Hulse, Ian; (1998) Hume's Principle exhumed. Masters thesis (M.Phil), UCL (University College London).

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Abstract

This study is a critique of Fregean Platonism as advanced by Crispin Wright and Bob Hale. Fregean Platonism is founded upon an argument that purports to attain three objectives. The first of these is to explain why the natural numbers are not epistemologically suspect in the ways supposed by nominalists, i.e. to show how we can acquire the concepts required to form beliefs about the natural numbers, how we can refer to them and how we can know about them. The second objective is to demonstrate the existence of the natural numbers, construed as Fregean Objects. The third is to found number-theoretic logicism. This study is concerned with the success of the argument only with respect to the first two objectives. The argument makes crucial use of a certain sentence, Hume's Principle (HP). (HP) is the statement that the number of F's equals the number of G's if and only if the F's can be bijectively mapped to the G's (for any concepts F and G). Two readings of the argument are distinguished. The first takes (HP) to be a contextual explanation of the concept natural number. It is argued that the argument on its first reading fails, that (HP) cannot successfully explain the concept natural number. Derivatively, it fails to demonstrate the existence of the natural numbers. No firm conclusion is reached with respect to the argument on its second reading. It is argued that (HP) is apriori under Christopher Peacocke's analytic theory of the apriori and that this might be used to overcome objections to the analyticity (hence, apriority) of (HP) suggested by George Boolos.

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