Why does Kant think the antinomies provide an indirect proof of transcendental idealism? How convincing is this argument?

Submitted for PH201 (History of Modern Philosophy) Summer Exam

One of Kant’s aims in the Critique of Pure Reason is to provide a foundation for metaphysics, which has hitherto made no progress because its practitioners could not agree on the appropriate method or appropriate first principles. The Antinomies are a set of contradictory conclusions that metaphysicians have drawn. Kant intends to show that his critical philosophy, and in particular his doctrine of Transcendental Idealism (henceforth, TI) – that space and time are neither things in themselves nor properties of things in themselves, but forms of intuition shaped by subjects’ cognitive faculties – can resolve these matters. In particular, he argues that since the opposite assumption of Transcendental Realism (henceforth, TR) leads inexorably to these contradictory conclusions, this is a proof by contradiction for TI. I argue that the argument is ultimately uncompelling.

Kant claims that the Antinomies arise from Reason’s inevitable tendency to overreach. Reason is about drawing inferences from what one knows, so we can have better understanding; a rational explanation thus consists in showing how something follows necessarily from something else. In other words, we observe the “conditioned”, some state of affairs; and we reason (as it were) backwards, to understand why that state of affairs arose; and then why that state of affairs arose; and so on, until we arrive at the “unconditioned”, something which is not itself in need of explanation. The issue is that by the unconditioned, one might mean the first member of that series, or the series taken as a whole; either explanation is equally valid, and yet they contradict each other. For four questions in metaphysics, he takes the former explanation as the Thesis, and the latter as the Antithesis; the contradiction is the Antinomy. For instance, one is about whether matter is finitely divisible (Thesis) or infinitely divisible (Antithesis); another is about whether there is some necessarily existing being (Thesis) or if all beings are contingent (Antithesis). Each contradiction flows from the assumption of TR; thus, TR is false.

Even before we present Kant’s solution to the Antinomies using TI, there are several objections one might raise at this point. It is not self-evident, for instance, that the arguments for all Theses and all Antitheses are equally compelling and valid. It has not been the view of preceding metaphysicians that matter is both finitely divisible and infinitely divisible; rather, different philosophers have taken different, consistent perspectives, each arguing that her position is correct. One might thus claim that no contradiction emerges if one simply takes one side as being correct, and thus the inference to TI is flawed. Moreover, the “proof” of TI seems to depend on the “Supreme Principle of Pure Reason”, that “if the conditioned is given, then the whole sum of conditions, and hence the absolutely unconditioned, is also given.” (KrV A 20 / B 34). But the Transcendental Realist may simply deny this principle; then again, the arguments for the Theses and Antitheses would not be sound, so no contradiction emerges. Indeed, Kant himself does not think the Supreme Principle is knowably true: “Such a principle of pure reason, however, is obviously synthetic; for the conditioned is analytically related to some condition, but not to the unconditioned.” (KrV A 308/B 364).

These objections are unproblematic for Kant’s ultimate objective in this section, which is to say, securing a basis for metaphysics and creating agreement on first principles and method so that its practitioners’ views might converge. Kant himself need not accept every argument which has appealed to various philosophers on these matters, so long as he shows that they are all operating under the assumption of TR, and that rejecting that stance would resolve their disagreement. In particular, he has already provided positive arguments elsewhere in the Critique for TI, so the argument is not circular. However, as it relates to this indirect argument for TI, it is certainly a problem if no contradiction actually must follow from TR. Moreover, it remains to be seen if TI actually solves the Antinomies, as Kant claims; otherwise, we simply return to a state of ignorance. Thus, we shall have to consider the specifics of Kant’s arguments to determine if his proof is robust.

Let us first take Kant’s exposition and solution to the Second Antinomy, about whether there exist simple parts of matter, or if matter is divided to infinity. Suppose that TI is false, or equivalently that TR is true. Then exactly one of these disjuncts can hold, and moreover space and time must exist independently of our cognitive faculties, as properties or frameworks pertaining to things in themselves. Suppose matter is composed of simple, indivisible parts; then it would be impossible for these indivisible simples to constitute extended objects. Thus, matter must be infinitely divisible; but then an infinite regress of divisions is required, and it does not seem possible that actual objects can be so divided. So we have a contradiction: TR is false. Contrarily, suppose TI is true. Then we see that material bodies are not things in themselves, but mere appearances; since we can always divide matter infinitely in thought, matter is plainly infinitely divisible – there is no problem of actual, real objects somehow actually being divided into infinite parts (KrV A 434-36 / B 462-64).

One might object to this attempted reductio ad absurdum by noting again that the arguments given for the proposition that matter can be neither finitely divisible or infinitely divisible under TR are hardly unarguable. One might argue, for instance, that it is possible for continuous, extended objects to be built out of discrete elements in the same way that infinite sets in mathematics can be defined using finite elements combined with each other (for example, the recursive definition of the natural numbers). Equally, it might be argued that although it is difficult to see how a physically real object can be infinitely divided, this is not a compelling case for the proposition being contradictory. One could advocate for either of these arguments, or else advocate for the same epistemic humility advocated for by Kant regarding transcendentally real objects, without rejecting the view that space and time are properties of things in themselves. This brings us to Kant’s suggested resolution: as critics like Ameriks have noted, it does not really answer the question about matter. Instead, he simply shifts the question to a different topic, namely what is true about our ideas or perceptions. Certainly, if his doctrine of Noumenal Ignorance is true, then the problem of whether matter is finitely or infinitely divisible is relegated as unanswerable. But this is merely the same state of ignorance that pertained before regarding the status of matter understood as a thing in itself. Metaphysicians before could equally well have made arguments for the finite versus infinite divisibility of our idea of matter, but it is a substantially different question. Moreover, it is not obvious that Kant’s solution in this realm is not equally prone to Antinomies: one might argue that we cannot divide matter infinitely in thought, since we are finite beings, for instance.

Therefore, the general criticisms considered before remain devastating in the case of a particular Antinomy. It is beyond the scope of this essay to argue for all four Antinomies; nevertheless, the structure of argument will clearly apply in all cases. The argument that the assumption of TR leads inevitably to contradiction, and thus must be rejected in favour of TI, which resolves the Antinomies, is flawed because the arguments for the Thesis and Antithesis are not necessarily valid (a proposition which must be considered on a case-by-case basis for each Antinomy), or sound, because of status of the Supreme Principle of Reason. Most importantly, the same move Kant makes, about considering appearances rather than objects, is available even to the Transcendental Realist; it does not answer the question, nor demonstrate that TI resolves the contradiction. Hence, the indirect proof Kant offers is ultimately unconvincing.

Result

Mark: 74% (Low First), averaged across this and two other answers.