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.
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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 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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