Before going off for Christmas I made a doomed attempt to buy second-hand books as presents, and succeeded only in buying myself a few slim tomes (although one of those, In Defence of War by Nigel Biggar, did turn out to be a present for my wife).One of which was the said Kant's Dialectic by Jonathan Bennett, 1974. I'm mostly interested in this via Popper (see Kant’s cats) who believed the Antimonies were designed to demonstrate how reason goes astray when unconstrained by reality. I think that's a good interpretation though (as I said there) I'm doubtful whether that was actually Kant's intent; certainly, IMO, if you're going to do something like that you should clearly state it, which Kant never does.
Sadly that doesn't get addressed in KD1. Instead, despite a refreshing beginning summarising the contents and some well-turned flings against Kant, we degenerate too much into philosopher-ese. My doubt now is to how far I bother go in discussing this.
Substance
In antient philosophy, people were interested - amongst a great many other things - in what the world is made of. Recall that they didn't know if matter is fundamentally "atomic" or continuous, and so the question of what is a fundamental "substance" arises. Section 19 offers "The concept of substance, dropped in §14, must now be picked up again. We have met the idea of a substance as something indestructible, but our considerations of the Dialectic will involve the stronger thesis that a substance cannot come into or go out of existence, or, as I shall say, cannot be originated or annihilated. By this criterion, a must be sempiternal, i.e. must exist at all times". That would have made reasonable sense all through classical antiquity and to Kant, but makes no sense by 1974, when we have had mass-energy equivalence and the creation and destruction of particles for more than fifty years. The section continues onwards, wurbling happily about philosophical things, totally unmoored by reality, almost as though determined to demonstrate Popper's version of Kant's point. Similar problem occur elsewhere.
As a slight aside, one can consider "the soul" under this rubric; if feeling religious, you consider "the soul" in it's usual "woo" fashion; if not, you consider consciousness instead. But either way the question arises: is it a "substance", i.e. indivisible? This, then has some eery echoes of the "splitting brains" discussions that Parfit was so fond of. There I've argued, effectively, that consciousness is indivisible; but I don't think it is meaningful to call it a substance.
Extension and divisibility
Kant presents arguments why extended things cannot be indivisible, largely following Descartes. But he is wrong, because, as we now know, matter is fundamentally "atomic"2, which I'll put in quotes, because as-we-all-know somewhat confusingly for conversations like this, the things we call atoms are not "atomic". But nevermind, electrons are "atomic", i.e. indivisible, and are extended in space, although in a slightly confusing way. Now we know that, we of course re-examine his argument for the crucial and illuminating error. But unfortunately it is simply and uninterestingly "if a thing is extended in space (and space is divisible) then we can consider the thing to have parts and so be divisible". All of the fascinating bits of QM that this has (inevitably, for its time) failed to take account of are the bits of interest. Sadly, KD fails to go that route, instead preferring to merrily emit a long string of words. See-also Ye workes of ye Francis Bacone.
As a sort-of ironic post-script, part of that stream-of-words is a discussion of Our Author's pet idea that compositeness, i.e. divisibility, might be nicely discussed in terms of breakability. But this fails, or at least is complexified, unbeknownst to him, due to quark confinement in protons.
Aside, in update: I think the modern notion that things can have several instrinsic properties also doesn't fit well with what Kant and Descartes and a host of other extension-is-primary people say. Electrons have mass, spin, charge, and something that can be considered extension. All of these different properties are intrinsic.
Infinite time
Having been nothing but critical I should leave you with the one where I do feel sympathy, which is the discussion of the finiteness, or otherwise, of past time. Kant's actual discussion of this is often uninteresting, because he doesn't know about infinity, Cantor being fairly new at that point and not something Kant has studied. But in place of his argument against the past being infinite, I'd put the rather handwavy "as we know, it takes about 13 b yr to get from formlessness to us, really there can't have been infinite time".
Kant's argument against "the world" having begun at some point is that there would be empty time before this. That makes sense in a Newtonian universe; but (I think; don't push me on this I'm weak on GR) doesn't in a GR universe with big bang: instead, time starts. Again, one doesn't blame Kant for missing this; I do blame Our Author for not mentioning it; because really it is the only interesting point in an otherwise long dreary stream of words.
Notes
1. From the head of chapter 7 will probably do: "In Kant's usage, an "antinomy' is a pair of good-looking arguments for apparently conflicting conclusions. In the chapter on the Dialectic to which I now turn, he offers four antinomies, each purporting to exhibit a conflict which can be resolved only with help from Kantian philo- sophy. Sometimes Kant suggests that his principles discredit the ques- tions to which the antinomal arguments offer answers, but he also suggests that in the first two antinomies each of the opposing conclusions may be false, while in the third and fourth both conclusions may be true. Indeed, no one account will do. The chapter is in fact a medley, and the several sorts of unity claimed for it are all spurious".
2. I know: we have no final theory. QM might get overthrown. But I'm betting on it to this extent, at least. Ditto on electrons being the bottom. If absolutely necessary I recast my argument into the form "there is a model of reality in which...", which suffices.
3. Since I have space, I'll include this here (from Critique of Pure Reason): It is not so extraordinary as it at first sight appears, that a science should demand and expect satisfactory answers to all the questions that may arise within its own sphere (questiones domesticae), although, up to a certain time, these answers may not have been discovered. There are, in addition to transcendental philosophy, only two pure sciences of reason; the one with a speculative, the other with a practical content-pure mathematics and pure ethics. Has any one ever heard it alleged that, from our complete and necessary ignorance of the conditions, it is uncertain what exact relation the diameter of a circle bears to the circle in rational or irrational numbers? By the former the sum cannot be given exactly, by the latter only approximately; and therefore we decide that the impossibility of a solution of the question is evident. Lambert presented us with a demonstration of this. The Lambert he refers to is Johann Heinrich Lambert, who proved in 1761 that pi is irrational. But WTF is Kant trying to say here? If he is trying to say that pi is irrational, he is choosing a wilfuly obscure method of doing so. Even "the question" at hand in "the impossibility of a solution of the question is evident" is obscure; the only question he has actually asked is "Has any one ever heard...", but he can't mean that. But the ratio of circumference to diameter is known exactly; it is pi; that pi doesn't have a finite decimal expansion doesn't mean we don't know its exact value. I think that just as he doesn't understand infinity, he isn't really comfortable with irrationals, which is like weird because sqrt 2 has been known to be irrational for a loong time.
Refs
* What's the difference between a mathematician and a philosopher? All a mathematician needs: pencil, paper, and a trash can. All a philosopher needs: pencil and paper. Source.
