Corcoran on Corcoran: a 2017 BIO.pdf

John Corcoran (born 1937, Baltimore) is a logician, philosopher, mathematician, linguist, and historian of logic. He is known for his philosophical work on the nature of logic, the nature of mathematical logic, information-theoretic foundations of logic, the conceptual structure of metalogic, the relationship of logic to epistemology, and the roles of proof theory and model theory in logic. Corcoran’s papers have been translated into Arabic, Greek, Persian, Portuguese, Spanish, and Russian. His 1989 signature essay “Argumentations and logic” was translated into four languages. Fourteen of his papers have been reprinted; one was reprinted twice. He has been principal author on over 40 co-authored works. His 2015 article “Existential import today”, coauthored with the Iranian logician Hassan Masoud, is currently first on its journal’s most-read list with over 5000 readers. His 1972 work on Aristotle’s logic of the Prior Analytics is regarded as being highly faithful both to the Greek text and to the historical context. It is the basis for many subsequent investigations. It was adopted for the 1989 translation of the Prior Analytics by Robin Smith and for the 2009 translation of the Prior Analytics Book A by Gisela Striker. The 2009 article “Aristotle’s Demonstrative Logic” presents an amended and refined version of the philosophical and historical consequences of the 1972 work without the mathematics to reach a broad audience. Education: Pre-doctoral studies: Baltimore Polytechnic Institute, Engineering 1956, Johns Hopkins University BES Engineering 1959, MA Philosophy 1962, PhD Philosophy 1963. Dissertation: Generative Structure of Two-valued Logics; Supervisor: Robert McNaughton (PhD student of Willard Van Orman Quine). Post-doctoral studies: Yeshiva University Mathematics 1963–4, University of California Berkeley Mathematics 1964–5. Corcoran’s student years, the late 1950s and early 1960s, were wonderful times to be learning logic, its history, and its philosophy. His first logic teacher was Albert Hammond, who passed on from his own dissertation supervisor Arthur Lovejoy the tradition of the history of ideas—a tradition that his university, The Johns Hopkins University, had become famous for. Corcoran studied Plato and Aristotle with Ludwig Edelstein, the historian of Greek science and medicine who taught at the University and at the School of Medicine. His next two logic teachers were both accomplished and knowledgeable symbolic logicians: Joseph Ullian, a Quine PhD, and Richard Wiebe, a Benson Mates PhD who had studied with Carnap and Tarski. Corcoran’s dissertation supervisor, his doctor father, was Robert McNaughton, a Quine PhD who had already established himself in three fields: the metamathematics of number theory, the theory of formal languages, and the theory of automata. McNaughton encouraged Corcoran to do postdoctoral studies at Yeshiva University in New York City with Raymond Smullyan and Martin Davis, both doctoral students of Alonzo Church. McNaughton later encouraged Corcoran to go to UC Berkeley, the world center for logic and methodology, and he recommended Corcoran to Berkeley for a Visiting Lectureship. McNaughton was also instrumental in Corcoran’s move to his first tenure-track position, in Linguistics at the University of Pennsylvania, where McNaughton was a Professor of Computer and Information Science. In those early years Corcoran also attended semester-long courses and seminars by several other logicians, including John Addison, a Stephen Kleene PhD, Leon Henkin, another Church PhD, and John Myhill, another Quine PhD. Corcoran often mentions his teachers with great respect and warmth. History of logic: Corcoran’s work in history of logic involves most of the discipline’s productive periods. He has discussed Aristotle, the Stoics, William of Ockham, Giovanni 1

