The Axiomatic Method in the Empirical Sciences'

l. Introduction. My original intention was to give a talk primarily on the theory of models as applied to the theory of measurement in the empirical sciences. Conversations with Tarski earlier in the symposium changed my mind. We agreed that it would be desirable to have a survey, even if superficial, of the place of the axiomatic method and the theory of models in the empirical sciences. And so my present intention is to attempt such a survey. I recognize the difficulties, and consequently, ask in advance for your indulgence. The survey will necessarily be idiosyncratic-restricted to those topics I know something about. I shall begin with measurement, go on to physics and end with natural language. Throughout I shall try to emphasize open problems. Before I begin, however, I want to record my own intellectual indebtedness to Alfred Tarski, both directly and indirectly. Not long after coming to Stanford in 1950, I began to attend Tarski's seminar in Berkeley. In 1951 J. C . C . McKinsey joined the faculty at Stanford, and in 1952 I taught a course in the philosophy of science at Berkeley, which included as undergraduate students Richard Montague and Dana Scott. The years of close contact with McKinsey and Scott have been of permanent significance to me, and it is fair to say both of them were probably influenced more by Tarski than by anyone else. When McKinsey and I first began to think about working on the axiomatic foundations of physics in 1951, we discussed our plans and line of attack with Tarski on more than one occasion, and his sympathetic advice and support were important to both of us. It is a pleasure to record on this most appropriate occasion my debt to Alfred Tarski and the value I place on our friendship of many years.