about is whether it is possible to find an interpretation of the texts in question that rather more takes Descartes at his word. As scholars, we should undoubtedly pause before attributing the kind of lapse to Descartes that Moore wishes to impute to him. Further, while Descartes certainly puts things in terms of the dependence thesis that both Moore and Patterson discuss, it is unavoidable that he also puts matters in terms of alternative possibilities – there are other things that God could have done, for example, he could have made 1+2=4, but he did not do so (and of course, this links back to the question of divine indifference). So, can we find an interpretation of Descartes that avoids accusing him of a major lapse and perhaps gives a more natural reading of Descartes’ references to alternative possibilities and indifference of the will? There are a couple of strands in Descartes’ thought that can perhaps help us, and I will discuss these both briefly in turn before I conclude: 1) Descartes’ commitment to a strong form of divine simplicity (noted by Patterson (8-9), and 2) the distinction drawn by Conant between conception and apprehension in Descartes’ epistemology (1991, 120).

One of the many intriguing points that Patterson raises as potentially significant is Descartes’ approach to divine simplicity (8), the claim that God has no parts and his essence is inextricably intertwined with his attributes: “All the attributes which we include in the concept of the divine nature are so interconnected that it seems to us to be self-contradictory that any one of them should not belong to God”. (Descartes 1984, 107) Though the doctrine of divine simplicity is generally agreed upon, there is quite some contention in the theological tradition regarding how this plays out in greater detail. Descartes seems to have a commitment to a strong version of this doctrine, according to which we cannot even conceptually distinguish between different facets of the divine (see Kaufman 2003a for an examination of this view). It is this claim that ultimately commits Descartes to voluntarism, for there is nothing logically to pre-determine God’s decision to create the eternal truths. It just happens ‘all at once’, as it were. But I think we might consider whether this doctrine also might help resolve the apparent tension that we find in Descartes’ texts.

As I mentioned earlier, while Descartes certainly does not want to undermine divine omnipotence by holding that God’s will is pre-determined by his nature, neither does he want to state that God’s will is merely arbitrary. I think a hint of this is found in a quote from Descartes’ conversation with Burman, from 1648: “For although God is completely indifferent with respect to all things, he necessarily made the decrees he did, since he necessarily willed what was best, even though it was of his own will that he did what was best. We should not make a separation here between the necessity and indifference that apply to God’s decrees; although his actions were completely indifferent, they were also completely necessary”. (1991, 348) How should we make sense of this quote? Though it seems paradoxical, Descartes claims the Cartesian God is both free and necessitated. Insofar as the divine will is not pre-determined by the divine intellect, voluntarism is true: God created the necessary truths freely by an act of will. Though we cannot conceive of it, we can nevertheless grasp in some sense that things could have been otherwise with regard to the necessary truths and God could have (in some sense) created things in that way (and it is here that I refer to the second strand, where we follow Conant (1991, 120) in distinguishing between conception and apprehension in Descartes’ epistemology – I apprehend that the eternal truths could have been different, even though I cannot strictly conceive of it). However, at the same time, once we grasp the interconnecting nature of divine simplicity, we see that (in another sense) God could not have created things in another way. God’s nature as a whole acts as a simultaneous constraint on what he can will, but this is not a constraint that would negate the freedom of his will and a commitment to voluntarism (insofar as the will is not pre-determined). It is perhaps in this way that we could combine the convincing argument found in this paper concerning the dependence thesis with Descartes’ apparent reference to God being able to act otherwise. Regardless, the importance of Descartes’ notion of divine simplicity seems to me to be of particular importance here and thus of something potentially worthy of further discussion in regard to this topic.

j.m.head@keele.ac.uk

REFERENCES

Conant, James. 1991. “The Search for Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus”. Philosophical Topics 20 (1): 115-80.

Descartes, Rene. 1984. The Philosophical Writings of Descartes: Vol. 2. Translated by John Cottingham, Robert Stoothoff and Dugald Murdoch. Cambridge: Cambridge University Press.

Descartes, Rene. 1991. The Philosophical Writings of Descartes: Vol. 3. Translated by John Cottingham, Robert Stoothoff, Dugald Murdoch and Anthony Kenny. Cambridge: Cambridge University Press.

Kaufman, Dan. 2003a. “Divine simplicity and the eternal truths in Descartes”. British Journal for the History of Philosophy 11 (4): 553-79.

———2003b. “Infimus gradus libertatis? Descartes on Indifference and Divine Freedom”. Religious Studies 39 (4): 391-406.

Moore, Adrian. 2020. “What Descartes ought to have thought about morality”. In The Logical Alien: Conant and His Critics, edited by Sofia Miguens, 101-16. Cambridge, MA: Harvard University Press.

Patterson, Sarah. 2022. “Descartes on Modality and the Eternal Truths”. Public Reason 13 (2)-14 (1): 3-17.

1] Unattributed references are to Patterson (2021).

© 2022 by Public Reason

Public Reason 14 (1): 23-37

Infinity and Beyond? Learning How to be Finite Jennifer Bunker

Roehampton University Abstract. This article discusses the newly added Chapter 16 and Chapter 17 of Adrian W. Moore’s latest edition of The Infinite from 2019. The article interprets Moore’s focus on metaphysical infinity and finitude via his trialogue between Spinoza, Hegel, and Nietzsche. Then, it continues to examine Moore’s mode of addressing nihilism, which consists of reckoning with the infinite as a concept we appeal to when trying to express the insights which sustain value and our moral lives. Following this discussion, four questions are posed to Moore: two regarding his interpretation of the history of philosophy, upon which his views are based; and two regarding his own views. One question focuses on differentiation in Spinoza. The second question concerns the interpretation of Nietzsche’s Eternal Return. The third asks for a motivation for superseding Nietzsche’s finitism. The fourth calls into question the strength of Moore’s proposal of “reckoning with” the infinite.

Keywords: Spinoza, Hegel, Nietzsche, infinity, finitude, value, nihilism, Wittgenstein, Deleuze, Eternal Return, differentiation, delineation, negation, metaphysics, Adrian W. Moore.

1. Exposition

In 2019 Professor Moore – Adrian – published the latest edition of his very first book, The Infinite. With this new, third edition came a new, third part named “Infinity superseded”. One of the major conclusions of the earlier editions was that the concept of the metaphysically infinite is incoherent. It is something of which we cannot make sense, and it can have no application for us. Moore’s central concern in the final chapter of those editions had been to consider the predicament of human finitude and our consciousness of it. These new chapters revisit those themes. Moore begins by looking again at the infinite, the transcendent, and the finite in the work of three figures: Spinoza, Hegel, and Nietzsche. He draws out the existential and ethical implications of this history and ends by outlining what legitimate role the infinite can continue to play in our thinking and practice.

Chapter 16, “Infinity reassessed. The history reassessed anew” is, then, advertently structured around this trialogue between Spinoza, Hegel, and Nietzsche. It focuses on the metaphysics of infinity and finitude and is resolved in favour of Nietzschean finitism. Chapter 17, “Learning how to be finite”, meanwhile, is guided by a more ambient, tacit dialogue between Deleuze and Wittgenstein. Though less explicit, this dialogue is by no means hidden – Adrian points us to it in his preface to the third edition. There, he commends Deleuze as a thinker who was absent from the first two editions but whose work Adrian now sees as pivotal to the subject of the infinite and to the challenge of negotiating finitude. This chapter builds on the closing reflections of the previous editions to advocate for the concept of the infinite. It is a concept we appeal to when trying to express those insights which sustain our moral lives with the hope that value is real.

In very broad terms, I see the argument of the new section as unfolding in the following way. In Chapter 16, we have the trialogue between Spinoza, Hegel, and Nietzsche. We start with Spinoza, who offers an account of reality which is purely positive and has no room for negation, but which is static, lacking in dynamism. Hegel’s world spirit, on the other hand, is characterised by movement. It develops purposefully towards the rational, and is fuelled by negation – the destruction of each finite thing by its opposite. With both thinkers, though, we can distinguish elements of transcendence. In Spinoza’s case, the infinite nature of God or substance marks it as transcendent, almost in spite of Spinoza himself. Equally Hegel’s Absolute, in its infinitude, is beyond our experience and understanding and therefore should be understood as transcendent, on Moore’s construction of the term.

Nietzsche rejects the (metaphysical) infinite and with it, transcendence. Nor is there room for negation in this thoroughly affirmatory set-up. Being is replaced by becoming. Moore very plausibly suggests that Nietzsche, in denying the existence of a transcendent entity identified as the being of all other entities, took the step that Spinoza should have done, and was therefore better able to ward off the challenge from Hegel. Chapter 16 ends on an intriguing note. Moore considers our frustrated attempts to formulate Nietzsche’s denial of entityhood to being and submits that they point to ineffable insights. This raises the prospect of a role for the infinite in our thinking after all.

Chapter 17 addresses the threat of nihilism. Naturalistic, relativist accounts of value like Spinoza’s prompt the nihilist’s question “so what?”. Nietzsche responds to this challenge with the doctrine of Eternal Return, letting each ‘so what?’ be answered by a new creation of values. This cure comes at a price, however: it seems to demand the abandonment of our cherished ideas of humanity and the infinite. Moore undertakes a rescue in each case. He points us to accounts which outline a shared human nature without appealing to the concept of infinity. But he also maintains that we are entitled to use that concept – and its fellows, transcendence and God – though they have no application to reality, though our attempts to refer to them are nonsensical. In fact, Moore concludes, in learning to be finite we cannot do without the infinite.

2. Chapter 16

Moore begins by expressing a wish to revisit certain material from the earlier editions, and to, as he says, “develop its arguments in what now seem to me important new directions”. (238) He draws our attention to the near thirty-years that lapsed between the writing of the original work and this supplement. Though he notes that there will be very little in it he will retract outright, he starts with one aspect of the study about which he now feels uncomfortable: the account given of Spinoza in chapters five and seven.

In those earlier sections, Moore had emphasised the religious, even mystical, character of Spinoza’s thought. While still affirming that, on appropriate construals of those terms, Spinoza can be understood as a theorist of the religious, the ineffable, and the transcendent, Moore now shifts focus to Spinoza’s unorthodoxy, his naturalism, and his confidence in our capacity to understand. Moore’s summation of Spinoza’s project introduces what I see as a guiding concern of these two new chapters, and I quote it here (238): Spinoza’s aim was to provide a naturalistic basis for ethics. He wanted to make broad sense of our situation as finite individuals in an infinitely complex world, and to give an account, in those terms, of what our well-being consisted in.

Now, whether Moore himself ultimately endorses naturalism, or countenances the metaphysically infinite, we can hope to tease out as we read through this supplementary section. But it is sure that he approves Spinoza’s aspiration to take stock of our nature as finite beings, and shares Spinoza’s vital/animating interest in the question of how, in our finitude, we can live well.

Moore also wants to examine differences between Spinoza and Hegel which may have been elided in his earlier, briefer treatment of the two philosophers. First, he points out a fundamental divergence in their respective conceptions of God. “God”, per Moore, is the name Spinoza gives to the being of entities, which he treats as an entity in its own right. God is identical to the one existing substance, to nature, or reality, as a whole. Hegel’s God, as a person with purposes of his own, is less unorthodox. Other profound differences are canvassed, but the most significant divergency for Adrian’s discussion concerns the two thinkers’ treatments of the negative and negation.

For Spinoza, Being, God, is purely positive – negation has no role in being as such, though it does articulate the delineation of finite beings. Hegel derided Spinoza’s Being as a ‘dark, shapeless abyss’ and charged him with reviving a kind of Eleatic monism which figured being as abstract and homogenous. According to Parmenides, being was indeed a unified and indivisible One, in which all apparent change and diversity was merely illusory. But Spinoza is not Parmenides. His One – God, or substance – is really differentiated. Neither, though, is Spinoza Hegel, because, Moore says, that differentiation is not to be understood in terms of negation, but in purely positive terms.

Meanwhile for Hegel, negation is “at work in being itself”, as Moore puts it. (243) A finite being and its negation are essentially opposed to one another. Any finite thing must become its opposite and ultimately be destroyed as Being absorbs and eliminates falsity in its development towards truth. Such movement would not be possible without negation. For Hegel, then negation is part of Being, part of the infinite, part of what is. For Spinoza… negation is not!

There’s one further concept Moore wants us to have in mind before Nietzsche enters the discussion: transcendence. Moore defines the transcendent as what lies beyond our experience and understanding. Given that Spinoza’s goal is to find a naturalistic basis for ethics, he might be expected to reject the transcendent entirely. But God is infinite, and therefore, according to Spinoza’s epistemology, beyond our understanding – in other words, transcendent. Hegel, similarly, feels compelled to say that as finite beings we can only make sense of what is finite – which would suggest that his Absolute, in its infinitude, must also be transcendent. So thanks to their commitment to the infinity of being, we have, in both Spinoza and Hegel, what Moore calls “intimations of transcendence”.

Nietzsche’s role here, as Moore sees it, is to transform Spinoza’s ideas in such a way as to better keep Hegel at bay. First, Moore notes another development in his own thinking since the earlier editions, concerning the highly contested doctrine of Eternal Recurrence or Eternal Return. Moore comments that, while what he said about Eternal Return in Chapter 7 may have been strictly correct, he no longer stands by the most natural interpretation of it, which is that Nietzsche envisaged “an endlessly recurring cosmic cycle of many years” (246). Now Moore instead understands Nietzsche as suggesting that in each moment all other moments, both past and future, recur (as past and future), but reconfigured from the perspective of the new current moment. That, at least, is my understanding of Moore’s understanding of Nietzsche’s understanding of the Eternal Return! If Moore’s reading of the doctrine is correct, he says, it “has a vital bearing on the dispute between Spinoza and Hegel” (246).

Moore’s next step is to argue that Spinoza should not have countenanced the existence of a transcendent entity, the being of all other entities, as he did. Nietzsche, with, as Moore says, a naturalistic vision so similar to Spinoza’s own, takes the step Spinoza should have done, and denies that the being of entities exists as an entity in its own right. Through the doctrine of Eternal Return, interpreted as discussed, Nietzsche replaces being as an entity with endlessly changing entities – that is, with becoming. Moore had concluded chapter 7 of this book by remarking on the infinite aspect of the Eternal Return. Now understanding Nietzsche in an avowedly Deleuzian way, Moore revises this. He submits that the self-affirmation of endless becoming leaves no room for any negation, any transcendence, or any infinitude. This is the step Nietzsche takes beyond Spinoza. Nietzsche’s divergences from Hegel are far more marked. He repudiates Hegel’s vision of a metaphysically infinite whole and the idea that it works through negation to realise its purposes and make ultimate sense.

Moore promises that his final chapter will consider the significance – in particular the ethical significance – of the differences between these three thinkers. First, and as the final move in this chapter, he revisits the discussion of the infinite and the ineffable in Part II of the book. He calls our attention to a problem which arises when trying to deny entity-hood to being itself. For Nietzsche, as Moore has put it, being should not be understood as a noun – being is not itself, as Spinoza had thought, an entity. Instead, being should be understood as a verb; but how do we express this? How do we refer to it? As Moore asks, “[h]ow can we say that there is no such entity as being, without – simply through our use of the word “being”… – committing ourselves to their being such an entity?”[1] He notes that similar problems have arisen in his discussion of the infinite – for instance, the problem of expressing a denial that the truly infinite exists. It may be, Moore hypothesises, that these kinds of failed formulations point to failed attempts to put something ineffable into words. That is, something we are being shown about the nature of being but cannot express.

If this is right, then what could it be that we are being shown? What is the ineffable knowledge at stake in interpreting Nietzsche’s understanding of being? It could be, Moore suggests, knowledge of what it takes to be finite. But he asks us, if we are indeed being shown that, and are trying to put it into words, why can’t we say the same for the kind of talk Nietzsche disallows – why not the same for the infinite, the transcendent, and so on? Could we not also countenance this kind of talk as an attempt to put some ineffable knowledge, something we are shown, into words? This is the question with which Adrian leaves us at the end of Chapter 16.

3. Chapter 17

Moore starts this chapter with a section on the ethical import of the trialogue expounded in the previous one. Spinoza’s naturalistic ethics maps the route to our well-being, especially through understanding what befalls us. Hegel, against Spinoza, denies that finite things make their own sense – they endure affliction in the process towards realisation of the infinite whole, the site of absolute value. For Spinoza value is relative – a Spinozan individual holds a thing good if it contributes to its well-being. At the same time, Spinoza advocates understanding reality sub specie aeternitatis, from the point of view of eternity. Moore’s concern is that this way of seeing the world may tempt us to nihilism, because, from this remote perspective, value is liable to appear illusory. All that seems to remain is endless, pointless activity, leaving the nihilist’s question: “so what?” unanswerable.

Nietzsche, once his Schopenhauerian years were behind him, sought to repel this nihilism, according to which all of our suffering seems pointless. He nonetheless rejected the Hegelian picture of suffering being for the end of something of infinite value. Value, for Nietzsche, was not objective, and suffering was indeed purposeless. He offers us resources for overcoming nihilism not by trying to make sense of our lives from an eternal perspective, but by making sense of things from within their midst. And precisely by making sense: not discovering but creating it, creating meaning and value through the living of our lives. But could the nihilists’ unanswerable “so what?” not be confronted once again by each of these created values, so that, ultimately, each can only be seen as “a senseless palliative to our senseless suffering?” (254) No, thanks to the doctrine of eternal recurrence. There is no ultimate perspective in this way, just an endless succession of new sense making, new perspectives on reality, new evaluations of it. Every time the question arises, it can be answered anew – eternally. Through the concept of eternity, mathematical infinitude plays a role, for Nietzsche, but the cost of all this is recognising metaphysical finitude. Not just that there is no God, it also follows that we ourselves are finite and more fragile than we like to think. Moore next turns to address these threats to religion and humanity.

Facing the former head on, he argues that the slogan ‘God is dead’ is best understood to be saying that a concept, a way of making sense, had run its course. As God lost his vitality he became emptier, transforming into the Kantian thing-in-itself. The solace of God was replaced by the solace of the rational individual. But that too cannot survive Nietzsche’s twilight of the idols. Our identities emerge out of our animal drives and are continually rewritten and contested. Our species identity, too, has vindicated Nietzsche by splintering as the distinction between human and non-human (whether that be animal or technological) became increasingly unclear.

But as we are now, all of us considering these questions, we are human, and our thinking – especially when practical – is fundamentally shaped by that. We can only carry out sense-making – Moore channels Wittgenstein here – from within a form of life: very roughly, a cultural context. And each of our forms of life, Moore proposes, are ineliminably human. So for us to no longer think about basic practical questions from a shared human viewpoint would take a radical transformation. “Ethics itself”, Moore writes, “would be called into question” (259). Moore suggests it is helpful to return to Spinoza - his idea of good was anthropocentric (concerned with the good for ‘us’, as humans) otherwise it would have been relativist in a dangerous way. Because there are dangers – that is human dangers – in wishing to leave behind a human evaluative viewpoint. We should tread carefully.

Assume rejecting the metaphysically infinite does mean we must discard a capital G God, or a concept of the metaphysically infinite in ourselves like the Kantian faculty of pure reason. It may mean leaving behind certain seductive models – humanity as a Platonic idea, the self as an independent Cartesian subject – but we should not go too far. There may, for instance, be models of human nature which do not invoke metaphysical infinitude.

The difficulty, though, is that we crave infinitude itself – particularly, something metaphysically infinite which transcends our finite world and gives it meaning. But that, for Nietzsche, is an illusion and seeking it is life denying. Can Nietzsche himself consistently insist that we must cast off theism forever? He surely can’t foreclose the possibility of God returning, reconfigured, as the endless movement of meaning making goes on. Again, look at Murdoch’s atheism, Moore recommends, (an area of philosophy/theology, which is currently attracting increasing interest) according to which, though God does not exist, his idea plays a critical role in our lives, and what leads us to conceive of God does exist and is experienced.

So do we need to live without the infinite? These examples suggest not entirely. Moore’s final subsection is entitled “Reclaiming the infinite”. And he had already indicated two legitimate uses of it in section 15.3 – a regulative use and a use in “describing the attempt to put certain in expressible knowledge into words”. (263) Consider our craving for the infinite as the only thing that can allow us to answer the “so what?”. We saw the problem arise because a naturalistic, relativistic account of ethics, such as Spinoza’s, cannot seem to ground value as real. Robert Adams, as Moore notes, goes further and argues that any account we give will remain open to question – no human account can ever settle the question of real value, and that is because value, the good, is transcendent. But, Moore asks, what can the appeal to the transcendent, understood as that beyond experience and understanding, do for us – can it even make sense?

Moore’s response may be a little shocking, but on the foundation of the earlier editions, it should not, perhaps, be surprising. An appeal to the transcendent may not make sense – but to quote the nihilist, so what? Its not making sense may not matter. In particular, its not making sense may not harm its capacity to overcome the nihilistic threat. As Moore sees it, the reason we cannot give an account of things that can secure real value is not because we’ve focused our accounts on the way things are in our finite experience instead of focusing on the infinite, transcendent reality. It is because, as he says, “real value is not a matter of how things are at all”. (264) If we do have any knowledge of real value, then, it can’t be knowledge of how things are. It must instead, Moore argues, be inexpressible knowledge. But then, if we can be said to have inexpressible knowledge concerning real value, why can’t “appeal to the transcendent, or to the Infinite, or to God, be part of what we resort to, however nonsensically, when we try to express it?” (264). If we do indeed have this knowledge, it is not knowledge of how things are, and it is not knowledge that we can express. Perhaps, therefore, we are entitled to reach for concepts of the infinite and the transcendent – though they don’t themselves make sense – in our inevitably nonsensical attempts to express what cannot be expressed.

On Moore’s construction, it isn’t that we have insights into a transcendent or infinite reality which we can only express through nonsense (as the religious positivists would have it). Rather, we have insights, and we are liable to appeal to the infinite and transcendent in our nonsensical attempted expressions of them. Moore employs the terms “infinite”, “transcendent”, and indeed “God” to characterise the talk we engage in when we try to express our inexpressible insights, not to characterise the nature of those insights – of what they are into. So while it inevitably uses such terms, his account of this nonsense talk is not itself nonsense – “although it is of the essence of such nonsense that we cannot make sense with it”, he trusts, “we can nevertheless make satisfactory sense of it”. (265) How can we legitimately employ the concept of infinity in our thinking, given that it doesn’t make sense? It depends on the who the “we” concerned is. We as humans, trying to understand value, being granted insights, trying to – as is impossible – express them, are liable to reach for such terms as “infinite” and “transcendent”. What we use those terms to say will be nonsense, because we are trying to express the inexpressible. We as philosophers can use the same terms to describe those very attempts – hopefully what we say will not be nonsense!

Perhaps this seems a rather undistinguished ending for the venerable concept of the infinite and its fellows. Moore, however, turning to the concept God in particular, encourages us that it can play a truly meaningful role in our lives. He had ended the earlier editions by examining what it would mean to live by what we were shown, he summarises it now as follows: “[M]y accepting what was still possible and what was no longer possible; my hoping that the most important possibilities would never be closed off; and my hoping that the possibilities with which I was still confronted were enough to give my life sense”, now adding “my trusting that we do well to think about the most basic practical questions of life from a human point of view”. (266) These hopes are supported by ideas of the infinite, the transcendent and of God used regulatively to sustain our values. Such a usage of the idea of God does not require that his existence should be credible, or even intelligible. The very fact that it transcends understanding and experience may indeed qualify it to anchor value in this way.

Moore’s conclusion, then, is that “nothing should tempt us into abandoning the concept of the infinite altogether, not even a clear demonstration that the concept has no direct application to reality”. (267) To say that the infinite doesn’t exist, even that it doesn’t make sense, is not to say we should do without the concept. Our most fundamental practical questions relate to what surpasses the finite. To make sense of ourselves, we must reckon with our own finitude, which must itself be understood in relation to what surpasses it – that is, the infinite.

4. Interpretation and Analysis

I’ve rather loftily called this section “interpretation and analysis” but I’m really just taking it as an opportunity to ask for a bit of a masterclass from Adrian, if I may! Adrian’s writing is known for its clarity, and these chapters are no exception to that rule. They do, though, cover much fascinating and difficult material, and I would be interested to hear more from Adrian on many of the ideas and arguments addressed. I’ve limited myself, after some internal wrangling, to four questions: one about Spinoza, one about Nietzsche and two about Moore’s own propositions.

A Question About Spinoza… Negation and Delineation This concerns what is, of course, a deep and intractable problem in Spinoza scholarship, but should only be a fairly quick question to start us off here. That is, in a nutshell, does Adrian, do you, hold that there are two kinds of differentiation at work in Spinoza’s Ethics?

There is a history of Spinoza’s commentators claiming that he is unable to account for real individuation. Hegel, as we saw, was of that party. He identified Spinoza’s metaphysical picture with Eleatic monism, in which individuality disappears. Moore differentiates Spinoza from Parmenides because Spinoza differentiates: there is differentiation both within and between God’s attributes, according to Spinoza.

Moore notes that Spinoza’s God is purely positive – Spinoza, he says, stipulatively aligns positivity with whatever is and God is another name for being – for what is. The only role for negation is in the delineation of what is finite, Moore says. (239) To take Moore’s example, a house and a garden each have positive existence in their own right, but the house is not the garden, it “lacks being in the garden outside it”, as he puts it (241).

When distinguishing Spinoza from Parmenides, though, as a philosopher who does allow for differentiation, this doesn’t seem to be the model of it that Moore has in mind. He says that for Spinoza, this differentiation “had better not be understood… in terms of negation” but rather in a “purely positive way”. (240) Hence my question of whether there are two different kinds of differentiation here – or perhaps better, is there delineation (which distinguishes a finite being negatively from what it is not) and differentiation which is purely positive?

If so, the further question arises of how – in virtue of what – this purely positive differentiation is possible.[2] Moore gives the examples of a finite body being distinguished from its surroundings and of bodies being distinguished from ideas. Perhaps the first of these would be explained by Spinoza’s claim that bodies are distinguished from one another in terms of motion and rest.[3] Or, perhaps what Moore has in mind here is a thing’s conatus, its striving to persevere in its being, which Spinoza calls its actual essence. Each of these concepts is examined in The Evolution of Modern Metaphysics. The second example is the differentiation of a mind from a body on the basis of the differentiation of the attributes as distinct essences of God. Can a pattern of motion and rest be picked out other than by negation, by what it is not? Can an essence – whether an essence of an individual, or an attribute as an essence of substance? In summary, my questions to Adrian are simply do you understand the delineation of the finite through negation to be one thing and distinct from the second, purely positive kind of differentiation? And how do you characterise the latter, in order to safely navigate Spinoza between the Scylla of an amorphous unity and the Charybdis of negation?

A Question About Nietzsche… Eternal Return Moore outlines Nietzsche’s concept of eternal return very succinctly in chapter 16, though it recurs in 17, so I shall take up his invitation to look to his fuller discussion of the topic in The Evolution of Modern Metaphysics. There, he describes the dispute as to what the status of the eternal return idea is: whether it is meant as a genuine, metaphysical doctrine or rather as a sort of ethico-existential thought-experiment to test what a person is capable of affirming. Moore illuminatingly points out that this dispute overlays another about what, in either case, Nietzsche is saying the eternal return is (what returns? In what way does it return?).

Historically, the doctrine has widely been treated as a revival of the pre-Socratic idea of a repeating cycle of history.[4] Perhaps, then, it was in part out of charity – to avoid attributing this absurdity to Nietzsche as a literal, metaphysical claim – that so many commentators glossed the eternal return as simply a thought experiment, offered as a test of affirmation. Must we give up on a metaphysical reading of the eternal recurrence? Deleuze proposes a new version. We should not be looking for the return of something that is the same. Instead, it is the eternal return itself that provides the “sameness” element. “It is” as Moore explains “the inexhaustible renewal of the ever-differing moment of becoming”. (TEOMM 402) Deleuze is saying that the moment repeats endlessly, but what flows through it is endlessly changing and new.

Moore – quite rightly, I think – feels a bit short-changed by Deleuze’s account, in as much as it seems to miss the idea of something returning. There is the repetition of the always-different moment, but nothing which itself comes back, which surely is what the idea of eternal return connotes. However, Deleuze’s interpretation does help to inspire Moore’s own, and both maintain that we should conceive of the eternal return as a real feature of the world. Moore argues that the eternal return is the amalgamation of two Nietzschean ideas: that ‘everything is knotted together’ and that “change is ceaseless” (402). Because of the knotting together of everything, change in anything means change in everything. In the ceaselessly changing moment, everything else, both past and future, come together, also changed. Moore summarises it as “the eternal return of all things, but ever different”. (403) Now, is this reading rather minimalist or rather radical? When Moore writes, “[w] hat happens at any moment, on this account, happens at every moment – albeit at some moments as future, at some moments as present, and at some moments as past” (403) this might not be saying much more than that, at any given moment, there is a past and a future, so that as each moment passes and is replaced with a new moment, again there will be a past and an endless future of moments that, in a sense, come with it.

I think it is more than that – the past and the future are also changed with each passing moment, on Moore’s account. But again, I think this could be interpreted in either a more modest or a more radical way. To take the more radical first, does it imply that 1) the past and future actually exist in some concrete way and 2) they also change at every moment, as the present ceaselessly changes? This seems somewhat metaphysically liberal. However, Moore follows the quotation just given with this: “each moment affords its own different perspective on the whole, its own different point of view from which to interpret the whole”. (403) Again, this perhaps suggests a more modest interpretation: that the past and future are simply understood differently with each changing moment. But understood by whom?

In fact, Moore refers to interpretation rather than understanding, and suggests that the agent making these reinterpretations is the will to power: “[e]ach moment enables the will to power to make an associated sense of things”, Moore continues. He concludes the passage with the following quotation from The Will to Power: the world has “a different aspect from every point; its being is essentially different from every point”. Even Nietzsche’s two separate clauses here may suggest quite different interpretations. To say that the world, or that the past and future, has a different aspect from every point is one thing, to say that they are essentially different seems to specify this in a way that makes a substantial metaphysical commitment.

I think, perhaps, what all of this really amounts to is that I would like to get a bit clearer on the change involved in the eternal return. If change, here, consists in reinterpretation, does that merely imply that, subjectively, past and future are seen in different ways at each moment? Or rather that, objectively, the will to power reconfigures them? I suspect that, in the end, the answer may well be that the distinctions shaping my questions here – between perspective and essence, between subjective and objective – simply break down with respect to a concept like the will to power.

…And Two Quick Questions About Moore 1. Is Nietzsche Enough, Or Do We Need Mo(o)re?

My question is, simply, does Nietzsche’s affirmation of value creation, as you have described it, offer a live, viable alternative to your own answer to the nihilist? Why did we need to move on from Nietzsche? Nietzsche’s response might seem to have an advantage in that it is thoroughly immanent and concrete: we create new values, to eternity, in the face of the nihilist’s “So what?”. He insists, as Adrian explains, that hankering after transcendent values while denigrating the this-worldly is itself nihilistic.

