Solving the proper problem : Wittgenstein, fictionalism and the applicability of mathematics
This thesis proposes a solution to the problem motivating Albert Einstein's question, 'How can it be that mathematics âŠ is so admirably appropriate to the objects of reality?'; the problem of mathematical applicability. It considers Mark Steinerâs anthropocentric non-naturalist attitude to the problem in the light of Hartry Field's fictionalism, contending that Field's proposed solution, though prima facie naturalist in character, in fact inherits non-naturalist commitments which were problematic in anthropocentric solutions. Specifically, Field's solution retains a view of the grammar of our mathematical expressions as based on the model of object-and-designation. However, Field finds importance in the notion that what mathematicians know is non-propositional in the sense of being concerned with inference rules rather than assertions of existence, and a way of exorcising the rogue grammatical commitment in question from the fictionalist account can develop from a focus on this aspect of our talk about mathematics tout court rather than just epistemologically. The view that emerges when we do this, in the first instance enables a naturalistic and wholly adequate solution to the problem of mathematical
Clark, Robert
Solving the proper problem : Wittgenstein, fictionalism and the applicability of mathematics. This thesis proposes a solution to the problem motivating Albert Einstein's question, 'How can it be that mathematics âŠ is so admirably appropriate to the objects of reality?'; the problem of mathematical applicability. It considers Mark Steinerâs anthropocentric non-naturalist attitude to the problem in the light of Hartry Field's fictionalism, contending that Field's proposed solution, though prima facie naturalist in character, in fact inherits non-naturalist commitments which were problematic in anthropocentric solutions. Specifically, Field's solution retains a view of the grammar of our mathematical expressions as based on the model of object-and-designation. However, Field finds importance in the notion that what mathematicians know is non-propositional in the sense of being concerned with inference rules rather than assertions of existence, and a way of exorcising the rogue grammatical commitment in question from the fictionalist account can develop from a focus on this aspect of our talk about mathematics tout court rather than just epistemologically. The view that emerges when we do this, in the first instance enables a naturalistic and wholly adequate solution to the problem of mathematical
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