Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics.In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources.Both versions of logicism—strong and weak—maintain that in expressing them; or, as Kant might have preferred it, by virtue of internal relations among the concepts involved.
Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal.
It will be recognized as the most powerful presentation yet of a neo-Fregean program.
doctrine that can be advanced with respect to any branch of mathematics.
Another consequence of successful logicist reduction of a given branch of mathematics is that mathematical certainty (within that branch) is of a piece with certainty about logical truth.
The same holds for necessity; and for the character of the knowledge concerned.