My most important recent effort has been the extensive collaboration with David Krantz, Duncan Luce and Amos Tversky in the writing of our two-volume treatise Foundations of Measurement , the first volume of which appeared in 1971. At the time of writing this autobiography, we are hard at work on Volume II. My present feeling is that when Volume II is published I shall be happy to let the theory of measurement lie fallow for several years. It is, however, an area of peculiar fascination for a methodologist and philosopher of science like myself. The solution of any one problem seems immediately to generate in a natural way several more new problems. The theory nicely combines a demand for formally correct and explicit results with the continual pursuit of analyses that are pertinent to experimental or empirical procedures in a variety of sciences but especially in psychology, where the controversy about the independent measurability of psychological concepts has been long and intense. The theory of measurement provides an excellent example of an area in which real progress has been made in the foundations of psychology. In earlier decades psychologists accepted the mistaken beliefs of physicists like Norman Campbell that fundamental measurement in psychology was impossible. Although Campbell had some wise things to say about experimental methods in physics, he seemed to have only a rather dim grasp of elementary formal methods, and his work in measurement suffered accordingly. Moreover, he did not even have the rudimentary scholarship to be aware of the important earlier work of Helmholtz, Hölder, and others.

The work of a number of people over the past several decades has led to a relatively sophisticated view of the foundations of measurement in psychology, and it seems unlikely that any substantial retreat from this solid foundation will take place in the future. I am somewhat disappointed that the theory of measurement has not been of greater interest to a wider range of philosophers of science. In many ways it is a natural topic for the philosophy of science because it does not require extensive incursions into the particular technical aspects of any one science but raises methodological issues that are common to many different disciplines. On the other hand, by now the subject has become an almost autonomous technical discipline, and it takes some effort to stay abreast of the extensive research literature.

Although important contributions to the theory of measurement have already appeared since we published Volume I of Foundations of Measurement , I do think it will remain as a substantial reference work in the subject for several years. What is perhaps most important is that we were able to do a fairly good job of unifying a variety of past results and thereby providing a general framework for future development or the theory.

Having mentioned the seminars of Tarski earlier. I cannot forbear mentioning that perhaps the best seminar, from my own personal standpoint, that I ever participated in was an intensive one on measurement held jointly between Berkeley and Stanford more than ten years ago when Duncan Luce was spending a year at the Center for Advanced Study in the Behavioral Sciences at Stanford. In addition to Luce and me, active participants were Ernest Adams, who is now Professor of Philosophy at Berkeley and was in the fifties my first PhD student, and Fred Roberts, who was at that time a graduate student in mathematics at Stanford and is now a member of the Department of Mathematics at Rutgers University. William Craig also participated on occasion and had penetrating things to say even though he was not as deeply immersed in the subject as were the rest of us. Our intensive discussions would often last well beyond the normal two hours, and it would not be easy to summarize all that I learned in the course of the year.

There is also a pedagogical point about the theory of measurement, related to what I have said just above about measurement in the philosophy of science, that I want to mention. The mathematics required for elementary examples in the theory of measurement is not demanding, and yet significant and precise results in the form of representation theorems can be obtained. I gave several such examples in my textbook in logic (1957a) and also in my paper ‘Finite Equal-interval Measurement Structures’ (1972d). I continue to proselytize for the theory of measurement as an excellent source of precise but elementary methodology to introduce students to systematic philosophy of science.