Now, I doubt that Adrian’s account is guilty of this. He notes Robert Adams’ claim that the only successful response to the “So what?” question posed by the nihilist is to cast value as transcendent. Moore’s own response is rather more complex: we have inexpressible insights into “the value of things” – when we try to put these into words, we are liable to talk, though nonsensically, of a transcendent reality. (264) Nonetheless, concerning the idea of God Moore does remark that it may be able to uphold value in the way he suggests “because it is an idea of something that both transcends and sustains all that (merely) exists”. Does this escape Nietzsche’s critique of nihilistic focus on the transcendent? Maybe so, since Moore is referencing a regulative idea rather than a constitutive belief and because it is one that sustains our action and living in this world, rather than denigrating it.

But if Moore’s account doesn’t have the cost Nietzsche thinks it essential to avoid, does Nietzsche’s view have the cost about which Moore is concerned? And more importantly, is it a cost at all? It is when discussing the idea of post-humanism that Moore leaves Nietzsche behind and nails his own colours, somewhat circumspectly, to the mast of humanity. Now, this post-humanism isn’t prima facie part of the eternal return and its role in the response to nihilism as expressed by Moore, though it may well be implicit elsewhere in Nietzsche’s work. More important, though, is the question of whether it really constitutes a cost. Moore maintains 1) that those of us reading his work, those of us considering these questions, are human, and that our thinking – especially when practical – is fundamentally shaped by that. Moreover, 2) that for us to no longer think about basic practical questions from a shared human viewpoint would take a radical transformation, and again, 3) that ethics would be called into question, so we should tread carefully. Moore suggests it is helpful to return to Spinoza whose idea of good was anthropocentric (concerned with the good for ‘us’, as humans) rather than relativist in a dangerous way. Because 4) there are dangers – that is human dangers – in wishing to leave behind a human evaluative viewpoint.

These may indeed sound like serious risks, but perhaps they can be understood in a way that makes them seem less threatening. As regards point 1), it is very natural to call ourselves human, if we imagine that the alternatives are to be animal, alien, or artificial. But it may not seem absurd to imagine that The Infinite could find readers who were post-human in the sense of being technologically enhanced, or even who were übermenschen, in Nietzsche’s sense. On point 2) the transformation might be radical, but it could – Moore himself says it would – be gradual and piecemeal rather than revolutionary. (259) To respond to point 3), is it not, for Nietzsche, an aspect of our flourishing to overcome (our) humanity? That is, isn’t his vision also, like Spinoza’s, directed to ‘our’ good? This, of course, depends on the idea that though we are human, we – the readers of Nietzsche and Moore – may not only be such. Perhaps not all of our interests are identified with our humanity – we may have goods relative to our other identities too. Adrian also warns that we need to consider the dangers – including perhaps non-human dangers – of undue conservatism. (260) I would be intrigued to hear whether you had in mind the dangers that might threaten things other than “we” humans, or whether you countenance the possibility of an “us” that is other than human?

2. A Worthy Fate for the Infinite?

If the infinite has no direct application to reality, if the truly infinite does not exist, if it can only be spoken about through nonsense, can we really say that the concept remains important for us? And say the same for the concept of God? Certainly, Adrian holds them to be so. They constitute our response to insights into real value, they frame our most fundamental practical questions and are essential to reckoning with our own finitude. It is worth investigating how, precisely, the concepts play these roles – on a first look, one suggestion may appear a little underwhelming and the other a little under-supported.

To take the former, Adrian suggests that the idea of God, with its connotations of steadfastness and constancy, could be put to regulative use to sustain my ability to make sense of things. But consider that this usage does not even require God’s existence to be intelligible. Is it satisfying – even possible – to use an idea in this way if it is neither credible nor intelligible? Moreover, the contradiction of these regulative ideas of God and the infinite could conceivably play exactly the same role for me. I could be shown, as Adrian puts it, that God exists, or equally that God does not exist. This might seem to further diminish the role of the infinite and of God. However, it is of the nature of regulative ideas that they are used, regardless of truth values, in order to sustain and make our moral lives meaningful and coherent. Adrian therefore has Kant on his side in holding this to be a substantial and dignified role for the idea of God.

Adrian concludes this section by submitting that we need to reckon with the infinite as we negotiate how to be finite – the concept remains necessary to us and we must not abandon it. This is the claim that I suggest might strike us as a little under-argued, as it appears in these final two paragraphs of the section. Compared to the first, this claim seems rather stronger, the language a little vague. Let us look briefly at what is offered, in these final paragraphs, to persuade us that the concept of the infinite remains vital to our ethical and existential reasoning.

The following quotations all come from page 267, the final half-page of our section. First, we have “in trying to make sense of ourselves, we are trying to make sense of the infinite”. In the very last line, we have “we shall never know how to be finite if we do not reckon properly with the infinite”. Now of course, actually making sense of the infinite is impossible to achieve. It is not that an understanding of the infinite helps us to understand ourselves and our finitude and teaches us how to live with it. All we have to support these vital endeavours is a “trying to understand” and a “reckoning with”. In between these two claims, we get a third “ [w]hat all the most basic practical questions of life come back to” is “how we, in our finitude, relate to what surpasses that finitude”. This might also raise an eyebrow, assuming “what surpasses” finitude to be understood as the infinite – can it really be said to underlie all of our most basic practical questions? The problem, I suggest, is that talk of “reckoning with” and “relating to” the infinite looks rather weak, while the claims that this is vital to learning to be finite and all our most fundamental practical questions seem rather strong.

Of course, though, these concluding statements are founded on all that has gone before. I submit that we can best parse the reasoning which supports them by reminding ourselves of the following two points in particular. First, the model of using ideas regulatively might dispel the concern that notions of “trying to understand” and “reckoning with” seem underpowered. The concept of the infinite is not something we can understand or make sense of, but this doesn’t undermine its power to shape our understanding and actions as a regulative idea. Merely keeping it in play, merely reckoning with it, is sufficient. Second, the need to secure value against the nihilist’s “so what?”, I think, gives us the link between our most basic ethical concerns and the concept of the infinite, along with its fellows, God and the transcendent. If “most basic” mean those that have to do with the reality of value, and if the infinite is among the concepts we reach for to keep the possibility of enduring value alive, then it does indeed underpin our fundamental practical concerns. I’m aware I’m going out on a bit of a limb in suggesting these last questions might demand a response and I’m doing the same in my attempt to answer them. It may well be that Adrian himself had other parts of his argument in mind as supporting these final claims for the infinite.

5. Conclusion

The section we looked at, building on a book stuffed full of intricate arguments and an embarrassment of historical sources is, of course, extremely rich, and there are many more questions that I would have loved to have asked. One concerned whether Spinoza’s concept of natura naturans (counterbalances the understanding of God as the being of entities and) offers any prospect of explaining God’s transcendence in terms of aspects rather than parts. A second, related to why Adrian adopted the expression “being shown” rather than “seeing”, and what the relationship and ordering is between using the idea of God regulatively and being shown something, such as the idea “God exists”. However I’m well aware that I might have worn your patience, and even more so Adrian’s, very thin by now, so I will draw to a conclusion. The majority of the questions I did ask centred on issues of the correct interpretation of Spinoza or Nietzsche. Of course, this sort of detailed historical reconstruction is not the object of “Infinity Superseded”, and I want to finish by returning to what I consider to be the real achievement of what we have read.

The Infinite offers a masterly historical analysis of the title topic, detailing its mathematical technicalities and philosophical profundities. Not content with that, Adrian does as Spinoza did, and puts metaphysics into the service of ethics.[5] In spite of the seriousness with which he takes the paradoxes of the infinite, Kant’s injunction on the limits to what we can know, and Wittgenstein’s dictum on what is beyond expression, he is able to offer a genuine response to the nihilist’s challenge to value. In these last two chapters in particular, Adrian addresses some of our deepest and most important concerns. While respecting what we might call the bounds of sense as he has mapped them, he nonetheless makes an original and subtle proposal as to how we can best negotiate our finitude. In particular, he indicates how the possibilities of meaning and value might be kept open, how profound but inexpressible insights can shape our lives, how God may play a role in that and why the infinite remains a legitimate and indeed vital concept to reach for.

Perhaps this is what is most remarkable and significant about “Infinity Superseded”: the case it makes for why the infinite and its ungraspability matters to us existentially and ethically. But in these two chapters alone, that case is built on philosophical history and analysis of huge erudition and brilliance. We are offered profound and often novel studies of Spinoza, Hegel, and Nietzsche, reasoning shaped by Adrian’s authoritative knowledge of Kant and Wittgenstein and benefiting too from his openness to take on and absorb a new approach in the work of Deleuze. I have already mentioned the parallel with Spinoza’s mission, but I hope Adrian won’t mind me adding that these qualities reflect his own character as I experienced it too: brilliant, mindful of human needs, and always ready to listen to a new argument.

I have to finish by mentioning one other trait Adrian is well-known for – his sense of humour! Perhaps we can even detect a hint of irony in this new section’s title, ‘Infinity Superseded.’ It might as justly have been named ‘Infinity Triumphant’ - or rather, ‘Infinity Resurrected,’ reflecting this section’s work to rehabilitate the infinite after consignment to the death of senselessness and inapplicability. Indeed, I enjoyed Adrian’s own slightly mischievous allusion to the possible resurrection of God following Nietzsche’s announcement of his death. Maybe likewise, reports of the infinite’s death have been greatly exaggerated.

J.Bunker@roehampton.ac.uk

1] This will also be true of any equivalent expression.

2] Moore mentions differentiation within and across attributes (the former of which “allowed finite bodies to be distinguished from their surroundings” (240) so differentiation presumably isn’t distinguished from delineation simple in terms of the kind of things it individuates).

3] And further, that an individual can be identified by a maintained pattern of motion and rest among its parts. Moore refers to the relevant Definition and Lemmas of EIIP13 in The Evolution of Modern Metaphysics.

4] There is a more subtle variation on the cosmological interpretation: that given finite resources and infinite time, every configuration that has existed will eventually recur. Moore has it (citing arguments from Richard Schacht) that even this version is easily refuted.

5] “Metaphysics in the Service of Ethics” – the (sub?)title of AWM’s Spinoza chapter in EOMM.

© 2022 by Public Reason

Public Reason 14 (1): 38-43

Learning How to Be Infinite

Pablo Montosa

University of Barcelona

Abstract. This paper focuses on some of the more controversial points in Jenny Bunker’s reply to Adrian W. Moore concerning his account of Spinoza. In particular, it raises the question of whether Moore has conceived of certain aspects of the relations between modes in a substantial manner and points to some of the consequences that would follow. Finally, it argues, contra Moore, that the perspective sub specie aeternitatis does not imply draining reality of all value and meaning but conceiving of values as relative. In contrast, the perspective in mediis rebus implies conceiving of values as substantial attributes of things, being the cause that ultimately leads to nihilism, understood as contempt for the world.

Key words: Bunker, Moore, Spinoza, infinite, substance, modes, nihilism, values.

1. Towards the end of her reply, Jenny Bunker points out that Adrian Moore has built the case of the two new chapters of The Infinite on “philosophical history and analysis of huge erudition and brilliance” (2021, 37). In highlighting Moore’s scholarship and analytical depth, Bunker refers to his remarkable work as a historian of philosophy, drawing on his philosophical knowledge to illustrate the various conceptions of infinity held by some of the most influential philosophers, logicians and mathematicians. The label “philosophical history”, however, suggests that Moore has not merely operated as a historian of philosophy but also as a philosopher of history, using historical sources to illustrate the central thesis of his essay: the infinite is ungraspable, since it does not refer to anything actually existing, but, at the same time, it is an indispensable notion for dealing with our lives on the ethical and existential dimensions.

This thesis, as Bunker observes, is “shaped by Adrian’s authoritative knowledge of Kant and Wittgenstein” (37). The Kantian influence is apparent in presenting infinity as a regulative idea. If we were to act only based on our finitude, we would not set out on essential endeavours that we could hardly undertake in the span of our short lives. However, if we believe that we have an infinite amount of time to accomplish them, there would be nothing to prevent us from procrastinating. I fancy James Dean must have had something similar in mind when he urged us to dream as if we would live forever and to live as if we would die today. Now, since the notion of infinity, according to Moore, is essentially nonsensical and incomprehensible, one can only show its occurrence while avoiding any temptation to explain it, according to the famous Wittgensteinian distinction between showing and saying.

The problem, subtly hinted at by Bunker, is whether Moore’s legitimate philosophical interests have interfered with his account of Spinoza, Hegel, and Nietzsche. It is thus a question of elucidating what Moore has not found in these authors when looking at them through the Kantian glass. Hence, Bunker focuses the majority of her questions “on issues of the correct interpretation of Spinoza and Nietzsche” (36). Among the four questions that Bunker explicitly poses: “one about Spinoza, one about Nietzsche, and two about Moore’s own propositions” (30), I will focus on the one concerning Spinoza, which I think is of most interest. In my view, Bunker’s question about Spinoza leads us to a significant criticism of Moore’s interpretation, namely, his inability to explain the differentiation of Spinoza’s modes in a purely positive way. After developing this point, I will turn to another important aspect of Spinoza’s thought that both Moore and Bunker seem to have overlooked: the role that Spinoza’s concept of infinity and the subsequent relativity of values play as an antidote to nihilism and remorse.

2. The question Bunker addresses to Moore is related to the role of negation in Spinoza’s understanding of finite modes. This is the question Bunker raises explicitly. But this does not prevent her from mentioning, at the beginning of her conclusion, some of the many questions she has refrained from asking him. Among them would be the question of “whether Spinoza’s concept of natura naturans (counterbalances the understanding of God as the being of entities and) offers any prospect of explaining God’s transcendence in terms of aspects rather than parts” (36).

In this single sentence, Bunker encapsulates an objection of far-reaching significance: Moore has neglected the crucial distinction in Spinoza’s thought between the substance and its modes. In depicting Spinoza’s God as “the being of entities”, a kind of ontological equivalent of the Set of all Sets, Moore has neglected that the modes of the substance are not properly “entities”, or at least not in the same way as the substance is. In Moore’s own words: “When he [Spinoza] argued that there was an absolute unified simple eternal substance of which everything else was but a mode, he was really just treating the being that was common to every entity as itself an entity” (2019, 238). To counter Moore’s reading, we can summarily say that, for Spinoza, the distinctive feature of a substance is to be the cause of itself. Thus, a substance does not need something else to be or to be conceived. For this reason, a substance must be infinite since, if it were to be finite, it would have to be conceived as such from something else that limits it. This leads him to conclude that the substance can only be unique. Accordingly, the things of the world, ideas and bodies, can only be conceived as modes, that is, as being in something else in virtue of which they are conceived. If this is so, things cannot be conceived of as finite, independent, and self-subsistent substances, but in an intrinsically relational way. Hence, finitude can be conceived of neither substantially nor as a property of existing things conceivable by itself.

This brings us to the question explicitly posed by Bunker about the soundness of Moore’s distinction between two possible ways of conceiving the individuation of modes: by “differentiation” and by “delineation” (2023, 25-26). As Bunker points out, according to Moore’s account, negation in Spinoza would explain the delineation of finite things. In the case of the delineation of bodies, Moore uses the example of the house and the garden to show how finite bodies are distinguished from their “surroundings”: “a house and a garden each have a positive existence in their own right, but the house is not the garden, it ‘lacks being in the garden outside it’, as he [Moore] puts it” (10). According to this, bodies would be defined by a merely negative trait: their lack of being. To clarify this point, Moore compares Spinoza’s account of negation with his conception of error: “if one is right to reject p, and if someone else A accepts p, then, in Spinoza’s view, this indicates something lacking in A. All contents of A’s mind – all of A’s ideas, in Spinoza’s own terminology – are part of what is, and they pertain to what is, and they contain no error. The error comes about only because A is ignorant of what lies beyond these ideas and proceeds in a way that is appropriate to what is not” (2019, 242). But in his Ethics, Spinoza carefully distinguishes error from ignorance. Error is not ignorance, but the deprivation of knowledge implicit in inadequate ideas (2p35d).[1] And an idea becomes inadequate when we consider the idea perceived by the human mind together with the idea of something else (2p11c). For example, if Oedipus had grown up an orphan, he would not know who his mother is, but he would know that he does not know. But by believing that his mother is Merope, he does not even know that he does not know. We say that Oedipus is deprived of knowledge of his mother by considering the idea in Oedipus’ mind (the idea that his mother is Merope) alongside another idea outside his mind (the idea that his mother is Jocasta). Therefore, error, as a privation, is something that happens to ideas when considering them in relation to other ideas, but it does not express anything positive about them. And what has been said about ideas, following Moore’s analogy, must be applied to bodies. Thus, finitude, understood as “delineation”, can only have a privative sense: it is a property that supervenes on bodies by relating them to one another, but it does not define them. On the contrary, “delineation” presupposes the previous “differentiation” of bodies and is built upon it.

That is why Bunker suggests a conception of bodies more faithful to Spinoza’s thought: bodies distinguish themselves as proportions of “motion and rest” (10). Indeed, motion does not imply the negation of rest, nor vice versa. Motion and rest are not contrary terms but correlative. Yet, if we accept that bodies distinguish themselves and differ from each other relationally, we will see that the example of the house and the garden will simply not do. Firstly, because nothing prevents us from conceiving the house and the garden as finite substances existing by themselves and conceivable independently of each other: we can conceive of a house without a garden and a garden without a house. And, secondly, because not being a garden does not express any positive feature of the house, just as not being a house does not say anything about the garden. Thus, as Bunker notes, by presenting finite bodies as the outcome of a delineation process, Moore envisages Spinoza’s bodies in a Cartesian manner, that is, as the “parts” that result from dividing extension. To illustrate and further develop the interpretation of Spinoza’s account of bodies suggested by Bunker, I propose to imagine them as chess pieces. The knight is not distinguished from the bishop by its figure, nor even because it lacks something that the bishop has, but by the distinctive moves it can carry out. In turn, the actual mobility of a knight at a given position and time can only be adequately conceived by considering the position and potential moves of the surrounding pieces on the chessboard. In that sense, the knight is not distinguished from its surroundings by a negative feature since its singular essence (its capacity of movement in certain and determined circumstances) includes the complete configuration of the remaining pieces of the board that condition and determine it. And so, since each finite mode implies each of the infinite configurations of pieces that can be arranged on a chessboard, these modes, as Bunker proposes, should be conceived as “aspects” rather than “parts” or, in other words, as each of the infinite gestures of an infinitely expressive face.[2]

3. I now turn to an aspect of Moore’s interpretation of Spinoza that Bunker has not addressed in her reply. It regards the anthropological significance of infinity and its relation to nihilism and the relativity of values. I aim to stress several points of Spinoza’s thought that I think Moore has failed to notice and that differ considerably from his own views on the matter. For Spinoza, the human mind is nothing but the idea of a body (2p13). But the mind does not know itself except by the affections that its body experiences when it is determined by an external body (2p23). Moreover, the idea of this affection does not imply an adequate idea of the body itself (2p19) or the external body (2p25). Consequently, our immediate perceptions appear to us as conclusions without premises, mutilated and detached from the set of relations that determines them. And this is what explains the human inclination to regard the things of the world as finite substances, that is, as free or causes of themselves, for to imagine something as free is simply to imagine it (5p5). Only the idea of God (understood but not imagined) will enable us to escape from the prison of finitude and conceive of ourselves and the things around us as modes of an absolutely infinite substance.

Conversely, in conceiving of things as substances, we believe that we like something because it is good: we like ice cream because it is good, or we are fond of a particular fellow because he is nice. Goodness is an attribute of ice cream, regardless of who tastes it. But when those same things, as we change our disposition towards them and how they affect us, do not meet our expectations, we will consider them deprived of the goodness we once attributed to them and thereby we despise them. In this way, we will fall into contempt of the world, or as Nietzsche would say, into the ascetic ideal. Indeed, one could argue that, for Spinoza, contempt is the quintessential metaphysical passion insofar as it leads us to focus on what is not rather than on what is (3p52s). Instead, by conceiving things as modes, we will understand that ice cream is only good insofar as we like it. Moreover, instead of despising the things of the world, deriding, or condemning them, we will try to understand how they enable us to enjoy their potentialities to the best of our ability. Therefore, the relativity of values in Spinoza does not lead us, as Moore believes, to nihilism (2019, 252-3) but rather constitutes its antidote.

But this entails another critical side of Spinoza’s relativism that neither Moore nor Bunker have considered. For it is the same antidote that spares us from falling into nihilism that allows us to free ourselves from remorse, as long as conceiving of things as modes involves conceiving ourselves as so. Only by conceiving ourselves as substances, that is, as the cause of our affections and actions, can we regard ourselves as the cause of our sadness, adding to it remorse and abjection. In this sense, the other side of contempt for the world is contempt for oneself. Thus, for instance, if I believe myself to be the cause of my own jealousy, I will add to this sorrow the hatred I feel for myself as the cause of this despicable passion (4p54). If, on the other hand, I remove free will from the equation and conceive of my affections as modes, I will understand that my jealousy is the necessary and inevitable effect of the relations I establish with my environment, which determine me. Thus, instead of cursing myself and trying to repress what I feel, I will look for ways to escape this situation, provided it is within my reach.

4. I still vividly recall when, many years ago, my old logic professor, Calixto Badesa, proposed The Infinite as recommended reading in his subject. The clarity and depth of its analysis, the enormous erudition, and the originality of its philosophical proposal made a deep impression on me. Since then, Moore’s book has become an inseparable companion and an obligatory reference on the subject of infinity, making me reread it several times. I immediately got a copy when I discovered that Moore had published a third edition in which he expanded his account of Spinoza. I hoped to find something I had missed in the previous editions, such as, for instance, a thorough treatment of the concept of infinity that Spinoza expounds in his famous letter to Lodewijk Meyer or an interpretation of his unique conception of the mediate and immediate infinite modes. Although Moore cites the Letter on the Infinite in a footnote (2019, 249 n. 8), his interest in Spinoza leads him to focus on other aspects of his thought, especially those of an ethical and moral character, which he manages to integrate into his essay without undermining his central thesis: “Hardly anything in what follows will constitute an outright retraction of what has gone before” (237). I believe, however, that by overlooking those features of Spinoza’s thought most at odds with his views, Moore has missed the opportunity to engage with a real devil’s advocate, which might have led him to refine and reinforce his claims.

In my reply, I have deliberately chosen to emphasise the most controversial points of Bunker’s reply and pinpoint other problem in Moore’s interpretation of Spinoza that in my view she omits. However, these critiques do not take away from my deep agreement with Bunker about the importance of this book, not only as a major philosophical contribution but also as an unavoidable reference for those interested in the history of the concept of infinity and its philosophical complexities. In addition, the divergences I have stressed between Spinoza’s and Moore’s philosophical propositions should not conceal their deep affinity, as Bunker has pointed out in her reply. Anyone who opens for the first time the third book of the Ethics may have the strange impression that Spinoza has tried to work a love-story or an elopement into the fifth proposition of Euclid. With his essay, Moore has undeniably shown the intimate implications that a concept as seemingly abstract and mathematical as the infinite has in the ethical and existential domain of our lives.

montosa@ub.edu

REFERENCES

Bunker, Jenny. 2023. Infinity and Beyond? Learning How to Be Infinite. Public Reason 13 (2): 23-37.

Lin, Martin. 2006. Substance, Attribute, and Mode in Spinoza. Philosophy Compass 1 (2): 144-53.

Moore, A.W. 2019. The Infinite, 3rd edn. London: Routledge.

———. 2023. Replies. Public Reason 13 (2): pp. 97-121.

Spinoza, Benedictus de. The Collected Works of Spinoza. Vol. 1, ed. and trans. by Edwin Curley. Princeton: Princeton University Press.

1] All references to the Ethics are to Curley’s translation: Spinoza 1985.

2] On the conception of modes as gestures see Lin 2006, 151-152.

© 2022 by Public Reason

Public Reason 14 (1): 44-67

The Possibility of Kantian Armchair Knowledge[1]

Sorin Baiasu

Keele University Abstract. In his masterful essay, “Armchair Knowledge: Some Kantian Reflections”, A.W. Moore claims that Kant lapses into contradiction as a result of invoking transcendental idealism as a solution to the puzzle of what Moore calls “armchair knowledge”. Moore talks about “the incoherence of transcendental idealism” and, through a discussion which includes the question of whether different subjects possess different categories, offers an account of armchair knowledge without transcendental idealism. He suggests we should abandon the Kantian a priori intuitions and, with them, also Kant’s synthetic a priori judgements. In this paper, I examine some of the problems identified by Moore in Kant’s account. I do not aim to show that there is no internal inconsistency in Kant’s thought or that Moore (perhaps continuing in this way Kant’s project of uncovering the deceptions of transcendental judgements) might not be right to point to potential problems in Kant’s texts; my claim is rather that there are resources in the Kantian corpus to explain away the main contradictions and conflicts Moore identifies in Kant.

Key words: Kant, Adrian W. Moore, transcendental idealism, knowledge vs. cognition, armchair knowledge, things in themselves.

1. Introduction

In the Critique of Pure Reason, in the second division of Transcendental Logic (namely, Transcendental Dialectic), Kant aims to uncover the illusion of transcendental judgements and to keep it from deceiving us; he notes, however, that Transcendental Dialectic cannot make that illusion disappear and warns us that it will hoodwink and thrust reason incessantly into momentary aberrations, which we will then need to remove. (A297-8/B354-5)[2]

In his masterful essay, “Armchair Knowledge: Some Kantian Reflections”, A.W. Moore claims that Kant lapses into contradiction as a result of invoking transcendental idealism as a solution to the puzzle of what Moore calls “armchair knowledge”.[3] Moore talks about “the incoherence of transcendental idealism” (33)[4] and, through a discussion which includes the question of whether different subjects possess different categories, offers an account of armchair knowledge without transcendental idealism. He suggests we should abandon the Kantian a priori intuitions and, with them, also Kant’s synthetic a priori judgements.

In what follows, I will examine some of the problems identified by Moore in Kant’s account, with particular focus on the contradiction he thinks Kant commits as a result of being forced to accede to synthetic armchair knowledge of how things are in themselves.[5] I discuss Moore’s notion of armchair knowledge, Kant’s distinction between cognition [Erkenntnis] and knowledge [Wissen], the conflict Moore identifies between the necessity and contingency of synthetic armchair knowledge, and the claim that Kant has to be incoherently committed to synthetic armchair knowledge of things in themselves. I will also make a brief note on Moore’s discussion of whether different subjects can have different pure concepts.

I do not aim to show that there is no internal inconsistency in Kant’s thought or that Moore (perhaps continuing in this way Kant’s project of uncovering the deceptions of transcendental judgements – hence the subtitle of his talk, “Kantian Reflections”) might not be right to point to potential problems in Kant’s texts; my claim is rather that there are resources in the Kantian corpus to clarify the significant conflicts Moore thinks Kant ends up with.[6]

2. PUZZLES: ARMCHAIR KNOWLEDGE AND KNOWLEDGE OF WHAT IS NECESSARY AS NECESSARY MOORE DEFINES ARMCHAIR KNOWLEDGE AS “KNOWLEDGE THAT IS INDEPENDENT OF EXPERIENCE, IN THE SENSE THAT IT IS NOT WARRANTED BY EXPERIENCE”. (23) THIS IS NOT ARMCHAIR-RELATED KNOWLEDGE (SAY, OF HOW COMFORTABLE THE ARMCHAIR IS), BUT KNOWLEDGE ACQUIRED BY THE SUBJECT[7] WHILE SEATED IN THE ARMCHAIR. THE TERM “ARMCHAIR KNOWLEDGE” IS USED BY MOORE TO REFER TO A PARTICULAR TYPE OF A PRIORI KNOWLEDGE, NAMELY, A PRIORI KNOWLEDGE THAT IS INDEPENDENT OF EXPERIENCE.[8],[9] ONE FEATURE MOORE TAKES TO BE CRUCIAL FOR ARMCHAIR KNOWLEDGE IS THAT IT DOES NOT INVOLVE ANY APPEAL TO ANY PARTICULAR ENCOUNTER WITH ANYTHING BEYOND THE SUBJECT.[10]

Moore thinks that accounting for armchair knowledge is one of the oldest philosophical puzzles. It is generated by the fact that there seems to be such knowledge (and, hence, it is acquired without any use of any particular encounter with anything beyond the subject) and, yet, some of it appears to concern what is beyond the subject. Moreover, some such knowledge concerns not only just some of what is beyond the subject, but all of what could possibly be beyond the subject.[11] The puzzle is summarised by Moore as follows: (i) there is armchair knowledge; (ii) some armchair knowledge (if such there be) concerns what is beyond the subject; and

(iii) armchair knowledge does not involve any appeal to any particular encounter with anything beyond the subject. (24)[12]

There are philosophers who think the puzzle can be solved, and adopt a form of idealism: they claim that some of what is beyond the subject has a form – a range of essential features – that depends on the subject. (25)[13] Hence, no use needs to be made, in acquisition of this knowledge, of any particular encounter with anything beyond the subject. (25)[14]

Moore attributes this view to Kant. He thinks the attraction of this view is not limited to the puzzle of armchair knowledge, but goes beyond to account for some knowledge of what is necessary. Moreover, “it can be used to account for (some) knowledge of what is necessary, as necessary.” (25 - e.o.) After all, according to Moore, Kant takes it that all armchair knowledge, simply qua armchair knowledge, is knowledge of what is necessary. For example, some armchair knowledge might be knowledge to the effect that whatever has the given form is of such and such a kind; then, for Moore, Kant’s view is that some of this knowledge is also knowledge to the effect that whatever has the given form must be of such and such a kind.

This, however, (namely, how to account for knowledge of what is necessary as necessary) is, according to Moore, another old philosophical puzzle. The puzzle is given by the implication that, finite and contingent beings like us, who have knowledge of what is necessary, must have “epistemic access to all the ways things might have been”. (25)[15] A solution to this puzzle, Moore claims, is to find a grounding for necessity in contingency. On his view, Kant attempts to offer a successful account of this kind.

This is how Moore interprets Kant: Kant’s idealism maintains that the part of the subject’s armchair knowledge, which pertains to the given form, is knowledge from a particular point of view; a point of view admits of alternatives; hence, the subject’s having this point of view is the contingency in which necessity is grounded; this does not compromise necessity, since there is not “anything in his idealism to preclude the subject’s continuing to have, and continuing to exercise, knowledge from the given point of view”; (26) such knowledge, however, cannot itself include acknowledgement of the idealism.

