"Intuitionism and Model Theory:  Two Ways of Thought in the Foundations of Mathematics?"

Brouwerian intuitionism and contemporary classical model theory are generally, and rightly thought to be opposed approaches to the foundations of mathematics.  At the very least, Brouwer  rejected the formalization of mathematics that lies at the heart of model theory.  However, I will point to a paradox in intuitionistic mathematics whose solution requires attributing to intuitionism some ways of thought indigenous to model theory.  Having made this point, I will turn to the question of what then is the deep difference between these two approaches to the foundations of mathematics.  If there is time, I will suggest that this discussion bears on some broader issues beyond the foundations of mathematics. Though the first part of the talk mentions some technical notions, I will approach them heuristically and avoid technical details.