This talk will bear on three topics: the analysis of feasible computability, vagueness, and strict finitism as a philosophy of mathematics. Dean will begin by reviewing some facts about proof theoretic speed-up and Parikh's notion of an almost consistent theory which were originally inspired by Dummett's paper "Wang's Paradox".  After this, Dean will suggest that reactions to strict finitism point towards a semantics for vague predicates in the form of non-standard models of weak (bounded) arithmetical theories of the sort originally introduced to characterize the notion of feasibility as understood in computational complexity theory.  Such an approach eschews the use of non-classical logic and related devices like supervaluation while also being compatible with classical model theory of the sort widely employed in natural language semantics. Time permitting, Dean will discuss applications of measurement theory (in the sense of Krantz et al. 1971) to vagueness in the non-standard setting.