To: Gordon F.
From: Geoffrey Klempner
Subject: Parallels between theories of space and theories of time
Date: 8 January 2007 11:42

Dear Gordon,

Thank you for your email of 26 December, with your final essay for the Possible World Machine, in response to the question, 'What illuminating parallels can be drawn between a philosophical account of the nature of space and a philosophical account of the nature of time?'

So my guess that you were inspired by McTaggart seems to be correct! I take it that, like McTaggart, you are responding to the challenge of creating something analogous to time without temporality as such (the A-series) but more time-like than mere 'spatialised' time (the B-series).

I feel ever more confident that you will read Alexander, Whitehead and McTaggart with great pleasure.

Space and time

I didn't have any particular parallels in mind when I composed this question. An obvious one would be the question of infinity vs finitude explored by Kant in the Antinomies of Pure Reason, in the second part of the Critique of Pure Reason. ('Space is finite' vs 'Space is infinite', 'Time has a beginning' vs 'Time does not have a beginning'.)

However, the theme which emerges for me is much more to do with the lack of parellism between space and time. As I see it, this comes out in two ways:

Richard Swinburne, in his excellent book 'Space and Time' gives an intriguing argument for a disanalogy between the claim that it is logically possible to have an unoccupied space, and the claim that it is logically possible to have a period of time without any events. (I may have mentioned this before, sorry if I'm repeating myself.) The argument goes like this:

Imagine a space containing several objects. Now take the objects away, one by one (don't ask how, just annihilate them - we are investigating logical, not physical possibility). At last, we take away the final object and the space is empty. Now try to put one object back. There is no 'place' to put it because place is logically defined in relation to existing objects.

Now consider time. The universe comes to a halt for one minute. Then it starts up again where it left off. No-one is the wiser. No clue is left. By contrast with space, this is logically possible, because the time when the universe was at a standstill is fixed, determined by its relation to the previous times and the times that came after.

This suggests a disanalogy between time and space, and also suggests a possible reason for claiming that time is capable of 'making boundaries' in a way that space is not.

As you argued, every spatial boundary is a mere transition from one kind of 'stuff' to another. Whereas the mere passage of time is intrinsically 'boundary-making'. That's just an idea - I haven't anything more to say about it.

The second point is for me the more fundamental: McTaggart is wrong. The reality of the A-series cannot be denied on the basis of a mere claim about logical inconsistency. What McTaggart's argument succeeds in showing is that it is impossible, using language (and there is admittedly no other means of expression) to say what the passage of time consists in, no way to express the fact that the time is now: just as there is no way to express the fact that I am I. My conclusion from this is that a complete metaphysical description of reality must acknowledge 'indexicality' as an aspect of what is real. The eternal view cannot capture the nature of time. Time adds something to the world which cannot be seen from a viewpoint sub specie aeternitatis.

This is what I argue in my book 'Naive Metaphysics', although the main emphasis is on 'I' rather than 'now'. In fact, what I am arguing for is the undeniable reality of the 'I-now'. If this leads to inconsistency, then we must embrace inconsistency. That's the price you have to pay for attempting to tell the whole truth rather than just the part that you can conveniently package into a consistent philosophical 'theory'.

You are fortunate indeed to be able to feel that you have a lot of work still to do on your project. I hoped this too when I wrote my book: but instead my metaphysical investigations came to a dead end. The Metaphysics program managed to find more things to say that aren't in the book, but the clash between the objective and subjective worlds - or the world of 'I-now' and the world of 'all that is the case' - is one that I have never succeeded to this day in elaborating on or taking a step further. Maybe I am wrong and McTaggart (or Mellor, see his book 'Real Time') is right. The discovery that this was the case would at least be a spur to further investigation. But I'm not counting on it.

Anyway, I've enjoyed our correspondence on the central questions of philosophy. I have a strong feeling that your thoughts and ideas have developed a lot through our exchanges. I have certainly found your contributions very stimulating.

All the best,

Geoffrey