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McTaggart's Paradox: Two Parodies

  • Kenneth Rankin (a1)
Abstract

To be truly provocative and outrageous the superior philosophical sophistry will commonly possess four somewhat adventitious features. I shall rate it as classic if it has all four. First, and least adventitiously, the argument will be crisp and initially seductive. Second, by the standard the sophistry sets direct rebuttal will be laborious and diffuse. Third, the recipe for the latter will prescribe that we pick out some hitherto unarticulated logical principle (e.g. ‘Existence is not a real predicate’) such that if the principle be true then the sophistical argument must be invalid, and then, on the strength of that consequence assume the principle to be true. Consequently and fourth, as an antidote parody is supreme. With a persuasive absence of fuss and bias we can turn the tables if we show that, if the sophistical argument were really valid, then some structurally similar argument would prove just as consummately far too much. In short, from the rhetorical point of view at least, Gaunilo is more lethal than Kant. Even if the similarity is defective, the sophist will lose some of his adventitious and insufferable poise, if he ventures to show why.

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1 There are two versions of McTaggart's paradox. The first appeared in ‘The Unreality of Time’, Mind, New Series, No 68 (October 1908), reprinted in Sherover, The Human Experience of Time (New York, 1975), 278–296. The second occupies a pivotal position in his major opus The Nature of Existence (Cambridge University Press, Vol. 1, 1921, Vol. 2, 1927). The latter is the primary object of analysis in this paper, and all sectional references throughout are to it. However I shall discuss the bearing of the first version upon the second in further footnotes. For comments on the difference between the two versions see also Sanford David, ‘McTaggart on Time’, Philosophy 53 (1968). I am grateful to Dr Robert Fahrnkopf for drawing Sanford's paper to my attention.

2 For an assessment of this part of his project see my paper forthcoming in Dialogue, ‘McTaggart, Mereology, Substance and Change’.

3 In the Mind article (see footnote 1) McTaggart drew a distinction between a vicious circle and a vicious regress, both alleged to be implicit in the direct rebuttal. Of the two forms of vice, it is the latter that comes closest to the regress he adduces in the book. He argues that ‘[i]f we avoid the incompatibility of the three characteristics by asserting that M is present, has been future, and will be past, we are constructing a second A-series, within which the first falls in the same way in which events fall within the first’ (Sherover, op. cit., 291). He then proceeds to cast doubt on the intelligibility of this and further regresses of A-series before objecting, as in the book, that it removes the contradiction from one place only to transfer it to another. In the book, on the other hand, there is no attempt to represent the regress as a regress of A-series. It is, however, in the other charge of vice that the major difference between the two versions lies. The rebuttal he says (in the article) is viciously circular because ‘it assumes the existence of time in order to account for the way in which moments are past, present and future’ (Sherover, op. cit., 290). He can argue in this way here only because he has already defined time in terms of the A-series and a further C-series, whereas in the book a similar definition is introduced only later (§ 348).

4 For a further discussion of vicious regress see my ‘The Duplicity of Plato's Third Man’, Mind (April 1969).

5 In ‘The Tenses of Verbs’ in his Elements of Symbolic Logic (Macmillan, 1947). See also Prior's Arthur further comments in Past, Present and Future, Chap. I (Oxford: Oxford University Press, 1967).

6 However, he does seem to take exception to the iterativeness of iteration in so far as in his article (see footnote 3) he represents the iterativeness of A-determinations as a proliferation of A-series, and goes on to remark ‘It may be doubted whether any intelligible meaning can be given to the assertion that time is in time’ (Sherover, op. cit., 291).

7 One consideration leading him to suppose this is less to the fore in the book than at the point in the article (see footnote 3) where he argues that the direct rebuttal is viciously circular. The reason he gives for that allegation there is ‘that the A-series, together with the C-series, is sufficient to give us time’ (Sherover, op cit., 290). The suggestion appears to be in what follows that it is only in application to the C-series that the A-series acquires tense.

8 See Broad C. D., An Examination of McTaggart's Philosophy, Vol. II, Part I (Cambridge University Press, 1938), 3. 11, and Christensen Ferrel, ‘McTaggart's Paradox and the Notion of Time’, The Philosophical Quarterly 24, No. 97 (10 1974).

9 E.g. Dunne J. W. in An Experiment with Time (London: Faber, 1927).

10 E.g. Russell in ‘On the Experience of Time’, Monist 25 (1915), and Smart J. J. C., ‘The River of Time’, Mind (1949) reprinted in Essays in Conceptual Analysis, A. G. N. Flew (ed.) (London: Macmillan, 1956).

11 Those acquainted, as I had yet to be, with George Schlesinger's ingenious reconstruction of the paradox in Chapter III of his stimulating book Aspects of Time (Hackett, 1980) may wonder whether this disclaimer is the effect of backwards causation. Schlesinger motivates the Basic Paradox by postulating that basically events are instantaneous. That, indeed, is McTaggart's own view. Consequently: (I) the successive instantiation by a basic event E of futurity, Presentness and pastness at M1, M2, and M3 respectively cannot exempt it from contradiction in quite the same way as more standardly the successive instantiation by a temporally extended entity of contrary properties, e.g. heat and cold by a poker, exempts it from contradiction. Thus E cannot be future in the first of three successive temporal parts, present in the next, and in the last part past. Instead, Schlesinger infers: (2) the successive instantiation these three A-determinations must be reducible to three B-relationships respectively, viz. E's being after M1, simultaneous with M2 and before M3, in the conjunction of which there is no contradiction. However: (3) with this result McTaggart cannot rest, holding as he does that without A-change there can be no time at all. Hence: (4) each of the three B-relationships has in turn to instantiate successively all three A-determinations, thus creating the need to avoid contradiciton anew and regressively. This novel suggestion, however, will do neither as an interpretation, nor a validation, of McTaggart's actual argument. The latter expressly precludes step (2) by denying (a) that A-terms are definable and (b) that the regress arises form the impossibility of defining them without using the terms in their own definition. Furthermore, to avoid contradiction, the iterativeness of A-determinations can be invoked, instead of step (2), without requiring E to by temporally extended.

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Philosophy
  • ISSN: 0031-8191
  • EISSN: 1469-817X
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