The interaction between intuitions about inference, and the normative constraints that logical principles applied to mechanically-recognizable derivations impose on (informal) inference, is explored. These intuitions are evaluated in a clear testcase: informal mathematical proof. It is argued that formal derivations are not the source of our intuitions of validity, and indeed, neither is the se...

The nexus of predication is accounted for in di¤erent ways in di¤erent theories of universals. We brie‡y review the account given in nominalism, logical realism (modern Platonism), and natural realism. Our main goal is to describe the account given in a modern form of conceptualism extended to include a theory of intensional objects as the contents of our predicable and referential concepts.