To: David F.
From: Geoffrey Klempner
Subject: Kant's argument for the necessary unity of space
Date: 20 March 2006 10:58

Dear David,

Thank you for your email of 10 March, with your further thoughts on units 10 and 11 of Possible World Machine and fourth essay in response to the question, ''The real existence of a physical object, as opposed to existence as a hallucination or in a dream, involves being in a spatial relation to HERE.' Comment on this argument, derived from Kant, for the claim that there cannot be more than one space.'

The first point to make is that the background to Kant's argument is the 'Refutation of Idealism' (Critique of Pure Reason, 2nd edition) which takes as the premiss, 'I have experience' and argues for the conclusion that this MUST be 'experience of an external world'.

Kant describes this as a response to Cartesian scepticism. The difficulty is that the conclusion, 'empirical realism', would not satisfy Descartes. Empirical realism, in Kant's view, is consistent with transcendental idealism, the view that space and time are merely 'forms of experience' and that 'things in themselves' (or 'noumena') are neither spatial nor temporal. Descartes is a transcendental realist, in Kantian terms. Mind and matter are, for Descartes, the ultimate 'things in themselves'.

So we have to rephrase Kant's conclusion: experience is necessarily AS OF an external world. Any possible experience, is experience as of ONE space, the space which I 'construct' on the basis of my experiences.

It seems plausible to say, as you do, that we have (in a sense) to regard each subject as constructing his own 'space' which I can never enter into. But Kant never says this. Other persons are necessarily located in my space, the only 'space' that I can intelligibly imagine or conceive. What exists beyond 'my space' is just the reality of non-spatial, non-temporal things in themselves.

But let's leave noumena behind, because arguably they do not make any difference one way or another. If I want to think about objects in space, then there is only one way to do it, according to Kant, and that is by constructing a theory on the basis of my experience. The truth or falsity of any statement about the world of my experience involves placing objects in a single space, because this is the only intelligible way to make sense of causal relations between the objects of my possible perception.

Your argument, 'I don't care about truth or falsity, so long as I can speculate about the bare existence of other spaces' would not impress Kant. What is it to speculate about something? Let's say I speculate that every morning when he is alone in the bathroom, George Bush practices his 'quick draw' gun fighting skills in front of the mirror. It is pleasing to imagine this, no doubt. But I am not merely imagining this (the way I might imagine, e.g. being President of the United States or being a champion gunslinger). My pleasure comes from the thought that, 'It might actually be true.' My speculation, untestable though it may be, is aimed at reality. It might, for all I or anyone else - even Bush's wife - could ever know, be the case that this IS what GWB does.

If Kant were merely arguing that it is impossible to verify the existence of another space, then the realist response would be to say that there can be truths which are not verifiable. But that is not the argument. The argument is that the very notion of another space is unintelligible, given the role which Kant assigns to spatial concepts in making sense of experience. A second space has no possible role to play, it is just 'a wheel which turns, although nothing turns with it' (Wittgenstein).

So far so good. This was the generally accepted view until an article appeared by Anthony Quinton, 'Spaces and Times', (Philosophy, 37, 1962, pp.130-147) which gave a plausible scenario in which a single subject inhabits two spaces. Every time I go to sleep, I 'dream' of an alternative existence as a poor but happy fisherman in a village in the mountains. When I go to sleep in my fisherman's world I wake up in this world. My fishing dreams become increasingly coherent, until I find that the two dreams are equally coherent. Applying Kant's own principles, neither experience can be dismissed as a mere 'dream', so both must be regarded as 'experiences of a world in space'. But no mention of how the two spaces are connected.

The second dialogue contains the vestiges of a memorable argument I had with my then supervisor P.F. Strawson. Strawson was favourable to the idea that there could be 'causal relations' between objects in different spaces. That was how he defended Quinton. I replied with the argument which I attribute to Kant in the dialogue.

The assumption behind Quinton's article is that the Kantian argument is the best one available. If we reject the whole Kantian apparatus of 'constructing' a spatial world, does that provide a way to allow a plurality of spaces? In writing the Space Hopper story, my thought was that it does. The very notion of physical space depends on whatever is regarded at the current time as the 'best explanation' for observed phenomena. Hence the claim that space, according to physics has a particular size and shape. There is no reason, in principle, why the best available physical theory should not posit two or more spaces, if the result is simpler, more elegant than any of the available alternatives.

All the best,

Geoffrey