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

6   A-THEORY: REVISED EXPOSITION

I argued above that if our immediate experience is capable of telling us anything, then it tells us that time is as described by A-theory. There must therefore be some way around McTaggart’s argument that A-theory is self-contradictory. Here I attempt to supplement this existence argument with an account of how A-theory can be stated in a self-consistent manner.

An immediate response to McTaggart’s argument that the contradiction appears at each level of the regress is to say that it is also eliminated at each level. It was based on a misconception at the first level, and the same is true at all other levels. We introduce the iteration of tenses as the natural and correct way of curing this misconception, and when it tries to raise its head at the second level, we introduce a third level to eliminate it there, and so on. The regress is virtuous, because at each turn we eliminate the misconception on which the contradiction is based.

In the regress we zig-zag between the appearance and elimination of the contradiction. The pessimist (McTaggart) says that we always have a contradiction. The optimist replies that we always eliminate it. On average we appear to have half a contradiction. Given this, it is better to avoid even the transient appearance of a contradiction by eliminating the misconception at source rather than by the iteration of tenses, which never succeeds in achieving a decisive elimination.

An A-theoretic reply to McTaggart was given by Broad. His basic argument is that McTaggart went wrong in assuming that moments exist tenselessly, and then have tenses tenselessly attributed to them. If we insist that our attributions of properties to temporal objects must always be tensed, then the McTaggart contradiction can not get started. This is precisely the role of tenses - to allow objects to have different properties at different times without contradiction.

This allows us to leave paradox behind, but we still have a regress which prevents us explaining in words the tenses mean, explaining the fact that the future tense of attributions is not a permanent property of the attributions but will ultimately give way to a present tense and then a past tense for these same attributions. It prevents us from explaining just how tense differs from date. We can say that date avoids contradiction by making the attributions to different objects, while tense does this for attributions to the same object, but there our explanation halts. The natural picture to use, of the present moving through the attributions, turning future into past as it goes, fails to work because it invoke the notion of change, the very thing we set out to explain. This forces us to choose between:

• everything can be described in words - and so the failure of our description of tenses shows that time in the A-theory sense does not exist, and
  
  
• time is a reality, but is that part of reality which is unsayable.

We no longer have the immediate disproof of the reality of A-theoretic time threatened by the contradiction, but we can only retain reality at the cost of abandoning the completeness of language. This way of expressing the outcome of the McTaggart regress was advocated by Dummett:

“If this last piece of reasoning, to the effect that the belief that time is unreal is self-refuting, is correct, then McTaggart’s argument shows that we must abandon our prejudice that there must be a complete description of reality. This prejudice is one that lies very deep in many people. I shall not here attempt to explore it further, to find out whether it can be supported or what mistakes, if any, it rests on. It is enough if I have succeeded in showing that it is to this prejudice that McTaggart is implicitly appealing, and that it is this which must be extirpated if his conclusion is not to be accepted, and above all that his argument is not the trivial sophism which it at first appears.”

Of course there is a way of expressing what tenses mean by using the element of time itself within language. An example given by Findlay is of the description of a man diving. Initially we say:

“He is on the diving board, he will be diving and a little later he will be in the water.”

Then, when appropriate we say again:

“He was on the diving board, he is diving and he will be in the water.”

Finally we can say:

“He was on the diving board, then he was diving and now he is in the water”.

In practice children learn how to use tenses accurately by abstracting from such examples within a year of starting language use (even though their grasp on the exact dimensions and structure of the past and future may still be rather hazy). The McTaggart regress does not hinder their understanding, though within a few years they often become aware of it in the form of paradoxes such as, “Tomorrow never comes, because when it comes it is today”.

In this way we succeed in communicating facts about time, and the general phenomenology of passage, but it is done by introducing passage itself as an integral part of our explanation. It is analogous to supplementing a linguistic description of a triangle with a picture of a triangle, supplementing saying as the means of communication with depicting. But the lesson we draw from McTaggart is that, in the case of passage, the introduction of depicting into the explanation is unavoidable; the mechanism of saying alone is unable to communicate the nature of time.

Of course the reference of all expressions referring to items in the world beyond language has initially to be established by some form of ostension. Depiction is a means of assisting this ostension. What is different about the passage of time is that the depiction must continue in our use of the expressions, after the explanation has been achieved. This element of depiction is concentrated in the tenses. This allows all the other expressions to have unchanging references, that is, references fully expressed by means of the mechanisms of saying. However if today I say,

“It is raining now.”

then the word “now” (taken as the embodiment of the present tense) has a different reference to the one it will have if I were to use the same sentence tomorrow. (Since the two sentence-tokens can have different truth-values, the reference of one of the components must have changed.)

The number of tenses in a sentence can be reduced to one. If we are talking about things happening at different times within a sentence, this can be done with multiple tenses, but it is not necessary to do so. The other way is to use B-relations or dates to describe the temporal relations. But one tense is still needed to fix the relations or calendar of dates to the reality of Now. The fundamental assertion of A-theory is that until this is done the reference of the sentence has not been finally established. Suppose one came across a text describing various events using an unknown calendar. Then one would not be able to tell if this was describing past history, predictions of the future or a mixture of the two. This, says A-theory, means that reference, the link to the world, has not been fully made.

Of course with permanent, printed records, it is impracticable to update the tenses continuously. The solution in practice is to leave the sentences untensed, and then have the completion of reference external to them, in the form of a calendar which tells us what today’s date is. (With electronic text, by contrast, such updating, using the computer’s internal clock and calendar, is easy.)

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