At this point, Moore introduces the notion of i-dependence, the dependence posited by the idealist (of the form of what is beyond the subject on the subject). With this notion, he claims, transcendental idealism can be read as a version of idealism in which i-dependence is not itself included in whatever has this form. By contrast, empirical idealism is idealism in which i-dependence is included. Kant’s idealism is transcendental, since it assigns contingency to the i-dependence: (for it allows that there might not have been any such subject, nor therefore any such form depending on any such subject), and this contingency, simply qua contingency, must transcend the necessity attendant on whatever has the form in question. (26) Next, Moore focuses on the distinction between analytic and synthetic armchair knowledge. He notes that, for Kant, we can distinguish between these two kinds of armchair knowledge, a distinction related to Kant’s distinction between intuitions and concepts. The subject is given various objects of knowledge by means of intuitions and she thinks about these objects by means of concepts. Moreover, Moore observes that any knowledge, “at least if it has what Kant calls ‘content’”, must make use of both intuitions and concepts. (27) Distinctive about analytic knowledge, Moore remarks, is that the exercise of concepts does all the relevant work: the subject can know that what is being thought is true by appeal to the concepts involved and by analysis of them. By contrast, in the case of synthetic armchair knowledge, the subject must also appeal to the intuitions involved. This would seem to suggest that no analytic armchair knowledge concerns what is beyond the subject.[16] Yet, Moore maintains that we are not forced to conclude this: There is a perfectly good sense of ‘concern’ in which the subject’s analytic armchair knowledge that all vixens are female, say, concerns vixens, not the subject’s concept of a vixen, nor any part of the subject’s conceptual repertoire. […] Indeed my own view is that Kant allows for analytic armchair knowledge that lacks content, that is to say analytic armchair knowledge in which the concepts involved do not relate to intuitions, and that even knowledge of this kind can, in the relevant sense of ‘concern’, concern what is beyond the subject. An example might be the subject’s knowledge that things in themselves are things irrespective of how they are given to us, knowledge which concerns things in themselves. (27-8 - e.o.) The first point noted by Moore in this quotation is that analytic armchair knowledge, although true only by appeal to the concepts involved and by analysis of them, nevertheless also concerns what is beyond the subject. This is significant, since it suggests there is analytic armchair knowledge. The second point noted by Moore here is that this analytic armchair knowledge can concern things in themselves. I discuss these claims in more detail, in the next two sections, and I start with Moore’s notion of armchair knowledge and its relation to Kant’s distinction between cognition [Erkenntnis] and [Wissen].

3. ARMCHAIR KNOWLEDGE, KNOWLEDGE [WISSEN] AND COGNITION [ERKENNTNIS]

Immediately following the previous quotation, Moore inserts the following footnote: Note that the distinction between knowledge and cognition that many Kant exegetes draw is very pertinent to what I am suggesting here and may help to make what I am suggesting appear less exegetically contentious. (28 n19) In order to try to mitigate unnecessary exegetical contention, in this section, I will focus on Kant’s distinction between knowledge and cognition, and their relation to Moore’s armchair knowledge. In this footnote, Moore makes reference to another footnote, from his chapter on Kant (2012: Ch. 5) in The Evolution of Modern Metaphysics. (2012: 112-3 n13) My starting point will be this second footnote, which is quite substantial and exegetical.

First, the context in which, in The Evolution, Moore discusses Kant’s distinction between knowledge and cognition is given by a discussion of Kant’s distinction between “truths that can be known a priori and truths that cannot”. (2012: 112) The respective footnote then follows. In this footnote, Moore notes that he uses ‘knowledge’ for Kant’s ‘cognition’. He says he agrees with the translation of Kant’s ‘Erkenntnis’ by ‘cognition’, as he thinks that whatever Kant means by ‘Erkenntnis’, it is not ‘knowledge’. This raises the following question: if Erkenntnis, the term in Kant usually translated by cognition, is not knowledge, then why does Moore use ‘knowledge’ for Kant’s ‘cognition’? We will examine his justification for this, but for the moment, let us follow Moore’s discussion in this footnote further.

He notes that Kant takes ”Erkenntnis” to be “the conscious representation [Vorstellung] of an object”[17], and notes that this excludes some knowledge [Wissen] and includes some non-knowledge. The Wissen that Erkenntnis excludes, Moore continues, is “knowledge that is purely conceptual and makes no reference to any object”, but, Moore notes, this is not the same as analytic Wissen (which is purely conceptual and need not make reference to any particular object either, although (as we have seen at the end of the previous section) Moore introduces a sense in which it “concerns” objects or what is beyond the subject).[18] By contrast, the purely conceptual Wissen without reference to any object that Moore has in mind seems to be Wissen of things in themselves, for instance, “knowledge that there are things in themselves” (2012: 133 - e.o.), which he also offers as an example in the paper I am currently discussing.[19]

This suggests that Moore may accept analytic Wissen (perhaps even analytic knowledge of things in themselves) as the kind of knowledge included by Erkenntnis. The kind of knowledge that is excluded is, therefore, (perhaps merely) synthetic knowledge of things in themselves. As suggested just above and as we will see further on in this paper, Moore thinks that Kant incoherently must nevertheless make room for this kind of knowledge as part of cognition.

The non-Wissen that Erkenntnis includes is “the conscious representation of an object that contains some error”.[20] If Erkenntnis excludes some Wissen and includes some non-Wissen, then, at best, ‘Erkenntnis’ and ‘Wissen’ can overlap. Now, one reason why Moore wants to talk in terms of ‘knowledge’, when Kant uses ‘cognition [Erkenntnis]’, is that (he says) it “connects better with my broader concerns”; his justification for using ‘knowledge’, however, is that: in all the relevant contexts, the questions that Kant raises about cognition, and the answers that he gives are equally questions and answers about knowledge. When he asks, for example, how cognition of a certain kind is possible […],[21] the kind of cognition in question is likewise a kind of knowledge (m.e.).[22]

Hence, Moore relies on the fact that the notions overlap in all the relevant contexts; in the relevant contexts, the kind of cognition Kant discusses is also a kind of knowledge. This is how footnote 13 in The Evolution of Modern Metaphysics, Ch. 5, ends. In the next section, I focus on the relation between Moore’s armchair knowledge and Kant’s distinction between Erkenntnis and Wissen.

4. KNOWLEDGE [WISSEN] AND COGNITION [ERKENNTNIS]

When Moore talks about Kant’s Erkenntnis, one passage to which he refers from Kant is the famous Stufenleiter passage at A320/B376-7 (e.o.), where Kant refers to a chart of kinds of presentations: The genus is presentation [Vorstellung] as such (repraesentatio). Under it falls presentation with consciousness (perceptio). A perception that refers solely to the subject, viz., as the modification of the subject’s state, is sensation (sensatio); an objective perception is cognition (cognitio). Cognition is either intuition or concept (intuitus vel conceptus). An intuition refers directly to the object and is singular; a concept refers to the object indirectly, by means of a characteristic that may be common to several things.

”Cognition” is defined here as objective presentation with consciousness. ‘Objective’ seems to mean reference (whether direct or indirect) to an object, distinct from the subject. In the ”Dohna-Wundlacken Logic”, the passage to which Moore refers clarifies these notions further: the consciousness which accompanies the objective presentation is described as “an action in the mind […a] (presentation of our presentation), which is lacking in obscure presentations.” (24:701 - e.o.)[23] In the ‘Jäsche Logic’, Kant offers also an example; he explains that to cognise is “to be acquainted with something with consciousness” and adds that “[a]nimals are acquainted with objects too, but they do not cognise them”. (9:65 - e.o.) This suggests that, on Kant’s account, (some) animals have “obscure” presentations of objects, are acquainted with them, but without having also presentations of the respective presentations of the objects (that is, consciousness). Hence, they lack cognition of objects, although they have presentations.

One thing to note is that there are variations in the ways Kant defines Erkenntnis. For instance, in the KrV, he talks about the presentation of an object with consciousness, whereas in the ‘Jäsche Logic’ he talks about being acquainted with an object with consciousness. A second thing to remark is that, in some places at least, for Kant, both intuitions and concepts on their own count are cognitions. They refer (directly or, respectively, indirectly) to an object, and are conscious. The third interesting point is the distinction between the ways in which intuitions and concepts refer to objects – they, to use Moore’s terminology, “concern” objects in different ways.

The second aspect just mentioned (that intuition and concepts are on their own cognitions) offers an opportunity for a clarification. As suggested above, the Kantian notion of cognition, Erkenntnis, which Moore seems to have in mind in his discussion (let us call it EM), is broader than the notion of cognition requiring both intuitions and concepts, a notion that Kant also formulates explicitly (call this, EK). Thus, Kant says: [S]ynthesis of a manifold (whether this manifold is given empirically or a priori) is what first gives rise to a cognition. […] Bringing this synthesis to concepts, on the other hand, is a function belonging to the understanding; and it is through this function that the understanding first provides us with cognition in the proper meaning of the term. (A77-8/B103 - e.o.)[24]

Here Kant talks about EK. The different ways in which intuitions and concepts concern objects are thereby a bit further clarified by Kant: objects are given through intuitions and they are thought through concepts. This is a sense specified also by Moore. Hence, as mentioned above, the kinds of cognitions Moore seems to have in mind (EM) correspond in Kant to cognitions which require intuitions and concepts (EK), but also cognitions, where the presentation of objects with consciousness is given only by concepts or only by intuitions.

Now, as Moore notes, one way in which Erkenntnis is different from Wissen in Kant is that Erkenntnis need not refer to true presentations and, hence, includes what Moore calls “non-knowledge”. Thus, Kant notes that “if a cognition does not agree with the object to which it is referred then it is false, even if it contains something that might well hold for other objects”. (AA58/B83) But, if we focus on EM (which includes cognitions requiring both concepts and intuitions, but also cognitions involving only concepts or only intuitions) and set as condition that we refer only to true cognitions of the type EM (call this class of cognitions ET), are all cognitions in this special class cases of knowledge [Wissen], as Moore suggests? In other words, is knowledge in Kant a true presentation, accompanied by consciousness, which refers to an object either thought through concepts or given through intuitions or both given through intuitions and thought through concepts?

Kant’s discussion of knowledge [Wissen] in the ‘Canon of Pure Reason’ suggests the answer is negative: even the more restricted kind of Erkenntnis (ET) does not correspond to an appropriately restricted Wissen. Thus, in the Canon, Wissen is briefly introduced as a special case of assent or holding-to-be-true or considering-true [Fürwahrhalten]. ‘Assent’ is defined as “an event in our understanding that may rest on objective bases but that also requires subjective causes in the mind of the person who is judging”. (A820/B848) Hence, to know something is to assent to it in a particular way, as a result of judging it. This requires some subjective “causes” and may also require objective bases or grounds. In particular, Kant specifies that “assent that is sufficient both subjectively and objectively is called knowledge [Wissen]”. (A822/B850 - e.o.) Knowledge is the result of subjective causes, which convince me of the object of my assent, and of objective grounds, which give certainty about it. (A822/B851) As a form of assent, however, Wissen is distinct from Erkenntnis, which is a type of presentation – objective presentation accompanied by consciousness. What I assent to is a presentation, but, in addition to this presentation (which may be the object of a cognition of type EM), Kant specifies the need for some subjective and objective support, which, respectively, are sufficient to convince me of the truth of the presentation and to provide certainty for everybody.

How does this bear on Moore’s discussion so far? First, Moore’s justification for the use of ‘knowledge’, where Kant uses ‘cognition’, does not seem to hold, given that the notions are not the same even when the focus is on a narrower range of cases. An instance of Erkenntnis might be part of an instance of Wissen. For instance, an objective presentation might be the object of assent supported by sufficient subjective and objective grounds. Moreover, such an objective presentation may function as (or as part of a) sufficient objective ground for the object of a propositional attitude (in this case, assent). (Willaschek and Watkins 2020: 3210) Yet, contrary to Moore’s comments, Erkenntnis and Wissen are not overlapping concepts, in the way in which, say, the groups of possessors of mobile phones and of TV sets are; rather they are more similar to the concepts of triangles and quadrilaterals.

Moore says that Erkenntnis excludes Wissen that makes no reference to any object; however, Wissen that makes reference to an object is still distinct from Erkenntnis, although they both share the objective character (the reference to the object). By analogy, for instance, we can say that the class of triangles excludes concave quadrilaterals, since no triangle has angles over 180 degrees, although convex quadrilaterals and triangles are still distinct concepts, despite the fact that they share the property that their angles are not over 180 degrees. Moore also claims, as we have seen, that Erkenntnis includes non-Wissen, namely, the conscious representation of an object that contains some error. Yet, the conscious representation of an object that is true is not automatically Wissen. Similarly, we can say that the class of quadrilaterals includes some non-quadrilaterals, namely, those geometrical figures, which do not have only three sides. Nevertheless, these geometrical figures do not immediately count as quadrilaterals. This suggests that a reconsideration of the notion of armchair knowledge might be in order for Moore.

Secondly, consider Moore’s view that: There is a perfectly good sense of ‘concern’ in which the subject’s analytic armchair knowledge that all vixens are female, say, concerns vixens, not the subject’s concept of a vixen, nor any part of the subject’s conceptual repertoire. (27-8) The discussion of Erkenntnis in Kant shows that, as such, this suggestion by Moore about analytic armchair knowledge is quite unproblematic for the framework of Kant’s terminology. As we have seen (the third aspect I mentioned above, namely, the different ways in which intuition and concept refer to objects), Kant says that intuitions are singular and refer to objects directly, whereas concepts are general and refer to objects indirectly. Concepts refer to objects indirectly, since concepts include ‘marks’ or features, which are common to several objects, so they refer to a particular object through a particular feature, a feature which may be shared by other objects too. This also explains why concepts are general. Hence, we can see that analytic armchair knowledge can concern objects and indeed it concerns them in a different way than the type of cognition or Erkenntnis requiring both concepts and intuitions (EK) or the Erkenntnis, which consists of an intuition (as part of EM).

What may seem puzzling in Moore’s idea of analytic armchair knowledge, which concerns things in themselves, becomes clear when we consider EK, the restricted notion of cognition. If Moore uses “knowledge” when Kant uses “cognition”, and if we take “cognition” to refer to the notion that Kant regards as “cognition in the proper meaning of this term” (A78/B103)[25] – what I have labelled EK –, then we end up with a contradiction. Thus, EK requires both concepts and intuitions; at the same time, however, analytic cognition does not require intuition. Hence, Moore’s ‘analytic armchair knowledge’ becomes contradictory, since analytic Kantian cognition (analytic EK) would at the same time require and not require intuition.

Still, we have seen that the best way to interpret Moore’s understanding of ‘cognition’ is as a less restricted notion of cognition (EM, not EK), one which may include concepts and intuitions, but may also just consist of concepts or just of intuitions. On this broader notion of cognition, we can talk unproblematically about analytic cognition.

5. THE INCOHERENCE OF TRANSCENDENTAL IDEALISM AND OTHER CONTRADICTIONS WITH THESE TERMINOLOGICAL CLARIFICATIONS IN PLACE, LET US LOOK FURTHER AT MOORE’S ARGUMENT. HE RAISES TWO ASSOCIATED QUESTIONS, WHOSE FORCE CAN BE APPRECIATED IF WE NOTE THAT ANALYTIC ARMCHAIR KNOWLEDGE CAN BE REGARDED AS PART OF THE ORIGINAL PUZZLE OF ARMCHAIR KNOWLEDGE, SINCE, AS WE HAVE SEEN, FOR MOORE, THIS TYPE OF KNOWLEDGE, TOO, CONCERNS WHAT IS BEYOND THE SUBJECT.

Now, Moore thinks that Kant holds that transcendental idealism is needed to solve the puzzle with regard to synthetic armchair knowledge, but only with respect to synthetic armchair knowledge. (28) He thinks Kant’s reasons for holding this are not apparent yet. The two questions which arise are the following: (Q1) whether Kant would allow that transcendental idealism be invoked to solve the puzzle with regard to analytic armchair knowledge, even if it does not have to be invoked; (Q2) what it is about synthetic armchair knowledge that would make Kant think that transcendental idealism must be invoked to solve the puzzle with respect to synthetic armchair knowledge. (28) Moore thinks that, for Kant, the puzzle of armchair knowledge can be solved for analytic armchair knowledge by noting that the subject can acquire such knowledge just by analysing the concepts involved, even if we were to acknowledge that analytic armchair knowledge concerned what is beyond the subject.[26] There is no need to invoke i-dependence and transcendental idealism. Yet, Moore wonders whether, despite the fact that there is no need to do this, Kant would have anything against doing this.

The way Moore presents the situation is as follows. He asks us to imagine a philosopher who thinks that the form of what is beyond the subject (which, Moore adds, “depends on the subject and to which the subject’s armchair knowledge pertains”) is not confined to the features Kant asserts (spatio-temporal conditions, causality, etc.), but extends to “all those of its essential features that are in any way conceptual, such as the feature of being, if a vixen, female”; moreover, this philosopher thinks that the contingency of the i-dependence belongs equally to “the subject’s general conceptualisation of things” and to “the subject’s spatio-temporal intuition of them”. (29) Moore’s answer is that Kant would have something against this. This is because, on Moore’s account, Kant thinks a subject can have thoughts concerning things in themselves, for instance, as suggested above by Moore, some analytic armchair knowledge or, in its absence, the thought that we are free. If we think that the subject’s conceptualisation contributes as much to the contingency of the i-dependence as the subject’s spatio-temporal intuitions do, then the subject’s thinking, just like the subject’s intuiting, is always of appearances.[27]

But would this really be Kant’s concern? Let us stick for a moment to Kant’s model of the mind, which includes among its a priori structures pure intuitions, categories and ideas, but not other concepts. On this model, Kant claims we can think of things in themselves. But Kant does not believe that we can think of things in themselves specifically with the help of empirical concepts, which are not part of the a priori structure of the mind. He thinks we can think of things in themselves whatever we want as long as we are not contradicting ourselves and as long as we are aware that what we are thinking about through a concept might have no object corresponding to it (both in the sense that some concepts might not have real possibility, and in the sense that we might never cognise the object of some really possible concept, when we consider it as it is in itself). (Bxxvi n)[28] Hence, extending the a priori structure of the mind to include essential features that are conceptual is not going to make a difference to our capacity to have thoughts concerning things in themselves (at least as this capacity is understood by Kant).

So Moore here does not quite capture Kant’s reservation for the extended model of the mind and the extended solution to the puzzle of (analytic and synthetic) armchair knowledge. But even if he did, the question would still be whether Kant would be justified in rejecting this extended model and the associated solution. Moore thinks an answer to this question depends on an answer to the following question: [W]hen Kant argues from the existence of armchair knowledge concerning what is beyond the subject to the truth of transcendental idealism, at what point in his argument does he make crucial appeal to the fact that the armchair knowledge is synthetic, and, relatedly, what, in his own terms, would preclude someone’s extending the argument to armchair knowledge that is analytic? (30) Moore imagines two replies Kant might give to this question (which is a version of Q2). First, Kant might say that his argument for transcendental idealism is an inference to the best (and only) possible explanation. Extended to analytic armchair knowledge, the argument for transcendental idealism would no longer be the best possible explanation: the simpler explanation involving only the subject’s analysis of the concepts involved would be available. Secondly, on Moore’s account, Kant might say that the extended version of the argument rules out thoughts about things in themselves, which he is obliged to allow for “otherwise there would follow the absurd proposition that there is an appearance without anything that appears”. (30)[29]

Moore thinks that these responses are not “entirely satisfactory”. (30) With regard to the first, he thinks there would be a presupposition Kant would make, according to which the unity and power of an explanation that applies to all armchair knowledge is more significant than the simplicity of an explanation that applies only to analytic armchair knowledge. Yet, “there would be an obvious answer to this question if the first response were buttressed by the second”. (30) More exactly, if the second answer showed why the unity of the explanation was needed, the first answer’s presupposition would be justified. Still, Moore thinks that the second response also begs some questions about the coherence of Kant’s transcendental idealism.

As we have seen, however, on its own, the extended version of the argument does not challenge Kant’s requirement that we be able to think about things in themselves. Moreover, concerning the first reply, it is still unclear transcendental idealism would be an appropriate account of analytic armchair knowledge (even with the extended model of the mind stipulated by the imaginary philosopher mentioned above).

To answer Q2[30], Moore begins with a presentation of other positions, distinct from transcendental idealism and which are not even versions of idealism, which can claim to account for knowledge of what is necessary, as necessary. He gives the example of the view according to which the subject’s knowledge that vixens are female consists in command of a particular rule that prohibits counting a creature as vixen without also counting that creature as female.

Moore acknowledges that this is knowledge of a contingency (for there might never have been any such rule), but he thinks the necessity concerned is not compromised: If there had never been any such rule, vixens would not have failed to be female. Rather, what sex vixens are would not have been an issue for anyone: no-one would have thought in those terms. Vixens would not have failed to be female, because vixens must be female. And this ‘must’ is as hard as it either can or need be. (31 - e.o.)[31]

Moore calls this a Wittgensteinian view and regards it as “a variant of Kant’s view of analytic armchair knowledge”. (31)[32] He thinks that, by exploring how this Wittgensteinian view would not be similar to Kant’s view of synthetic armchair knowledge, we will be helped with addressing Q2. Moore begins with the observation that, on a Wittgensteinian view, given any relevant item of knowledge (e.g., the knowledge that vixens are female) sheer familiarity with the concepts involved ensures that one can see the truth of what is known.[33] By contrast, Kant insists that one cannot see the truth of what is known in the case of synthetic armchair knowledge without appeal to the intuitions involved. (31-2) Moore thinks that even in this case, Kant would accept that sheer familiarity with the concepts involved ensures that “one can see how things must be for what is known to be true [or…] that one can see, not the truth of what is known, but the truth conditions of what is known”. (32 - e.o.) [34] The example Moore gives is of the claim that the sum of the angles in a triangle is equal to two right angles. To show that this is not an analytic truth, we would need alternatives in which the sum of the angles is something other than two right angles (and these alternatives need not be realised; they only need to exist). Without such alternatives, there would be a sense in which sheer familiarity with the concepts involved would ensure that one could see the truth of what is known. (32) This, Moore thinks, leads us to an answer to Q2: synthetic armchair knowledge admits of alternatives qua synthetic; yet, qua armchair knowledge, admits of no alternatives. It is knowledge of both a contingency and of a necessity.

This is not the case for the knowledge that vixens are female, on the Wittgensteinian view. On this view, there seems to be no conflict between contingency and necessity – this is because the necessity attaches to the known truth itself (vixens are female), whereas the contingency is of the second-order truth that there is a rule in force whose statement consists in the enunciation of the first-order truth. The alternative is to that second-order rule’s being in force. By contrast, on Kant’s view, the alternatives “are alternatives to the known truth itself: in the example considered above, they are alternatives to triangles’ having angles whose sum is equal to two right angles”. (33 - e.o.)[35] Kant and Wittgenstein make “an attempt of sorts to ground necessity in contingency”; yet, whereas Wittgenstein does not need to appeal to transcendental idealism, Kant does, since Kant needs to “allay what would otherwise be a simple conflict between a claim of necessity and a claim of contingency with respect to one and the same truth”. (33)[36]

I find the assertion that there is a conflict between a claim of necessity and a claim of contingency in Kant problematic. I agree that Kant takes the truths of disciplines, such as geometry, to be necessary. He is trying indeed to account for this necessity. Pure intuitions (and transcendental idealism) play indeed here a crucial role and, without pure intuitions, he takes the claim that the sum of a triangle’s angles is two right angles to be contingently true. The concept of the sum of a triangle’s angles (call this concept S) does not include as an essential feature the concept of two right angles (call this concept P). Yet, this fact about the relation between S and P, namely, that S does not include P, is not changing when we consider the triangle’s angles and right angles as geometrical objects. The claim about geometrical objects can be necessary, even though the distinct claim about the concepts of those geometrical objects is not.[37] It is, therefore, unclear that a conflict exists between the necessity and contingency of the same truth.

This, however, is not the most serious objection Moore formulates against Kant. Moore thinks that Kant solves the conflict between contingency and necessity by introducing some appropriate relativisation: He holds that the truth in question is necessary from a particular point of view, the very point of view that the subject’s knowledge is from, constituted, in part, by the intuitions to which the subject appeals in having the knowledge. But when the truth is not considered from that point of view – when a step back is taken to reflect on why appeal to these intuitions is necessary to have knowledge of the truth, which is done precisely by not appealing to them but rather by duly prescinding from them – then Kant thinks that the truth can be conceived as admitting of alternatives. (33 - e.o.)[38]

Moore notes that Kant’s transcendental idealism is introduced “to explain how the subject can have armchair knowledge of what admits of such alternatives”. (33) The relation of i-dependence follows from this. This relation, Moore adds, “has to be conceived as transcending the necessity in question. For the i-dependence cannot so much as be entertained until that step back is taken from the original point of view”. (13)[39] We get in this way to Moore’s discussion of the incoherence of transcendental idealism.[40] Moore acknowledges that Kant is vindicated in his claim that transcendental idealism is needed to solve Kant’s puzzle of synthetic armchair knowledge. Yet, he thinks that Kant’s account quickly runs into difficulties. The step back from the original point of view is not to another point of view, but to no point of view at all, it is a step to thinking how things are in themselves. Yet, Moore claims: This would be all very well if such thinking were only ever mere thinking. Kant is not involved in any internal inconsistency simply in allowing us thoughts about things in themselves. The problem is that, by Kant’s own lights, such thinking sometimes amounts to knowledge. (34 - e.o.) The example given by Moore is the thought that there is synthetic armchair knowledge. This, Moore claims, is a piece of knowledge and, moreover, a piece of synthetic armchair knowledge. It is not analytic and it is not based on experience. Hence, Kant “is, by his own lights, forced to accede to the very thing that it is his business to deny, synthetic armchair knowledge of how things are in themselves”. (34) This, Moore thinks, shows that Kant ends up with a contradiction; it does not invalidate the argument for transcendental idealism, but, in order to avoid the contradictions to which transcendental idealism leads, we can reject synthetic armchair knowledge. We might reject it because there is no armchair knowledge or there is only analytic armchair knowledge or there is something wrong with the distinction between analytic and synthetic armchair knowledge or for some other reason.

6. A Kantian Solution to the Metaphysical Contradiction

I think Moore’s argument is the following: Kant wants to account for (what he takes to be) the necessity of certain claims in disciplines, like geometry. A claim like the one we discussed above, concerning the angles of a triangle, will appear as necessary when the pure intuitions of space and time are regarded as constitutive of experience. Pure intuitions can be regarded as constitutive of experience, when they are acknowledged as a priori structures of the subject (hence, when i-dependence is acknowledged), that is, when they are regarded from a different point of view than that of the subject. This different point of view, however, is not that of another subject, but is supposed to be no point of view at all, the perspective independent from that of the subject and, hence, the perspective of things in themselves. In general, to account for synthetic armchair knowledge, we need to acknowledge i-dependence, which Moore thinks moves us into the no-perspective position of things in themselves. Hence, knowledge[41] that there is synthetic armchair knowledge is synthetic[42], is not empirical[43] and is about things in themselves.[44]

Now the claim that there is synthetic armchair knowledge is indeed a synthetic claim, as any existential claims are. Moreover, I agree that it is not an empirical claim. As Moore notes, Kant provides an argument in support of the claim that a particular claim or other is synthetic a priori. The a priori character of a claim cannot be justified by appeal to experience. The claim that there is synthetic a priori knowledge seems therefore also to be a piece of knowledge (perhaps even in accordance with Kant’s notion of knowledge [Wissen]) and, more precisely, a piece of synthetic knowledge, which is not based on experience. This is why Moore regards it as a piece of synthetic armchair knowledge. Moreover, since to show that a particular claim is synthetic a priori knowledge we need to invoke an argument about i-dependence and the status of pure intuitions, Moore thinks that Kant puts here forward a piece of synthetic armchair knowledge about things in themselves. Yet, he takes this to be incoherent, since he takes Kant to deny synthetic armchair knowledge of how things are in themselves.

There are two issues here. First, the claim that there is synthetic a priori knowledge is not a claim about how things are in themselves. It is a claim about the existence of a particular type of knowledge, namely, the synthetic a priori type. The concept of synthetic a priori knowledge refers to knowledge about phenomenal entities, such as triangles. So the claim is that there is knowledge about phenomenal entities, not things in themselves. I will return to this, but consider first a possible reply from Moore: what is the status of a claim that there are things in themselves, a claim to which some commentators say Kant is committed (for instance, see n49 below)? Is this not synthetic a priori knowledge of things in themselves – is this not synthetic armchair knowledge of things in themselves?

First, a clarification: at Bxxvii, Kant makes the claim Moore quotes repeatedly in his paper, namely, that, without things in themselves, “an absurd proposition would follow, viz., that there is appearance without anything that appears”. Yet, Kant takes this absurd proposition to be the conclusion of a reductio whose starting point is not that things in themselves exist, but that we must be able to think of things in themselves.[45] Kant also explicitly acknowledges that we might not be able to cognise things in themselves.[46] He explains, in a footnote (Bxxvii n), that to cognise an object I must be able to “prove [beweisen] its [real] possibility”, and he contrasts merely logical possibility (which is a condition for an object to be thought) and real possibility, which shows the “objective reality” of a concept. (Bxxvi n) He specifies that, to show the real possibility of an object and, hence, to cognise it, I can proceed from “its actuality as attested by experience, or a priori by means of reason”. (Bxxvi n) At the end of the footnote, Kant seems to specify that showing the real possibility of the concept of a thing in itself by means of reason is possible with “practical” sources of cognition.[47] Here, Kant talks about theoretical cognition in the restricted, “proper” meaning of the term (EK). As we have seen above, this requires both intuitions and concepts. Moreover, it also becomes clear that, insofar as cognition requires the real possibility of the object to be cognised, a cognition in the extended sense (including those presentations given by concepts only) does not qualify as such, since, as we have seen, concepts refer to objects only indirectly, through a characteristic mark, which can belong to several objects. Similarly, while intuitions are cognitions which can show the actuality of their respective objects, on their own, without the understanding, the cognitions they would provide would be limited to this actuality.

So, on the basis of theoretical sources of cognition, with regard to things in themselves, we cannot show that they exist (that they are really possible), although Kant seems to suggest that we can show that they exist as objects of our thought (that they are logically possible). Hence, Kant’s claim concerning the existence of things in themselves refers to their possibility. The epistemic claim concerning things in themselves, more exactly the fact that we do not have epistemic access to them, is about cognition [Erkenntnis]. Given that Moore uses ‘knowledge’ for Kant’s ‘cognition’, he is right to interpret Kant as claiming that we cannot have knowledge (cognition, in the restricted, “proper” meaning of the term) of things in themselves. This is because, by definition, we cannot have intuitions of things in themselves. It becomes also clearer that Kant’s focus is on the restricted notion of cognition.

Now, consider the case where the claim ‘there are things in themselves’ is a knowledge claim in the Kantian sense of ‘knowledge’. It is a synthetic claim, since it is an existential claim. It is not derived empirically, since we cannot have intuitions of things in themselves. The synthetic link between the concept of a thing in itself and the concept of existence is not grounded in an a priori intuition. Here the reductio might work as a justification of our assent to the synthetic claim that things in themselves exist. If we assume appearances exist and are not mere illusion, then things in themselves exist too, since without them we would have the absurd claim that appearances exist and are illusions at the same time.[48]

The difference between a cognition of things in themselves and knowledge of things in themselves is that a cognition (EK) offers a presentation of the object (by appeal to both intuition and concept), whereas knowledge is justified assent to a presentation. This justification, however, need not make reference to intuition, but can be any objective support for the given presentation. As a result, Kant has sometimes been interpreted as being committed to the existence of things in themselves, in virtue of the sufficient objective and subjective justification of assent to this existence: the synthetic presentation of things in themselves as existing has been regarded as objectively justified by arguments independent from a cognition of things in themselves, which would imply intuition.[49]

This would seem to suggest that Moore is right – Kant asserts that we have knowledge of a synthetic a priori cognition concerning things in themselves, knowledge which he, at the same time, denies. Yet, and this is the second issue I wanted to mention, it is unclear what we have here is a genuine contradiction. The claim that things in themselves exist is indeed a synthetic claim. What this claim implies is that things in themselves are not only logically possible, but also really possible. Kant suggests, however, that the first reductio mentioned above does not yet prove the real possibility of things in themselves. Things in themselves are regarded as necessary presuppositions of the appearances that we encounter in experience; yet, the reductio only works if we attribute certain other features to these appearances, such as empirical reality.

