CONTENTS

1   INTRODUCTION

2   TECHNICAL DEVELOPMENTS

3   B-THEORY: EXPOSITION

4   A-THEORY: EXPOSITION AND PARADOX

5   ARGUMENTS FOR A-THEORY

6    A-THEORY: REVISED EXPOSITION

7    TIME AND ASSERTION

8    THE PAST-FUTURE ASYMMETRY

9    CONCLUSIONS

4   A-THEORY: EXPOSITION AND PARADOX

The basic objects of A-theory are the enduring objects. They are not temporally composite (although of course they may be spatially composite). Rather they have a potential, and in most cases actual, multiplicity of states. I was a child, now I am a middle-aged adult, and if I live that long I shall be an old man. These states are logically incompatible. Contradiction is avoided by the mechanism of tense: the states are attributed to the object in different ways. Contradiction occurs only if incompatible states are attributed to the object using the same tense. Change, pace Russell, involves difference, but it is a special type of difference. It involves a difference between the attributes of the same object (and not just between attributes of different components of the same temporal composite.)

According to A-theory the use of tense is irreducible. Russell’s reduction succeeds only by virtue of losing reference to an important part of reality. The present is all the reality that there is. This does not mean we deny reality to the past, saying that it is just a figment of our imagination. Rather we attribute reality to the past using the was method of attribution. Our statement about the present being all that there is, is tautologically true because “is” is irreducibly tensed. Similarly we attribute a reality to the future, using the will-be method of attribution. (A-theory is often associated with a belief in an open, indeterminate future, with the passage of time seen as resolving indeterminacies. This linkage is not necessary. It happens that the future is considerably less epistemologically accessible to us than the past. The passage of time resolves our epistemological uncertainties over the way things will be - by making them present. But I would argue that logically and ontologically, statements about the future have well-defined truth-value. The statement “A man will land on the moon in 1969” was true in 1960 - and indeed in all years prior to 1969 - even though we had no way of finding this out for certain in 1960.)

Here we encounter our first difficulty in enunciating what A-theory is trying to say. We want to say that there is something in common between the different tense-attributions, namely reality, but we deny that there is a tenseless reality. We can not extract this common feature and display it separately. To do so would be to lapse into the very ontology of B-theory which we wish to deny.

This does not mean that we can not create B-theoretic models of the temporal world as useful devices for helping us think about time. As human beings with the faculties of memory and anticipation which can operate over indefinitely large tracts of time, and with the power of conceptual thought which allows to express the contents of the faculties, explore the logical implications thereof, we are uniquely capable of creating B-models. We can thereby live across time, rather than in an eternal present. Having these models in which memory, present knowledge and anticipation are all bundled together is indispensable to living as functional human beings. Once we have mastered the technology of writing (external information storage) we draw spatial pictures of these models, for example to illustrate the course of history or to plan the course of our projects.

These models, however useful they are for displaying the contents of a temporal reality, must not, according to A-theory be confused with reality. The radical distinction between the three tenses is absent from the model. B-models are Wittgensteinian ladders, to be used for climbing, but then firmly kicked away once we have achieved our objective.

A-theory stands Weyl on his head. The happening world is the reality, and the tenseless manifold is a product of our subjective imaginings. We can express this by (mildly) parodying his famous B-theoretic pronouncement.

The objective world happens, it does not exist as a timeless whole. It consists only of the present (it consisted of the past and will consist of the future but these are different attributions). Only in the subjective realms of our individual imaginations, and in the inter-subjective realm of our collective cultural imagination, is there a manifold in which past, present and future have an equal, tenseless ontological structure.

This statement of A-theory works well within a single present moment. In this context there is a unique present, past and future. But obviously this is not all there is to time. It is important to our understanding of the future that it will be present, and of the past that it was present. To me as a child in the 1960s, 1998 seemed impossibly deep in the future. And yet here it is, large as life and just as vividly present as any other year. And 1968, once so passionately present, is now a distinctly faded memory. My recent family holiday in Florida was for many months an anticipation. Then it turned into a present reality. Now it is over and is rapidly disappearing down the plug-hole of memory. This is the fundamental phenomenology of the passage of time which motivates A-theory.

And yet, as McTaggart showed, attempts to express these basic facts about A-theory lead promptly to either a vicious circularity or to a vicious regress. The only way we appear to have at our disposal to explain what we mean by tenses is to recycle the tenses themselves. If we take the present as the fundamental measure of reality, then we try to explain the will-be reality of the future in terms of will-be present. In the notation developed in Section 2, this attempt can be written as

                        Tense-xs (x)  = Tense-xs (Tense-0x(x)) .

Here we are treating the truth of the tensed statement as an event which can be assigned a tense. Not to make this attempt is to leave the future and past as being permanently different, which is quite untrue. But while the iterated tense statements are true (and are the basis for the tense-logic developed by Prior), they lack the explanatory power.

Worse than that, argued McTaggart, this circularity or regress leaves us unable to resolve a contradiction that appears in our attempts to describe A-theoretic time. To paraphrase McTaggart’s let us revert to a three-fold system of tenses (the argument goes through a fortiori with a continuum of tenses). Consider a moment in time, M. Three mutually incompatible things can be said of M, namely P(M), N(M) and F(M), being past, present and future respectively. One and only one of these is true of M. On the other hand, to express the fact that past, present and future are not permanent attributions, we must say that all of them a true of M. There is a clear contradiction between these two statements about the attribution of tenses.

The natural way to attempt to remove this contradiction, which occurs automatically when tensed language is used, is to say that, of course, the three incompatible attributions are not true of M simultaneously. But to say this requires the iteration of tenses. The threefold attribution to M is expressed in one of three ways:

            N(N(M))ÙF(P(M))ÙP(F(M)), corresponding to N(M), or

            P(N(M))ÙN(P(M))ÙP(F(M)), corresponding to P(M), or

            F(N(M))ÙF(P(M))ÙN(F(M)), corresponding to F(M).

But, argues McTaggart, the contradiction reappears at the new level. In the first case for example we have N(N(M)), but, for the same reason as at the first level, we must also have P(N(M)) and F(N(M)), which is a contradiction. To remove it we would need a new iteration of tenses which would re-introduce the contradiction at the next level up.

It is this persistence of contradiction at each iteration which makes A-theoretic time paradoxical, not simply the existence of the regress. He explains the situation in the following terms.

“It may be worth while to point out that the vicious infinite has not arisen from the impossibility of defining past, present, and future, without using the terms in their own definitions. On the contrary, we have admitted these terms to be indefinable. It arises from the fact that the nature of the terms involves a contradiction, and that the attempt to remove the contradiction involves the employment of the terms, and the generation of a similar contradiction.”

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