Hilary Putnam' has recently proposed that a reconception of the logic embodied in quantum theory permits a consistent, realistic interpretation of the quantum formalism. Putnam also argues that the adoption of a quantum logic eliminates the paradoxes of measurement in quantum theory. If he is correct, then a great deal of what has been written about the interpretation of quantum mechanics and the epistemology of logic is wrong. Our aims are to provide a formal semantic framework for Putnam's proposals, to investigate alternative ways of realizing his program, and to come to some tentative conclusions concerning the promise and significance of the enterprise.