The empirical reality of the objects we encounter in experience might be the best possible explanation we can have given our experience. The same goes for the reality of our freedom – it seems to us we are both free and subject to laws of nature, and the question is how to reconcile these claims. Hence, at most, such arguments show the necessity of assuming things in themselves exist as (possible) objects of thinking. This is not surprising, because we do not have intuitions of things in themselves, so the only cognition we can have is indirect, through the concept of a thing in itself and without direct reference to a specific thing in itself or other. But the truth of such a presentation only shows something about all the other things which stand under the concept. The experience of a specific object will give me that object and, hence, will show that the concept of that object has at least one instantiation. The concept of a specific object will only refer to the group of the objects falling under the concept, but, if it is not possible to have intuitions of specific objects of that type, then all an argument can show is that it is possible to draw a distinction and think in terms of that concept.

Before moving on to some concluding remarks, I would like to return to the question of the status of the claim that there is synthetic a priori knowledge. Consider the following reply: since this is a claim of existence, it is a synthetic claim; moreover, its truth does not rely on an empirical encounter of such knowledge, but on the argument in support of the particular synthetic a priori knowledge item under discussion (say, that about the sum of the triangle’s angles). Defenders of Kant might want to say that this is not a claim about things in themselves, as I have also argued above; yet, as we have seen, the claim relies on the assumption of i-dependence (the dependence of the form of what is beyond the subject on the subject), which is formulated from the perspective of things in themselves. When I step back from my limited perspective into the absolute world of things in themselves and I make a claim, is this not a claim about things in themselves or, rather, a claim about its object considered as a thing in itself?

My response, for the particular case considered by Moore, is negative. To see this, consider an analogy with a picture, which seems to me to have been taken with a camera, which had an orange-tinted lens. The assumption of the constitutive chromatic filter, which contributes to the picture, is analogous to the assumption of the a priori intuitions of space and time, which are constitutive of experience. These assumptions introduce a distinction between the appearance given by experience and the way things would be independently from the elements which constitute the experience. Now, my claims that the picture is necessarily orange, when taken with that camera, and that the sum of a triangle’s angles necessarily equals two right angles have an apodictic character, but they are claims about how we experience the objects, rather than about how objects would be in themselves. If a priori intuitions are contingent on the epistemic agent, then the claim about the triangle’s angles considered in itself would be assertoric, rather than apodictic. Similarly, the claim about the chromatic properties of the photographed landscape would be assertoric, if I were to regard the photographed landscape independently from the orange-tinted lens.

In addition and importantly, the claims which rely on the assumption of some constitutive elements, and, hence, which introduce the distinction between appearances and things as they are in themselves (and, hence, between the limited perspective of the epistemic agent and the absolute world of things in themselves) do not rely on any implicit appeal to intuitions of things in themselves. The assumption of the constitutive elements is one way of accounting for what is experienced, and the apodictic character of these claims or of the claims that things as they are in themselves are different from the way they appear to be are simply logical inferences from that assumption.

5. Concluding Remarks

Moore’s text continues with an advice that we should abandon the view that there are a priori intuitions (a view Moore calls the Intuition Thesis). These, he says, are necessary in order for there to be synthetic armchair knowledge.[50] Without the Intuition Thesis, however, there is still the Concept Thesis – the thesis that there are pure concepts. If we accept the Concept Thesis, but abandon the Intuition Thesis, then we do not need to accept transcendental idealism. This holds even if we accept what Moore calls the “Relativised Concept Thesis’. (35) The latter allows for the possibility that different subjects (humans and extraterrestrials, for instance) possess different pure concepts. It is a thesis similar to the Relativised Intuition Thesis (which claims that different subjects possess different pure intuitions), which Kant explicitly endorses.

Moore notes two aspects of the relativised theses. First, concerning the Relativised Intuition Thesis, he observes that it is this thesis which may seem to make Kant’s commitment to transcendental idealism mandatory. Yet, Moore claims, what makes a commitment to transcendental idealism mandatory for Kant is the contingency Kant endorses in those intuitions’ being the way they are. Secondly, the contingency in the subject’s possessing such and such pure concepts is similar to the contingency in the subject’s abiding by such and such a rule on the Wittgensteinian view.

We are not forced to a relativisation of the necessities the subject acknowledges: if the subject’s possessing such and such pure concepts involves and is involved in the subject’s acknowledging that things must be thus and so, it does not follow that things might not be thus and so for subjects not possessing those concepts. Subjects not possessing those concepts will not have an issue with whether things are thus and so – they do not think in those terms. In the final section of his paper, a notion of armchair knowledge which is not of what is necessary (but admits of alternatives) is presented. (40) On the basis of this notion of armchair knowledge, the argument for transcendental idealism, Moore claims, fails. He constructs two possible accounts of armchair knowledge, one inspired by Spinoza and one, by Aristotle. These are all fascinating topics on their own, but within the confines of this paper, I cannot investigate and evaluate them further.

Before, I conclude, I want to make a brief comment on Moore’s discussion of the Relativised Concept Thesis. Moore thinks this is of philosophical interest, since it may lead to the same problem he formulated against Kant before (the Modal Contradiction): the contingency of the subject’s pure concepts is the ground for the necessities the subject has armchair knowledge of; to acknowledge this contingency, the subject must take a step back from her point of view, and this, Moore claims, “is to credit her with the capacity to gain insight into how things are in themselves of just the sort Kant insists is impossible” (40) (leading to the Metaphysical Contradiction). However, if I am right and the various conflicts Moore points to do not in fact obtain, then this would not only relieve the transcendental idealist of some of the worries expressed by Moore, but may also explain why Kant does not discuss the Relativised Concept Thesis in his work.

As Moore notes, “it would be setting the bar too high to insist that one cannot make best sense of what Kant says unless one absolves him of all internal inconsistency”. (40) Absolving Kant of all internal inconsistency was certainly not my aim in this paper – my aim has been to address the important internal inconsistencies presented by Moore and to argue that they are less problematic than he suggests.

s.baiasu@keele.ac.uk References

Baiasu, S. 2016. “Is Kant’s Metaphysics Profoundly Unsatisfactory? Critical Discussion of A.W. Moore’s Critique of Kant”, in Kantian Review 21(3): 465-81.

———. 2013. “Kant’s Rechtfertigung and the Epistemic Character of Practical Justification”, in M. Timmons and S. Baiasu (eds) Kant’s on Practical Justification: Interpretive Essays. New York: Oxford University Press.

Kant, I. (1900-) Kants gesammelte Schriften. Ed. By the Königlich Preußischen Akademie der Wissenchaften, subsequently Deutsche, now Berlin-Brandenburg der Wissenschaften (originally under the editorship of Wilhelm Dilthey) (Berlin: George Reimer, subsequently Walter de Gruyter).

———. 1992. Lectures on Logic, J. M. Young (trans. and ed.), Cambridge: Cambridge University Press.

———. 1996. [KrV] Critique of Pure Reason, W. S. Pluhar (trans.), Cambridge, MA: Hackett.

———. 1998. [KrV] Critique of Pure Reason, P. Guyer and A. W. Wood (trans.), Cambridge: Cambridge University Press.

———. 1987. [KU] Critique of Judgement. W. S. Pluhar (trans.), Cambridge, MA : Hackett.

———. 2000) [KU] Critique of the power of judgement, P. Guyer and E. Matthews (trans.), P. Guyer (ed.), Cambridge: Cambridge University Press.

———. 2002. “Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward as a Science”, G. Hatfield (trans.), in Theoretical Philosophy After 1781, H. Allison and P. Heath (eds), Cambridge: Cambridge University Press.

Moore, A. W. (Forthcoming) “Armchair Knowledge: Some Kantian Reflections”, in Public Reason.

———. 2016. “Reply to Sorin Baiasu and Edward Kanterian”, in Kantian Review 21(3): 495-506.

———. 2012. The Evolution of Modern Metaphysics: Making Sense of Things. Cambridge: Cambridge University Press.

Willaschek, M. and Watkins, E. (2020) “Kant on Cognition and Knowledge”, in Synthese 197: 3195-3213.

1] Acknowledgements: I am grateful to participants to the 2019 'Rousseau' Annual Conference (which took place online in July 2021), particularly to Adrian Moore and Zachary Vereb, for their comments, questions and discussion. Part of the work on this paper was carried out while I was on institutional research leave. I am grateful to Keele University for making possible this period of research.

2] I am mainly relying on Werner S. Pluhar’s translation, in the 1996 unified edition of KrV, and on the translation by Paul Guyer and Allen W. Wood, in the 1998 CUP edition. Pagination references in the text and footnotes are to the volume and page number in the German edition of Kant’s works, Kants gesammelte Schriften (1900-). References to the KrV follow the A (first edition), B (second edition) convention. The translations I use are listed in the bibliography with any abbreviations mentioned after the publication year. Changes to the translation are indicated by “translation (slightly) modified”. The abbreviations “e.o.” and “m.e.” represent, respectively, “emphasis in the original” and “my emphasis, S.B.”

3] Moore’s paper is the text of his 2019 ‘Jean-Jacques Rousseau’ Annual Lecture, published in Moore (2023).

4] In what follows, unattributed page references are to Moore’s ‘Rousseau’ Annual Lecture in Moore (2023).

5] Below (see n40), this is called the Metaphysical Contradiction. I also discuss here two other contradictions: the Thinking Contradiction and the Modal Contradiction (see ns27 and 36).

6] In his paper, Moore refers to our previous exchange (2016) as a stimulus for part of the discussion in his ‘Rousseau’ Lecture. My aim in the contribution to the 2016 exchange was also to clarify away the significant contradictions he identified in Kant in his Kant chapter of The Evolution of Modern Metaphysics (2012).

7] “Subject” is Moore’s term and he refers to Kant for remarks pertinent to his (Moore’s) use of the term (23 n1).

8] There is also a priori knowledge that could have been independent of experience. For instance, knowledge of a mathematical truth based on an appeal to authority does not qualify as armchair knowledge, but does qualify as a priori in this sense. This is Moore’s example: “my own knowledge that every natural number is the sum of four squares is based on an appeal to authority. So it is not included in what I am calling ‘armchair knowledge’. But it is included in what, on this broad usage, would be called ‘a priori knowledge’, since it is knowledge of a mathematical truth that could in principle have been independent of experience”. (24 n3)

9] Moore also notes the use of ‘a priori’ to refer to truths (Moore gives the example of potential items of armchair knowledge), rather than knowledge, and also to non-propositional entities, such as concepts (Kant’s categories, for instance). (1 n3) Finally, another reason for talking about ‘armchair’, rather than ‘a apriori knowledge’ is offered by Moore later in his paper: he thinks it would be regarded as more acceptable to claim that I have armchair knowledge of my own existence than to classify such knowledge as a priori. (41 n57)

10] In the KrV, Kant claims that “even though all our cognition [Erkenntnis] starts with experience, that does not mean that all of it arises from experience”. (B1) If all our cognition, including that which does not arise from experience (and is, hence, a priori), starts with experience, then there is some ‘use’ of some particular encounter with something beyond the subject in the case of Kant’s a priori cognition. Moore does not discuss this distinguishing aspect of Kant's account.

11] Moore’s reference to Kant (B3-4) here suggests he has in mind knowledge of the conditions which make experience and cognition in general possible.

12] Moore notes that some philosophers try to solve the puzzle by denying (i), (ii) or (iii): some empiricists deny (i); other empiricists accept (i), but deny (ii); for them, all armchair knowledge concerns the subject’s command of language or the subject’s conceptual repertoire or something of this kind; some Platonists accept (i) and (ii), but deny (iii); they claim that armchair knowledge is acquired through acquaintance with one or more Platonic Ideas. (24-5)

13] I think there will be a difference here between the position of those who think that some of what is beyond the subject has a form that depends on the subject, on the one hand, and, on the other, the positions of those for whom some of what is beyond the subject has a form, which does not depend on the subject, but nevertheless is a form which corresponds to the form that the subject also has and that the subject needs in order to make sense of what is beyond her.

14] Again, it depends depends on what “use” means means, but we can also say that the subject is an epistemic agent with the mind structured by the form.

15] It seems that the idea here is that, to have knowledge of what is necessary is to have knowledge that that which is necessary could not have been otherwise; and, to know that things could not have been otherwise (than how they necessarily are) implies that we, finite and contingent beings, have epistemic access to all the ways things might have been. This, however, must be an accurate presentation of a situation in which a finite and contingent being tries to show that knowledge of X is knowledge of what is necessary; if we start with the assumption that knowledge of X is knowledge of what is necessary and try to understand how this might be possible, this puzzle does not seem to emerge.

16] Hence, given the way the puzzle of armchair knowledge was formulated by Moore above, it seems that ii) only applies to synthetic armchair knowledge.

17] He refers here to A320/B376-7 and the “Dohna-Wundlacken Logic” (24: 702).

18] It should be noted, however, that Kant does not talk about analytic Wissen in his work. (Willaschek and Watkins 2020: 3211 n45) For the discussion of Kant’s distinction between Erkenntnis and Wissen, I am relying on my “Kant’s Rechtfertigung and the Epistemic Character of Practical Justification”. (2013) I have also found very useful Willaschek and Watkins (2020), although there are a few important aspects (some mentioned in this paper), where my reading of Kant is slightly different from theirs.

19] Moore makes reference to a section of his chapter, where he talks about knowledge of things in themselves. There are other examples he gives there: “space represents no property at all of any things in themselves nor any relation of them to each other (A26/B42)” or “[time] cannot be counted either as subsisting or inhering in the objects in themselves (A36/B52)” or “objects in themselves are not known to us at all (A30/B45)”. The assumption here seems to be that there is a distinction between objects and things in themselves (and perhaps between objects and objects in themselves, to include the expression at A30/B45), and the knowledge excluded by cognition is of things in themselves. To be sure, there is practical cognition of specific things in themselves (such as God or freedom), but no knowledge of specific things in themselves (at least, if Kant were to be consistent). My focus in what follows is on knowledge claims concerning things in themselves, which are formulated in positive terms. Those formulated in negative terms (as are the examples given above in this footnote) can easily be accounted for; for instance, they can be presented “through all the predicates that are already contained in the presupposition that the object has as a property nothing belonging to sensible intuition”. (B149)

20] Moore refers here to the “Blomberg Logic” (24:93-4 and 105) and the “Jäsche Logic” (9:53-4).

21] He refers here to B19ff. and Prolegomena (§5).

22] He makes further reference here to Bvii-x and Prolegomena (4:371).

23] Translation slightly amended.

24] Willaschek and Watkins (2020: 3199-200) identify a passage at A92-3/B125, as the place where Kant would introduce EK. There, according to them, Kant seems to suggest that “cognition of an object requires both an intuition and a corresponding concept”. (2020: 3200 – e.o.) Yet, Kant talks about “two conditions under which alone the cognition of an object is possible [zwei Bedingungen, unter denen allein die Erkenntnis eines Gegenstandes möglich ist]”. (A92/B125) But this can be interpreted also as stating two separate conditions which can individually make possible the cognition of an object. The quotation I provide in the text is much clearer about the need for both conditions (and I make haste to add that it is also referred to by Willaschek and Watkins). On page 27 of his text, as e have seen, Moore talks about EK, as knowledge with content.

25] As mentioned above, when Moore justifies his use of ‘knowledge’ for Kant’s ‘cognition’, he refers to B19ff., where Kant talks about the possibility of synthetic a priori judgements, which require both concepts and intuitions.

26] Moore notes in a footnote (29 n23) that the concepts involved in analytic armchair knowledge refer to what is beyond the subject, when the concepts involved do apply to what is beyond the subject. He gives the example of knowledge that mermaids have fishes’ tails as another example of analytic armchair knowledge, which can (“arguably”) be said (“in the same attenuated sense of ‘concern’”) to concern mermaids. This raises, of course, a question about the difference between what Moore means by applying to, or concerning, what is beyond the subject and what Kant does; for Kant, the important distinction is between a concept’s logical possibility and its real possibility, a distinction which Moore’s example suggests Moore is not considering. Moore says (see below in this paper) that analytic armchair knowledge is provided by linguistic rules in force and their necessity is not affected by the contingency of their being in force.

27] Let us call this the ‘Thinking Contradiction’; this would be committed by Kant (as read by Moore), since, on the one hand, Kant thinks we can have thoughts concerning things in themselves; on the other hand, however, Kant does not seem to allow room for such thinking. This is because a priori concepts contribute to the “contingency of the i-dependence”, that is, contingency of the form of what is beyond the epistemic agent. Hence, the subject’s thinking through these a priori concepts is of appearances. But if the subject cannot think about things in themselves with the help of a priori concepts, it seems even less likely that she will be able to think about things in themselves with the help of empirical concepts.

28] This would then solve the Thinking Contradiction by dissolving the problem. The assumption that we can only think about things in themselves with the help of some specific concepts, in particular, concepts which are not part of the a priori structure of the mind, is an unusual presupposition. There is in particular the puzzle of the a priori ideas of God, freedom and world as a whole, which makes the problem acute, since these ideas are the conceptual means by which we can uniquely refer to some specific things in themselves, rather than generically to the class of things in themselves.

29] This seems to refer to the previous argument which I questioned, namely, that including essential features of a conceptual nature among the a priori elements of the mind makes it impossible for us to think about things in themselves. I have called this alleged problem in Kant the Thinking Contradiction (see n27 above) and argued that it has a solution (n28 above).

30] Recall Q2: What is it about synthetic armchair knowledge that makes Kant think that transcendental idealism must be invoked to solve the puzzle with respect to it? (28)

31] Here we end up with a tension between the claim that knowledge that vixens are female is knowledge of a contingency, on the one hand, and, on the other, the claim that vixens must be female, with a strong sense of ‘must’. Given this ‘must’, it seems that knowledge that vixens are female is knowledge of a necessity. What is contingent is the having of this knowledge, not the content known; this is because, for Moore, without the particular rule connecting vixens and female, “no-one would have thought in those terms”, so no-one would have had the knowledge that vixens are female, although vixens would still have been, since they must be female. (31)

32] He also notes, however, referring to Moore (2019: §1), that differences are important, indeed crucial, insofar as, due to these differences, the Wittgensteinian view might count as a rival to Kant’s view.

33] A clarification is introduced by Moore here: the truth of the item of knowledge is not derived from the familiarity with the concepts; rather, one counts as familiar with the concepts when one has command of the relevant rule – presumably one can accurately say whether the item of knowledge is true or not.

34] He contrasts this with the logical form of what is known, “which leaves the truth conditions of what is known undetermined”. (32) A qualification is added here: there is no such a thing as ‘the’ logical form of what is known; to talk about this, Moore suggests, would involve “tendentious” considerations about complete logical analysis. (32 n32) Moore thinks this explains why, if I wanted to show that what is known is not an analytic truth, I could not appeal to a procedure purporting to show that what is known is not a logical truth. More precisely, Moore adds that to show that what is known is not a logical truth, one would specify a false proposition with the same logical form, whereas to show that it is not an analytic truth, one would have to consider alternatives to that very truth. This presupposes the availability of alternatives.

35] This is not quite so: when Kant gives the example of ‘7 + 5 =12’, he does not really consider the possibility that the sum or 7 and 5 is different from 12, but the possibility that the concept of the sum of 7 and 5 may not presuppose as an essential feature number 12.

36] Call this Kant’s Modal Contradiction: Kant claims that the same truth is necessary and contingent.

37] What is contingent is the relation between the concepts of a triangle’s angles and of two right angles. What is necessary is the distinct relation between a triangle’s angles and two right angles. This is not much different from the ‘Wittgensteinian’ alternative favoured by Moore, and answers the Modal Contradiction.

38] This can also be read as follows: Kant says that the judgement is synthetic, since the concept of the subject does not presuppose as a part the concept of the predicate. The contingency is the result of this relation between the subject and the predicate, as far as we consider only the concepts of the subject and the predicate. The necessity is given indeed from a particular point of view, namely, that of the spatio-temporal agent and is indeed the result of the constitution of the relation between the subject and the predicate by the a priori intuitions.

39] Say that no step back is taken from the original point of view; say I have two claims: ‘A triangle has three sides’ and ‘A triangle has angles whose sum is equal to two right angles’. Without any stepping back, I can see, through familiarity with the terms of the first claim, that it has to be true; at the same time, I can see that, despite my familiarity with the terms of the second claim, the notion of the sum of the angles of a triangle does not presuppose that of two right angles and, from that perspective, alternatives are open for consideration.

40] Call this Kant’s Metaphysical Contradiction: according to Moore, Kant’s thinking of how things are in themselves sometimes amounts to knowledge; for instance, the thought that there is synthetic armchair knowledge is of things in themselves, is not analytic and is not based on experience, so it can only be synthetic armchair knowledge of how things are in themselves. Yet, on Moore’s account, Kant also rejects the possibility of synthetic armchair knowledge of how things are in themselves.

41] “This, by his own lights, is a piece of knowledge – if only because he has arrived at it as a result of what he takes to be a decisive argument”. (34)

42] “For Kant would surely deny that it depends on sheer analysis of the concepts involved”. (34)

43] “[H]e would also surely deny that it depends on experience”. (34)

44] The change of perspective introduced by i-dependence “is a shift from considering things from one point of view to considering them from no point of view at all, from thinking about how things appear to thinking about how they are in themselves”. (34)

45] “[W]e must be able at least to think […] the same objects also as things in themselves. For otherwise an absurd proposition will follow, viz., that there is appearance without anything that appears”. (Bxxvi-xxvii)

46] “[W]e must be able at least to think [denken], even if not cognise [erkennen], the same objects…” (BBxxvi – e.o.)

47] As a result, in Kant, we can have practical cognition [Erkenntnis] of specific things in themselves, such as God, but not theoretical cognition. Moreover, assent to this practical cognition can be justified as an instance of belief or faith [Glauben], but not of knowledge [Wissen].

48] There is, in addition, by the way, another reductio formulated by Kant in the same context; this is an argument concluding that the distinction between objects of experience and the same objects as things in themselves is needed to make sense of the fact that we are free and subject to natural laws. (Bxxvii)

49] See for instance Willaschek and Watkins (2020: 3211-2).

50] In n49, Moore explicitly states his interpretative assumption that “only by appeal to a priori intuitions can the subject have synthetic armchair knowledge”. Here Moore mentions a set of references from KrV, where Kant explains how a priori intuitions are necessary for synthetic a priori cognitions (in the narrow sense EK). He also acknowledges that there may be instances where Kant seems to contradict himself in this respect (the example given is from the KU, although I think it refers to something slightly different). Additionally, Moore mentions that his talk of synthetic a priori knowledge “already involves departure from Kant’s own way of framing these ideas”. (39 n49) In this paper, I have accepted Moore’s assumption that a priori intuitions are necessary for synthetic a priori cognitions (although only theoretical cognitions). I have argued that the contradiction Moore mentions in this footnote (which is one of the three contradictions I consider in this paper – the Metaphysical Contradiction) can be briefly answered as follows: if theoretical synthetic a priori cognitions require a priori intuitions, then a theoretical synthetic a priori knowledge claim about things in themselves (such as, the claim that there are things in themselves) cannot be a piece of theoretical cognition, but can be a piece of knowledge (in the Kantian sense of Wissen), for which a priori intuitions are not necessary.

© 2022 by Public Reason

Public Reason 14 (1): 68-75

Kantian Reflections on Conceptual Limits Zachary Vereb

University of Mississippi Abstract. This paper reflects on Kantian exchanges between A. W. Moore and Sorin Baiasu. After briefly situating their exchange, I highlight Baiasu’s clarification regarding Kant’s distinction between knowledge and cognition. Although convincing, I suggest that Baiasu’s objections could be strengthened with further discussion of the notion of a thing in itself as a limiting concept, as well as emphasis on Moore’s use of ‘concern’, which might require further clarification. I conclude with broader reflections on what is at stake: not just armchair knowledge, but the coherence and relevance of Kant’s practical philosophy under the assumption of its dependence on transcendental idealism.

Key words: Kant, limits, metaphilosophy, transcendental illusion, armchair knowledge.

What is it about Kant’s philosophical thinking that makes it continually relevant, despite endless attempts at refutation?[1] Numerous answers could be given, but Kant’s injunction to remain vigilant in the face of transcendental illusion stands out. For Kant, transcendental illusion does not cease even though it is uncovered and its nullity is clearly seen into by transcendental criticism […] The cause of this is that in our reason (considered subjectively as a human faculty of cognition) there lie fundamental rules and maxims for use, which look entirely like objective principles, and through them it comes about that the subjective necessity of a certain connection of our concepts on behalf of the understanding is taken for an objective necessity, the determination of things in themselves. [This is] an illusion that cannot be avoided at all, just as little as we can avoid it that the sea appears higher in the middle than at the shores, since we see the former through higher rays of light […] (KrV A297/B354)[2]

Throughout the Critique of Pure Reason, Kant urges that we remain indefatigable in shining the critical spotlight, dissipating but never fully extinguishing illusion, illusion that “has portrayed a reality to them when none is present” (KrV A501/B530).[3] Yet questions remain: Does Kant succumb to transcendental illusion with his idealism? Whence necessity? Is Kant committed to noumenal knowledge in the philosophical enterprise of drawing boundaries between the phenomenal and noumenal? What is the epistemic status of knowledge (supposing it obtains) that we have synthetic a priori knowledge?

It indeed remains possible to reflect upon Kant’s critical flashlight, illuminating cracks in the edifice that shines them. A. W. Moore (2012) attempts as much, returning with his more refined essay “Armchair Knowledge: Some Kantian Reflections.” Moore’s strategy is threefold: First, he identifies two central puzzles in philosophy (i.e. the possibility of armchair knowledge and grounds of necessity). Second, he specifies how Kant tries but fails to resolve them. And third, he attempts to move beyond Kant’s letter, with his solution reflecting its title in Kantian spirit.

This paper engages with two ideas developed out of Baiasu’s reply to Moore, especially as they pertain to limits. After briefly situating their philosophical exchange (§ I), I highlight Baiasu’s helpful clarification regarding Kant’s distinction between knowledge and cognition. Although largely convincing, I then suggest (§ II) that Baiasu’s objections could be strengthened with further discussion of things in themselves, as limiting concepts, and of ambiguity in Moore as to what knowledge ‘concerns’. I conclude (§ III) with broader reflections on what is at stake: not just armchair knowledge, but the coherence of Kant’s practical philosophy under the assumption of its loose dependence on transcendental idealism, and its relevance for today.

I. PHILOSOPHICAL PROBLEMS KANT TRIES TO RESOLVE TWO IMPORTANT PHILOSOPHICAL PROBLEMS. FIRST, HOW ARE WE TO ACCOUNT FOR WHAT MOORE CALLS ARMCHAIR KNOWLEDGE, I.E. THE JUSTIFICATION OF A PRIORI KNOWLEDGE?[4] IN PARTICULAR, “THE QUESTION: ‘HOW IS SYNTHETIC A PRIORI KNOWLEDGE POSSIBLE?’ THUS ASSUMES A MUCH WIDER SIGNIFICANCE FOR KANT. IT EVENTUALLY COMES TO EMBRACE THE QUESTION ‘HOW IS KNOWLEDGE OF AN INDEPENDENT REALITY POSSIBLE?’ OR, MORE BROADLY ‘HOW IS REPRESENTATION POSSIBLE?’” (MOORE 2012, 119). SECOND, THERE IS THE RELATED BUT DISTINCT PHILOSOPHICAL QUESTION OF ACCOUNTING FOR NECESSITY. THERE ARE MANY REASONS TO CARE ABOUT JUSTIFYING NECESSITY AND A PRIORI KNOWLEDGE BEYOND THE SUBJECT, SUCH AS SAVING MATHEMATICS FROM THE EMPIRICIST DIFFICULTIES. KANT SEES STRENGTHS IN THE EMPIRICIST POSITION, BUT HE IS WORRIED OF TROUBLESOME IMPLICATIONS. CONSIDER, FOR EXAMPLE, HUME’S NEGATIVE CONCLUSIONS ABOUT THE NECESSITY AND A PRIORITY OF GEOMETRICAL KNOWLEDGE IN A TREATISE OF HUMAN NATURE. ACCORDING TO HUME, GEOMETRY […] NEVER ATTAINS A PERFECT PRECISION AND EXACTNESS […] THE REASON WHY I IMPUTE ANY DEFECT TO GEOMETRY IS, BECAUSE ITS ORIGINAL AND FUNDAMENTAL PRINCIPLES ARE DERIV’D MERELY FROM APPEARANCES […] I OWN THAT THIS DEFECT SO FAR ATTENDS IT, AS TO KEEP IT FROM EVER ASPIRING TO A FULL CERTAINTY. (HUME 1978, 70-1) HUME, WHO ARGUES THAT FUNDAMENTAL GEOMETRIC PRINCIPLES ARE DERIVED FROM APPEARANCES ALONE, THINKS MATHEMATICIANS COMMIT CONCEPTUAL ERRORS BY REASONING A PRIORI. CONCEPTUAL ERRORS ARE SIMILARLY MADE, HE THINKS, BY METAPHYSICIANS WHO ATTEMPT TO REASON BEYOND EXPERIENCE IN DEFENDING NECESSARY KNOWLEDGE ABOUT REALITY. KANT, BY CONTRAST, IS CONCERNED TO DEFEND THE NECESSITY AND SYNTHETIC CHARACTER OF MATHEMATICAL KNOWLEDGE: I CANNOT, HOWEVER REFRAIN FROM NOTING THE DAMAGE THAT NEGLECT OF THIS OTHERWISE SEEMINGLY INSIGNIFICANT AND UNIMPORTANT OBSERVATION [I.E. MATHEMATICS’ SYNTHETIC A PRIORITY] HAS BROUGHT UPON PHILOSOPHY. HUME, WHEN HE FELT THE CALL, WORTHY OF A PHILOSOPHER, CAST HIS GAZE OVER THE ENTIRE FIELD OF PURE A PRIORI COGNITION […] INADVERTENTLY LOPPED OFF A WHOLE (AND INDEED MOST CONSIDERABLE) PROVINCE OF THE SAME, NAMELY PURE MATHEMATICS. (PROL 4: 272) NOT ONLY SHOULD MATHEMATICAL KNOWLEDGE BE NECESSARY AND PRECISE, BUT THE DEFENSE OF SUCH KNOWLEDGE – AS KANT SUGGESTS IN THE PROLEGOMENA TO ANY FUTURE METAPHYSICS – SETS THE STAGE FOR HIS DEFENSE OF JUSTIFIED METAPHYSICAL KNOWLEDGE.

Now Kant’s specific way to resolve these interconnected philosophical problems hinges, as Moore argues, on his transcendental idealism,[5] and resolving them has for Kant both theoretical and practical import. Yet, for Moore, the panacea of transcendental idealism is also a poison: it entails a contradiction in Kant’s own system. In other words, Kant’s idealism saves armchair knowledge but only at the cost of a transcendental illusion it was supposed to guard against, namely being committed to knowledge about things in themselves exceeding the human standpoint. Related problems surrounding transcendental idealism have been extensively discussed elsewhere, so I will not touch on them here.[6] Salient aspects of these discussions, however, include questions as to whether noumena constitute real entities about which we can have knowledge, as well as more fundamental questions about drawing limits. Baiasu aims to disclose the roots of Kant’s apparent error. In doing so, he reconsiders the contradiction that Moore claims follows from Kant’s commitment to transcendental idealism, as well as his general project of drawing limits. Even if Kant has some internal problems, Baiasu submits that Kant has resources for recovery.

