Formalism and Structuralism, a Synthesis: the Philosophical Ideas of H. B. Curry.

The call for the conference “The Emergence of Structuralism and Formal- ism” contrasts formalism, which it describes as the manipulation of meaningless symbols, with structuralism, which it describes as treating mathematics as a subject with a subject matter. H. B. Curry identified himself as a formalist, probably because of the in- fluence of David Hilbert (under whose direction he earned his doctorate in 1928–29), but believed that all mathematical statements have a definite subject matter. What really distinguished Curry’s views is that he thought that the only subject matter that mathematics has is generated by mathematics itself. This might lead to a view that we humans are programmed to engage in some mathematical activity, and this is where mathematics starts. I believe that Curry is better considered to be a kind of structuralist than a formalist the way those words are used today.

Authors

• Jonathan P. Seldin

Keywords

• Formalism
• Structuralism