Logical and Epistemic Modality

This essay examines the interaction between the project of metamathematics and the cognitive science of concepts. The aim of metamathematics, i.e., the methodology of the deductive sciences, is to provide a precise characterization of the concepts figuring in rigorous, formal theories (Tarski, 1930/1983). The concepts at issue include those familiar frommetalogical inquiry – e.g., completeness and categoricity – as well as formal concepts admitting material conditions on their satisfiability, such as the concept of truth. The philosophical significance of the examination is that – while many formal properties can be readily accommodated within cognitive-scientific theories of mental representation, by, e.g., enriching the expressive resources of the languages in which the properties are defined – there are some ineliminable metamathematical concepts, the ontological commitments of which would appear to be more demanding. Whereas most concepts in the methodology of the deductive sciences are consistent with the extensional characterization of the mathematical languages at issue, the latter, ontologically inflationary metamathematical notions can be distinguished e.g. by their constitutively intensional properties. In this essay, I examine, in particular, the interaction between the philosophy See also the project of reverse mathematics pursued by Friedman (1975/ms) and Simpson (1999).