David Corfield

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It is important to note that a presupposition made by all parties to these debates is the recognition of a distinction between gerrymandered concepts and those ‘good for the life of mathematics’, even if they disagree about where the boundary lies. Weil (1960) talks of sculpting from porphyry when working on analogies between function fields and number fields, and moulding with snow when giving axioms for uniform spaces. Philosophers cannot choose to ignore this difference. Following this lead they will encounter further questions: Is ‘good for the life of mathematics’ a mind-independent quality or connected to the ways in which our embodied minds work or have been trained to work? Are mathematicians engaged on a never-ending quest, or do we foresee the arrival at a terminus? Weil A. (1960) ‘De la Métaphysique aux Mathématiques’, in : Collected Papers (1979), Vol. 2, Springer-Verlag, 408-412.

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