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Conversation with Stewart Shapiro

di Sebastiano Moruzzi, Andrea Sereni

Stewart Shapiro (1951) insegna presso la Ohio State University, ed è uno dei massimi esponenti della filosofia della matematica e della filosofia della logica contemporanee. In filosofia della matematica è noto per la sua originale versione di strutturalismo. In filosofia della logica, è noto per le sue analisi sulla logica del secondo ordine e sulla nozione di conseguenza logica. Abbiamo intervistato Shapiro in occasione di una sua recente visita in Italia, chiedendogli di raccontarci della sua formazione filosofica e di soffermarsi sugli aspetti principali della sua vasta produzione filosofica.

1. Prof. Shapiro, you are one of the leading philosophers in contemporary philosophy of mathematics and philosophy of logic. Beside being the author of some essential books and a vast number of papers on these fields, you are one of the main proponents of the view known as structuralism, and you have suggested original views concerning, for instance, second-order logic and vagueness. We assume that your interest in these issues comes from your studies in Buffalo with John Corcoran. Would you help our readers understanding how you decided to get involved professionally in these areas of philosophy, which colleagues or philosophers inspired or guided you in making this choice, and why you decided to be a philosopher in the first place?

SS. Although it has been a long time, and my memory is not very reliable, I'll begin with the last question. Even as a small boy, I was attracted to mathematics – I was something of a nerd. Way back in junior high school, I stumbled onto some popular works describing advanced mathematics, and was immediately hooked. I was profoundly fascinated by the notion of rigorous proof, with the very idea that through careful reasoning, one can (apparently) decide the truth of some proposition, putting it beyond all doubt. My seventh-grade mathematics teacher, Samuel Traficant, was most encouraging, giving me literally hours of his time after school. During high school, I attended a National Science Program in mathematics, held each summer here at Ohio State University. It was directed by Arnold Ross, a wonderful teacher and leader. At this program, there was a course in mathematical logic, taught by Ivo Thomas. I was then introduced to Gödel's completeness and incompleteness theorems, and fell in love with them. When I enrolled at Case Western Reserve University, to begin my university experience, I already knew that I wanted to study logic. I was surprised and delighted to learn that it was possible (at least in theory) to devote one's career to this. At Case, I was also blessed with wonderful teachers, including Ray Nelson and Howard Stein, introducing me to various aspects of mathematical logic and set theory. My interests also began to turn philosophical, and toward the end of my college career, I managed a double major, in mathematics and philosophy. I then entered the Ph.D. program in mathematics at the State University of New York at Buffalo, in 1973, but switched to philosophy a year later. My ability to find outstanding teachers continued there. First and foremost, of course, was my advisor, John Corcoran. At that time, Buffalo was a veritable powerhouse in logic – covering philosophy, mathematics, and computer science. The list includes John Kearns, Nicolas Goodman, John Myhill, John Case, Richard Vesley, Harvey Friedman, Leo Harrington, and Thomas Jech. There was also a wonderful spirit of cooperation among the logicians in the various departments. It was a great place to be trained in logic, both philosophical and mathematical. Of course, the subject matter itself is important to me. I am attracted to the fact that logic is a central branch of both mathematics and philosophy. One can, it seems, shed light on deep and interesting philosophical problems, concerning epistemology, language, and even metaphysics, through rigorous, formal techniques. Here is one place where certain formal theorems have profound ramifications for central philosophical issues.

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