Titlebook: Wittgenstein, Mathematics and World; Bob Clark Book 2017 The Editor(s) (if applicable) and The Author(s) 2017 Mathematics.Wittgenstein.Ein

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Fictionalism,ertions. This needs careful unpacking, and this chapter is possibly the most technically demanding part of the book philosophically and logically. A key notion in contemporary philosophy of mathematics is that of .. In short, the idea is that science—particularly contemporary physics—is . mathematic

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Infinity and Concept-Determination,es clear. Returning to the main thread and looking at the notion of ., the chapter then investigates two specific ways this latter notion has been treated historically as part of mathematics. One of these ways, due to Georg Cantor, is relatively well-known, as perhaps is Wittgenstein’s own criticism

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The Logical ,,e says might seem to lead him to a conventionalist view of mathematics, thereby denying the necessary nature of mathematical claims. Michael Dummett, in his review of Wittgenstein’s ., famously saddled Wittgenstein with an extreme kind of conventionalism about mathematics; in fact Dummett labelled W

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The Problem Solved,e chapter moves on from this example to relate this illumination, together with the work covered in earlier chapters, to a specific contemporary dialogue between two distinguished philosophers of mathematics, Mary Leng and John Burgess. The dialogue centres on some work of Rudolf Carnap, and a disti

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lay their eggs in water, and are called Anamniota because the embryo is not so protected. Finally, a distinction can be made between the fishes and the tetrapods, the former with fins and the latter with pentadactyl limbs. Distinctions based on the amnion or the limbs emphasize the essentially aquat

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