To: Gordon F.
From: Geoffrey Klempner
Subject: How does space pose a problem for philosophy?
Date: 28 November 2006 11:04

Dear Gordon,

Thank you for your email of 22 November, with your essay for Possible World Machine, in response to the question, 'In what ways does the nature of space pose a problem for philosophy?'

In your essay, you have posed several ways in which space might be a problem for philosophy.

1. Measurement. You almost get to the point of posing the question here, but not quite. As you observe, certain fundamental physical quantities are interdefinable. As a result of history, we are stuck with a rather awkward number for the length of a meter, but the point is that assuming the constancy of the speed of light, any quantities defined in terms of this will be equally constant.

But suppose someone suggested that, for all we can know through observation and experiment, the actual length of a meter, as defined in terms of the speed of light, is shrinking, correlatively with all other physical quantities defined in terms of the length of a meter. There are two possible responses: (a) the hypothesis is unmeaning (b) the hypothesis is unverifiable. The equivalence of (a) and (b) can only be assumed if you hold a verificationist theory of meaning. Does that mean, if you are not a verificationist, that it is really possible that the universe is expanding or contracting in a way that can never be measured by any instrument? or is the absurdity of this hypothesis an argument in favour of verificationism?

2. The unit on space poses the idea of two or more spatially unrelated 'spaces'. This is similar to, but not the same as the theory put forward by David Lewis according to which every possible world exists in its own space and time, the difference between other possible worlds and the actual world being merely one of local perspective.

The many-worlds interpretation of quantum mechanics comes somewhere in between, in that the many worlds are a subset of all the possible worlds, namely those that can be reached by considering alternative histories of the universe starting out with 'the' big bang, or those consistent with the actual laws of physics. (These are equivalent only on the assumption that there is a world for every possible variation of the 'big bang' consistent with the laws of physics.)

The objection to Lewis is that he has turned possible worlds in to actual worlds. This ignores the essential difference between possibility and actuality. In terms of ontology, the realm of the possible should be seen as sui generis, not reducible to the actual.

3. The existence of the vacuum is a conundrum as old as philosophy. The Greek atomists defined space as 'non-being', the absolute opposite of being, in defiance of Parmenidean monism. This is not space as we would understand it, however.

If the ultimate constituents of the universe are particulate then there seems no objection in principle to defining a region of space where all particles have been removed. If the ultimate constituents are not particulate, on the other hand, then there is no method in principle of reducing the concentration of material in a given region to zero. But couldn't we just get lucky, anyway? couldn't there be regions completely devoid of material even though we can never know this, because the concentration is so low? Once again, the verification principle looms.

4. In the unit of the Metaphysics program dealing with Kant's 'Refutation of Idealism' I consider the possibility that Kant's argument for the necessity of 'space' only goes so far as establishing the need for a pre-spatial 'matrix' which can be any number of dimensions apart from three. This would be enough for 'objective experience' according to Kant's argument, even if this is not what Kant himself held.

Provided that the subject has a 'theory' of what is external to perception, in relation to which seeming perceptions are capable of being judged veridical or otherwise, one has all the structure necessary to resist the naive idealist view that 'all that exists are my own perceptions'. In effect, however, this is just a more sophisticated version of idealism.

5. Correct me if I am wrong, but I thought that all the problems of infinity - infinitesimals, transfinite numbers etc. - can be raised with time as well as with space. If that is true, then the concept of space as such is not the source of these problems.

All the best,

Geoffrey