Is Logic Empirical? - Hans Reichenbach

Hans Reichenbach

Reichenbach considered one of the anomalies associated with quantum mechanics, the problem of complementary properties. A pair of properties of a system is said to be complementary if each one of them can be assigned a truth value in some experimental setup, but there is no setup which assigns a truth value to both properties. The classic example of complementarity is illustrated by the double-slit experiment in which a photon can be made to exhibit particle-like properties or wave-like properties, depending on the experimental setup used to detect its presence. Another example of complementary properties is that of having a precisely observed position or momentum.

Reichenbach approached the problem within the philosophical program of the logical positivists, wherein the choice of an appropriate language was not a matter of the truth or falsity of a given language – in this case, the language used to describe quantum mechanics – but a matter of "technical advantages of language systems". His solution to the problem was a logic of properties with a three-valued semantics; each property could have one of three possible truth-values: true, false, or indeterminate. The formal properties of such a logical system can be given by a set of fairly simple rules, certainly far simpler than the "projection algebra" that Birkhoff and von Neumann had introduced a few years earlier. However, because of this simplicity, the intended semantics of Reichenbach's three-valued logic is unsuited to provide a foundation for quantum mechanics that can account for observables.