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Boolos, G. and Heck, R. [1998] “Die Grundlagen der Arithmetik §82–83”, in Boolos [1998]: 315–338. Burgess, J. [1984], Review of Wright [1983], Philosophical Review 93: 638–640. Clark, P. [2004], “Frege, Neo-logicism and Applied Mathematics”, in Stadler [2004]: 169–183, reprinted below as chapter 3. Cook, R. [2002], “The State of the Economy: Neologicism and Inflation”, Philosophia Mathematica 10: 43–66, reprinted below as chapter 12. Cook, R. [2003], “Aristotelian Logic, Axioms, and Abstraction”, Philosophia Mathematica 11: 195–202, reprinted below as chapter 9.

It is essential to the proof of Frege’s theorem that octothorpe be so construed. Thus octothorpe denotes a total function from concepts to objects. x #F = x is true. It will not guarantee that HP is. HP entails, as Wright has put it with exemplary force and Cartesian clarity, that there is a partition of concepts into equivalence classes, in which two concepts belong to the same class if and only if they are equinumerous. If there are only k objects, k a finite number, then, since there are k + 1 natural numbers ≤ k, there will be k + 1 equivalence classes, viz.

147–170. 9 Is Hume’s Principle Analytic? “extension” may mean, the extension of the Fs is the extension of the Gs; and (c) if the antecedent holds, then the concepts Fand G bear a relation to each other that Frege called the analogue of identity. Thus under each of three familiar systems of formula-evaluation, Vb can never turn out false. In the case of both HP and Basic Law V, we have a principle whose left-to-right half requires that there be a function from concepts to objects respecting certain non-equivalences of those concepts.