A423/B451
Thing is, we are only impartial umpires for someone else’s judgements as expressed in his language. For each of us, for whatever our own reason concludes, there can be no impartiality, insofar as there are no disputants in a singular cognitive system.
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“…. In the course of our discussion of the antinomies, we stated that it is always possible to answer all the questions which pure reason may raise; and that the plea of the limited nature of our cognition, which is unavoidable and proper in many questions regarding natural phenomena, cannot in this case be admitted, because the questions raised do not relate to the nature of things, but are necessarily originated by the nature of reason itself, and relate to its own internal constitution.…”
So it is that reason always concludes to an answer its own questions, insofar as it is its nature to do so, but may without contradiction invoke different judgements as ground for them, insofar as its internal constitution is always a logical syllogism. It’s no different
in principle than considering getting to Chicago from Tampa by way of St. Louis (the thesis), or considering the same thing but instead, by way of Seattle (the antithesis). Doesn’t matter….you get there either way (the conclusion) and while one route may be better in one respect (faster, cheaper, the major premise in a syllogism), it may be better in another (you get to stop in and see Grandma and Grandpa, the major in a different syllogism). As you say, on the one hand, a logical disjunction, but not on the other, a contradiction.
Going to Chicago is of course not a transcendental notion, but the logical method is the same as an antinomy. And while the antinomies themselves in the text exhibit negation…beginning of the world/no beginning, etc….in principle the trip to Chicago is thetic/antithetic as well, re:, go this way/don’t go this way, and furthermore, even if empirically conditioned hence certainly determinable
post hoc by experience, the syllogistic method remains
cum hoc consistent with reason itself.
The whole point of the antinomies is that for any transcendental idea, not just the four listed major examples of one, there is an antithesis for it, which follows logically from the fact any idea presupposes its own negation. And while it may be only the philosopher that dreams this shit up, every human is capable of it, assuming his sufficient rationality. Just because he seldom if ever does, doesn’t mean he can’t, and pursuant to the proper interest of philosophy, we want to know what we can do, along with the consequence of it, not what we can’t be bothered doing.