Is Hume’s Principle Analytic?
There are a number of issues on which Crispin Wright and I disagree, some of them substantive and some merely terminological. For example, we disagree over whether the term “analytic” can be suitably applied to HP and whether a derivation of arithmetic from HP would establish a doctrine appropriately called “logicism.” I also have certain reservations, which I shall set out later, about his notions of explanation and reconceptualization. However, I think the areas of agreement about the interest of Frege’s derivation of arithmetic are both wide-ranging and far more significant than those of disagreement. In particular I want to endorse Wright’s closing suggestion that “the problems and possibilities of a Fregean foundation for mathematics remain [wide?] open” and the remark made earlier in his paper that “The more extensive epistemological programme which Frege hoped to accomplish in the Grundgesetze is still a going concern.” I also want to emphasize that I consider Wright to have made a great scientific contribution in showing contemporary readers how the deduction of the Peano postulates from HP could be carried out and in formulating the conjecture, subsequently verified, that HP is consistent.
KeywordsAnalytic Truth Ontological Commitment Cardinal Number Logical Truth Natural Reading
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