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A-series and B-series accounts of time


To: Chris M.
From: Geoffrey Klempner
Subject: A-series and B-series accounts of time
Date: 19th October 2010 14:17

Dear Christian,

Thank you for your email of 12 October, with your essay for the University of London BA Metaphysics module, in response to the question, ''Time should be understood as a series of events ordered by notions such as before or after, we do not need tense invoking concepts like past, present and future.' Discuss.'

Time understood as a series of events ordered by before-and-after is McTaggart's 'B-series' while time understood in terms of past, present and future is McTaggart's A-series. Although you offer a critique of McTaggart's argument for the unreality of time, the real question being asked here is not whether it is possible to demonstrate the incoherence of the A-series, but rather whether a theory formulated in terms of the B-series is sufficient to capture our 'understanding' of time.

McTaggart rejects both the A-series and the B-series. He is not arguing for the B-series without the A-series. There is no B-series because time is unreal. What he proposes instead is the C-series, which no-one would mistake for our 'understanding' of time. There is a series, all right, but it isn't a 'time' series.

So the bulk of your argument needs to concentrate on the question of the sufficiency of the B-series. If sufficiency could be established, then we would simply not need any destructive critique of the kind that McTaggart offers.

However, you do have a proposal of your own which looks very interesting (I have not come across this before). As I understand it, what you are suggesting is that we regard each passing moment of time as a discrete B-series. The result is a matrix. My (or our) position in time is identified as a line in the matrix. But which line? The problem is, if you start out describing the matrix of B-series's from an external point of view, then all you have done is replicate the B-series in a redundant fashion, as in a hall of mirrors. What you want to say is that NOW is THIS line in the matrix. But how can you say that, in terms of this picture?

Beyond all the talk of 'contradictions' what McTaggart's argument ultimately relies on is the fact that there is no meaningful way to state which time is 'now'. All we can do is utter the tautology, 'now is now'. In just the same manner (as I argue in my book 'Naive Metaphysics') we seem to have no way to express the evident fact that 'I am GK' (or 'I am CM', or Thomas Nagel's 'I am TN' in 'The View From Nowhere'). All I am saying is 'I am I'. The fact which is 'evident' to me, isn't a fact so far as you are concerned. GK is GK.

You give a good selection of the opposing arguments, although I would have liked to have seen Mellor ('Real Time') mentioned here, as he really takes the bull by the horns and tries to offer an explanation, in terms of a B-series theory, of the significance of the 'present' in terms of human agency. My strong suspicion, as your discussion to some extent bears out, is that proponents and opponents of the B-series view are locked in a battle which can never be lost or won.

*Of course* you can give truth conditions for A-series 'time' if you help yourself to temporal indexicals. The ruse is transparent. *Of course*, if you offer a B-series theory of truth conditions for tensed statements, something 'seems' to be left out -- but this 'something' cannot be said. As Wittgenstein comments about the beetle in the box, 'a nothing would serve as well as a something about which nothing can be said. A-theorists are merely insisting that there *is* a beetle in the box, while B-theorists steadfastly refuse to allow that this 'insistence' cuts any ice.

So I fully agree with you that we are left with a 'question begging chain of argument and counterargument on both sides'. However, the issue is not, as you immediately go on to say, 'whether the notion of A-series is not contradictory'. The question is whether or not talk of the A-series is ultimately *redundant*. Which merely takes us back to the 'chain of argument and counterargument'.

What is a theory of time? What is it for? One can accept that it is a very useful project to try to give truth conditions for natural language, along Davidsonian lines. It explains something (sc. how we can understand a potentially infinite number of sentences on the basis of knowledge of a finite number of words semantic parts). But to 'explain something' about time (what a speaker 'knows' when they are competent in the use of tensed statements) isn't to say what time *is*.

I suspect that the real motivation for B-series theorists is that they don't want to be left with this intractable metaphysical problem. They want a cut-and-dried theory which leaves nothing 'unexplained'. However, there is another, less inflationary way of responding to this which is simply to say that if you accept that a theory of truth conditions doesn't 'explain everything', it doesn't follow that you are left with an 'unresolved problem'. Some things just are what they are, the ultimate sui generis notions which constitute our conceptual scheme.

All the best,