Journal Article

Infinite Sequences: Finitist Consequence

Martin C. Cooke

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 54, issue 4, pages 591-599
Published in print December 2003 | ISSN: 0007-0882
Published online December 2003 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/54.4.591
Infinite Sequences: Finitist Consequence

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A simultaneous collision that produces paradoxical indeterminism (involving N0 hypothetical particles in a classical three-dimensional Euclidean space) is described in Section 2. By showing that a similar paradox occurs with long-range forces between hypothetical particles, in Section 3, the underlying cause is seen to be that collections of such objects are assumed to have no intrinsic ordering. The resolution of allowing only finite numbers of particles is defended (as being the least ad hoc) by looking at both ω-sequences (in the context of a very basic supertask, in Section 4) and ω*-sequences (reversed ω-sequences, in the form of paradoxical results from the recent literature).

Introduction

The simultaneous collision

The paradox in other contexts

The basic problem is N0 things

The recent literature

Generating N0 things

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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