We will explain, via the simple example of propositional logic, the process by which a well-behaved logic with a classical semantics may be given a generalized algebraic semantics, and then turned into a "syntactic algebra" forming the universal such semantics, which is then (in the best cases) recoverable from the space of all classical models equipped with suitable "dual" structure. Time permitting, we will briefly sketch how similar ideas can be carried over to first-order logic.