Logic and time

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Abstract
‘In Time rigorous abstraction, in Time the highest, in Time divine knowledge, is comprehended’Atharva VedaFollowing McTaggart [17], we may distinguish two aspects of time: The A-series, running through the past to the present and on into the future, and the B-series, running from earlier to later. In Indo-European languages at least, verbs are tensed, so we cannot help but place whatever we speak of in one of the three divisions of the A-series. But these divisions are not permanent: what is present was future and will be past. Hence a typical statement, e.g. ‘Socrates is sitting’, may well be true at one time and false at another. The instability of truth-value over time was a commonplace among pre-Renaissance logicians, but most modern writers have ‘abstracted from’, i.e. ignored, this feature of ordinary language.Early logicians were quite interested in time: Aristotle questioned the applicability of the excluded middle to predictions of future contingencies in the famous ‘sea-fight’ passage of On interpretation. Later Greek logicians debated whether that which neither is nor will be can legitimately be called possible, and whether, in order for the conditional ‘if p, then q’ to be true, it is required that ‘not both p and not ∼q’ be true (not just now but) always. Mediaeval logicians in Western Europe struggled with logical difficulties created by the Dogmas of the Church, Omniscience and Free Will. Their counterparts in the Islamic world puzzled over the semantics of the temporal adverbs, ‘always’, ‘usually’, ‘often’, ‘sometimes’, ‘seldom’, ‘never’.

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