The mathematics of McTaggart's paradox

Manuscrito 35 (2):233-67 (2012)
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Abstract

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

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References found in this work

A Theory of Conditionals.Robert Stalnaker - 1968 - In Nicholas Rescher (ed.), Studies in Logical Theory. Oxford,: Blackwell. pp. 98-112.
Elements of symbolic logic.Hans Reichenbach - 1947 - London: Dover Publications.
The unreality of time.John Ellis McTaggart - 1908 - Mind 17 (68):457-474.
Tense and reality.Kit Fine - 2005 - In Modality and Tense: Philosophical Papers. Oxford, England: Oxford University Press. pp. 261--320.
Real Time.David Hugh Mellor - 1981 - British Journal for the Philosophy of Science 34 (2):197-200.

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