Abstract: From the beginning, much of Tarski's work in logic was motivated by a preference for "mathematical", or "very mathematical" definitions of logical concepts, over metamathematical ones. Fraisse's characterization of elementary equivalence by means of a "purely mathematical" definition, as Tarski called it, is one example. Vaught suggests in his account of Tarski's work in model theory [1], that Tarski's guiding principle, as we will call it, resting as it does on the distinction between the "purely mathematical" and the metamathematical, may not have a precise content, "as a precise distinction between "mathematical" and "metamathematical" might well be considered to be impossible because of Tarski's definition of truth."
In this talk I will suggest that Vaught's remark has interesting foundational implications, both for any consideration of Tarski's own view and in terms of the wider foundational ramifications.
[1] Alfred Tarski's Work in Model Theory, The Journal of Symbolic Logic, Vol. 51, No. 4 (Dec., 1986), pp. 869-882