Outlines of a Formalist Philosophy of Mathematics

by Haskell B. Curry

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Genres: Philosophy

Hardcover

First published January 1, 1970

Reviews

[Lucille Nguyen · Rating 5 out of 5]

Every so often, when I find myself wondering what exactly I am doing when I am doing mathematics, I refer back to Haskell Curry's book. A short treatise of only 80 pages in length, it sketches out mathematics as the study of structure and formal systems as such, and delegates the issue of logic and mathematics and definitional.

Hilbert's formalism may have been dealt a death blow by Godel, but the formalism of Curry is more that of a structuralist of Benacerraf or Shapiro. It bears asking what exactly these structures and relations we seek are. As Curry writes: "Mathematics is the science of formal systems," though in his later work he might have said that it is more the science of formal methods. What is the nature of those structures, those methods, these systems? That has driven the structuralist schools over the last few decades, from in re to ante rem to Benacerraf's eliminative post rem structuralism.

And to think that it all of this could be contained in a thin little book.