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

7   TIME AND ASSERTION

The changing reference of tenses presents us with two options. We can express this fact about changing reference by saying that talk about time and changes is irreducibly token reflexive. This option takes the sentence type to be defined purely by its lexical content. The difference in reference of the sentence uttered at different times can be explained in terms of a reference to the difference in token. Alternatively, since the time of utterance has semantic significance, we can say that it is part of the essential features which define the sentence type. Despite their lexical identity, the utterances today and tomorrow are in fact different type-sentences.

Which ever way we choose to express it, the conclusion is that if A-theoretic time is a feature of the world (and our experience suggests very strongly that it is), then it is a feature which affects the power of language to say things. To protect the ontological neutrality of language, we try to make the workings of language isolated from, and indeed prior to the contents of the ontology they are supposed to describe. With A-theoretic time this attempt fails.

A consequence of the semantic significance of the time of utterance means that there is a significant difference between our two traditional methods of assertion:  speech and writing. These are two quite different ways of displaying a sentence token, either for the purposes of assertion or otherwise. Speech is evanescent by its nature, and is therefore useful when one wants to assert something just at one time, and not having the token remain there on display continuously making an assertion, possibly unintended at some later time. Of course even before the recording of speech, human memory was able to retain a record of the display of the token, leading to the possible retort, “But you said that X”. To this, if the assertion is no longer intended, the reply could be, “X was true then, but this is no longer the case”, or “I believed X then, but subsequent events have led me to change my mind”. On the other hand, if you want to persist in an assertion, then the same spoken display of a token has to be made over and over again.

Writing, by contrast, while not being absolutely permanent, does not have the intrinsic ephemerality of speech. It therefore has the opposite advantages and disadvantages to speech. For a permanent assertion, such as some religious dogma one wishes to propagate, it is ideal. The invention of writing paved the way for the establishment of the religions of the book. On the other hand one might not want the token to be there permanently, going on making an assertion on one’s behalf whether wished or not. To avoid this one might seek to destroy one’s offending writings, but the development of printing and now of electronic text, means that the multiplication of tokens of the original writing can make such erasure much harder.

A less drastic solution is to agree to the convention that the assertion is made only when the writer is actually performing the writing, and that thereafter what remains on paper is a record of a past assertion rather than a means of continuing assertion (in the same way that, in pre-literate times, the memories in the heads of the listeners functioned.) In fact we use an mixture of the two assertion conventions, depending on what we guess the intention of the writer was. Consider the two ways of saying almost the same thing:

“Darwin argued that evolution is driven by natural selection.”

“Darwin argues that evolution is driven by natural selection.”

The use of the present tense in the second formulation of course does not imply that we believe Darwin is still alive and arguing. We use this convention to imply that Darwin intended an ongoing assertion, and that this assertion can take its place in modern arguments about evolution long after the man who made it died. If on the other hand we were writing a history of thought, then we would be more likely to use the past tense, to indicate that the assertion was made at some historical moment.

Where McTaggart drew the conclusion that there was something wrong with time, the A-theorist draws the conclusion instead that there is something wrong, or at least limited, with our ability to speak about time. This is Dummett’s conclusion, namely that “we must abandon our prejudice that there must be a complete description of reality”. Although Dummett explicitly states he is not going to pursue the matter further, we can find earlier in the same essay a hint of just what might be going wrong with the mechanism of saying.

“I can make drawings of a rock from various angles, but if I am asked to say what the real shape of the rock is, I can give a description of it as in three-dimensional space which is independent of the angle from which it is looked at. The description of what is really there, as it really is, must be independent of any particular point of view. Now if time were real, then, since what is temporal cannot be completely described without the use of token-reflexive expressions, there would be no such thing as the complete description of reality. There would be one, as it were, maximal description of reality in which the statement ‘The event M is happening’ figured, others which contained the statement ‘The event M happened’,  and yet others which contained ‘The event M is going to happen’.”

I conjecture that the cause of the failure of the mechanism of saying is what might be called Radical Multiplicity. A radical multiplicity is one in which the different elements are not components of some over-arching whole. Objects in space are the classic example of an ordinary multiplicity. They can be regarded as the components of a spatially extended composite object. By contrast, if events in time are seen as parts of some B-theoretic (and hence spacelike) whole, then a key element of temporal phenomenology is lost. If we try to put it back by having the property of being present moving through the manifold, turning future into past, then we begin a regress or circularity.

The working of the mechanism of saying depends upon the assumption that after all the details have been included in the sentence type, the final two-fold distinction, between truth and falsity, can be indicated by simply displaying a token of the sentence to indicate truth. For this to work it has to be the case that the token either is or is not displayed. This assumption fails when the saying is done within a radical multiplicity. Within one element a sentence either is, or is not asserted, but elsewhere it may have another assertion status. We can not state that assertion takes place if a token is displayed within at least one of the elements, because this quantification over the elements assumes the existence of a totality; radical multiplicity is precisely the absence of this totality.

The interpretation of McTaggart’s result developed here can also be expressed in terms of the distinction between knowledge and understanding (see the essay entitled “Knowledge and Understanding”). The way time works (at least in situations where Galilean relativity is a good approximation) is known intimately by us, but when try to articulate this knowledge, as Augustine lamented, we run into unexpected difficulties. McTaggart seems to have proved that this is not just because we have not been good enough at philosophical analysis, but rather because, in the case of time, a full understanding, in the sense of articulation in language, is strictly impossible. We have a perfectly good way of sharing our knowledge about time, using residual depiction, and encounter difficulties only when, like Augustine, we try to say what it is we know.

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