Full Idea
I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology.
Gist of Idea
Mathematics and logic have no border, and logic must involve mathematics and its ontology
Source
Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.-17
A Reaction
I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics.