My aim in this paper is to take issue with Graham Bird's treatment of Kant's mathematical antinomies in The Revolutionary Kant (TRK)Footnote 1 It is an imposing and magisterial commentary, running to over 800 pages, every one of which contains significant insights and displays admirable scholarship. My disagreement, in such a context, is minor. That said, at the end of the essay I shall suggest, albeit very inchoately, a way in which this disagreement connects with some reservations that I have about Bird's fundamental project, which is to repudiate what he calls ‘traditionalist’ interpretations of Kant in favour of what he calls a ‘revolutionary’ interpretation. I subscribe to what (I am fairly sure) Bird would call a traditionalist interpretationFootnote 2 – though I admit to being altogether less clear about the contrast than he is.Footnote 3

My focus, as I have already indicated, is Bird's treatment of the mathematical antinomies, which constitutes chapter 26 of his book. I have no special quarrel with his treatment of the details of the antinomic arguments. My concern is rather with his treatment, in §3 of the chapter, of what he calls ‘the character of the conflicts’.

As I understand it, Bird's conception of Kant's conception is roughly as follows. We are part of a physical reality which is largely independent of us. We can obtain knowledge of this reality, and of what pertains to it, such as our own psychological states, although we cannot obtain knowledge of anything else. All the knowledge that we do obtain relates to experience. But it also involves certain a priori concepts. And we can put these concepts to a further, independent use: to entertain the idea of an experience-transcendent reality, the reality of ‘things in themselves’ such as God. We cannot however obtain any knowledge of such a reality. We cannot even know whether things in themselves exist. But, once we have entertained the idea, it is irresistible for us to speculate about such things, and indeed to try to obtain knowledge of them, by pure reason. Moreover, in certain cases, we are subject to a powerful illusion of having succeeded. In the specific case of the cosmological questions with which the mathematical antinomies are concerned, our mistake consists in:

• • starting with perfectly legitimate scientific questions about the structure of physical reality;

• • using certain a priori limit concepts to address these questions;

• • wrenching those concepts from that use;

• • using them instead to raise questions about the experience-transcendent limits of physical reality itself;

• • addressing these questions by pure reason; and

• • fancying that we have answered the questions. (See especially §3.1.)

There are two points in particular that Bird emphasizes as part of this conception:

1. (1) It is a mistake to think that we can settle issues about the character of the physical universe by pure reason (671 and, a little more cautiously, 674).

2. (2) The particular issues about the character of the physical universe that we do think we can settle by pure reason we cannot settle at all: our attempts to settle them constitute ‘an erroneous and undecidable’ pseudo-discipline (674 and 680).

My own view is that there is a problem in ascribing (1) to Kant, and that, although he takes (2) to be true of the issues that arise in the dynamical antinomies, he does not take it to be true of the issues that arise in the mathematical antinomies. (This indeed marks one of the most important contrasts between the two sets of antinomies.)

Let us begin with (1). Before we can properly consider Kant's attitude to (1), we need to clarify what is meant by ‘pure reason’ in this context. If the term is used in the way in which Kant sometimes uses it – whereby to settle an issue by pure reason is simply to settle it a priori (B20, A712/B740 and Prol 4: 280) – then there is no question but that he would deny (1). For he would count what he achieves in the three Analogies of Experience (A176/B218ff.) as a counterexample. Come to that, he would count what can be achieved in pure mathematics as a counterexample (A157/B196). More often, however, and certainly in the passages that are most directly relevant to the Antinomies, Kant uses the term ‘pure reason’ in such a way that not only must pure reason be free of any appeal to experience, it must be free of any appeal to intuition as well (e.g. A306/B363 and A750–1/B778–91). Then it is altogether less obvious what Kant would say about (1).Footnote 4

Bird cites, in this connection, A409/B436. This is the passage in which Kant specifies a natural principle of pure reason: that if the conditioned is given, then the unconditioned must be given also. This passage certainly highlights a mistake that Kant thinks we naturally make when we try to address issues about the character of the physical universe by pure reason, perhaps indeed the chief mistake: the mistake, namely, of taking this principle to be a truth about the physical universe.Footnote 5 But it does not suggest that the mistake is ineradicable; nor, in particular, that the mistake cannot be eradicated by pure reason; nor, crucially, that once the mistake has been eradicated, pure reason lacks the resources to address the original issues.Footnote 6 It is quite compatible with what Kant says in this passage that we can settle issues about the character of the physical universe by pure reason.

Be that as it may, my concern hereafter will be with (2), which states that we have no way of settling such issues. That there is something awry with Bird's attribution of (2) to Kant is reflected in a crucial asymmetry between what Kant wants to say about the truth or falsity of the conclusions in each of the mathematical antinomies and what he wants to say about the truth or falsity of the conclusions in each of the dynamical antinomies. I do not mean the familiar point that he accedes to the falsity of both conclusions in the former case and to the truth of both conclusions in the latter case. I mean the less familiar point that he recognizes a modal contrast too. He says that the conclusions in each of the mathematical antinomies must both be regarded as false; and that the conclusions in each of the dynamical antinomies may both be regarded as true (e.g. A531–2/B559–60; see also Prol 4: 341–2 and 4: 343–7). The ‘must’ indicates that he does indeed think we can settle what to say in the former case: this is reflected in the pithy summary that he gives (A506–7/B534–5) of the argument for transcendental idealism from the reasoning in the First Antinomy.Footnote 7 Bird, significantly, says merely that ‘in the two mathematical antinomies both sides can be wrong’ (674; emphasis added); and later, that ‘Kant … allows the conclusions to the mathematical antinomies to be both false’ (681; emphasis added). This second quotation is not, admittedly, in propria persona; but nor is there any indication that Bird would demur.

What grounds this modal distinction? The answer is: another distinction which Kant draws in the Transcendental Doctrine of Method (A740–1/B768–9). There he divides the misguided efforts of metaphysicians into two broad classes, according to whether their questions are ill-conceived or well-conceived.Footnote 8 Kant's idea is this. These metaphysical questions always involve some idea of reason, that is, some a priori concept of the understanding freed of whatever conditions allow it to be applied empirically. Such a question is ill-conceived if it involves a confused amalgam of an idea of reason with some concept that can be applied only to objects of possible experience. It is well-conceived if it involves ideas of reason without any such distortion. In the former case, the question has no answer. Or rather, it has no answer as intended. Thus if the question is which of two apparent contradictories holds, each involving the confused concept, then the answer is neither (A503–5/B531–3). In the latter case the question has an answer, even as intended, but only at the level of things in themselves, which means that we lack the resources to ascertain what that answer is. The questions addressed in the mathematical antinomies are of the former kind: they are ill-conceived. The questions addressed in the dynamical antinomies are of the latter kind: they are well-conceived.

Although my principal concern in this paper is with the mathematical antinomies, I want to take a brief digression to discuss the dynamical antinomies. There is an issue about what exactly Kant takes the arguments in the dynamical antinomies to establish, once the illegitimate inference to how things are in themselves is separated off. Consider in particular the Third Antinomy. The question there is whether there is any such thing as freedom, and Kant takes the arguments to leave open the possibility that there is, at the level of things in themselves, even though there is not in physical reality. The argument for the antithesis is in this respect fairly straightforward. Kant takes that argument to establish just what it purports to establish: that there is no freedom in physical reality because ‘everything [there] happens in accordance with laws of nature’ (A445/B473). But what of the argument for the thesis? What Kant himself says, in his remark on it – and unlike Bird (693) I take Kant to be speaking in his own voice in his various remarks on these arguments – is this:

What Kant takes this argument to show, it seems to me, is that there must be something uncaused grounding whatever happens in accordance with laws of nature. This relates to something else that I think Kant thinks we know: that there must ultimately be something unconditioned corresponding to whatever is conditioned (see Bxx). This is of course to be distinguished from the assumption cited above, which Kant certainly holds to be illusory: that there must be something unconditioned and physical corresponding to whatever is conditioned and physical. It is also, in my view, evidence of another error on Bird's part: the error of holding that Kant denies us any knowledge concerning things in themselves, even knowledge of their existence.Footnote 9

To return to the mathematical antinomies: the questions addressed in these antinomies are, to repeat, ill-conceived. The question addressed in the First Antinomy, for example, involves the concept of the physical universe as a whole. But this is a confused amalgam of the idea of unconditionedness and the concept of physical reality (A422/B450Footnote 10). The physical universe as a whole, if there were such a thing, would have to be both physical and all-encompassing. But the only physical things that can exist are objects of possible experience.Footnote 11 And no object of possible experience can be all-encompassing. That is, no such object can encompass the whole of physical reality (4: 340–2). The source of our mistake, when we conflate these concepts in this way, is a genuine item of knowledge that we have, the very item to which I just referred: that there must ultimately be something unconditioned corresponding to whatever is conditioned, and in particular corresponding to whatever is conditioned and physical. What we fail to appreciate, however, is that such unconditionedness must reside in things in themselves, which physical things are not. We naturally assume that some physical thing must be unconditioned, the very assumption that we have already seen Kant reject; or, to put it another way, that there must be such a thing as the physical universe as a whole, finite or infinite as the case may be. Once we drop this assumption, we can acquiesce in the conclusion that every physical thing is part of some other physical thing that is older and bigger – as the earth, for instance, is part of the solar system – though there is no one physical thing of which every physical thing is part (‘Transcendental Dialectic’, book 2, passim, esp. §§IVff.; A338–704/B397–732, esp. A592/B620ff.).Footnote 12

How exactly does this account set me apart from Bird? There is of course the point that I, unlike Bird, allow us, on Kant's behalf, a minimal item of knowledge concerning things in themselves. But there are differences even apart from that. Bird again and again insists that in the mathematical antinomies we are, in Kant's view, addressing questions that are undecidable for us. I disagree. Kant stands by the correctness of the arguments in these antinomies, except of course for what he sees as their erroneous shared presuppositions (4: 339–40);Footnote 13 and he takes them to show exactly how to decide the questions addressed. We have first to reject those shared presuppositions (A481–2/B509–10), then apply the arguments. Thus the correct verdict in the case of the First Antinomy is that it is false that the physical universe as a whole is finite, and false that the physical universe as a whole is infinite, because it is false that the physical universe as a whole is (A501–2/B529–30 and A506–7/B534–5).Footnote 14

In the section beginning at A476/B504 Kant is explicit that we must not treat our failure to reach a satisfactory verdict on such matters as an excuse to say that they are beyond us. Bird refers to this passage. He mentions in particular Kant's objection to our pleading ‘unavoidable ignorance’ (A477/B505). ‘What [Kant] objects to’, Bird comments, ‘is not the fact of our ignorance but the failure to explain it’ (676). Yes, in the case of the dynamical antinomies. No, in the case of the mathematical antinomies.Footnote 15

I want finally to fulfil the promise I made earlier, by relating this discussion to Bird's fundamental project. I shall say very little, however. The matter is far too complex for me to go into detail here. It would be nice for me if I could claim that only an interpretation of the sort I favour – a sort that Bird would call traditionalist – can accommodate Kant's insistence that there is no such thing as the physical universe as a whole. I do think that such an interpretation is particularly well placed to accommodate that insistence, because I think that it is particularly well placed to explain Kant's repudiation of experience-transcendent facts about physical reality, of which any fact about the physical universe as a whole would be an instance. (Cf. A503–5/B532–3.) It is particularly well placed to explain Kant's repudiation of such facts because it entails, in a fairly direct way, that there is, for Kant, nothing to physical reality beyond what is capable of being given in experience. But that is as much as I want to claim. I do not want to claim anything stronger because an interpretation of the sort Bird favours can also, I believe, explain Kant's repudiation of experience-transcendent facts about physical reality, albeit more subtly. Indeed I find the position in question – the combination of the broad view that Bird finds in Kant with a repudiation of experience-transcendent facts about physical reality – extremely attractive. The problem is that, great as my admiration for Kant is, not even a principle of charity allows me to convert my sympathy for the position into sympathy for the corresponding exegesis.Footnote 16