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For me, the Transcendental Deduction aims at proving two things:

  1. Categories or pure concepts of understanding must be applied to the manifold of intuitions, i.e, they are necessary for cognition.

  2. Categories or pure concepts are legitimate insofar as they apply to intuitions.

I am not clear on the second part of the argument, nor can I find any passage directly aiming at the second point.

Also, I also understand that some people associate the second argument to Transcedental Schemata portion of the book. However, to me that section only elucidated how inner-sense/time is a common thread between the heterogeneous faculty of sensibility and understanding. That only proves 'how' the two faculties are linked, not why they should be.

Also, if you think this argument is rather given in Schemata, or ALSO given in schemata (since some papers indicate this as well), please explain that. Some papers also indicate that Schemata is redundant since this problem was solved in B-deduction, hence this question.

To summarise: I understand the argument for intuitions without concepts cannot constitute knowledge but what's the argument for the proposition that concepts without intuitions also cannot claim objective knowledge?

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  • A knowledge of something has to be in correspondence with that something. How would empty concepts be brought into a correspondence with anything else without getting linked to intuitions?
    – Conifold
    Jun 18, 2020 at 17:41
  • Like that of metaphysics. That's knowledge that doesn't correspond to intuitions. So it is a knowledge about 'something' but that something is not intuitions. Kant needs to prove that the usage of categories should not be allowed to used on anything that doesn't have intuitions. Jun 18, 2020 at 18:08
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    That is why pre-Kantian metaphysics was nonsensical, its practitioners overlooked that there was no way to bring it into any correspondence. So "like that" does not refer to anything. The burden is not on Kant to prove a negative, it is on those claiming a positive to produce a candidate for what that is supposed to be. Historical candidates include divine revelation and ESP, but epistemic magic, like all magic, is commonly viewed with understandable skepticism.
    – Conifold
    Jun 18, 2020 at 19:49
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    I honestly think you are too hung up on the term objective knowledge in the sense one would take it contemporarily (this is a translation of a text that is 240 years old, after all). What we call objective knowledge is rather framed as certain and necessary knowledge in Kant. It would probably be better to think in terms of actual knowledge about objects of experience. And since experience in general and its objects in particular are given through intuitions, the problem dissolves.
    – Philip Klöcking
    Jun 18, 2020 at 23:31
  • Hmm. I am still having trouble. See rationalists like Leibniz or Descartes never claimed that God or Soul are located in time or space. They said we have a priori reasoning that allows us to prove they exist. They never said they correspond to 'objects'. So when Kant terms them dogmatic, he needs to prove that the a priori 'reasoning' they are using, is only valid insofar as they do it on 'objects'. Now he has proved that objects correspond to intuitions. But he hasn't proved that a priori categories should only be applied to on objects, otherwise it is invalid. Jun 19, 2020 at 8:48

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The Schematism is the Transcendental Deduction. It's the TD continued. The reason why, I assume, Kant considered the "B" Deduction superior to the "A" version is exactly that it is structured in a way that immediately suggests that the Schematism constitutes the completion of the whole reasoning.

I only partially agree with your account of the Deduction. Indeed, the first part of the TD-B demonstrates that any object of intuition is a possible object of judgement, which is broadly equivalent to what you said. But the Deduction doesn't provide any constraint on non-empirical use of the categories. Kant assumes that any object of our cognition must be externally given when he says that judgement is a mere act of combining/synthesis. Then, afterwards, he presents what he calls an 'indirect proof' of this proposition in the Transcendental Dialectic by showing that going beyond the bounds of experience leads to dialectical contradictions and thus no knowledge can be acquired this way. The second part of the TD-B aims to show that objects intuited in space and time, necessarily subject to the categories as far as they're to be cognized, can at all be cognized, i.e. subjected to the categories. Kant speaks of intellectual synthesis (of intuitions as such) and figurative synthesis (of intuitions with some form). This provides a smooth transition into the Schematism chapter where pure time-determinations are finally derived from the categories (which is the sole purpose of the Transcendental Deduction).

Your confusion might stem from the fact that, indeed, the Transcendental Deduction with the Schematism elaborate the, using a phrase of Strawson, "bounds of sense" - from the inside of experience in which pure intellectual concepts and spatio-temporal intuitions. But to recognize a boundary isn't yet to forbid crossing it - that's the goal of the Transcendental Dialectic - that is the answer to the question in the last paragraph.

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