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.
Highlights
Wittgenstein’s atomist picture provides us with an extremely elegant, combinatorial picture of modality
Possibilities are generated by combinations of atomic propositions, which are in turn generated by combinations of simples
I shall think of the possibilities as points in a logical space. (We can call these possibilities ‘possible words’, and call logical space ‘the possible universe’; nothing will turn on this terminology)
Summary
Wittgenstein’s atomist picture provides us with an extremely elegant, combinatorial picture of modality. Subject only to constraints on their logical types, any arbitrary recombination of simples yields an atomic proposition. : given an atomic proposition, a, replacing the (names for) simples in a with (names for) other simples of the same logical type yields another atomic proposition. These atomic propositions generate the possibilities in logical space, via two principles ([10]: 4.211, 4.26–4.28, 5.134): Modal-Valuationism. : any combinatorial possible assignment of truth values to atomic propositions yields a possibility. These three principles record the atomist picture. It provides an elegantly simple of logical space.
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