Single Idea 8744

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

Full Idea

The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.

Gist of Idea

Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own

Source

Stewart Shapiro (Thinking About Mathematics [2000], 5.1)

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.113


A Reaction

This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.