II. DEFENDING KANT

To address Moore’s puzzles with armchair knowledge, Baiasu unpacks several important distinctions. This allows him to push back against Moore without having to draw from resources external to Kant’s works. As Baiasu notes, “Moore defines armchair knowledge as ‘knowledge that is independent of experience, in the sense that it is not warranted by experience’ […] The term ‘armchair knowledge’ is used by Moore to refer to a particular type of a priori knowledge, namely knowledge that is [as distinct from could have been] independent of experience” (Baiasu 2). Yet for Kant, we can first distinguish knowledge (Wissen) from cognition (Erkenntnis). The latter “is defined here [KrV A320/B376-7] as objective presentation with consciousness,” where objective “seems to mean reference (whether direct or indirect) to an object, distinct from the subject” (Baiasu 7). Further, cognition is used by Kant in at least two separate ways, one requiring concepts and intuitions (cognition in the classic, narrow sense, e.g. KrV A77-8/B103), and the other in the wider sense where Kant admits that “intuitions and concepts on their own count as cognitions” (Baiasu 7; cf. to RGV 6:181 and “practical cognition […] resting solely on reason […]”). Baiasu notes that Moore seems to use the wider-sense variant for his purposes (the question of making sense of things), but often refers to this wider-sense cognition as ‘knowledge’.

Things are further complicated with knowledge since it is not the same as Kantian cognition. It requires not only a presentation with objective reference, but also assent (KrV A820-2/B848-51; Log 9: 70), which is to say, “the need for some subjective and objective support, which respectively, are sufficient to convince me of the truth of the presentation and to provide certainty for everybody” (Baiasu 8-9). Since cognition and knowledge are not reducible concepts, as Moore apparently entertains, Baiasu concludes that he ought to rethink his notion of armchair knowledge at the basis of his critique.[7] Further, as Moore thinks that some armchair knowledge “appears to concern what is beyond the subject” (Moore 1), it is helpful that Baiasu problematizes Moore’s notion of armchair knowledge. Following this cue, it may also be helpful to problematize Moore’s sense of what it means for knowledge to concern something in the first place.

This is one aspect of Moore’s argument that rightly puzzles Baiasu, namely the former’s claim that we can coherently be said to have knowledge concerning things in themselves. (This is a problem for Moore in that it suggests to him that Kant’s idealism is self-stultifying, but I do not consider that here.) Baiasu’s conceptual clarification is helpful not only for suggesting potential pitfalls with Moore’s initial definition of armchair knowledge,[8] but also because it helps to show why Moore’s puzzle about analytic armchair knowledge of things in themselves is not what it seems. There are at least two additional modes of attack that Baiasu could have taken at this juncture to strengthen his critique. First, he could have pressed more explicitly on the ambiguities surrounding the use of ‘concerning’ language in Moore’s argumentation.[9] Second, since his approach aims to remain immanent to Kant’s critical system, he could have utilized textual remarks on the nature of things in themselves understood as “boundary concepts.”[10] The first would be an external objection (namely that perhaps Moore is potentially equivocating, remaining imprecise in his language as Wittgenstein might say), while the second would be internal. Before concluding, I would like to reflect on the implications of Baiasu’s defense for Kant by exploring what is at stake should the defense be unsuccessful.

III. CONCLUDING REFLECTIONS AT FIRST GLANCE, IT IS NOT OBVIOUS THAT THE QUESTION REGARDING THE POSSIBILITY OR COHERENCE OF KANTIAN ARMCHAIR KNOWLEDGE HAS ANY BEARING ON KANT’S ETHICS OR POLITICAL THOUGHT. YET WE NEED NOT LOOK FAR TO SEE IMPLICATIONS FOR KANT’S PRACTICAL PHILOSOPHY. WE MIGHT CONSIDER, FOR INSTANCE, BAIASU’S OWN DEFENSE OF KANTIAN METAPHYSICS IN HIS CHAPTER “METAPHYSICS AND MORAL JUDGEMENT” (2011). THERE, BAIASU ARGUES THAT KANT’S TRANSCENDENTAL APPROACH TO METAPHYSICS IS NEEDED TO MAKE HIS ETHICAL THEORY MORE PERSUASIVE. MORE SPECIFICALLY, COMMENTATORS OF KANT’S ETHICS WHO BRACKET HIS METAPHYSICS, BAIASU SHOWS, HAVE A PROBLEM EXPLAINING THE NATURE OF CONTRADICTION IN THE APPLICATION OF THE CATEGORICAL IMPERATIVE. BAIASU, NOT WITHOUT GOOD REASON THEN, BELIEVES WE MUST “RETRIEVE SOME OF THE KANTIAN METAPHYSICS WHICH IS USUALLY LEFT BEHIND”, IF “KANT’S ETHICS IS TO HAVE ANY CHANCE OF BEING A GUIDING THEORY” (BAIASU 2011, 174). NON-METAPHYSICAL PRACTICAL PHILOSOPHIES REPRESENT, FOR BAIASU, A POTENTIAL ETHICAL DEAD-END.

If this is all true, then much is at stake with Baiasu’s defense of Kantian armchair knowledge, and so it is worth highlighting. In other words, if Kant’s theoretical philosophy hinges on his idealism, then one of two things is likely to follow. If Moore’s critique of the contradictions of transcendental idealism is successful, it is even more devastating than he lets on (and so another lesson from Strawson 1966 is in order, but this time via a practical angle).[11] Supposing Moore is right could have long-reaching implications for the coherence of Kantian moral philosophy; unless we can think of things in themselves, we cannot make sense of freedom, nor could we make sense of Kant’s juridical and legal ideas: that is, how we follow political laws not just as a matter of sensible incentives, but because they are right. Thinking of laws from the perspective of freedom is necessary to know how to change positive laws. On the other hand (and Baiasu is probably keen on this, given Baiasu 2011 and 2016b), the success of Baiasu’s defense would underscore that the status of Kantian metaphysics – often thought a mere artifact for philosophers of history – therefore has potential consequences for making sense of freedom and of law relevant for today.

As seen, the question of Kantian armchair knowledge has important implications beyond metaphilosophy. It might motivate us to rethink the internal unity of Kant’s system if transcendental idealism, which he took to be a heart to his system, is compromised. Clearly, then, Kantian reflections have import for rethinking applied problems today, as a reminder of the importance for thinking about limits and the sustainability of conceptual systems. Let us circle back to the question posed at the outset. What is it about Kant’s thought that invites revisitation? Do commentators not merely beat a dead horse? Moore’s response is keen: The importance of Kant’s doctrines does not depend on their detailed truth. It does not even depend on their broad truth. Kant may be fundamentally wrong. But if he is, his errors are of that deep sort that can still instruct us, prompt us, stimulate us, and guide us, opening up significant new possibilities for us to explore. (Moore 2012, 116) Just as James Joyce once wryly remarked that scholars will continue to puzzle over his gestures toward the limit of language,[12] so also does Kant’s thought continue to challenge us. Even if Kant’s philosophical foundations waver, it is nonetheless profitable to reflect on the way he thinks. For Kant’s way of thinking in the Critique of Pure Reason presses us to think about limits – not only in metaphilosophy, but the limits of nature, language, metaphysics, and even religion – just as it has challenged thinkers of the past.[13] As for the dead horse, let us not forget that Kant’s father was a horse-harness maker. Kant’s architectonic, when we think about it philosophically, should never be viewed in stasis, despite his armchair reflections. A proper design is resilient and flexible, so it should not surprise us that a return to Kant, in his armchair-drawing carriage, would make for a journey worth taking. Indeed, like a reliable horse-harness, it promises to take us somewhere new, even as we encounter novel limits in a changing world.

ztvereb@olemiss.edu

REFERENCES

Allison, Henry E. 2004. Kant’s Transcendental Idealism: Revised and Enlarged Edition. New Haven and London: Yale University Press.

Baiasu, Sorin. 2011. Metaphysics and Moral Judgement. In Baiasu, Sorin; Williams, Howard & Pihlstrom, Sami (eds.) 2011. Politics and Metaphysics in Kant. Cardiff: University of Wales Press.

———. 2016a. Is Kant’s Metaphysics Profoundly Unsatisfactory? Critical Discussion of A. W. Moore’s Critique of Kant. Kantian Review, 21(3): 465-81.

———. 2016b. Right’s Complex Relation to Ethics in Kant: The Limits of Independentism, in Kant-Studien 107: 2-33.

———. Forthcoming. The Possibility of Kantian Armchair Knowledge. Public Reason.

Baiasu, Sorin, Williams, Howard & Pihlstrom, Sami (eds.) 2011. Politics and Metaphysics in Kant. Cardiff: University of Wales Press.

Bird, Graham. 1962. Kant’s Theory of Knowledge: An Outline of One Central Argument in the Critique of Pure Reason. New York: Humanities Press.

Friedman, Michael. 2001. Dynamics of Reason. Stanford: CSLI Publications.

Grier, Michelle. 2001. Kant’s Doctrine of Transcendental Illusion. Cambridge: Cambridge University Press.

Hume, David. 1978. Ed. L. A. Selby-Bigge. A Treatise of Human Nature. Oxford: Oxford University Press.

Kant, Immanuel. 1998. Critique of Pure Reason. Trans. and ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.

———. 1993. Opus Postumum. Trans. and ed. Eckart Förster and Michael Rosen Cambridge: Cambridge University Press.

———. 1997. Prolegomena to Any Future Metaphysics that Will Be Able to Come Forward as Science. Trans. and ed. Gary Hatfield. Cambridge: Cambridge University Press.

———. 1996. Religion within the Boundaries of Mere Reason. Trans. and ed. Allen W. Wood, and George di Giovanni. Religion and Rational Theology. Cambridge: Cambridge University Press.

Kanterian, Edward. 2016. Reason’s Disunity with Itself: Comments on Adrian Moore on Kant’s Dialectic of Human Reason. Kantian Review, 21(3): 483-93.

Lu-Adler, Huaping. 2022. Kant on Lazy Savagery, Racialized. Journal of History of Philosophy ٦٠: ٢٥٣-٧٥.

———. 2023. Kant, Race, and Racism: Views from Somewhere. New York, US: Oxford University Press.

Makkreel, Rudolf A. & Luft, Sebastian (eds.) 2009. Neo-Kantianism in Contemporary Philosophy. Bloomington: Indiana University Press.

Moore, A. W. 2012. The Evolution of Modern Metaphysics: Making Sense of Things. Cambridge University Press.

———. 2016. Reply to Sorin Baiasu and Edward Kanterian. Kantian Review, 21(3): 495-506.

———. Forthcoming. Armchair Knowledge: Some Kantian Reflections. Public Reason.

Pickering, Mark. 2011. The Idea of the Systematic Unity of Nature as a Transcendental Illusion. Kantian Review, 16(3): 429-48.

Strawson, P. F. 1966. The Bounds of Sense: An Essay on Kant’s ”Critique of Pure Reason”. London: Methuen & Co. Ltd.

1] Many commentators retool Kant’s philosophy for problems he did not address. For scientific, cultural and political puzzles, see Friedman 2001; Makkreel and Luft 2009; and Baiasu, Pihlström, and Williams 2011. Others challenge his thought (e.g., Lu-Adler 2022).

2] Parenthetical references to the Critique of Pure Reason refer to the first prints of the two editions of that work. Other references to Kant’s writings refer to the Royal Prussian Academy edition (Kants gesammelte Schriften) using the standard abbreviations. Unless noted, translations are from The Cambridge Edition of the Works of Immanuel Kant.

3] See Grier 2001 and Pickering 2011 on Kant’s account of transcendental illusion.

4] Armchair knowledge for Moore includes both analytic and synthetic varieties so long as the knowledge ‘concerns what is beyond the subject’. See Bird 1962 and Strawson 1966 for classic takes. For resources contrary to Moore, see the defense of transcendental idealism in Allison 2004.

5] Kantian a priori knowledge is thought justified by appealing to the contribution of fundamental features of human mentality, i.e. that objects of knowledge appear constrained within space, time, and the categories. Necessity is justified by its grounding in the relative contingency of the human standpoint. Both are basic features of Kant’s idealism. If Kant is correct that there is only one set of pure concepts and they happen to be Eurocentric ones, would human cultures that appear to make use of different, possibly non-individualist concepts (e.g. not making use of ‘substance’, but instead a more collective or processual concept) be denigrated as cognitively deficient? This is worrisome, for ‘conceptual imperialism’ could be used to justify subordination (see Lu-Adler 2023). Consider Kant’s rejection of the “monstrous [Ungeheuer] system” of Daoist philosopher Lao Tzu (whom he calls “Lao-Kiun”) in EAD 8: 335. Kant rejects Lao Tzu’s apparently substance-less mysticism, while Lao Tzu rejects reified concepts that Kant views essential to experience. I highlight this because it reveals an implication that falls out of Baiasu’s discussion of Moore’s “Relativised Concept Thesis” (Baiasu 20), but I cannot discuss this further.

6] See Baiasu (2016a), Kanterian (2016), and Moore (2016). Their exchange touches on concerns of the present paper, as well as specific contributions to this special issue. The engagements there, just like the present issue’s, are not unlike the objections/replies to Descartes’s Meditations (which keep in spirit with Moore’s historically informed approach to philosophical puzzles).

7] Even if Moore admits that his definition would require some fine-tuning, this will not obviously address his underlying Wittgensteinian questions: How can Kant draw limits between the phenomenal and the noumenal, one of which is apparently unknowable? Second, where to draw that line without any epistemic (theoretical) acquaintance with the other side? “Kant’s project seems to involve drawing a limit to what we can make sense of. But that in turn can seem an incoherent enterprise” (Moore 2012, 135); cf. Prol 4: 360-2 where Kant discusses his “[…] use of the metaphor [Sinnbildes] of a boundary in order to fix limits of reason […]”). Moore’s question originates from the Preface of Wittgenstein’s Tractatus: “in order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable (i.e. we should have to be able to think what cannot be thought).”

8] Since cognition in the wide sense can obtain with mere concepts and their objective reference, it seems that the cognition of our concept for ‘thing’ would concern things in themselves. Baiasu cites Moore’s example of analytic armchair knowledge we have of things in themselves “knowledge that things in themselves are things irrespective of how they are given to us, knowledge which concerns things in themselves” (Baiasu 6). But, as Baiasu shows, to say that we have knowledge of things in themselves goes too far, since that would require both a presentation and (subjective and objective) grounds for assent, neither of which we have for things in themselves. Baiasu identifies the problem to lie with Moore’s conflation of knowledge and the different senses Kant makes for cognition. Additional problems arise from this move (see footnote 10 below).

9] What, for example, does it mean for knowledge to ‘concern’ things in themselves? Baiasu does highlight how Moore’s particular use of this language raises questions, but a more direct discussion is needed. It is unclear that Moore’s example of vixens (see Baiasu 9) concerns objects rather than ways that we make use of concepts and language. Extra attention to the question as to whether (and in what way it could be justified that) cognition in the wide sense could concern objects metaphysically and not merely reflexively (so as to charitably avoid equivocating ‘concern’) would deepen the critique, and Kant does have resources for this (recall Kant’s discussion on transcendental illusion).

10] Moore finds it reasonable that we have bare knowledge of things in themselves as (existing, or possibly existing things), but even this inference is too hasty, for the category ‘existence’ is itself a mere piece of our mental machinery. To apply that concept beyond possible experience would be unjustified, though we can think the existence of things in themselves by analogy to our phenomenal experience. To avoid inferences of this sort and thereby evade problems concerning analytic armchair knowledge, Baiasu could have distinguished the ways that Kant discusses things in themselves, pointing to Kant’s emphasis on their use as ‘boundary concepts’ (e.g. KrV A255/B311; cf. KpV 5: 54 and Prol 4: 355). It can be illuminating to compare what Kant has to say on this with the incomplete Opus Postumum. Kant’s admittedly unsystematic final reflections show him ever interested in dealing with problems relating to Moore’s puzzle. There, the thing in itself is “only a thought-entity without actuality (ens rationis), in order to designate a place for the representation of the object” (OP 22: 31); as “merely a principle” (22: 34); and a “thought-object” that “stands only like a cipher [Ziffer]” (22: 37).

11] Similar debates are ongoing – not on the dependence of Kant’s practical on the theoretical philosophy, but within the practical, i.e. with questions as to the (in)dependence of the categorical imperative on the universal principle of right. Baiasu 2016b takes a stand in this debate as well, so certainly he is concerned with practical implications from Moore’s critique.

12] Since contributions in this special issue deal with Kant and Wittgenstein, the image of a philosophically scholastic-trained James Joyce, rebelling against the limits of language, is not, I think, unfitting. And as Moore is wont to engage both analytic and continental traditions insofar as they reflect on limits, we should also not be surprised to recall that Derrida would find Joyce’s reflections illuminating for his own philosophical investigations that are not necessarily dissimilar in spirit from Moore.

13] Philosophical minds as diverse as Hans Christian Ørsted, Charles Sanders Peirce, Martin Heidegger, and Móu Zōngsān have expressed kindred influence from Kant, even in moving beyond him.

© 2022 by Public Reason

Public Reason 14 (1): 76-92

Nonsense and the General Form of the Sentence

Michael Morris

Sussex University

Abstract. In his paper ‘The Bounds of Nonsense’ Adrian Moore defines sentences for Wittgenstein’s Tractatus as those items to which truth-operations apply, and understands this as a disjunctivist theory. I consider whether this view can plausibly be attributed to Wittgenstein, whether it is compatible with the way Wittgenstein draws the distinction between propositions (narrowly construed) and nonsensical pseudo-propositions, and whether it is compatible with the more general philosophy of the Tractatus. Understanding the Tractatus in the way suggested by the disjunctivist definition of sentences transforms the way we read the text.

Keywords: Sentence, proposition, nonsense, disjunctivism, form, syntax, realism, idealism, clarity.

1. The Claims

In his fascinating paper (Moore 2019), Adrian Moore presents two (connected) striking claims which he takes Wittgenstein to be committed to in the Tractatus:

(1) Sentences are those items to which truth-operations apply (Moore 2019, 63)

(2) Sentencehood has no independent essence of its own (Moore 2019, 64)

I want here to consider what these claims mean, whether Wittgenstein can be taken to accept them, and what difference that makes to our understanding of some of the central themes of the Tractatus.

2. Broad and Narrow Definitions

First, the background. Adrian begins with a familiar tripartite classification which distinguishes between these three categories:

thoughts

tautologies and contradictions

nonsensical pseudo-propositions

Thoughts are bipolar: they are true or false, and if true could have been false, and if false could have been true. This means they have sense; they picture reality. Tautologies and contradictions are true (if they’re tautologies) or false (if they’re contradictions), but they’re not bipolar. They are senseless, though not nonsensical. Nonsensical pseudo-propositions are neither true nor false: they are nonsensical.

A question arises immediately. How are we to describe the three kinds of thing which the tripartite classification classifies? That is, how are we to distinguish all of these three kinds of thing from other things for which the issues which divide them are simply of no concern (things such as trees and continents and nationalities, for example)?

One word we might use is “proposition”. But someone might think that only thoughts, in Wittgenstein’s sense, are propositions: neither tautologies and contradictions, on the one hand, nor nonsensical pseudo-propositions, on the other, are, strictly speaking, propositions, on this view. This would be a super-narrow definition of “proposition”. It seems clear that Wittgenstein himself does not adopt this definition. Alternatively, we might think that we could usefully count both thoughts, on the one hand, and tautologies and contradictions, on the other, as propositions, while denying that nonsensical pseudo-propositions are propositions. This would be to adopt what we might now call a narrow definition of “proposition”, in line with what Adrian calls the narrow interpretation of Wittgenstein’s use of the term. Or again, we might adopt a broad definition of the term “proposition”, and count even nonsensical pseudo-propositions as propositions, in line with what Adrian calls the broad interpretation of Wittgenstein’s use of the term “proposition”.

Adrian then proposes to use the word “sentence” to cover all three of the categories: that is, in a way which coincides with the broad definition of “proposition”, but without taking a stand on the term “proposition” itself. (Though “sentence” is in fact a natural translation of the word “Satz” in the German text of the Tractatus–that is, of the word which “proposition” translates in the established English translations.)

3. Disjunctivism

It is a consequence of Adrian’s view that the actual choice of word here is not all that important. One of the morals to be drawn from Adrian’s paper is that it is also not all that important whether the Narrow or the Broad interpretation is right about the use of the word “proposition” in the (English) text of the Tractatus. (In my view, there are quite significant literary reasons for that too: the Tractatus presents itself as a kind of scientific treatise, but it is in many ways more appropriately thought of as a kind of poem. The kind of poem it is means that it is legitimate, and in some circumstances simply right, for the same word to be used slightly differently at different points.)

Two things, however, are important. The first is the distinction between the things which the narrow interpretation counts as propositions and the things it doesn’t: that is, the distinction between the first two of the three categories, on the one hand, and the third, on the other. And the second is between the things which the Broad interpretation counts as propositions and the things it doesn’t: that is, the distinction between all three of the specified categories, on the one hand, and everything else (such as trees, continents, and nationalities), on the other.

The first distinction is what Adrian calls the principal distinction: it is the distinction within the class of what he calls sentences, between those which are not nonsense and those which are. Let us call the second distinction the background distinction. It is the background distinction which Adrian in effect defines by the two claims which I quoted at the outset:

(1) Sentences are those items to which truth-operations apply;

(2) Sentencehood has no independent essence of its own.

Adrian notes an obvious objection to claim (1):

(TON) Truth-operations apply only to items that are truth-valued (p.9).

That might seem to make claim (1) define, not sentences (as Adrian understands the term), but propositions, on the narrow definition of “proposition”. But (TON) depends on a narrow conception of “truth-operation”. We could instead understand it broadly, and claim this:

(TOB) Truth-operations apply only to items that appear to be truth-valued.

If we adopted (TOB), claim (1) would be tantamount to this:

(1*) Sentences are those items which appear to be truth-valued.

What is it for something to appear to be truth-valued in whatever way is required to make (1*) true, given that sentences, which (1*) defines, are supposed to be exactly those items which fall into one of our three initial categories? Here Adrian proposes that we may contrast what we can call a highest-common-factor with a disjunctivist approach, using those terms in a way which is borrowed from the philosophy of perception.

The highest-common-factor conception can be formulated as follows:

(HCF) To appear to be truth-valued in the way relevant to (1*) is to have some common essence E distinct from either (i) being truth-valued or (ii) merely appearing to be truth-valued.

The disjunctivist conception can be formulated as follows:

(D) To appear to be truth-valued in the way relevant to (1*) is just either (i) to be truth-valued, or (ii) to merely appear to be truth-valued.

Adrian’s claim (2) is a rejection of the highest-common-factor view, and an endorsement of disjunctivism. To spell his view out precisely: he takes (1), understood by way of (TOB)–that is, as (1*)–and (D) to define sentencehood. We might call this view, in full, the disjunctivist truth-operation view of sentencehood. I will call it the disjunctivist view, for short.

4. Three Questions and Two Forms of Disjunctivism

At this point three questions naturally arise:

(A) Does Wittgenstein hold the disjunctivist view?

(B) Is the disjunctivist view compatible with the way Wittgenstein draws the principal distinction?

(C) Is the disjunctivist view compatible with the philosophy of the Tractatus in general?

In addressing these questions I think it will be helpful to have in mind two different forms of the disjunctivist view. Remember Adrian’s claim (2), which is his commitment to disjunctivism:

(2) Sentencehood has no independent essence of its own.

This is neutral between two ways of understanding the significance of the disjunctivist view. To get a grip on this, we need to elaborate the notion of essence here a bit. Sometimes people take the essence of something to be no more than the set of its essential properties, where a thing’s essential properties are simply those without which it could not exist as the thing it is: this is a purely modal conception of essence. But historically essence has generally meant much more than that: the essence of something, on this more traditional understanding, is what makes it the thing it is. On this second conception, the essence of something is explanatory, and not purely modal.

I think it’s most revealing if we take “essence” in Adrian’s claim (2) in this second, richer way. Now we can see two ways in which (2) might be true:

(2a) The disjunctivist view gives the explanatory essence of sentencehood;

(2b) There is no explanatory essence of sentencehood; the disjunctivist view just states what all sentences have in common.

Call (2a) an expression of a strong disjunctivist view, and (2b) an expression of a bland disjunctivist view.

For a parallel here, consider the case where the idea of disjunctivism has its home: perceptual experience. A disjunctivist claim there comparable to the disjunctivist truth-operation view of sentencehood might be put like this:

(PD) Perceptual experience is either (i) being evidently in touch with an independent reality, or (ii) merely seeming to be in touch with an independent reality.

I think we would expect (PD) to be offered as a characterization of the explanatory essence of perceptual experience: being in touch with an independent reality is what perception is all about. It would be bizarre to claim that (PD) simply states what all perceptual experience has in common, but says nothing about what makes it what it is.

I will be considering the disjunctivist view as a claim about the explanatory essence of sentencehood: that is, I will be interested in the strong disjunctivist view. (I don’t know if this is what Adrian intended.) The reason is that this makes my three questions–(A), (B), and (C)–more interesting.

5. DOES WITTGENSTEIN HOLD THE DISJUNCTIVIST VIEW?

Recall that the disjunctivist view holds that Adrian’s claim (1), understood by way of (TOB) defines sentencehood. Here is the key claim again:

(1) Sentences are those items to which truth-operations apply.

The most direct support for the claim that Wittgenstein accepts this comes in 5 and 5.3 of the Tractatus. Here is the first of those remarks:

5 Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)

And here is the first sentence of the second:

5.3 All propositions are results of truth-operations on elementary propositions.

(The rest of 5.3 makes clear, what is anyway obvious, that a truth-operation can be applied to any proposition.)

Remark 6 gives formal expression to that point, using the N operator to give what Wittgenstein there calls both “the general form of the truth-function” and “the general form of the proposition”. One might then reformulate the point of 6 (slightly clumsily) like this:

6* The general form of the proposition is that it is either the basis or the result of truth-operations on elementary propositions.

Of course, we are talking about propositions here, and we shouldn’t rush to assume that propositions are sentences, in Adrian’s sense: that is, we shouldn’t rush to assume that the broad interpretation of “proposition” (to include the third of our original categories, as well as the first two) is correct. So let us suppose for the moment that “proposition” is defined narrowly, so that it applies just to the first two of our original three categories. Clearly, 5 and the first sentence of 5.3 apply to all propositions in this sense. And if we understand “result of a truth operation” narrowly–that is, as applying just to items which have a truth-value–then they will apply only to propositions in this sense.

But do they give the explanatory essence of propositions, in this narrow sense of “proposition”? There is some reason to think that they are meant to. This is because of the key point about remark 6, which I have formulated as 6*. Remark 6 is about form, and form is a key concept in the Tractatus. If we assume (not an obvious assumption, as I have already suggested) that the word “form” is used in the same way throughout the Tractatus, then form here, as elsewhere, is possibility of combination. Here are two key remarks:

2.0141 The possibility of its occurrence in atomic facts is the form of the object.

2.151 The form of depiction is the possibility that the things are combined with one another as are the elements of the picture.

What I think this shows is that form is basically concerned with syntax: in language, with precisely syntax; and in the world, with some worldly counterpart or analogue to syntax.

The reason why this seems to help the thought that 5 and 5.3 are at least meant to give the explanatory essence of propositions is that it is very natural and plausible to think that the explanatory essence of sentences–on an entirely everyday understanding of the term “sentence”–is something to do with their syntax. There is clearly something special about sentences–still in that ordinary sense–which makes it possible to consider, even if one were in the end to reject it, something like Frege’s context principle: the principle that it is only in the context of a Satz (a sentence, a proposition) that words have meaning (Frege 1884/1980: §62). The simple thought is that a sentence can be complete in a way that a mere list cannot: words can be added to or subtracted from a list quite arbitrarily, while still leaving us with a list; but they cannot be added to or subtracted from a sentence quite arbitrarily, while still leaving us with a sentence.

What remarks 5 and 5.3 of the Tractatus tell us, and remark 6 expresses formally, is that every proposition is either the base of a possible application of truth-operations or the result of the application of truth-operations. The immediate importance of this for that place in the Tractatus is what it shows about truth-functions. But for our purposes, what matters is what it shows about propositions: since everything which is the result of the application of truth-operations is also the (possible) base of an application of truth-operations, the claim of remarks 5, 5.3, and 6 is just this slight (propositional) variant of Adrian’s claim (1):

(1p) Propositions are those items to which truth-operations apply.

Remark 6 can now be understood to tell us this: (1p) gives the form of propositions. That is, the syntax of propositions is defined by the fact that they are those items to which truth-operations apply. We might reformulate this again: the distinctive syntactic completeness of propositions (Sätze) is defined by the fact that truth-operations apply to them (informally: that they can be combined truth-functionally).

So much for propositions, on an understanding of that term which does not involve our assuming that there are any propositions which have no truth-value. Adrian’s claim (1)–and hence the disjunctivist view as a whole–is about sentences, in the precise sense which includes things in all three of our original categories. So what about sentences, in this sense? Here is a plausible thought: if there is anything which unifies the category of sentences, in this precise sense, it is the same thing as what unifies the category of sentences on an everyday understanding of the term. But if anything unifies the category of sentences on an everyday understanding of the term, it is their syntactic completeness–or apparent syntactic completeness. But remark 6 of the Tractatus seems to say that the distinctive syntactic completeness of propositions–understood in such a way as not to suppose that there are any propositions which have no truth-value–is due to the fact that truth-operations apply to them. That seems to mean that remark 6 of the Tractatus is only plausible if the distinctive syntactic completeness–or apparent syntactic completeness–of sentences, in Adrian’s sense, is due to the fact that propositions, understood in the narrow way, are items to which truth-operations apply (i.e., (1p)).

There are two ways of making that plausible:

(a) Sentences are items which appear to be propositions (in the narrow sense);

(b) Truth-operations apply to things which appear to have a truth-value.

In effect, if we take a narrow (TON) view of truth-operations–if we think they apply only to things which have truth-values–then we can adopt (a); while (b) is just the broad (TOB) view of truth-operations.

I think there is little more than a terminological difference between these two approaches. What this means is that remark 6 of the Tractatus is only plausible if Adrian’s claim (1)–sentences are those items to which truth-operations apply–gives the explanatory essence of sentencehood, in both his and the everyday understandings of “sentence”.

But we should note both the point we’ve reached and the route we’ve taken to get here. In order to take remark 6 as giving the explanatory essence of sentencehood, I have had to take the core of the explanatory essence of sentencehood to be a matter of syntax. This is because 6 is about form, and form in the Tractatus is, in general and speaking a little roughly, syntax; and because syntax seems to be the core of the explanatory essence of the ordinary notion of sentence, which I’ve used to move from a claim about propositions, in the narrow sense, to one about sentences, in Adrian’s sense.

