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to Pacific Philosophical Quarterly, School of Philosophy, University of Southern nia, 90007, U.S.A. ..... Congress, Dalhousie, June 1981. 6 G.W.F. von Leibniz, ...
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'PHILOSOPHICAL \bl. 63, No. 2 April 1982

· Papers presented at the Society for Exact Philosophy Conference held in May 1 at Dalhousie University, Halifax, Nova Scotia. Guest Editor: Peter K. Schotch ~~~,~~~''X

a Philosophy of Becoming from Modern Physics

Richard T. W. Arthur 101

Are Novel Predictions Important?

Richmond Campbell and Thomas Vinci Ill Gary M. Hardegree 122

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1955 Axiomatization of Probability

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R. E. Jennings 146

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Hugues Leblanc 133

Infinitesimals .:;niSIUnlll

Robert P. McArthur 157 S. K. Thomason 168

Languages Via Alasdair Urquhart 186

than Late: On the Logical of the Thmporal Order

J ohan van Benthem 193

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BECOMING FROM MODERN PHYSICS BY

RICHARDT. W. ARTHUR

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The Society for Exact Philosophy in Halifax received support from the Social Sciences and Humanities Research Council of Canada. We wish to express our appreciation for that support.

seems to me an extraordinary fact that, in the longstanding dispute over the objectivity of becoming, exact philosophers have, almost without exception, come down against. As far as Western philosophy is concerned, of course, this side-taking began at the beginning when Parmenides and Zeno of Elea sharpened their emerging analytical abilities at becoming's expense. McTaggart and the early Russell one might also place in this tradition. But one would hardly expect modern philosophers of physics, whose disposition, after all, is more Ionian than Eleatic, to be similarly opposed; yet ranged against the objectivity of becoming we can find quotations from Einstein, Minkowski and Weyl, and explicit opposition from Gooel, Griinbaum, Smart, Putnam and, in their wake, the majority of modern philosophers of science. 1 But if I am right one of the main reasons for this opposition lies in the vagueness the expositions of becoming given by its proponents, and it is this deficiency I shall attempt to redress here.

Temporal Becoming First it is necessary to relate our subject to the theory of time. Now becoming

•is usually conceived in the form of a "tide" sweeping from past to future: that has become is in the past, everything that is yet to come is in future, and the set of things or events that is in the present marks the ever:«:lumgiing border between the two. But there are insuperable problems with this account. In the frrst place, as Russell, Griinbaum and others have argued,2 the conception of a