Girolamo Saccheri, George Boole, Richard Dedekind, Giuseppe Peano, Gottlob Frege, Bertrand Russell, the American Postulate Theorists, David Hilbert, C. I. Lewis, Alfred Tarski, Willard Van Orman Quine, and Warren Goldfarb. His 1972 interpretation of Aristotle’s Prior Analytics, proposed independently by Timothy Smiley of Cambridge University at about the same time, has formed the basis for subsequent investigations by Edgar Andrade, Jean-Yves Beziau, George Boger, Manuel Correia, Paolo Crivelli, Newton da Costa, Catarina Dutilh, Paolo Fait, Nicolas Fillion, James Gasser, Klaus Glashoff, John Martin, Mary Mulhern, Michael Scanlan, Robin Smith, Neil Tennant, Jan Von Plato, and others. As mentioned, it was adopted for the 1989 translation of the Prior Analytics by Robin Smith and for the 2009 translation of the Prior Analytics Book A by Gisela Striker. His 1980 critical reconstruction of Boole’s original 1847 system revealed previously unnoticed gaps and errors in Boole’s work and established the essentially Aristotelian basis of Boole’s philosophy of logic. In a 2003 article he provided a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic. His collaboration with Alfred Tarski in the late 1970s and early 1980s resulted in publications on Tarski’s work including the 2007 article “Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski” which traces Aristotelian and Boolean ideas in Tarski’s work and which confirms Tarski’s status as a founding figure in logic on a par with Aristotle and Boole. Mathematical logic: His mathematical logic treats propositional logics, modal logics, identity logics, syllogistic logics, standard first-order logics, the logic of first-order variablebinding term operators, second-order logics, categoricity, definitional equivalence, model theory, and the theory of strings—a discipline first axiomatized in Tarski’s 1933 truth-definition paper. The theory of strings, also known as concatenation theory and as abstract syntax, is foundational in all areas of logic. Corcoran’s work in string theory dates to his earliest meetings as a graduate student with McNaughton who was then applying string theory to computer science and formal linguistics. String theory provides essential background for all of Corcoran’s other mathematical work and it plays a seminal role in his philosophy. Philosophy: In all of Corcoran’s philosophy, especially his philosophy of mathematics, he has been guided by a nuanced and inclusionary Platonism which strives to do justice to all aspects of mathematical, logical, and linguistic experience including those aspects emphasized by competing philosophical perspectives such as logicism, constructivism, deductivism, and formalism. Although several of his philosophical papers presuppose little history or mathematics, his historical papers often involve either original philosophy (e.g. his 2006 article “Schemata”) or original mathematics (e.g. his 1980 article “Categoricity”) and his mathematical papers sometimes contain original history or philosophy (e.g. the 1974 article “String theory”). He has referred to the mathematical dimension of his approach to history as mathematical archaeology. His philosophical papers often involve original historical research. He has also been guided by the Aristotelian principle that the nature of modern thought is sometimes fruitfully understood in light of its historical development, a lesson that Corcoran attributes to Arthur Lovejoy’s History of Ideas Program at Johns Hopkins University. Corcoran’s attempt to integrate philosophy, mathematics, linguistics, logic, and history had been encouraged for many years by the late American philosopher and historian Peter Hare. References 1972. Completeness of an Ancient Logic, Journal of Symbolic Logic 37, 696–702. 1974. String Theory. (Co-authors: William Frank, Michael Maloney). Journal of Symbolic Logic 39, 625–37. 2

1980. Categoricity. History and Philosophy of Logic 1, 187–207. 1980. Boole's Criteria of Validity and Invalidity. (Co-author: S. Wood). Notre Dame Journal of Formal Logic 21, 609–39. 1989. Argumentations and Logic. Argumentation 3, 17–43. 2003. Aristotle's Prior Analytics and Boole's Laws of Thought. History and Philosophy of Logic. 24, 261–288. 2006. Schemata: the Concept of Schema in the History of Logic. Bulletin of Symbolic Logic 12, 219–40. 2007. Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski. Eds. C. Martínez et al. Current Topics in Logic and Analytic Philosophy / Temas Actuales de Lógica y Filosofía Analítica. Imprenta Univeridade Santiago de Compostela (University of Santiago de Compostela Press).145–178. 2009. Aristotle's Demonstrative Logic. History and Philosophy of Logic 30, 1–20. 2015. Existential import today: New metatheorems; historical, philosophical, and pedagogical misconceptions. (Co-author: Hassan Masoud). History and Philosophy of Logic 36, 39–61. Acknowledgements: Lynn Corcoran, Joaquin Miller, Frango Nabrasa, Paliath Narendran, Mary Mulhern, José Miguel Sagüillo, Jeffrey Welaish, and others.

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