This has a particular consequence in the context of the Tractatus. The central thesis of the philosophy of language of the Tractatus is that sentences have the same form as the world. That means that both sentences and the non-linguistic world have something like a syntax: both sentences and what makes sentences true are facts. This means that having the distinctive syntax of sentences does not distinguish between sentences and other facts. But being items to which truth-operations apply does distinguish between sentences and other facts. In effect, by suggesting that sentences have the syntax they have in virtue of being items to which truth-operations apply, we have not only offered an explanatory account of the essence of syntax: we have also provided a mark which distinguishes sentences from other facts. (We may then suggest that other facts are items which have the syntax they have in virtue of being items which make sentences true.)

The account which this gives us of the explanatory essence of sentencehood also seems clearly disjunctivist: there is no other essence of sentencehood which might be doing the work. The distinctive character of sentences derives entirely, on this account, from the fact that propositions, defined narrowly, are items to which truth-operations, also defined narrowly, apply; it can only also characterize other sentences–those which have no truth-values–in virtue of those other sentences appearing to be things which have truth-values.

I think this means that remark 6 of the Tractatus is only plausible if the disjunctivist truth-operation view of sentencehood is right. That’s close to a Yes to my question (A).

6. IS THE DISJUNCTIVIST VIEW COMPATIBLE WITH THE WAY WITTGENSTEIN DRAWS THE PRINCIPAL DISTINCTION?

What Adrian calls the principal distinction is the distinction between sentences which have truth-values and nonsensical pseudo-propositions. Wittgenstein famously explains how he understands the basis of what seems to be this distinction in the opening sentences of 5.4733:

Frege says: Every legitimately constructed proposition must have a sense; and I say: Every possible proposition is legitimately constructed, and if it has no sense this can only be because we have given no meaning to some of its constituent parts.(Even if we believe that we have done so.) Thus “Socrates is identical” says nothing, because we have given no meaning to the word “identical” as adjective.

This seems to allow that there can be propositions–at least that there can be sentences, in Adrian’s sense–whose syntax is fixed, even though they have no sense and no truth-value, because no meaning has been assigned to some of their constituent parts. For example, “Socrates is identical” is a sentence, but says nothing, and “identical” within it is an adjective, even though no quality (as we would put it) has been assigned as its meaning.

The mere fact that there can be sentences which have syntax, in a sense, without having sense or truth-value, is unproblematic once we have accepted Adrian’s flexibility about the possibility of a broad interpretation of the term “proposition”, combined with a disjunctivist account of what I have called the background distinction. What calls for a little thought is the way this is worked out in detail. The key thing here is that Wittgenstein’s whole account of language takes the meaning of sentences to be compositional: indeed, he takes this to be an argument for his picture theory of sentences (4.02). What this means is that a sentence can only be a sentence and lack sense in virtue of some of its constituent parts lacking a meaning. The question is how we can understand a sentence having constituent parts with a distinctive syntax–for example, “identical” in the sentence “Socrates is identical” being an adjective–if they have no meaning. The core problem is this: where does the syntax of the parts of a sentence come from?

A way of raising the problem is to look back at the notion of form as it applies to sentences. In the last section I mentioned these two remarks:

2.0141 The possibility of its occurrence in atomic facts is the form of the object.

2.151 The form of depiction is the possibility that the things are combined with one another as are the elements of the picture.

2.0141 describes the form of a constituent of a sentence-like item (a fact) in terms of the way it can combine with other such constituents within the whole: we might call this an external form–it is a matter of an item’s way of combining with things which are, in a way, external to it. 2.151 describes the form of a sentence-like item (a picture) in terms of the way that its constituents can be combined with one another: we might call this an internal form–it is the matter of the way things within an item can be combined with each other.

If we hold onto this picture, we expect constituents of sentence-like items to have external forms, and sentence-like items themselves to have internal forms. But sentences themselves must also have external forms: sentences can combine with other sentences to form sentences. And it is, of course, the external form of Sätze (sentences, propositions) which remark 6 of the Tractatus characterizes. The question, then, is this: how can the external form of sentences determine their internal form? How does the fact that sentences are those items to which truth-operations apply (Adrian’s claim (1)) determine their internal syntax?

There is a connection between this issue and the terms in which what is fundamental about sentences (as opposed to, say, lists) is characterized. In the last section I characterized what is distinctive about sentences as being that they have a certain completeness. But there is a tradition according to which what is distinctive is that they have a certain unity. Very roughly, the completeness characterization looks to external form, while the unity characterization looks to internal form. The difference between these approaches is not a superficial one: it has to do with what is taken to be fundamental. Put simply, the view that what is distinctive of sentences is that they have a certain unity takes the parts of sentences to be basic, and sentences to be unifications of those parts. In contrast, the view that what is distinctive of sentences is that they have a certain completeness takes whole sentences to be basic, and the parts to be derived in some way from them, as abstractions, or as commonalities between ranges of whole sentences.

It is clear that Wittgenstein takes whole sentences to be basic: this is evident in his clear commitment to a strong form of Frege’s context principle (see 3.3; 3.311), as well, of course, as in remark 6 of the Tractatus. So it is clear that Wittgenstein must take the external form of sentences, at least when characterized in terms of truth, to determine their internal form. What is not clear is how it can do that.

I will offer no solution here: we are on the very edge of one of the deepest issues in philosophy (one which is also relevant to the comparison with Kant which Adrian makes in his Appendix–surely no accident). What I will do is simply show the constraints which an attempt to work out a Wittgensteinian response must face.

First, it seems implausible that the mere idea of abstracting from, or finding commonalities between, whole sentences can itself explain the particular character of particular parts of speech: the adjectival character of “identical” in “Socrates is identical”, for example. This seems to mean that it is important that truth is involved in what determines the form of sentences: sentences are complete in whatever way is required for them to be true. Since truth requires some kind of relationship between sentences and the world, that relationship itself may be brought in to explain the particular character of particular parts of speech.

But, secondly, the particular character of particular parts of speech cannot just be borrowed or copied from the character of counterpart items in the world. So “identical” cannot be an adjective, for example, just because it is a quality which it purports to be correlated with. The reason is that if qualities had the relevant character independently of any relation to sentences, then worldly facts would have a fact-like character independently of their relation to sentences. And if worldly facts had a fact-like character independently of sentences, then it would be their correspondence to possible worldly facts which ultimately determined the syntax of sentences. The syntax of sentences would be as it is in virtue of the independently intelligible character which they share with independently fact-like worldly facts–and not in virtue of their being such that truth-operations apply to them. And that would undermine the thought that, for Wittgenstein, the disjunctivist truth-operation view gives the explanatory essence of sentences.

It seems to follow from this that if we are to make sense of the particular syntactic character of particular parts of speech we need to find some way of understanding what is involved in sentences being true, which is not merely a mapping between them and independently fact-like items in the world. But nothing yet stops it being the case that the internal form of sentences is determined by their external form–at least if their external form is determined by the fact that they can be true or false.

7. IS THE DISJUNCTIVIST VIEW COMPATIBLE WITH THE PHILOSOPHY OF THE TRACTATUS IN GENERAL?

Kant has already been hanging in the background. He now comes closer to the front of the stage. Let us begin by considering whether the disjunctivist view is compatible with the philosophy of language of the Tractatus. The central plank of the philosophy of language of the Tractatus is the application to language of a general theory of representation. The general theory of representation is expressed in these two remarks:

2.161 In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.

2.17 What the picture must have in common with reality in order to be able to represent it after its manner – rightly or falsely – is its form of depiction.

The application of this view to propositions (sentences) is made clear in this remark:

3.21 To the configuration of the simple signs in the propositional sign corresponds the configuration of the objects in the state of affairs.

This means that the form of the proposition (sentence) must also be the form of reality. And just as reality consists ultimately of facts (1, 1.1), so also:

The propositional sign is a fact (3.14).

How are we to make sense of this if the disjunctivist truth-operation view of sentences is right? It looks as if we cannot accept either of the two simplest ways of understanding how the form of language might be the same as the form of the world. One of these is a simple realist approach, which supposes that the world comes already composed of facts, articulated in objects, and language simply borrows or inherits this structure from the world: language is propositional because the world is. We have already seen that this is incompatible with the idea that the disjunctivist view gives the explanatory essence of sentencehood.

The other simple way of understanding the fact that language and the world have the same form is a simple idealist view, which supposes that language is in itself already propositional, and that a world with propositional structure is somehow created as a counterpart of it. But again, it is hard to see how that is compatible with the thought that being a possible base of truth-operations is the explanatory essence of sentencehood, and as we have seen, it seems to offer no way in which the particular syntactic character of the constituents of sentences can be explained.

This means that we are forced into something like the following picture, if we accept the disjunctivist view of the essence of sentences: there comes to be language with a propositional structure in virtue of sentences being held to be true or false of a world which is not in itself propositionally structured (is not already divided into facts); and that propositional structure is then projected back onto the world, to present it as a world that can be described. This is a familiar picture: it is a familiar form of Kantianism, and it faces a familiar problem. The problem is that it is hard to see how we are to make sense of–in particular, how we are to describe–the world which is not itself propositionally structured which lies at the base of this picture. The difference now is that the problem can be precisely located: its source is the central thesis of the Tractatus’ philosophy of language, the thesis that language and world must have the same form, if language is to be capable of picturing, describing, the world at all. It is this thesis which makes it so quickly impossible to describe the world as it seems to have to be in itself, not being in itself propositionally structured.

It is a delicate question whether the impossibility here is in fact the impossibility which led Wittgenstein to claim that the propositions of the Tractatus were nonsense (6.54). If there is an argument that the propositions of the Tractatus must be nonsense, it looks as if it is the argument about form which appears in the following remarks:

2.172 The picture, however, cannot depict its form of depiction; it shows it forth.

2.173 The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.

2.174 But the picture cannot place itself outside its form of representation.

And the point is applied to propositions (sentences) in 4.12:

Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it – the logical form.

To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.

If this argument is the basis of Wittgenstein’s view that philosophical propositions must be nonsensical, it seems that he must think that philosophical propositions are about form–in particular, the form of reality. (This is quite a plausible account of the problem with “formal concepts” at 4.1271-4.1272; and it seems naturally extended to the 6.4s and 6.5s.)

On the other hand, some of the imagery, both of the core argument here and of, for example, 5.61, and perhaps some parts of the Preface, seems to me to make good sense when applied to the predicament which the same-form conception of language puts one in over that kind of Kantian picture. In particular, the language of what is “inside” and what is “outside” seems to me to fit that predicament well. This imagery seems less precisely apt if the only source of philosophical impossibility is the impossibility of representing form.

There seem to be layers upon layers of modality here. At the base there is what one might call combinatorial modality. This is clearly expressed in these two claims:

2.022 It is clear that however different from the real one an imagined world may be, it must have something – a form – in common with the real world.

2.023 This fixed form consists of the objects.

We may put the thought here as follows. All possible worlds contain the same objects. Different non-actual worlds differ from each other and from the actual world only in how those objects are combined in facts. The possibilities of combination are determined in (perhaps by) the objects: the essence of the objects is the limit of the possibilities of their combination, and therefore of the range of alternative possible worlds.

At this base level we seem to have the following claim: the only possibilities are possibilities of combination, and the only necessity is that just these are the possibilities. There are two kinds of combination here, corresponding to the forms of objects and of facts: there are the ways in which objects can be combined in facts; and it seems there should be the ways in which facts can be combined with each other–which are the same as the ways in which sentences (propositions) can be combined with each other (that is, truth-functionally).

These possibilities of combination intersect quite interestingly with familiar kinds of contingency and necessity. Every possible combination of objects which forms a Sachverhalt (an atomic fact, or state of affairs) is a possible fact; and every actual such combination is a contingent fact. Things work a little differently for combinations of facts: in fact, it looks as if the way they work has to be described at the level of sentences. The truth-tables determine that some truth-functional combinations of sentences will represent possible facts–these are form the first of Adrian’s original three categories–while others will be tautologies, and others again contradictions. These latter two, which form the second of Adrian’s original three categories, represent no facts–there are no necessary facts, and no impossible facts–but have a modal status which clearly exploits broadly the same modality as that in virtue of which actually existing Sachverhalten (atomic facts, states of affairs) are contingent.

But then we can go one level up. The central thesis of the philosophy of representation of the Tractatus is that every picture–every representation–must have the same form as the reality it represents. This generates what we may call representational modality: because it is impossible for a representation to represent its own form, it is impossible for a representation to represent the form of any reality which it can represent. So in particular, it is impossible for us to describe or talk about combinatorial modality, since combinatorial modality is, precisely, form. This representational modality–the impossibility of representing form–seems to be different from combinatorial modality.

But the impossibility which arises from considering the consequences of accepting the disjunctivist view of the essence of sentences seems to be different again. The core claim of the philosophy of language of the Tractatus is that the form of sentences is the form of reality–the only reality which can be described. But the disjunctivist view of the essence of sentences seems to force us to think–or try to think–that there is a reality which does not have the form of sentences, and so a reality which, if the philosophy of language of the Tractatus is right, cannot be described. And this “cannot” seems to express an impossibility which is neither combinatorial modality nor representational modality.

There may be a concern that noticing these layers of modality is inconsistent with one of the famous and important claims of the Tractatus:

There is only logical necessity. (6.37)

And to the extent that the position is made more complicated on the disjunctivist view, there might be thought to be reason to doubt that the disjunctivist view of the essence of sentences is true to the spirit of the Tractatus. I think neither of these points is quite right: I think it will become clear why in the section after next.

8.Clarity

The larger aspect of the philosophy of the Tractatus which provides a reason to adopt the broad interpretation of the term “proposition” is the work’s commitment to what we might call clarity. This commitment appears in the following remark:

3.33 In logical syntax the meaning of a sign ought never to play a role; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presuppose only the description of the expressions.

The same thinking seems to be present in this important claim:

It is the characteristic mark of logical propositions that one can perceive in the symbol alone that they are true; and this fact contains in itself the whole philosophy of logic. (6.113)

And the point of this seems to be to deliver this result:

6.122 Whence it follows that we can get on without logical propositions, for we can recognize in an adequate notation the formal properties of the propositions by mere inspection.

This has extra significance in the light of the famous claim I mentioned at the end of the last section:

There is only logical necessity. (6.37)

The big philosophical idea seems to be this. All formal properties, and hence all modality, can be made visible in the logical syntax of sentences, and so be recognizable by “mere inspection”. This idea is what I mean by the clarity to which the Tractatus is committed.

The question is: what does the disjunctivist view do to this commitment to clarity? The first thing to note is that there is no incompatibility between the two. The issue turns on what is involved in “the description of the expressions”, as 3.33 puts it. The disjunctivist view and its “highest-common-factor” alternative give different accounts of this. The highest-common-factor view thinks there is some way of describing the syntax of signs which does not in the end depend on the fact that sentences are things which have or seem to have truth-values. The disjunctivist view thinks there is no such truth-independent way of describing the syntax of signs. But something can be identified as belonging to the class of things which either have or seem to have truth-values independently of actually fixing, or even considering fixing the meanings (referents) of its constituent parts. Even on the disjunctivist view, form can be identified by “mere inspection”.

But I think the disjunctivist view does make a difference to how the desire for clarity looks. Remember that the core of the disjunctivist view is this:

(D) To appear to be truth-valued [in the way relevant to defining syntax] is just either (i) to be truth-valued, or (ii) to merely appear to be truth-valued.

Whereas the highest-common-factor alternative is this:

(HCF) To appear to be truth-valued [in the way relevant to defining syntax] is to have some common essence E distinct from either (i) being truth-valued or (ii) merely appearing to be truth-valued.

These two approaches give a different sense of what is open to “mere inspection” in an adequate notation. On the highest-common-factor view, “mere inspection” reveals a genuine independent essence of sentences, syntax presenting itself as it is. On the disjunctivist view, on the other hand, what “mere inspection” reveals is nothing but appearance–appearing to be truth-valued. And what is achieved by “mere inspection” seems to be indifferent between the two options–between the inspected item’s actually being truth-valued, and its merely seeming to be truth-valued.

It seems extraordinary that Wittgenstein should care so little whether these sentences really have a truth-value or merely seem to. But I think it can be made sense of. It’s worth looking again at this remark:

6.122 Whence it follows that we can get on without logical propositions, for we can recognize in an adequate notation the formal properties of the propositions by mere inspection.

So far we’ve been concerned with the second clause here, and have simply passed over the first. But the first now takes on a new significance, if the disjunctivist view is right: if we take it seriously, Wittgenstein was not interested in tautologies–his concern was to identify them in order to dismiss them and pay no more attention to them. And for that purpose, it really does not matter whether a given sentence is really a tautology, or merely something which would be a tautology if it had a truth-value at all. Whereas other people–Ramsey, for example (Ramsey 1931: 4-5) –thought Wittgenstein had provided a way of identifying tautologies which was useful for logic, and might support a positive philosophy, Wittgenstein’s own concern seems to have been to be able to set them aside. It seems that for him insisting that the only necessity is logical necessity is a way of saying that no necessity (which can be articulated) is really interesting (philosophically, at least).

9. Where We End Up

If we take the disjunctivist view to be true to the spirit of the Tractatus, I think we end up with our view of the work subtly transformed, although perhaps in a direction which some of us should anyway have anticipated. I offer here a synoptic and partial sketch of the way the work seems when viewed in this way.

The work’s founding claim is, I think–at least for this partial sketch–the core idea of the picture theory: the idea that picture and pictured must share a common form–that is to say, that the ways in which the elements of the picture can be combined must be the same as the ways in which the elements of the pictured reality can be combined.

That founding claim has two sides to it. First, it involves a commitment to the view that the only modality which is officially acknowledged is what I’ve called combinatorial modality: the possibilities of combination of objects and facts (or names and sentences), and the necessity that these possibilities are possibilities. And secondly, because no picture can depict its own form, it ensures that those combinatorial possibilities, and that they are necessarily possibilities, cannot be depicted, because no picture can depict its own form. So the founding decision opens up a certain space–the space in which possibilities of combination would be visible as such–only to simultaneously shut it off.

Because the ways in which sentences can be combined are all truth-functional, on the theory of the Tractatus, it is inevitably possible to produce sentences which have a distinctive modal status–they are necessary or impossible–while still having a truth-value. The modality of these sentences, the tautologies and contradictions, is a kind of precipitate of combinatorial modality, and since these sentences do indeed have truth-values, Wittgenstein can now claim that “the only necessity is logical necessity” (6.37).

If we suppose that the disjunctive view of sentences is true to the spirit of the Tractatus, two additional complications are added. First, we cannot think of the isolation of tautologies and contradictions as a contribution to any positive philosophy: they can only be identified in order to be set aside and forgotten. And secondly, we cannot adopt either a simple realist or a simple idealist view of the relation between the syntax of sentences and the ways in which objects in the world can be combined: rather, it seems, a world for sentences to describe must be constructed along with the creation of sentences–out of materials which do not themselves have the form of language. But of course, the same-form assumption which founds the picture theory immediately also prevents us from describing either these pre-linguistic materials or the construction from them of a world of language. Once again, we have the distinctive pattern of a space being opened up, only to be at the same time shut off.

If this is right, then the disjunctive view of sentences simply presses harder a characteristic move which is already to be found in the work–given the founding claim that the form of the world and the form of language must be the same.

It is possible also to understand all this as an argument–or at least a vindication–of the founding claim itself. Wittgenstein does offer an argument of sorts for that claim. The picture theory is first announced here:

4.01 The proposition is a picture of reality.

The proposition is a model of the reality as we think it is.

And the remark which follows up on that is this one:

4.02 This we see from the fact that we understand the sense of the propositional sign, without having had it explained to us.

I take it that the idea is that the compositionality of meaning requires the picture theory: that is, it requires elements of reality to be associated with elements of sentences, with both elements having just the same possibilities of combining to form facts. I think this argument is quite plausible, if the choice is between the picture theory and some other view which holds that linguistic items are meaningful in virtue of being associated with parts of reality.

But I think the consequences of the founding claim of the theory which we have been looking at are at least part of the attraction of the theory for Wittgenstein. It is hard to read the Tractatus without thinking that he is pleased to have reduced all acknowledgeable necessity to logical necessity, and then to have been able to push it to one side; and also pleased to have shut off all discussion of issues which involve a larger, philosophical modality. And yet I think it is also hard to read the work without feeling that a mystical view of life was attractive to him, and so as revealing its author as someone who does not regret the fact that the core claim of the picture theory seems immediately to open up for some kind of contemplation the very space which it shuts off from discussion. I think it only enhances this view of the Tractatus if we see the work as being guided by the disjunctivist view of sentencehood.

m.r.morris@sussex.ac.uk

REFERENCES

Frege, G. 1984/1980. The Foundations of Arithmetic, trans. J. L. Austin. Oxford: Blackwell.

Moore, A. W. 2019. “The Bounds of Nonsense”, in his Language, World, and Limits: Essays in the Philosophy of Language and Metaphysics. Oxford: Oxford University Press.

Ramsey, F. 1931. The Foundations of Mathematics and Other Logical Essays, ed. R. B. Braithwaite. London: Kegan Paul, Trench, Tubner and Co.

Wittgenstein, L. 1922. Tractatus Logico-Philosophicus, trans. C. K. Ogden. London: Kegan Paul, Trench, Tubner and Co.

© 2022 by Public Reason

Public Reason 14 (1): 92-96

Truth-Functional Logic and the Form of a Tractarian Proposition

Oliver Thomas Spinney

Royal Holloway, London

Abstract. In this paper I argue against Michael Morris’ claim, that the Tractatus view involves holding that the possibility of truth-functional combination is prior to the possibility for sentential constituents to combine with one another. I provide an alternative interpretation in which I deny the presence of any distinction in the Tractatus between these two possibilities. I then turn to Adrian Moore’s ‘disjunctivist’ account of sentencehood, itself inspired by the Tractatus view. I argue that Moore’s account need not involve a commitment to the kind of priority Morris describes, and that it need not involve a commitment to transcendental idealism.

Keywords: Wittgenstein, Tractatus, truth-functional logic, propositions, sentences.

Adrian Moore’s (2019, 57-70) disjunctivist account of sentencehood may be briefly stated: a sentence is an item which is either capable of being the base of a truth-operation or appears to be capable of being the base of a truth-operation. Michael Morris claims that the capacity for a sentence to feature in truth-functional combinations constitutes its ‘external form’. Morris contrasts the notion of external form with internal form, and asks how the former determines the latter. Of particular interest to Morris is the question of how the syntactic categories of sub-sentential elements are determined, where the sentences they occur in are truth-valueless. Here I shall briefly argue that there is no such distinction between external and internal form at work in the Tractatus. I conclude that Morris reads into Moore a conception of priority which Moore need not accept. Moreover, Moore’s view may be interpreted as neutral with respect to the issue of realism.

Morris claims that the external form of a sentence is its capacity to combine with others truth-functionally; moreover, it is external, rather than internal form, which remark 6 of the Tractatus describes, and which Moore’s disjunctivist view characterises sentencehood in terms of. The internal form of a sentence, by contrast, is the capacity for its elements to combine with one another. Morris claims that the notion of external form is explanatorily prior to that of internal form. It is my claim, though, that this distinction collapses on Wittgenstein’s position. To see why, we must first examine what, according to Wittgenstein, truth-functional combination consists in. Wittgenstein writes

A proposition is an expression of agreement and disagreement with truth-possibilities of elementary propositions. (1963, 4.4)

Our truth-functionally combining some propositions consists in circumscribing, from a range of truth-value assignments, which combinations we wish to assert. In his Notes on Logic Wittgenstein says

What corresponds in reality to compound propositions must not be more than what corresponds to their several atomic propositions. Molecular propositions contain nothing beyond what is contained in their atoms; they add no material information above that contained in their atoms. (1961, 100)

The familiar truth-functional connectives are merely shorthand devices corresponding to the assertion of truth-possibilities (5.101). The molecular proposition ”p V q” does not assert the existence of a fact composed of the fact that p, the fact that q, and the logical object named ”V”[1]. Rather, ”p V q” is true just in case what ”p” represents and what ”q” represents do not both fail to obtain. This is a deflationary approach to truth-functionality. Consequently, for a sentence to be capable of truth-functionally combining with another is nothing more than for it to be capable of possessing the truth-values which the truth-tabular distribution requires. The ”external form” of a sentence is its capacity for truth and capacity for falsehood, tautologies and contradictions notwithstanding.

Internal form is, according to Morris, a ”matter of the way things within an item can be combined with each other” (7). Wittgenstein describes the relationship between form and the capacity for the constituents of a proposition to combine in the following way:

The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.

Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture. (1963, 2.15)

That the elements of a picture are capable of combining in the same way the objects for which they deputize are so capable constitutes the pictorial form of that picture. Possession of a pictorial form, of elements capable of combining in a certain way, is precisely what makes depiction possible:

What a picture must have in common with reality, in order to be able to depict it – correctly or incorrectly – in the way that it does, is its pictorial form. (1963, 2.17)

That a picture is capable of being true and capable of being false constitutes its capacity for truth-functional combination. That a picture is capable of being true and capable of being false, I submit, just is the fact that its elements possess the capacity to combine with one another in the same way the objects for which they deputize are capable of combining. There is, therefore, nothing more to an item’s being capable of truth-functional combination than that its names be capable of combining with one another in the relevant way. In other words, the possibility that some names are capable of combining with one another as the objects for which they stand are so capable is the possibility of truth and falsehood. The possibility of a proposition’s being capable of truth and capable of falsehood is the possibility of its being truth-functionally combined with another proposition. To put the matter differently, the capacity for a proposition to truth-functionally combine with another is the capacity for some names to combine so as to represent a state of affairs. Consequently, the external form of a sentence and its internal form are one and the same. Anscombe, in a different context, writes

Indeed, we should not regard Wittgenstein’s theory of the proposition as a synthesis of a picture theory and the theory of truth-functions; his picture theory and theory of truth-functions are one and the same. (1959, 81, emphasis original)

The view I am here presenting, on which the distinction between external and internal form of a proposition collapses, concords with Anscombe’s position[2]. The ”picture theory” describes the possibility of truth-aptness through a lens whose focal point fixes on the behaviour of propositional elements. The picture theory appears, therefore, to be a theory concerning the ”internal form” of propositions. Vitally, though, the picture theory of propositions is also a theory of what truth-functional combination consists in because the picture theory gives an account of what something’s being capable of truth and capable of falsehood consists in, and truth-functional combination, on Wittgenstein’s view, requires nothing more than that the items to be combined be capable of truth and capable of falsehood. Wittgenstein does not, in the Tractatus, give a description of how the behaviour of propositional elements contributes to the possibility of truth-aptness, and only subsequently show how propositions come to truth-functionally combine with one another. Rather, an explanation of truth-aptness which appeals to the combinatorial capacity of propositional elements is an explanation of truth-functional combination. Relatedly, Wittgenstein does not show how propositions come to be capable of truth-functional combination, and then apply this explanation to the question of how internal form is determined.

Morris, having argued that Moore’s position involves commitment to the priority of external form over internal form, asks how the former determines the latter[3]. This question of determination must be answered, according to Morris, if Moore’s view is to give the explanatory essence of sentencehood. What is strikingly characteristic of sentences is, in Morris’ view, their possession of a syntax. Moore’s view must show how syntactic categories are determined by external form, if Moore’s view is to give a definition of sentencehood while simultaneously illuminating what is clearly characteristic of sentences by means of that definition. Morris argues that a realist explanation of why sub-sentential components exhibit the syntactic features which they do is unavailable to Moore. The syntactic category of a given sub-sentential item cannot be explained through appeal to a form which is borrowed from an extra-linguistic item, for then the striking characteristic of sentences which is their syntax would not be explained by Moore’s definition, but by an alternative realism. Morris concludes therefore that Moore’s interpretation is in tension with a realist explanation of why items exhibit the particular syntactic features which they do.

If I am correct that the notions of internal and external form collapse for Wittgenstein, then it should be clear the question of how one determines the other is not applicable to the Tractatus view. We need not, therefore, read into Moore’s disjunctivist account a commitment to the priority of external over internal form. Relatedly, Moore’s approach may be read as neutral with respect to the issue of realism once the distinction between external and internal form has been dissolved. Moore claims that something’s counting as a sentence consists in its being capable of being the base of a truth-operation, or appearing to be capable of being the base of a truth-operation. I have argued that what it is for something to be capable of being the base of a truth-operation is for its constituent names to be capable of combining in a certain way. In other words, what it is for something to be capable of being the base of a truth-operation is for it to possess a pictorial form. The potential for truth-operability is the potential for constituent-combination of a particular kind. In turn, what it is for some constituents to be capable of combining in a certain way may, pending textual justification, be characterised in realist terms. That some constituents possess certain combinatorial capabilities may well involve appeal to the objects those constituents name. In other words, and crucially for present purposes, the first disjunct of Moore’s definition might involve a conception of truth-operability on which realism is bound up with that conception. To say that something is capable of being the base of a truth-operation is to say that it possesses a pictorial form. What it is to possess pictorial form may itself admit of a realist elaboration. In other words, the notion of truth-operability may be fleshed out via realist means. To invoke realism here would not be to place the explanatory power of our account of sentencehood outside of Moore’s definition, but only to claim that Moore’s definition is capable of including a realist commitment. Whether or not the disjunctivist view Moore describes does involve a realist commitment is an open question, but that it could involve such a commitment is not ruled out by anything Moore himself says. Accordingly, the Kantian picture Morris suggests that the disjunctivist view leads to is not an inevitability, though it remains, as with realism, a possibility.

Morris focuses his attention on the lead disjunct of Moore’s view, and interprets that disjunct as less flexible than I have claimed it to be. Accordingly, Morris draws certain conclusions from Moore’s view which I have argued need not follow; the lead disjunct of Moore’s definition may be viewed as more schematic than Morris allows. Moore’s position is, if my understanding is correct, equally compatible with realism, idealism, or transcendental idealism.

oliver.spinney@rhul.ac.uk

REFERENCES

Anscombe, G. E. M., 1959. An Introduction to Wittgenstein’s Tractatus. London: Hutchinson.

Moore, A. W., 2019. Language, World and Limits: Essays in the Philosophy of Language and Metaphysics. Oxford: Oxford University Press.

Winch, Peter, 1969. ‘Introduction: The Unity of Wittgenstein’s Philosophy’, in Studies in the Philosophy of Wittgenstein, edited by P. Winch, pp. 1–19. Oxford: Routledge.

Wittgenstein, Ludwig, 1963. Tractatus Logico-Philosophicus. Trans. D. F. Pears and B. F. McGuinness, London: Routledge and Kegan Paul.

1] See Wittgenstein (1963, 5.4).

2] See also Winch, who remarks that ”the structure of elementary propositions invades the field of truth-functional logic” (1969: 8). Winch describes the relationship holding between the structure of an elementary proposition and those truth-functional combinations in which the proposition is capable of occurring. It is on the basis of this relationship that the structure of an elementary proposition counts as a logical structure, according to Winch.

3] Of particular interest to Morris are cases involving nonsensical sentences. Morris asks how it is determined that ”identical” occurs adjectivally in the sentence ”Socrates is identical”. It is important to note here though that ”Socrates is identical” is a sentence, in Moore’s view, because it satisfies the condition of appearing to be a sentence. Correspondingly, the sign ”identical” is adjectival in the sense that it appears to be an adjective. What determines the adjectivality of ‘identical’ is, therefore, a matter of psychology, rather than logic.

