Is Logic Empirical?

"Is Logic Empirical?" is the title of two articles (one by Hilary Putnam and another by Michael Dummett) that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of reality. The replacement derives from the work of Garrett Birkhoff and John von Neumann on quantum logic. In their work, they showed that the outcomes of quantum measurements can be represented as binary propositions and that these quantum mechanical propositions can be combined in a similar way as propositions in classical logic. However, the algebraic properties of this structure are somewhat different from those of classical propositional logic in that the principle of distributivity fails. The idea that the principles of logic might be susceptible to revision on empirical grounds has many roots, including the work of W. V. Quine and the foundational studies of Hans Reichenbach. What is the epistemological status of the laws of logic? What sort of arguments are appropriate for criticising purported principles of logic? In his seminal paper "Two Dogmas of Empiricism," the logician and philosopher W. V. Quine argued that all beliefs are in principle subject to revision in the face of empirical data, including the so-called analytic propositions. Thus the laws of logic, being paradigmatic cases of analytic propositions, are not immune to revision. To justify this claim he cited the so-called paradoxes of quantum mechanics. Birkhoff and von Neumann proposed to resolve those paradoxes by abandoning the principle of distributivity, thus substituting their quantum logic for classical logic. Quine did not at first seriously pursue this argument, providing no sustained argument for the claim in that paper. In Philosophy of Logic (the chapter titled "Deviant Logics"), Quine rejects the idea that classical logic should be revised in response to the paradoxes, being concerned with "a serious loss of simplicity", and "the handicap of having to think within a deviant logic".