To: Peter B.
From: Geoffrey Klempner
Subject: Kant's First Antinomy
Date: 11 July 2003 14:49

Dear Peter,

Thank you for your e-mail of 1 July, with your first essay for your Associate program, 'An Essay on Immanuel Kant's Antinomy of Pure Reason - First Conflict of the Transcendental Ideas.'

Your essay is a carefully written and methodical piece of work. You first summarize the argument for the thesis, 'The world has a beginning in time, and is also limited as regards space,' then you give the argument for the antithesis, 'The world has no beginning, and no limits in space; it is infinite as regards both time and space' (N.K. Smith translation). You then give Kant's comments on these two arguments.

Commenting on the text, you observe that 'Perhaps the first notion that might occur to the reader, is that it is not so easy to distinguish between Kant's Highly concise presentation of the arguments and his own point of view. For he presents the arguments of the thesis and antithesis, in an almost satirical fashion...'

What are we to make of this? What does Kant think? Has he set out deliberately to contradict himself? Which side is Kant on? Those are the questions which would assault any reader who found these pages of the Critique of Pure Reason lying on a beach somewhere.

You comment, 'It should be taken into account that this is but one part of the whole work that makes up the Critique of Pure Reason.' However, it is not necessary to read the whole of the book to find out. After he has presented his four Antinomies, Kant goes on in the same section of the book to explain how these antinomies have arisen in the first place, and to offer a *third* alternative, which rejects both views, the thesis and the antithesis.

The crucial section, so far as the first antinomy is concerned, occurs at B 545-551, 'Solution of the Cosmological Idea of the Totality of the Composition of the Appearances of a Cosmic Whole'. Kant's thought is that what the antinomy shows is that there is something illegitimate about the question that leads us to pose the alternative, 'finite or infinite' with regard to time and also with regard to space. I will leave you to read this section and come to your own conclusions.

Thus, Kant's *own* argument, regarding the first antinomy is not the argument for the thesis, or the argument for the antithesis, but rather the argument for the view which rejects both alternatives.

If one is looking to criticize Kant's position, then there are various points at which one might object. Kant states at the beginning of his commentary on the thesis that he is not seeking to 'elaborate sophisms' (offer a 'lawyers proof' in your translation). Of course, that is what he would say. But we already know that the arguments cannot be *valid* arguments, so what's the interest in the subtle distinction (if there is one at all) between an invalid argument and a sophism? Kant's claim is that he is saying the very best that can be said in favour of the thesis and in favour of the antithesis. Above all, his concern is to defeat any suspicion that one or other of the two positions might be the correct one, after all.

So, this is one place where you might disagree. You might think that one of the two opposing theories is the right one.

Another question we can raise is about Kant's assumption that if the world is finite in space or in time, there ought to be a proof that it is finite, and if the world were infinite there ought to be a proof that it is infinite. From the fact that both arguments are invalid, one might just as well conclude that as a matter of contingent fact, the world just happens to be finite, or just happens to be infinite. Kant rejects this alternative too. What's his argument (if any) for doing so?

Finally, you might be fully convinced right up to the point where Kant offers his own 'third alternative', but feel that his solution is inadequate. In that case we would be in a position analogous to someone faced with an insoluble paradox.

Apart from exegesis, you do give one substantial argument of your own, 'If one is to talk about eternity, wherein the span of time is boundless, then there can be no state wherein it can be said that time has elapsed, since this would suggest imposing a cessation of time...'. Here's one possibility: Suppose that the world has a beginning in time, but no end in time. Then the span of time is indeed 'boundless', because it has no *furthest* limit, yet at every moment a precise amount of time has elapsed. Another possibility is that the world has an end, but no beginning. Suppose the latter were held to be the case. Kant's objection will be the one you have just quoted, that it is impossible for an infinite time to have already elapsed, because one would have to traverse an infinite series in order to reach the present moment. But are we forced to look at it that way?

All the best,

Geoffrey