© 2022 by Public Reason

Public Reason 14 (1): 97-122

Replies A. W. Moore

University of Oxford I should like to begin by expressing my deep thanks to Sorin Baiasu for organizing the 2020 Rousseau Annual Conference at which early versions of the essays in this volume were first presented, and for inviting me to deliver the Rousseau Annual Lecture that preceded the conference and that is the subject of his own contribution to the volume. I should like to express equally deep thanks to all the contributors for the great care and generosity with which they have engaged with my work. I have found it enormously gratifying to see some of my own ideas developed in such interesting ways, often taking them beyond anything that I had envisaged myself.

What unites all these essays? They range widely, but there is one significant concern that they share, both with one another and with the work to which they are responding: namely, the concern with limits and with what is involved in recognizing and acknowledging them. There is also a more specific concern, implicit if not explicit throughout, which is the concern with various problems that may afflict our acknowledging limits of our own. The most basic of these problems is that, in the case of at least some of these limits, it looks as though we cannot acknowledge them as long as we are subject to them.[1]

In Sarah Patterson’s and Jonathan Head’s essays, the crucial limits are limits to what we can recognize as possible. In Sorin Baiasu’s and Zachary Vereb’s essays they are the limits to our knowledge set by transcendental idealism. In Jenny Bunker’s and Pablo Montosa’s essays they are limits imposed by our very finitude. And in Michael Morris’s and Oliver Spinney’s essays they are limits to what counts as a sentence, on a technical conception of a sentence that I introduce in the work to which they are responding.

1. Reply to Sarah Patterson and Jonathan Head

There is a great deal in Sarah Patterson’s essay to suggest that she and I are close in our understanding of Descartes – closer, I think, than either of us is to Jonathan Head. One way to appreciate this is to consider the third paragraph of Head’s essay in which he provides a summary of Patterson’s exegesis, about which he subsequently expresses reservations: I would be happy to acknowledge his summary of her exegesis as a good summary of my own. Crucially, Patterson and I agree that, on Descartes’ view, God’s free creation of such truths as that one plus two is three is not antecedently constrained in any way by what is or is not possible, but rather that God Himself decides what is or is not possible by not only decreeing that such truths are true, but also decreeing that they are necessary. Patterson and I also agree that God’s decreeing that these truths are necessary does not just mean that things could not have been otherwise with respect to any of them; it means that God could not have decreed that things be otherwise with respect to any of them. One of the issues with which Patterson, Head, and I are all concerned is how this last consequence is to be reconciled with the freedom of God’s decrees.

A caveat before I proceed. Head puts the issue in terms of what he calls Descartes’ “voluntarism”.[2] This is a term that is often used in this context (though it is not used by either Patterson or me). Typically, what is meant is the view that necessary truths depend on God’s free creation. If the term is understood in this way, then it is quite wrong for Head to claim that I claim that “the voluntarism expressed in […Descartes’] correspondence and elsewhere is an unfortunate lapse.”[3] On the contrary, as I indicated in the previous paragraph, I take this to be Descartes’ fully considered view. So I assume that Head’s use of the term is unorthodox and that he has in mind some other view, presumably a view of the very kind that Patterson and I want to dissociate from this, about what God could have decreed with respect to any given necessary truth.[4]

Be the terminology as it may, the issue, as I have indicated, is how to reconcile the claim that God could not have decreed that things be otherwise with respect to any given necessary truth with the claim that God’s decreeing that things are that way is an act of free creation. How, for example, can it be an act of free creation on God’s part to decree that one plus two is three if God could not have decreed that one plus two be anything other than three? Towards the end of his essay Head answers this question by distinguishing senses: “in some sense,” he writes, “things could have been otherwise with regard to the necessary truths and God could have (in some sense) created things that way […but] (in another sense) God could not have created things in another way.”[5] The second of these senses is supposed to be connected with Richard LaCroix’s idea, to which Patterson has recourse in her essay, that although God is undetermined in His creation of the necessary truths, He is, in creating them, self-determined by His own creation.[6] This in turn is supposed to be connected with God’s simplicity – with there being no difference between God’s willing that something be so, His creating it to be so, and His understanding that it is so.[7]

I am not entirely sure how the distinction that Head draws on the strength of these supposed connections is to be understood. But, however it is to be understood, it surely compromises the necessity of the necessary truths. For the first of the senses that Head distinguishes involves the concession that, whatever the nature of the necessity that attaches to these truths, there is a more fundamental level at which they admit of alternatives (just as we can say that, whatever the nature of the necessity that attaches to the laws of physics, there is a more fundamental level, notably that of logical possibility, at which they admit of alternatives). To be sure, Head insists on Descartes’ behalf that the alternatives in question are alternatives that we can only apprehend, not conceive. But alternatives that we can only apprehend, not conceive, are none the less alternatives – unless what it is for them to be alternatives is for us to be able to conceive them (as in fact I think Descartes thinks), in which case what Head insists on Descartes’ behalf makes no sense. It seems to me that a proper approach to this issue needs to eschew distinctions of the kind that Head draws in favour of a single absolute conception of necessity whereby the necessity of one plus two’s being three means that it admits of no alternatives and that there is no relevant sense in which God could have decreed that things be otherwise. The challenge is to understand this in such a way that it poses no threat to the freedom of God’s decree. It is something of this sort that I attempt in the essay to which Patterson and Head are responding,[8] and I still see no reason to retract my attempt.

It is something of this sort that Patterson attempts too. As I have already intimated, we are exegetically close. Nevertheless, we differ. As Patterson points out at the beginning of §5 of her essay, some of what we both think we think for different reasons. The pivot of my interpretation of Descartes is an identification that I take him to make of what is possible with what does not conflict with our human concepts. In note 5 of my essay I admit that Descartes does not commit himself to this identification outright: he commits himself only to the hypothetical that, if this is what it is for something to be possible, then such and such follows. But I also claim that, in the context in which he says this, it is clear that he has no stake in endorsing any other conception of what is possible. Patterson demurs. She notes that Descartes does in fact go on to advert to other conceptions of what is possible without repudiating them. On her interpretation, what is possible depends, for Descartes, “not on human concepts, but on the essences freely created by God.”[9]

Even here, however, the disagreement between Patterson and me does not strike me as great. For one thing, I am happy to admit that what is possible depends, for Descartes, on the essences freely created by God. For I am happy to admit that God’s decrees about what is possible consist, for Descartes, in His creation of essences, where what Descartes means by essences, as Patterson reminds us towards the end of her essay, are true and immutable natures. The point, however, is that there is still an issue about what the immutability of such natures consists in; and I still think that Descartes understands this in terms of our human concepts. But even if I am wrong about this – even if Descartes has a more ontologically robust conception of the possible, as Patterson thinks – he still regards non-conflict with our human concepts as a symptom of possibility, if not a criterion.[10] And that is enough for my purposes in the essay to which Patterson and Head are responding.[11]

The fact remains that, on my interpretation, non-conflict with our human concepts is a criterion of possibility, not a symptom. It therefore behoves me to say something in response to Patterson’s explicit argument that this cannot be right. She cites a passage from Descartes’ Fifth Meditation in which he appears precisely to reject the idea that our human concepts determine what is or is not possible. The issue with which Descartes is concerned in this passage is the existence of God. Descartes not only thinks that God exists, he thinks that it is necessary that God exists. He insists, however, that it is the necessity that determines his thinking, not vice versa; he also insists that, just as his thinking that God exists does not make it true that God exists, neither does it “impose necessity on any thing”.

None of this troubles me, however. There are three propositions at stake here: (E) the proposition that God exists; (T) the proposition that Descartes thinks that God exists; (N) the proposition that it is necessary that God exists.

On my interpretation, (N) is true, not because of what Descartes thinks, nor therefore because (T) is true, but because of what Descartes, in common with the rest of us, cannot help thinking. And it is what Descartes cannot help thinking that determines what he actually does think. In other words, it is what Descartes cannot help thinking that determines that (T) is true, in line with what he insists in the passage from the Fifth Meditation. Moreover, Descartes is self-conscious about this. In particular, he acknowledges the truth of (N). And it is this that enables him to acknowledge the truth of (E), which in turn gives him reassurance concerning (T). For he infers the truth of (E) from that of (N). And his justification for making this inference – despite the fact that the truth of (E), but not that of (N), is independent of him – has to do, ultimately, with God’s benevolence,[12] which ensures that what Descartes, in common with the rest of us, cannot help thinking is true. Nothing in the passage from the Fifth Meditation seems to me incompatible with any of this. And indeed the sentence immediately preceding the passage seems to me rather neatly to encapsulate it: Descartes writes, “From the fact that I cannot think of God except as existing, it follows that existence is inseparable from God, and hence that He really exists.”[13]

There is another difference between Patterson and me. Patterson takes a somewhat different approach from mine to Descartes’ claim that he “would not dare to say that God cannot make [it…] that one and two should not be three.”[14] I say that such reticence is misplaced. Not that I am totally unsympathetic to Descartes: in note 10 of my essay I advert to the possibility that his reticence is due to a scholastic scruple of some kind, and later, relatedly, I mention Descartes’ reluctance to declare anything to be beyond the power of God – though I also add that he could and should have followed Aquinas by insisting that not being able to do the impossible is no limitation on the power of any being.[15] But Patterson, again following LaCroix, sees Descartes’ reticence more as a matter of rhetoric. She thinks that Descartes would not dare to say such a thing about God because doing so would be liable to misinterpretation. Even if she is right, however, it does not affect my principal contention. It remains the case, on my account, that what Descartes would not dare to say is something that he should say, however misleadingly, since it is a consequence of his basic conception of these matters.

Finally, in §6 of her essay, Patterson also takes issue with the way in which, at the end of my own essay, I relate my exegesis of Descartes to the question of what he thinks a deceiver of supreme power could do. Although I find Patterson’s alternative gloss on what Descartes says in this connection very attractive, I am not in the end persuaded that she does full justice to it (that is, to what he says). However, I shall leave the matter there. Patterson herself admits that what she proffers by way of elaboration of her alternative gloss is both brief and contentious,[16] and it would be inappropriate for me, especially within these confines, to speculate on what a detailed version of what she proffers would look like.

2. Reply to Sorin Baiasu and Zach Vereb

I will begin my reply to Sorin Baiasu and Zach Vereb by addressing various issues about the relations between what I have in mind when I talk about knowledge in the essay to which they are responding and what Kant has in mind when he talks about related notions.[17] Indeed I will devote the bulk of my reply to addressing these issues. They are admittedly not the most interesting issues. They are not even the issues where the most interesting disagreements between Baiasu, Vereb, and me arise. But they do affect almost everything else, and until they are addressed there is considerable scope for confusion.

We can start with the Kantian distinction between cognition and knowledge that Baiasu discusses in §3 of his essay. The two German terms that Kant uses are “Erkenntnis” and “Wissen”. To allow for the possibility that Kant is using these terms in a quasi-technical way, and to avoid begging any questions about how his use of either of them relates to my own use of “knowledge”, I shall retain the German originals.

What does Kant mean by “Erkenntnis”? This is a notoriously difficult question. I agree with Baiasu and Vereb that Kant gives at least two accounts of what he means which appear straightforwardly incompatible with each other. According to what he says at one point in Critique of Pure Reason, Erkenntnis requires both intuitions and concepts.[18] Later, he suggests that intuitions on their own and concepts on their own also count as instances of Erkenntnis.[19] Baiasu accordingly says that Kant has a single (ambiguous) label for two distinct notions.[20] Baiasu himself distinguishes these notions by labelling the former, narrower notion “EK” and the latter, broader notion “EM”. He further claims that, when I refer to Erkenntnis, I am referring to EM; and Vereb follows him in this regard.[21] But in fact this is not so. On the very few occasions on which I refer to Erkenntnis, either in my essay or in my book The Evolution of Modern Metaphysics, to which Baiasu and Vereb both also refer,[22] I have in mind EK, which I take to be, of the two, the notion that is of greater concern to Kant.

One of the occasions on which I refer to Erkenntnis is in a lengthy note in the chapter on Kant in my book.[23] And one of the things that I do in that note is to identify something which, in my own terms, counts as knowledge but which, in Kant’s terms, does not count as Erkenntnis, a kind of knowledge that I in turn characterize as “purely conceptual”. What I have in mind is analytic knowledge that concerns things in themselves, in the attenuated sense of “concern” that I introduce in my essay – knowledge in which no intuitions are involved.[24] (This is itself an illustration that what I think of as Erkenntnis is EK, not EM.) An example that I give in the essay is knowledge that things in themselves are things irrespective of how they are given to us.

Later in the chapter on Kant, where I give what might be deemed further examples of knowledge that is not Erkenntnis, I include the very knowledge that there are things in themselves, along with the knowledge that things in themselves are non-spatio-temporal. Baiasu interprets me as holding that these too are examples of purely conceptual knowledge concerning things in themselves.[25] However, given that by purely conceptual knowledge I mean a kind of analytic knowledge,[26] it follows, as I point out, that they cannot be so regarded. For they cannot be regarded as analytic. True, the idea that Kant accedes to synthetic knowledge of this kind concerning things in themselves should give pause. But, as far as that goes, the critical point is that, whereas the note is intended as an outline of what Kant himself would be prepared to say, the later material is intended as an indication of what, possibly despite himself, he is committed to saying.

Why do I say that these examples of knowledge cannot be regarded as analytic? In the case of the knowledge that there are things in themselves, partly because of what I see as Kant’s recoil from the very idea that an existential judgement can ever be analytic.[27] But is it as simple as that? In note 64 of the same chapter I allude to the possibility that our use of the expression “knowledge that there are things in themselves” may be a misleading label for knowledge that is not about what there is, but is rather knowledge that how things appear is only how they appear, in which case it may seem to be a compelling candidate for analyticity after all. Nevertheless in the same note I deny that it is. This is because of the “only”, which adverts to a contrast to which the mere concept of appearance does not.

Baiasu argues that the most that Kant thinks we have insight into is the logical possibility of things in themselves, not what Kant would call their “real” possibility, still less anything that might be characterized, however misleadingly, as their existence.[28] Vereb, towards the end of §2 of his essay, presents a similar argument, fastening on the idea that, for Kant, the concept of “things in themselves” is a “boundary concept” – which means, among other things, that it has a merely negative use.[29] I readily acknowledge the force and the importance of these arguments. All I can do in this context is to respond with the cavalier suggestion that any tension between what Kant allows himself to say concerning things in themselves and what I think he does say, or is committed to saying, is Kant’s problem, not mine. That said, it is not obvious to me that Kant’s granting us knowledge that there are things in themselves is, in itself, a problem for him (except insofar as the very distinction between appearances and things in themselves is a problem for him). He denies us Erkenntnis concerning things in themselves. But there is no suggestion, in anything I say, that the knowledge in question is that.[30]

In this respect, if not in respect of its syntheticity, our knowledge that there are things in themselves is like the analytic knowledge that Kant grants us that is (likewise) not Erkenntnis. Let us reconsider such analytic knowledge. As I have already indicated, it too concerns things in themselves, in the attenuated sense of “concern” that I introduce in my essay. But it does not make reference to any object in the way in which Erkenntnis – understood as EK – does. This is because it does not involve intuitions. It is not because it is analytic. We should not think that analytic knowledge, simply by virtue of the fact that it is justified by nothing but appeal to the concepts involved, automatically fails to count as EK. To say that such knowledge is justified by nothing but appeal to the concepts involved is not to deny that it involves intuitions too. In all but the exceptional case of analytic knowledge concerning things in themselves, it does involve intuitions too.[31] Thus when Kant himself refers to analytic Erkenntnis,[32] there is no reason to think that he is referring to anything other than a kind of EK. To repeat: what prevents analytic knowledge concerning things in themselves from being a kind of EK is that it does not involve intuitions.

But now two questions arise, one that Vereb urges directly and one that Baiasu urges indirectly. The question that Vereb urges directly is what I mean by this attenuated sense of “concern”. The question that Baiasu urges indirectly is whether I am justified in thinking that Erkenntnis and knowledge ever overlap, in other words that some instances of Erkenntnis are also instances of knowledge. (If I am not, then that is what prevents analytic knowledge concerning things in themselves from being a kind of EK.) To begin with the former question, Vereb complains that I am not clear about this.[33] The complaint is, in a way, entirely justified: I am not. Even so, given the context in which I invoke this sense of “concern”, the complaint is unfair. This is because my main point is that, even if we accept an attenuated sense of “concern” in which, on Kant’s view, we can have analytic knowledge concerning things in themselves, it will be sufficiently attenuated for this not to be a problem for him – just as it will be sufficiently attenuated for there not to be any need to invoke transcendental idealism in order to account for our analytic knowledge concerning things that are beyond us. Kant’s problem, as I try to indicate in §5 of my essay, lies elsewhere.

Now to the second question. The reason why I describe Baiasu’s urging of this question as indirect is that his focus is on the relation between Erkenntnis and Wissen, not on the relation between Erkenntnis and what I call “knowledge”. Were “knowledge” just my term for “Wissen”, then I would need to confront Baiasu’s intriguing challenge, endorsed and reinforced by Vereb, to the very idea that any instance of Erkenntnis can also be an instance of Wissen.[34] The challenge is grounded in the idea that Wissen includes assent while Erkenntnis precludes it. I am not entirely convinced,[35] though I regret that I do not have scope to pursue the issue here. However, what matters here is that, fascinating and difficult though these questions about the relation between Erkenntnis and Wissen are, I can simply bypass them on the grounds that I am not committed to an equation of knowledge with Wissen: even if Baiasu is right that Erkenntnis and Wissen are incompatible, it does not follow that Erkenntnis and knowledge are incompatible.

Very well, but is it not time, in that case, that I said what I meant by “knowledge”?

Perhaps it is. But my answer is simple. I intend my use of “knowledge” to be none other than its normal use. On its normal use, “knowledge” has a vast and varied range. It embraces: knowledge that 7 + 5 = 12; knowledge of the character of space and time; knowledge of Smith; knowledge of how to tie one’s shoelaces; knowledge of how to act rationally; and many more besides. I intend my use of “knowledge” to embrace all of these.[36]

This, incidentally, helps to explain why I am no more committed to an equation of knowledge with Erkenntnis than I am to an equation of knowledge with Wissen. For instance, and as we have seen, I grant that, on Kant’s view, there is knowledge concerning things in themselves, even though there is no Erkenntnis concerning things in themselves. (Moreover, as I point out in the lengthy note in my chapter on Kant to which I have already referred, some instances of Erkenntnis contain error in a way that precludes their counting as instances of knowledge.) I mention this because, at the beginning of §3 of his essay, Baiasu says something that might be interpreted as a claim that I am committed to an equation of knowledge with Erkenntnis. He is commenting on something else that I say in that lengthy note in my chapter on Kant, namely that throughout the chapter I put in terms of knowledge what Kant himself typically puts in terms of Erkenntnis. Baiasu goes on to say that I use the word “knowledge” for Kant’s “Erkenntnis”. But that is misleading, for the reasons given. Later Baiasu is more careful: he ascribes to me the belief that, in the relevant contexts, what Kant means by “Erkenntnis” overlaps with what I mean by “knowledge”. It is certainly true that, later in the note, I say that Erkenntnis overlaps with knowledge – and indeed I remain convinced that this is so, notwithstanding Baiasu’s challenge to the very idea that Erkenntnis is compatible with Wissen. (In fact I am even prepared to allow for the possibility that there are non-EK instances of EM that are instances of knowledge: the concept of gold, for example, may perhaps be identified with knowledge of what it is for something to be gold.) However, the crucial claim, which I also make later in the note and which appears similar to the claim that what Kant means by “Erkenntnis” overlaps with what I mean by “knowledge”, can nevertheless be interpreted much more loosely than that. It is the claim that “the questions that Kant raises about [Erkenntnis], and the answers that he gives, are equally questions and answers about knowledge”. That, I think, holds however exactly these various notions stand in relation to one another. If there is what I call synthetic armchair knowledge of necessities, then Kant’s questions undeniably pertain to it, as does the transcendental idealism that he champions in response to these questions.

In sum, then, my concern both in the essay and in the chapter on Kant is – quite simply – with knowledge, as it is normally understood. I do not refer to Wissen at all. And I refer to Erkenntnis only, in effect, to put it to one side.[37]

Let us now turn away from these taxonomical questions about the relations between knowledge, Erkenntnis, and Wissen and consider one of the principal questions that I raise in my essay: why would Kant reject an appeal to transcendental idealism to account for analytic knowledge? The answer I give is that this would make all our thoughts thoughts about appearances, never about things in themselves – whereas it is important for Kant’s purposes that we should be able to have thoughts about things in themselves. Baiasu seems to take my point to be that if our conceptualization of things contributes as much as our intuiting of things to the a priori structure of our minds, then it will follow that even our thinking, not just our intuiting, is only ever of appearances.[38] And he rightly rejects that – as would Kant. For Kant clearly does think that our conceptualization of things contributes as much as our intuiting of things to the a priori structure of our minds,[39] without supposing that this precludes thoughts about things in themselves. Baiasu has misunderstood me, however. My point is that if our conceptualization of things – that is, our sheer conceptualization of things, never mind the character of the concepts being exercised – contributes as much as our intuiting of things to the “i-dependence” that is posited by transcendental idealism – where by the “i-dependence” that is posited by transcendental idealism I mean the dependence that it posits of the form of what we have knowledge of on us – then it will follow that even our thinking, not just our intuiting, is only ever of appearances. And to invoke transcendental idealism in order to account for our analytic knowledge, including our analytic knowledge concerning such matters as God, freedom, and the immortality of the soul, is to be committed to the view that our conceptualization of things does indeed contribute as much as our intuiting of things to that i-dependence. Hence it is to be committed to the view that our thoughts must be as much thoughts about appearances as, on Kant’s view, our intuitions are intuitions of appearances.

Baiasu also attempts to rescue Kant from my claim that, in acceding to the possibility of truths that are both necessary and synthetic, Kant is bound to admit the possibility of truths that are somehow both necessary and contingent. Baiasu considers an item of geometrical knowledge that Kant would classify as both necessary and synthetic: that any triangle has angles that sum to two right angles.[40] He agrees that there is a contingency here. But he insists that what is contingent is a truth concerning the relation between the subject and the predicate of this item of knowledge, whereas what is necessary is a quite distinct truth concerning the geometrical objects themselves. No single truth, on this account, appears to be both necessary and contingent.

I confess I do not understand this. For one thing, I would have thought that the relevant truth concerning the relation between the subject and the predicate, which is that the latter is not contained in the former, is necessary, not contingent. (Surely we do not want to say that the concept of having angles that sum to two right angles might have been contained in the concept of a triangle, though it happens not to be?)[41] The closest that I can come to making sense of Baiasu’s claim is to think of it, not as a claim about two distinct truths, but as a claim about a single truth – that any triangle has angles that sum to two right angles – viewed in two distinct ways, first by taking account merely of the concepts involved, second by taking account also of the intuitions involved. The thought would be that, in the former case, we can acknowledge the truth as a contingency, but in the latter case we have to acknowledge it as a necessity, there being no incompatibility between these because the contingency and the necessity would each be relative to how the truth is viewed.

But if that is the kind of thing that Baiasu has in mind, then my concern is different. If, when we view the truth in the latter way, we really do have to acknowledge it as a necessity, then the necessity determines what we have to acknowledge when we view it in the former way too. By way of analogy, consider someone who claims that various truths can be acknowledged as contingent if we take account merely of the concepts involved and do not take account of logic. Thus they might claim that, if we take account merely of the concepts involved and do not take account of logic, then we can acknowledge the truth that any natural number is either odd or even as contingent; for, they might say, even if the predicate of this truth is in some sense contained in the subject, it is only a matter of logic that it is. I want to say that, given the necessity that attaches to logic, the sense in which the predicate of this truth is contained in the subject is the only sense that is relevant here: the necessity is itself part of the essential nature of the concepts involved, and to prescind from it is not properly to take account of them. (Kant would count the truth in question as an analytic truth.) Similarly in the case of the truth that any triangle has angles that sum to two right angles. Given the necessity that Kant thinks attaches to geometry, then the sense in which the predicate of this truth is contained in the subject is the only sense that is relevant here – unless Kant can find some pertinent difference between the necessity that attaches to geometry and the necessity that attaches to logic. To be sure, it might be countered on Kant’s behalf that he can indeed find a pertinent difference between these: the necessity that attaches to geometry, unlike the necessity that attaches to logic, can be duly relativized, albeit not in the way that was being considered above, namely to how truths are viewed, but rather in the way that I introduce in §4 of my essay, whereby it is necessity only from the point of view of beings with certain forms of intuition. In §5 of my essay, however, I urge that this creates further problems of its own.

I shall close this section by returning to Vereb’s essay. In §3 of his essay Vereb emphasizes the wider significance of the issues that I address in my essay about the alleged incoherence of transcendental idealism, and says that my critique, if successful, is “even more devastating than [Moore] sees.”[42] He goes on to mention the connection that these issues have for Kant with freedom, ethics, law, politics, religion, and more besides. I do not know whether there is an intentional suggestion here that I am unaware of these connections. I hope not. (Vereb would have to have a very dim view of my knowledge of Kant to think that I am.) Be that as it may, he is certainly right to emphasize the connections. And I am prepared to bite the bullet. To whatever extent any of Kant’s views rely on his transcendental idealism, then so much the worse, I say, for those views. But “to whatever extent” is the operative phrase. In very few cases, if any, is there nothing to be salvaged from the views, even once transcendental idealism is abandoned. And even if there are cases in which there really is nothing to be salvaged, to say so much the worse for the views is, for reasons that are implicit in the quotation from my book that Vereb gives on p. 73 and that he himself goes on to elaborate, very far from saying that they are worthless.

3. Reply to Jenny Bunker and Pablo Montosa

Jenny Bunker’s essay is in many ways the easiest for me to respond to, if only because she explicitly puts a series of questions to me. But before I turn to these questions, the first of which will also provide me with an opportunity to respond to Pablo Montosa, I wish to begin with a brief comment on Bunker’s exegesis. I think she gives a wonderful summary of my arguments in the two chapters of my book The Infinite on which she is focusing.[43] I even (absurdly) derived some satisfaction from the thought that my writing must have been exceptionally clear for Bunker to be able to summarize it so well! The credit, however, is hers, for her careful and patient reading. That said, I do have one small correction – although perhaps, in the light of some of what I shall say later, it will not seem so small. Ironically, it is a correction to something at the very end of her summary, and I mean at the very end: not even the final sentence, but the final clause, nay the final two words. Bunker makes a reference, mea nomine, to what surpasses our finitude and glosses this as “the infinite”. But I do not equate what surpasses our finitude with the infinite. What surpasses our finitude may just as well be some other finitude. And, very importantly, in the case of each individual among us, it may just as well be the finitude of any other individual among us. We shall return to these issues later.

Bunker’s first question is whether, in my interpretation of Spinoza, I acknowledge two kinds of differentiation; or better, whether I distinguish between delineation, understood as something that essentially involves negation, and differentiation, understood as something purely positive. And my answer is: yes, that is precisely what I do. But then the question arises how differentiation can be understood as something purely positive. And this is a very large question about which I try to say more both in the two chapters of The Infinite on which Bunker is focusing and at various points throughout The Evolution of Modern Metaphysics.[44] I do not doubt that far more needs to be said. Certainly far more needs to be said than I can proffer here. Nevertheless, it is worth reiterating one very simple point that I make in The Infinite, namely that I am, at least in part, appealing to an arbitrary stipulation, whereby positivity is aligned with whatever is and negativity with whatever is not.[45] Differentiation between two attributes can then be understood as purely positive on the simple grounds that it depends on the difference of kind that there is between these two attributes. Again, differentiation between two finite modes of the same attribute can be understood as purely positive on the simple grounds that it depends on the relations that there are between these two modes (in the case of bodies, relations of motion and rest). This is in contrast to the delineation of a finite mode, which has to be understood as involving negation on the equally simple grounds that it depends on where the mode is not.[46]

It is these and related issues concerning Spinoza’s ontology that are the foci of the various objections to my book that Montosa raises in his essay. Some of these objections concern what he sees as omissions, things that I do not say but should; others concern what he sees as errors, things that I should not say but do. Despite the fact that he includes some extraordinarily generous comments about my work elsewhere in his essay, for which of course I am grateful, each of his objections seems to me ill-grounded. In each case, with one exception, I agree with Montosa about what I should or should not say, but I disagree about what I do or do not say.

The exception is Montosa’s first objection. I claim that, for Spinoza, the being that is common to every entity is itself an entity and is what is meant by substance. Montosa’s objection is that I am thereby “[neglecting] the crucial distinction in Spinoza’s thought between […] substance and its modes.”[47] Since there is nothing more prominent in Spinoza’s thought than the distinction between substance and its modes, I would need to be guilty of singularly insensitive exegesis for this objection to hold. But I cannot see why Montosa thinks it does. He goes on to list various fundamental differences that Spinoza recognizes between substance and its modes, none of which I think I am committed to denying. He also says that, if modes of substance are entities at all, then they are not entities “in the same way” as substance is, and again I do not think I am committed to denying that. The word “entity”, as I am using it, is nothing but a maximally generic word that applies to everything. The quantifier “all entities” therefore does exactly the same work for me as the quantifier “omnia quae sunt” does for Spinoza. The latter is the quantifier that appears in the very first axiom of his Ethics.[48] And indeed that axiom, in conjunction with Spinoza’s third and fifth definitions, neatly captures what I have in mind by the claim to which Montosa takes exception. For what that axiom states, in my terms, is that all entities are either in themselves or in something else; and “entity that is in itself” is how “substance” has been defined in the third definition, while “entity that is in something else” is how “mode” has been defined in the fifth.[49] Since the fifth definition also includes an indication that what modes are in is substance, it follows that, for Spinoza, substance and modes alike are in substance. Indeed for both substance and modes to be at all is for them to be in substance. It does not seem to me a large step from there to an identification of substance with being. At any rate I cannot see why taking this step entails neglecting any of the fundamental differences between substance and its modes.[50]

Montosa’s second objection is that, in my exposition of Spinoza’s account of error, I align error with ignorance, whereas Spinoza himself carefully distinguishes them. I agree that Spinoza carefully distinguishes them. I disagree that I align them. My claim is that, for Spinoza, error comes about because of ignorance. Thus when a man errs, he errs because he lacks knowledge of what lies beyond him and thereby imagines that something quite different does; none of the contents of his mind, not even his imagining, is erroneous in itself, but his ignorance enables his imagining to lead him astray.[51] I cannot see any difference between what I have just claimed that Spinoza says, what Montosa claims that Spinoza says,[52] and what I claim in my book that Spinoza says.[53] Montosa’s objection thus leaves me mystified.

The mystery is compounded when he extends the objection to the related issue of what constitutes the finitude of a body. Montosa says, supposedly contra me, that, in Spinoza’s view, finitude, understood as “delineation”, can only have a privative sense: it is a property that supervenes on bodies by relating them to one another, but it does not define them. On the contrary, “delineation” presupposes the previous “differentiation” of bodies and is built upon it.[54]

Is that significantly different from what I say in my book? I claim that, in Spinoza’s view, given any finite entity x, there has to be something that lies “outside” it, y. This in turn means that, […] whereas whatever differentiates them has being, which is […] positive, x’s involvement in y’s being […] has a lack of being, which is negative […]. It is thus that the being of x is delineated.[55]

If there is a significant difference between that and what Montosa says, then, as before, I cannot see it.

