## Past, Present and Future

A. Prior. *Past, Present and Future*, Oxford University Press, 1967.

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#### Abstract:

This book gives a full account of the more informal aspect of symbolic tense-logic up to the time of writing, work which the author originated and has led in the last 15 years. Considerable reference is made to studies of time and tenses in previous logic, classical, medieval, and recent. A wide variety of calculi are introduced to investigate various problems. Fundamental technical problems, such as completeness proofs, are not dwelt on, but a fair amount of formal work is done. Chapter I reviews informal logic of tenses, particularly McTaggart on past-present-future and earlier-later. Chapter II reviews the solved problem of formalising Diodorean modality. Chapter III introduces two of the four main approaches to symbolising tense-logic: the calculi in the tense operators $P,G,H,F$ ("It has been the case that...", etc.), and the calculi in the relation $U$ between instants, within which $P,G,H,F$ can be handled. These calculi have intended interpretations in terms of time. Here and in Chapter IV the particular calculi corresponding to particular assumptions about time are discussed. (The relevant formal results of Cocchiarella, Lemmon and Scott, etc., are summarised in an appendix.) Chapter V is about the logic of "world-states". In Chapter VI the third main approach, metric tense-logic with operators such as $Fn$ ("It will be the case after an interval $n$ that..."), is introduced, and tentative postulates put forward. In Chapter VII determinism is discussed. A modal operator $L$ for "It is now-unpreventably the case that..." is introduced, and asymmetry between past-tense and future-tense expressions is set up. This is done in two ways, corresponding to two counters to Diodorus' "master argument". Intended interpretations in terms of branching time are given. Chapter VIII looks at the extending of tense-logic to include predicates and individual quantifiers, and the difficulties that arise. This book is a thorough survey of a field of symbolic logic of growing importance; it will be stimulating to those working with either traditional problems or contemporary mathematical techniques in logic.

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@BOOK{prior67:_past_presen_futur, title = {Past, Present and Future}, publisher = {Oxford University Press}, year = {1967}, author = {A. Prior}, abstract = { This book gives a full account of the more informal aspect of symbolic tense-logic up to the time of writing, work which the author originated and has led in the last 15 years. Considerable reference is made to studies of time and tenses in previous logic, classical, medieval, and recent. A wide variety of calculi are introduced to investigate various problems. Fundamental technical problems, such as completeness proofs, are not dwelt on, but a fair amount of formal work is done. Chapter I reviews informal logic of tenses, particularly McTaggart on past-present-future and earlier-later. Chapter II reviews the solved problem of formalising Diodorean modality. Chapter III introduces two of the four main approaches to symbolising tense-logic: the calculi in the tense operators $P,G,H,F$ ("It has been the case that...", etc.), and the calculi in the relation $U$ between instants, within which $P,G,H,F$ can be handled. These calculi have intended interpretations in terms of time. Here and in Chapter IV the particular calculi corresponding to particular assumptions about time are discussed. (The relevant formal results of Cocchiarella, Lemmon and Scott, etc., are summarised in an appendix.) Chapter V is about the logic of "world-states". In Chapter VI the third main approach, metric tense-logic with operators such as $Fn$ ("It will be the case after an interval $n$ that..."), is introduced, and tentative postulates put forward. In Chapter VII determinism is discussed. A modal operator $L$ for "It is now-unpreventably the case that..." is introduced, and asymmetry between past-tense and future-tense expressions is set up. This is done in two ways, corresponding to two counters to Diodorus' "master argument". Intended interpretations in terms of branching time are given. Chapter VIII looks at the extending of tense-logic to include predicates and individual quantifiers, and the difficulties that arise. This book is a thorough survey of a field of symbolic logic of growing importance; it will be stimulating to those working with either traditional problems or contemporary mathematical techniques in logic. } }

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