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By an extensional logic I mean a logic satisfying the following two requirements: a) all connectives are extensional, i.e., the truth-values of compound statements formed by means of them depend only on the truth-values, not the meanings, of the component statements; b) any two predicates of equal extension, no matter how different their meanings, are mutually substitutable in any context.

One of the striking differences between natural languages, both conversational and scientific, and the extensional languages constructed by logicians is that most conditional statements, i.e., statements of the form “if , then ,” of a natural language are not truth-functional. A statement compounded out of simpler statements is truth-functional if its truth-value is uniquely determined by the truth-values of the component statements.

The question chosen as title of this paper may strike the reader as peculiar. For it is often said that an operational definition of a concept is a definition in terms of operations of measurement. To be an operationist, many scientists would say, is to insist that scientific concepts be made precise and empirically applicable by defining them in terms of measuring operations. Does it not follow, then, that, if any concepts are operationally definable, then concepts of physical magnitudes are? However, the widely used term “operational definition” needs clarification. I shall specify in the course of this paper a sense in which such terms as “length,” “mass,” “temperature,” etc. are not operationally definable insofar as they enter into the mathematical formulation of physical laws; but I will also specify a sense in which they must be operationally definable if they are to have any physical significance.

Arthur Pap was born on 1 October 1921 in Zürich, Switzerland. His father was a successful businessman. Pap’s talent in music showed early. For a while, he studied with the classical pianistWalther Frey. During his gymnasium (high school) years, Pap developed a passion for philosophy, with a primary interest in Hegel and (neo-)Kantian speculative philosophy. While studying at Zürich University, he took some courses in philosophy and logic from Karl Dürr.

Remembering the life of Arthur Pap it is necessary to rely on his recounting of his early life in Europe. He spoke quite vividly of his childhood, education, emigration and early years in the U.S. I also remember vividly what he told me about those years, and in these notes have striven for authenticity–there is no invention and where speculating, I have said so. We first met in spring of 1946 when I was his student–an appreciative but lazy auditor–in an introduction to philosophy course at Columbia; we married in June of that year.

Reprints of parts of Pap’s major publications are not included. Citations of Pap’s works throughout this volume are made, not to this bibliography, but to the References for the entire volume.