Mereology in Philosophy of Mathematics

Por • 29 sep, 2014 • Sección: Leyes

Geoffrey Hellman

There is a surprising variety of programs in the philosophy and foundations of mathematics that have found mereology a useful and, in some cases, an indispensable tool. After emphasizing a number of key relevant features of mereology, we will brie.y examine four such programs, including (1) Goodman and Quine.s efforts to recover syntax of mathematical language as part of a .nitist, formalist philosophy of mathematics; (2) Field.s and Burgess.»synthetic mechanics» as an effort to recover nominalistically certain applications of mathematics in physics inspired by synthetic geometry; (3) Lewis.attempt to ground set theory on a combination of mereology and plural logic, which he called «megethology» (theory of size); (4) Hellman.s modal-structuralism employing the same machinery as (3) together with modal logic, but to provide an eliminative structuralist alternative to platonist, face-value readings of abstract mathemtical theories.

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