Any viable philosophy of mathematics must square with incontrovertible metamathematical results. Thus, as is well known, any version of formalism committed to identifying mathematical with provability in some formal system is to be rejected in light of Godel's first incompleteness theorem, according to which any consistent formal system capable of representing the primitive recursive numbertheoretic functions has an undecidable sentence. In fact, Godel showed how, given any such system, one could construct such a sentence which, on the standard interpretation of its symbols, makes a definite claim about natural numbers. Thus, either such a Godel sentence or its negation must be an truth, but neither is provable in the system for which it was constructed. Any formalist philosophy which respects arithmetical truth runs afoul of the first incompleteness theorem.' The impact of Godel's incompleteness theorems on logicism, however, is not so straightforwardly assessed. While there are independent grounds for regarding logicism (as conceived by Frege and Russell) as a lost cause, it remains instructive to examine the force of G6del's theorems in this quarter. In fact, a negative result (i.e., incompatibility of logicism with a metatheorem) could be quite powerful, especially if it does not depend on a particularly restrictive way of drawing the controversial line between logic and non-logic. The purpose of this note is to present precisely this kind of an argument: so long as logic is taken to be formalizable (i.e., logically valid formulas form a recursively enumerable set), a natural thesis of epistemological logicism is, modulo quite elementary assumptions, incompatible with Godel's second incompleteness theorem.2 However, for this argument, it needs to be assumed that the logicist system is to be finitely axiomatized. Extending the argument to the infinite case turns out to depend on a crucial step whose