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Exclusion Problems and the Cardinality of Logical Space

Button, T; (2017) Exclusion Problems and the Cardinality of Logical Space. Journal of Philosophical Logic , 46 (6) pp. 611-623. 10.1007/s10992-016-9412-z. Green open access

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Abstract

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended (in principle) in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability (in principle) of the atomist picture. The condition is: logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss (2012), which goes back to Carruthers (1990: 144–7). And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many.

Type: Article
Title: Exclusion Problems and the Cardinality of Logical Space
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10992-016-9412-z
Publisher version: https://doi.org/10.1007/s10992-016-9412-z
Language: English
Additional information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: Atomist picture · Logical space · Colour-exclusion · Color incompatibility · Logical independence · Tractarian metaphysics · Ludwig Wittgenstein · Tractatus Logico-Philosophicus · Sarah Moss
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy
URI: https://discovery.ucl.ac.uk/id/eprint/10085871
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