To: Mark S.
From: Geoffrey Klempner
Subject: Kant on synthetic a priori principles
Date: 11th October 2010 13:00
Thank you for your email of 30 September, with your essay for the University of London Modern Philosophy: Spinoza, Leibniz Kant module, in response to the question, 'Describe and assess Kant' s reasons for holding that mathematical (arithmetical and geometrical) knowledge, and some principles of natural philosophy (physics), are synthetic and a priori' (Q9 2006, Q11 2009 combined).
You have understood the question in a different sense from the way I think it was intended. In the sense in which you have understood it, you have made a case for denying Kant's claim about synthetic a priori judgements which appears to be based purely on a critique of Kant's use of these two terms. Although his definitions of 'synthetic' and 'a priori' are largely defensible (with a nod to Quine etc.) he has failed to overcome the dilemma expressed eloquently by Einstein (a quotation which I haven't come across before): 'In so far as the laws of mathematics refer to reality, they are not certain; and in so far as they are certain, they do not refer to reality.'
Despite the fact that Einstein said it, and despite also the reasonable assumption that Einstein was not unaware of Kant's philosophy, this is little better than a statement of the very thing that Kant spends pages and pages of the Transcendental Analytic arguing against. This is the challenge, which Kant is very much aware of. Indeed, you could see this concise statement as pinpointing the very problem which Kant has identified.
Kant doesn't accept (and neither do I) the possibility that arithmetic could be empirical, in Einstein's implied sense. Come to think of it, nor did Frege in his brilliant destructive critique of Mill's views in the Grundlagen ('Foundations of Arithmetic' translated by J.L. Austin). Geometry is a very different case. Whereas for arithmetic we have the challenge of Godel's theorem, which though fundamental merely rejects the belief that arithmetic is finitely axiomatizable, in Geometry we have proofs of the consistency of non-Euclidean geometries, not to mention the evidence from Relativistic physics that it is non-Euclidean geometry which correctly describes the actual world.
So, what exactly did Kant set out to prove? He employs a novel form of argument, 'transcendental argument' which appeals to the 'conditions for the possibility of experience'. As you quote Hanna, the apriority/ necessity which he is seeking could be described as 'a necessary truth with a human face'. I would only add that it is not specifically human beings for whom these propositions are necessary, but rather any beings who enjoy our 'forms of perception', viz. space and time.
You mention P.F. Strawson at one point: in his excellent commentary on Kant, 'The Bounds of Sense' (1966) Strawson seeks to defend Kant's transcendental arguments, by means of a certain amount of horn retraction. If it really was the world which told us that Quantum Mechanics is at least possibly true, then before we even look at Kant's argument for the necessity of determinism we more or less know that there must be a fallacy somewhere. And yet, there is something right about what Kant says.
Imagine a subject theorising about a possible world, on the basis of a stream of experience. If that experience is not ordered spatially as well as temporally, if the existence of space is not brought in from the start as a necessary a priori assumption, then the process can never get going at all. Strawson gives a nice account of how, in the absence of a spatial world, the self disappears, leaving only a momentary vanishing awareness. (This more or less what Kant seeks to show in the 'Refutation of Idealism' from the 2nd Edition of the Critique of Pure Reason.) The identity of the self presupposes, as the a priori condition for its possibility, that experience is interpreted as perception of an external world of objects in space, the self (the empirical self that is) being one of those objects.
But Kant realized that this wasn't enough. We need additional assumptions if this task of constructing a spatial world on the basis of experience is to get off the ground. The world changes, and yet, somehow, based on limited experience, we are able to track these changes. To do that, we need the concepts of 'substance' and 'cause'. On the assumption that there can be no truth value gaps, of any kind, not even in principle, Kant argues that whatever is identified as 'substance' must be necessarily indestructible (e.g. Newtonian corpuscles). There can be no exceptions to deterministic causation. This is where Strawson demurs: all Kant has shown is that for experience to be possible there must be 'sufficient' permanence and 'sufficient' lawlike regularity (whatever that means).
If you have read all the way through the Transcendental Analytic, you will know just how mind-bogglingly obtuse Kant can be. But there's really no substitute, so far as this essay topic (or topics) is concerned, to giving an exposition of Kant's transcendental arguments and an evaluation of their cogency.
All the best,