Abstract. — Precisifications of certain informal concepts could be thought of as instances of conceptual engineering: the concept of a Turing machine (human effective computability), the notion of a Kripke structure (possibility), the Kolmogorov axioms (probability), Tarski’s definition of truth in formal languages, to name just a few. Should we regard the technical notions these formalisms define as engineered concepts? In this talk I will present a critical view of the feasibility of conceptual engineering in logic and foundations of mathematics, drawing on a few key examples: the concept of “model,” which emerged slowly and under significant internal pressures; the concept of computability, and from my own work the concept of formalism independence/formalism freeness. The view taken here is that foundational formalisms such as these are not tracking conceptual change so much as invariant conceptual content. Time permitting, we venture into the sociology of mathematics as it bears on the control problem. Mathematicians are often resistant to new concepts (especially those coming from foundations). The bar may be set too high for conceptual engineering projects in mathematics if such projects do not deliver on conventional factors such as simplification (the complex number proof of the Fundamental Theorem of Algebra), establishing deep connections between mathematical subdisciplines (Hrushovski’s application of model-theoretic concepts to the Mordell-Lang Conjecture), the ability to prove new theorems (projective determinacy vis a vis regularity properties of the reals).

• Zoom meeting ID: 857 3025 53 80
• Zoom password: ACEW20 (Invite link)