Montosa makes some further moves in amplification of his conception of how bodies are distinguished from one another in Spinoza’s system which amount to a third objection. He emphasizes the importance of relations of motion and rest; and, when focusing on the essence of a body, he invokes an analogy with the power of a chess piece. He concludes that we should think of bodies as “aspects” of something rather than as “parts” of something. With a few exceptions that do not matter for current purposes, everything that he says in the course of making these moves strikes me as admirable.[56] What I cannot see is why he thinks any of it tells against me. Thus consider the example that I give to illustrate what I say in the quotation above: a house, I say, lacks being in the garden outside it. Montosa says that this example “will simply not do”.[57] But “will simply not do” for what purpose? All I take my example to illustrate is Spinoza’s own claim that “to be finite is in part a negation”.[58] Does my example not do that? I agree that it does not illustrate any claim about the involvement of negation in the essence of the house; nor about the involvement of negation in the essence of anything else; nor indeed about the involvement of negation in any other aspect of reality. Nor is it intended to. On the contrary, the very point of the section of my book in which this example occurs is that, for Spinoza, unlike for Hegel, negation is not at work in being itself. I struggle to see any of the moves that Montosa makes in the course of his third objection as rebukes.

Montosa’s fourth objection is that, when I say that the relativity of values in Spinoza “makes it that much easier to embrace the nihilistic thought that all there is, ultimately, is how things (non-evaluatively) are,”[59] I have things back to front: the relativity of values is rather the antidote to such nihilism. A further aspect of this objection, directed at Bunker as well as at me, is that we ignore the way in which conceiving all finite things, including ourselves, as modes of substance is likewise an antidote to nihilism. The connection is that the relativity of values is reckoned to be a corollary of that way of conceiving things; for that way of conceiving things is reckoned to entail seeing value as a by-product of the interaction of such modes, specifically as attaching to some of them relative to others that desire them, and, importantly, as attaching to some of them only relative to others that desire them.[60] As Montosa puts it, “by conceiving things as modes, we will understand that ice cream is only good insofar as we like it.”[61]

Again, I broadly accept what Montosa says I should say here. Moreover, I think I say it.[62] But I also think he has missed the crucial distinction that I draw in the relevant section of my book between viewing the world sub specie aeternitatis and viewing it in mediis rebus.[63] My point is that Spinoza’s relativism makes it that much easier for us to embrace the nihilistic thought when we view the world in the former way; for when we view the world in that way such relativism leaves us with the blank thought that some modes desire other modes, which in turn leaves us with an unanswerable “So what?” Once we view the world from our own point of immersion in it as desirers, on the other hand, the nihilistic thought is no longer compelling. And that seems to me implicit in what Montosa says too. We must, he urges, view all things, including ourselves, as modes of substance. That use of the first person, of which there are many other examples in his discussion,[64] precisely indicates a view of the world from our point of immersion in it. Yet again it is unclear to me why Montosa thinks that he is either correcting or significantly supplementing any points of my own.

It feels very ungracious to resist so much of what Montosa says in his essay, given the kindness and the generosity that he brings to it. But perhaps there is some recompense in the fact that all I am really trying to do is to indicate the extent of my agreement with him.

Let us now return to Bunker. Her second question concerns what sort of endless change I think is involved in Nietzsche’s eternal return; whether it is a matter of the same things appearing ever differently or whether it is a matter of ever different things appearing. Bunker suspects that my answer to this question will be that the question itself is shaped by a distinction that simply breaks down in Nietzschean terms. And she is exactly right. In a Nietzschean context, “appearing” amounts to being interpreted. But here we have to remember how radical Nietzsche’s conception of interpretation is. He tells us in his notebooks that there are no facts, only interpretations.[65] That is, there is no more to reality, on Nietzsche’s radical conception, than how it is interpreted. Hence the distinction between the same things appearing ever differently, which means the same things being interpreted ever differently, and ever different things appearing, which means ever different things being interpreted, is indeed a distinction, ultimately, without a difference.

Bunker’s third question connects with some of what I said in response to Montosa. It is the question, in effect, whether I exaggerate the dangers of our thinking about the most basic practical questions of life from something other than a human point of view. Actually, it is not so much a question as a cluster of questions – about how we might be able to overcome our own humanity, about the dangers of our doing so, about the converse dangers of conservatism, and suchlike. And, as Bunker rightly intimates, many of these questions are my own.[66] Much of the material to which she is responding is deliberately very circumspect. The really crucial point is the point that straddles pages 258-59 of my book: whatever radical changes await us, we have to get to there from here, in a gradual piecemeal way, and “here”, whether we like it or not, involves our humanity, at a very deep level, which means that, at least for now, the only way in which we can think sensibly about the costs and benefits of our coming to think about the most basic practical questions of life from something other than a human point of view is from a human point of view. That said, and in answer to Bunker’s more specific question – do I countenance the possibility of an “us” that is other than human? – I must. I cannot rule anything out. The very possibility of our coming to think about the most basic practical questions of life from something other than a human point of view, while it is a possibility concerning us human beings, is at the same time the possibility of our coming to reckon with a first-person plural that extends beyond us human beings.[67] Ironically, that relates back to the one quarrel that I had earlier with Bunker’s exegesis of me. For what may be at stake here is our surpassing our own finitude; but “our own finitude” here means our own current finitude, and our surpassing it will consist in our arriving at a new finitude, not in our becoming in any sense infinite.

Bunker’s fourth question is really more of a request: to say more than the little that I do say about why we need to reckon with the infinite as we negotiate how to be finite. I readily concede the paucity of what I say about this. This paucity is explained partly by the fact that I am as concerned to flag the possibility that this is something we need to do as I am with why, or how, or even whether we need to do it. That said, Bunker makes some comments of her own about what I might have in mind, and I simply note that in every case – except when she once again makes the assumption (which she flags as such) that I mean the infinite by what surpasses our finitude – she is exactly right. In particular: yes, I am envisaging our using the concept of the infinite as a regulative ideal; and yes, I think that our concept of the infinite can contribute something in that rôle towards protecting our sense of what ultimately matters. I try to say more in the book. What I say may not amount to much; but I am both gratified and grateful that it has proved enough for Bunker to see what I was getting at.

4. Reply to Michael Morris and Oliver Spinney

I need to begin this section with an apology and an explanation. Both are directed specifically at Oliver Spinney. The apology is that I have virtually nothing to say in response to his essay. The explanation is that I think it is superb: I find myself simply wanting to endorse it. Spinney has captured very well much of what I have to say in response to Michael Morris, and although I shall try to say some of it myself I am also content to defer to what Spinney has already said.[68]

Morris offers support for two key claims that I make in the essay on Wittgenstein on which he and Spinney are commenting.[69] Both claims concern the broad category of what I call “sentences”, a category of items with which Wittgenstein is concerned in his Tractatus.[70] These items fall into two sub-categories: the first sub-category comprises, in the terminology of the Tractatus itself, propositions that have a truth-value; the second sub-category comprises, again in the terminology of the Tractatus itself, pseudo-propositions, which lack a truth-value.[71] Propositions that have a truth-value are arguably not all propositions, because Wittgenstein arguably construes items in the second sub-category as propositions too.[72] Items in the second sub-category nevertheless attract the epithet “pseudo” because they appear to have a truth-value: they appear to be items in the first sub-category.

The first claim, which Morris labels (1), is that sentences can be characterized as those items to which truth-operations apply, where this obviously requires a suitably broad conception of truth-operations whereby their application extends to items in the second sub-category, which merely appear to have a truth-value, and not just to items in the first sub-category, which really do. The second claim, which Morris labels (2), is that sentencehood has no independent essence of its own: a sentence just is anything that either belongs to the first sub-category or belongs to the second. But Morris does more than offer support for these two claims. He takes the underlying ideas in fascinating new directions and teases out consequences that they have beyond anything that I myself was envisaging. I naturally welcome all of this. There are nevertheless one or two points in his essay that I want to take issue with.

Before I do that, however, I should like to register an important point of convergence. In §4 of his essay Morris says that he is considering claim (2) in the stronger of two senses that he identifies, as a claim about what the explanatory essence of sentencehood is, and not merely as a claim about what all sentences have in common and thus as a denial that sentencehood has any explanatory essence at all. He also comments in parenthesis that he is not sure whether this is what I intended. I can confirm that it is, at least insofar as I intended anything so determinate – for I must add that I had not properly considered this matter. I thank Morris for his clarification.

I turn next to a very minor corrective. Morris characterizes what I call the Principal Distinction, in other words the distinction between the two sub-categories of sentences, as that between those sentences that are not nonsensical and those that are.[73] But unless “nonsensical” is intended in an unhelpfully question-begging way here, as just a synonym for “pseudo-propositional”, it ends up begging another question: it ends up begging the question against people like Michael Kremer and Cora Diamond who think that some of the items in the second sub-category, for instance mathematical sentences, are not nonsensical.[74] The cleanest and simplest way to characterize the Principal Distinction is just this: it is the distinction between those sentences that have a truth-value and those that do not.

Now §6 of Morris’s paper is intended to answer the question whether claim (2) is compatible with how Wittgenstein draws the Principal Distinction. The reason Morris canvasses for thinking that it is not is, very roughly, as follows. Any sentence has both what Morris calls an “external” form and what he calls an “internal” form. Its external form, which is what is captured in claim (1), is its capacity to combine with other sentences to yield further sentences, through the application of truth-operations. Its internal form is the capacity of its constituents to combine together, which includes of course their capacity to combine together to form, in particular, it. Claim (2) implies that the external form of a sentence is primary; that what makes something a sentence is its capacity to combine with other sentences in that way, or rather in one or other of those two ways, depending on whether it has a truth-value or not. Its internal form, by contrast, must somehow derive from that. And this in turn means that the following cannot be true: (S) A sentence shares its internal form with something independent of it on which its truth or falsity might depend.

(S) cannot be true, since that would mean that the internal form of a sentence did not derive from its external form, but was rather borrowed or inherited from something independent of it. (There is a presumption here that for (S) to be true just is, at least in part, for the internal form of a sentence to be borrowed or inherited from something independent of it. We shall return later to the consequences of relinquishing this presumption.) On the other hand, Wittgenstein’s drawing of the Principal Distinction seems to require that (S) is true; for the difference between a sentence that has a truth-value and a sentence that does not, on Wittgenstein’s conception, is that while the internal form of each of them ensures that it has constituents that are suitably combined, in the former case there is also an assignment of Bedeutungen to those constituents such that whether the sentence is true or false depends on the obtaining or not of a possible combination of these Bedeutungen with the very same form, whereas in the latter case there is no such assignment.[75]

My concern about this train of thought, which I take to be essentially Spinney’s concern about it too, is that I do not see why claim (2) implies that the external form of a sentence is “primary” in any sense that requires its internal form somehow to derive from its external form. Why should we not acknowledge both that what makes something a sentence is its external form and that (S) is true, with the consequence that neither its external form nor its internal form is in any relevant sense prior to the other?

Here it is worth reflecting that the internal form of a sentence is really due to nothing more than its being a part of the world, that is to its being a fact.[76] Not all facts are sentences, to be sure; but all sentences are facts and it is because a sentence is a fact that it is fit to have a truth-value, even if, as it happens, it is one of those sentences that do not.[77] The distinction between a fact that is a sentence and a fact that is not – what Morris calls the Background Distinction – is the distinction between a fact that appears to have a truth-value, which is as much as to say a fact to which truth-operations apply, and a fact that does not. The distinction between a sentence that really does have a truth-value and a sentence that merely appears to have one – the Principal Distinction – is the distinction between a fact whose constituents have been assigned Bedeutungen and a fact whose constituents merely appear to have been assigned Bedeutungen (where it is important to note that the appearances, in the latter case, are a matter of psychology, not a matter of semantics[78]). I see no incompatibility between this way of drawing of the Principal Distinction and claim (2).

Now I have been talking about sentences’ sharing an internal form with possible combinations of Bedeutungen – thereby making (S) true. A more schematic way to put this would be as follows: (L) Language shares a form with the world.

But, as Morris points out in §7 of his essay, (L) can be construed in different ways. The train of thought above, in which Morris raised doubts about whether the internal form of a sentence could derive from its external form and at the same time be something that it shared with some possible combination of Bedeutungen, was motivated in part by what Morris would call a “realist” construal of (L). On a realist construal, language borrows or inherits the form of the world. (This is connected to the point that I made in parenthesis above about the presumption that was being made concerning what was required for (S) to be true.) But (L) is also subject to what Morris would call an “idealist” construal, on which it is the other way round: the world borrows or inherits the form of language. This means that, whereas on the realist construal the form of the world is intelligible independently of the form of language, on the idealist construal it is not; on the idealist construal, as Morris himself puts it, “language is in itself already propositional, and […] a world with propositional structure is somehow created as a counterpart of it”.[79]

In my remarks above I tried to resist the doubts raised by Morris; but not by resisting the underlying realism. What I said was entirely compatible with that.[80] The question therefore arises whether an alternative way of resisting these doubts would be to turn idealist.

Morris will say no, not without abandoning Wittgenstein’s way of drawing the Principal Distinction, which is incompatible with such idealism. For if the world is “somehow created as a counterpart of language”, how can there be any difference between those sentences whose constituents really have been assigned Bedeutungen and those sentences whose constituents merely appear to have been assigned Bedeutungen? Are the linguistic appearances not decisive?

I have posed these as rhetorical questions. But I certainly do not mean to suggest, either on my own behalf or on Morris’s, that there is nothing more to be said about the issue. No doubt there are all sorts of answers that these rhetorical questions might attract; and no doubt there are all sorts of further questions that any such answers might prompt. However, I shall say no more about the issue here. For Morris suggests an even deeper reason why it would be unacceptable, in Wittgensteinian terms, to turn idealist: such idealism would offer no way of explaining the internal form of sentences. This reason too, I think, can be presented as a pair of rhetorical questions. If the world is created as a counterpart of language, how can there be sentences at all? How can there be facts whose constituents so much as appear to have been assigned Bedeutungen?

Morris’s own view is that, granted claim (2), Wittgenstein must eschew both the realism and the idealism, then. But he believes that there is an intermediary position that Wittgenstein can adopt, whereby the world does not “in itself” share the form of language but the form of language is “projected back onto the world, to present is as a world that can be described.”[81]

Let us reconsider (L). This was my schematic recasting of the claim that sentences share an internal form with possible combinations of Bedeutungen. The intermediary position that Morris considers is, in effect, a rejection of that recasting in favour of a subtler one in which the claim is recast rather as follows: (L*) Language shares a form with the world-as-presented (or the world-as-describable, or something of the sort).

But unless the world-as-presented (or the world-as-describable, or whatever else needs to be put in place here) is just that which is “somehow created as a counterpart of language” – that is, unless this supposedly intermediary position is just a notational variant of the idealism – its subtlety is surely a subtlety too far. More specifically, it surely requires a Kantian distinction between appearances and things in themselves that is every bit as recondite and as problematical as Kant’s own distinction between appearances and things in themselves. Not that this is a rebuke to Morris. He would agree. This is exegesis; it is not philosophy in propria persona. Morris would see the problems that arise here as precisely those that Wittgenstein is wrestling with in the Tractatus.[82]

I wonder, though. Could we not step back from these problems, for at least a while longer, by adhering to my original recasting of the claim in question as (L), rather than as (L*), and by construing (L) neither in the realist way, whereby language borrows or inherits the form of the world, nor in the idealist way, whereby the reverse is true, but in a neutral way, whereby there is no borrowing or inheriting in either direction? Here I come back to the thought that the internal form of a sentence is due to nothing more than its being a part of the world. So too, more generally, language can be said to share a form with the world simply by virtue of being a part of the world. This would be a “no priority” view, of a piece with the view that I canvassed earlier whereby neither the external form of a sentence nor its internal form is in any relevant sense prior to the other.

adrian.moore@philosophy.ox.ac.uk REFERENCES

Conant, James 2020, “Replies”, in The Logical Alien: Conant and His Critics, ed. Sofia Miguens. Cambridge, Mass.: Harvard University Press.

Descartes, René 1984a, Meditations on First Philosophy, in his The Philosophical Writings of Descartes, Vol. II, trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press.

———. 1984b, Principles of Philosophy, in his The Philosophical Writings, Vol. I, trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press.

———. 1991a, “Letter to Arnauld”, in his The Philosophical Writings of Descartes, Vol. III (Correspondence), trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press.

———. 1991b, “Letter to More”, in his The Philosophical Writings of Descartes, Vol. III (Correspondence), trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch . Cambridge: Cambridge University Press.

Diamond, Cora 2011, “The Tractatus and the Limits of Sense”, in Oskari Kuusela and Marie McGinn (eds), The Oxford Handbook of Wittgenstein. Oxford: Oxford University Press.

Kant, Immanuel 1998, Critique of Pure Reason, trans. and ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press.

———. 2002, Prolegomena to Any Future Metaphysics That Will be Able to Come Forward as a Science, trans. Gary Hatfield, in his Theoretical Philosophy After 1781, ed. Henry Allison and Peter Heath. Cambridge: Cambridge University Press.

Kreis, Guido 2023, “Kant on Why We Cannot Even Judge About Things in Themselves”, in Jens Pier (ed.), Limits of Intelligibility: Issues From Kant and Wittgenstein . London: Routledge.

Kremer, Michael 2002, “Mathematics and Meaning in the Tractatus”, in Philosophical Investigations, 25(3): 272-303.

LaCroix, Richard R. 1991, “Descartes on God’s Ability to do the Logically Impossible”, reprinted in Georges J.D. Moyal (ed.), René Descartes: Critical Assessments, Vol. III.London: Routledge.

Moore, A.W. 2012, The Evolution of Modern Metaphysics: Making Sense of Things Cambridge: Cambridge University Press.

———. 2019a, The Infinite, 3rd edn. London: Routledge.

———. 2019b, “The Bounds of Nonsense”, in my Language, World, and Limits: Essays in the Philosophy of Language and Metaphysics. Oxford: Oxford University Press.

———. 2019c, “The Bounds of Sense”, reprinted in my Language, World, and Limits: Essays in the Philosophy of Language and Metaphysics. Oxford: Oxford University Press.

———. 2023 a, “Armchair Knowledge: Some Kantian Reflections”, in my The Human A Priori: Essays on How We Make Sense in Philosophy, Ethics, and Mathematics. Oxford: Oxford University Press.

———. 2023b, “What Descartes Ought to Have Thought About Modality”, reprinted with a new postscript in my The Human A Priori: Essays on How We Make Sense in Philosophy, Ethics, and Mathematics. Oxford: Oxford University Press.

———. 2023 c, “Sense-Making From a Human Point of View”, reprinted in my The Human A Priori: Essays on How We Make Sense in Philosophy, Ethics, and Mathematics. Oxford: Oxford University Press.

Nietzsche, Friedrich 1967, The Will to Power, trans. Walter Kaufmann and R.J. Hollingdale and ed. Walter Kaufmann. New York: Random House.

Spinoza, Benedictus de 2002a, Treatise on the Emendation of the Intellect, in his Spinoza: Complete Works, ed. Michael L. Morgan and trans. Samuel Shirley. Indianapolis, Ind.: Hackett Publishing.

———. 2002b, Ethics, in his Spinoza: Complete Works, ed. Michael L. Morgan and trans. Samuel Shirley. Indianapolis, Ind.: Hackett Publishing.

Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus, trans. D.F. Pears and B.F. McGuiness. London: Routledge.

1] This is connected with what I have elsewhere called “the Limit Argument”. The Limit Argument has two premises: that we cannot properly draw a limit to what we can make sense of unless we can make sense of the limit; and that we cannot make sense of any limit unless we can make sense of what lies on both sides of it. The argument’s conclusion is that we cannot properly draw a limit to what we can make sense of. See Moore 2012, 135. For an earlier reference to the argument, though not with that label, see Moore 2019c, 96.

2] PR, 13.

3] PR, 13.

4] Another possibility, of course, is that he has misinterpreted me, though there is plenty of evidence to the contrary in the rest of his essay, which seems to me to show a good grasp of my exegetical stance. I cannot however resist taking this opportunity to mention someone who has misinterpreted me, in precisely the way indicated: I have in mind James Conant, whose own exegesis of Descartes is the subject of the essay by me on which Patterson and Head are commenting, namely Moore 2021. Conant’s misunderstanding occurs in his response to my essay: Conant 2020, §§I – VII, esp. §VII. For a corrective see the postscript to my essay.

5] PR, 21, emphasis added.

6] LaCroix 1991.

7] See Descartes 1984b, Pt I, §23.

8] Moore 2021.

9] PR, 5.

10] Cf. Patterson’s concession that, for Descartes, “we know or recognise possibility through compatibility with our concepts.” (PR, 12)

11] That said, I must acknowledge the obvious complications that arise if non-conflict with our human concepts is only contingently a symptom of possibility. One way of addressing these complications would be to argue that, for Descartes, it is not only contingently a symptom of possibility: it is necessarily a symptom of possibility, because of God’s benevolence.

12] This of course brings into sharp relief the so-called Cartesian Circle, though this is not the place to address that.

13] Descartes 1984a, 46.

14] Descartes 1991a, 359.

15] I am therefore delighted by Patterson’s reference to Descartes 1991b, 363, a passage with which I was previously unfamiliar and in which, as Patterson points out, Descartes does precisely what I say he could and should have done. I thank Patterson for drawing my attention to this passage.

16] PR, 13.

17] The essay to which they are responding is Moore 2021.

18] Kant 1998, A50 – 51/B74 – 76.

19] Kant 1998, A320/B376 – 77.

20] A less charitable view would be that Kant is simply being careless in one of these passages.

21] Baiasu 2021, Vereb 2021 respectively.

22] Respectively Moore 2021, nn. 19, 50, and 53, and Moore 2012, Ch. 5, n. 13.

23] Moore 2012, Ch. 5., n.13. Incidentally, by highlighting Kant 1998, A320/B376 – 77 in that note, I certainly incur some blame for the misunderstanding to which I have just referred: this is the passage already mentioned in which Kant suggests that what he means by “Erkenntnis” is EM.

24] For arguments against the view that Kant would acknowledge any such knowledge see Kreis 2023, esp. §6. I remain unpersuaded.

25] PR, 54.

26] See Moore 2012, pp. 133 – 4. But if this too is a locus of misunderstanding, then I think I can explain why: in the note to which I have already referred (Moore 2012, Ch. 5, n. 13) I talk about purely conceptual knowledge that makes no reference to any object and then add parenthetically that this is not the same as what I am about to identify in the main text as analytic knowledge. My point, however, is not that the purely conceptual knowledge in question is not analytic. My point is rather that some analytic knowledge does make reference to an object and is (therefore) not purely conceptual. I hope that some of what I say below will cast further light on this.

27] See Kant 1998, A225/B272 and A594/B622ff.

28] PR, 56.

29] See Kant 1998, A255/B310 – 11.

30] What Baiasu says in §6 of his essay therefore strikes me as less opposed to what I say than it initially appears.

31] Cf. n. 26 above: this is what I had in mind when I said that some analytic knowledge is not purely conceptual.

32] E.g. Kant 1998, A151/B191.

33] E.g. n. 9.

34] Pp. 48-54 and 70-71 of their essays respectively.

35] For one thing, I wonder what Baiasu makes of Kant 2002, 4:371.

36] It is partly for this reason that Baiasu is wrong to say, near the beginning of §2 of his essay, that I use the term “armchair knowledge” to refer to a particular type of a priori knowledge. He is certainly right that I would classify some a priori knowledge, but not all of it, as armchair knowledge. But I would also classify some knowledge that is not a priori as armchair knowledge, for instance knowledge of one’s own existence (see §7 of my essay, and in particular n. 58). For the same reason Vereb is quite unwarranted in claiming, as he does in (the very puzzling) n. 4 of his essay, that “armchair knowledge for Moore includes both analytic and synthetic varieties so long as the knowledge ‘concerns what is beyond the subject’,” (emphasis added).

37] I am far from thinking, incidentally, that a satisfactory discussion of these issues, let alone a satisfactory discussion of these issues that is also intended to serve as serious exegesis, could allow for such nonchalance concerning how knowledge, Erkenntnis, and Wissen relate to one another. All I am doing is indicating what my own focus is. – Note: much of my response to Baiasu and Vereb so far has taken the form of bookkeeping. I have one final piece of bookkeeping, which in turn provides me with a welcome opportunity to record a debt to Baiasu. In n. 52 of his essay Baiasu mentions parenthetically that he reads Kant 2000, 5:197, n. 1 differently from how I suggest it should be read in n. 50 of my essay. And he is quite right to do so. The final sentence of my n. 50, in which I myself retract that suggested reading, appears in the published version of my essay, but did not appear in the version to which Baiasu had access. This sentence was prompted by Baiasu’s parenthesis, for which I am grateful.

38] Cf. his n. 31.

39] On page 55 of Baiasu’s essay, incidentally, he says that the a priori structure of our minds, on Kant’s view, includes pure intuitions, categories, and ideas, but not other concepts. This goes to show that he understands “the a priori structure of our minds” as designating something more restricted than merely the a priori content of our minds, presumably something originary: otherwise it would include concepts that are associated with pure intuitions, such as mathematical concepts (e.g. Kant 1998, A715/B743 ff.), as well as what Kant calls “predicables”, concepts that can be derived from the categories (Kant 1988, A81 – 82/B107 – 8). – While I am on this subject, I shall mention what I take to be a slip in Vereb’s essay: in his n. 5 he alludes to the possibility that Kant is correct that there is only one set of pure concepts, but then qualifies this by adding that the concepts in question may be Eurocentric and there may be human cultures that make use of different concepts. I take it that Vereb should not have included the correctness of Kant’s doctrine in the possibility to which he alludes. Otherwise this is extremely difficult to make sense of.

40] Let us for current purposes prescind from one awkward feature of this particular example, namely that it is not in fact an item of geometrical knowledge, because it is not in fact true.

41] Cf. Baiasu’s n. 39. What Baiasu is discussing here seems to me quite unlike the Wittgensteinian contingency that I discuss in my essay, which is not a matter of what any concepts are like, nor of what any rules are like, but is rather a matter of what concepts are actually exercised or what rules are actually in force.

42] PR, 72.

43] Moore 2019a, Chs 16 and 17.

44] See esp. Moore 2012, Ch. 21, §3.

45] Moore 2019a, 240-41.

46] The word “where” in this sentence need not be understood in literally spatial terms.

47] PR, 39.

48] Spinoza 2002b, Pt I, Ax. 1. In Shirley’s translation this quantifier is rendered “all things that are”.

49] Spinoza 2002b, Pt I, Defs 3 and 5.

50] It is worth noting what Spinoza says in Spinoza 2002a, p. 21, about Nature, which, in Spinoza 2002b, Pt IV, Pref., he identifies with substance: “This entity is unique and infinite; that is, it is total being, beyond which there is no being.”

51] See e.g. Spinoza 2002b, Pt II, Prop. 17, Schol., and Prop. 35, Schol.

52] Notice the pivotal rôle played in Molinero’s examples involving Oedipus by Oedipus’s ignorance that his mother is Jocasta. If Oedipus knew that his mother was Jocasta, he would not err in the way he does.

53] Moore 2019a, 242

54] PR, 40.

55] Moore 2019a, 241, transposed from the past tense to the present tense, emphasis in the original.

56] The exceptions include an unfortunate suggestion that there are infinitely many possible configurations of chess pieces on a chessboard (PR, 40-41)!

57] PR, 40.

58] Spinoza 2002b, Pt I, Prop. 8, Schol. 1; cf. Spinoza 2002b, Pt III, Prop. 3, Schol.

59] Moore 2019a, 253, transposed from the past tense to the present tense, emphasis in original.

60] Cf. Spinoza 2002b, Pt III, Prop. 9, Schol.

61] PR, 41.

62] See e.g. Moore 2019a, Ch. 17, §1.

63] Moore 2019a, esp. 252.

64] Many of these are uses of the first-person singular rather than the first-person plural, but that makes no difference to the point that I am making here. (One example of the use of the first-person plural, incidentally, is the very claim that ice cream is good only insofar as we like it. And notice the suppressed relativization “for us” that needs to be taken for granted in this claim after the “good”.)

65] Nietzsche 1967, §481.

66] For related treatment of them see Moore 2021.

67] I am assuming that it is not the possibility of our coming to reckon with a first-person plural that does not extend as far as that. It is worth noting, however, that I am assuming this on ethical grounds, not on logical grounds. For any of us to think about the most basic practical questions of life in such a way as to exclude any of the rest of us from the first-person plural would itself, it seems to me, be an affront to our humanity.

68] Not that these remarks should be taken to imply that I do not think well of any of the other seven essays, still less that the more I have to say about any of them the less well I think of it! There are all sorts of ways in which one can admire and appreciate other people’s work, and finding oneself wanting to endorse it, which is the form that my admiration and appreciation of Spinney’s essay take, is merely one of these.

69] Moore 2019b.

70] Wittgenstein 1961.

71] Wittgenstein 1961, e.g. 5 and 4.1272 respectively.

72] See e.g. 6.2. This is one of the issues that I address in Moore 2019b.

73] PR, 75. Not that he puts it in these terms. Rather, he characterizes the distinction as that between sentences that have a truth-value and what he calls “nonsensical pseudo-propositions”. But he gives no reason to think that he intends “nonsensical”, in its application to sentences, as anything other than equivalent to “pseudo-propositional” – hence no reason to think that, in his use of the expression “nonsensical pseudo-propositions”, he intends “nonsensical” as anything other than pleonastic. If he does, then my corrective takes a different form, namely that he has not taken into account all pseudo-propositions: cf. what I go on to say in the main text.

74] See Kremer 2002 and Diamond 2011.

75] I have retained the original German word “Bedeutungen” here, rather than use the standard translation “meanings”, in order to signal that, at least in the most basic case, what are assigned are the constituents of states of affairs: see Wittgenstein 1961, 2.01 and 3.203.

76] Cf. Wittgenstein 1961, 1.1 and 3.14 ff.

77] Cf. Wittgenstein 1961, 5.4733.

78] Ibid, 5.4733 is relevant again, as is 6.53.

79] PR, 85.

80] It was also, arguably, compatible with its denial. I depicted language as sharing a form with the world simply by virtue of being a part of the world, but this arguably did not preclude the world’s being “somehow created as a counterpart of language”, any more than an author’s appearing in their own fiction precludes the fiction’s being the author’s creation.

81] PR, 85.

82] See §7 of his essay.

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Table of Contents

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contents

Sarah Patterson - Descartes on Modality and the Eternal Truths

Jonathan Head - Divine Simplicity and Freedom in Descartes - Comments on Sarah Patterson’s ”Descartes on Modality and the Eternal Truths”

Jennifer Bunker - Infinity and Beyond Learning How to be Finite

Pablo Montosa Molinero - Learning How to be Finite

Sorin Baiasu - The Possibility of Kantian Armchair Knowledge

Zachary Vereb - Kantian Reflections on Conceptual Limits

Michael Morris - Nonsense and the General Form of the Sentence

Oliver Spinney - Truth Functional Logic and the Form of a Tractarian Proposition

Adrian W. Moore - Public Reason Replies

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