| John Corcoran | |
| Birth Date: | 20 March 1937 |
| Birth Place: | Baltimore, Maryland, U.S. |
| Fields: | Logic, history of logic, philosophy of logic, mathematical logic, philosophy of mathematics, epistemology, ontology, linguistics |
| Workplaces: | University at Buffalo (SUNY) |
| Alma Mater: | Johns Hopkins University |
| Doctoral Advisor: | Robert McNaughton |
| Known For: | Interpretation of Aristotle's Prior Analytics, reconstruction of Boole's original works, work on logic, work on mathematical logic, character-string theory, subregular polyhedra |
John Corcoran (; March 20, 1937 – January 8, 2021) was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof theory and model theory in logic. Nine of Corcoran's papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 "signature" essay[1] was translated into three languages. Fourteen of his papers have been reprinted; one was reprinted twice.
His work[2] on Aristotle's logic of the Prior Analytics is regarded as being highly faithful both to the Greek text and to the historical context.[3] It is the basis for many subsequent investigations.
His mathematical results on definitional equivalence of formal character-string theories, sciences of strings of characters over finite alphabets, are foundational for logic, formal linguistics, and computer science.[4]
Corcoran graduated from the Advanced College Preparatory Program (the "A Course") of the Baltimore Polytechnic Institute in 1956 and received the BES in Mechanical Engineering in 1959 from the Johns Hopkins University, where he received the PhD in Philosophy in 1963. His post-doctoral studies in mathematics were at Yeshiva University in1964 and at the University of California Berkeley in 1965. His dissertation topic was Generative Structure of Two-valued Logics.
Corcoran's first logic teacher was Albert L Hammond. Corcoran studied Plato and Aristotle with Ludwig Edelstein. His next two logic teachers were Joseph Ullian and Richard Wiebe. Corcoran's dissertation supervisor was Robert McNaughton. At Yeshiva University in New York City Corcoran studied with Raymond Smullyan and Martin Davis. Corcoran's first tenure-track position was at the University of Pennsylvania, where his dissertation supervisor was a Professor of Computer and Information Science.
Corcoran was Professor of Philosophy, University at Buffalo (SUNY) from 1970 to 1973; Associate Professor of Philosophy, University at Buffalo between 1970–1973;Assistant Professor of Linguistics, University of Pennsylvania between 1965–1969; Member ofLinguistics Group, IBM Research Center between 1963–1964.
Corcoran was Visiting Professor of Logic, University of Santiago de Compostela 1994; Visiting Scholar, Linguistic Institute, SUNY Oswego 1976; NSF Seminar Project Director, Linguistic Institute, University at Buffalo 1971; Visiting Associate Professor of Philosophy and Research Associate, University of Michigan 1969–1970; VisitingLecturer in Philosophy, University of California, Berkeley 1964–1965; Mathematician, General Electric Research Laboratory 1962; Mathematician, Aeronca Astromechanics Institute, 1961; Junior Instructor in Philosophy, Johns Hopkins University 1960–1961.
Corcoran's work in history of logic involves most of the discipline'sproductive periods. He has discussed Aristotle, the Stoics, William of Ockham, Giovanni Girolamo Saccheri, George Boole, Richard Dedekind, Gottlob Frege, Charles Sanders Peirce, Clarence Irving Lewis, the American Postulate Theorists, Alfred Tarski, Willard Van Orman Quine, and Warren Goldfarb.
His 1972 interpretation of Aristotle's Prior Analytics, proposed independently by Timothy Smiley at about the same time, has been found to be more faithful than previous interpretations both to the Greek text and to the historical context. It has formed the basis for subsequent investigations by Edgar Andrade, 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, and others. 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. A 2003 article[5] provides a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic; it also reveals the centrality of wholistic reference in Boole's philosophy of logic. According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole did not dispute one point that Aristotle made, but he did "go under, over, and beyond" Aristotle's logic by 1) providing it with mathematical foundations involving equations, 2) extending the class of problems it could treat—to assessing validity he added solving equations, and 3) expanding the range of applications it could handle—e.g. from propositions having only two terms to those having arbitrarily many.
More specifically, Boole agreed with what Aristotle said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say.First, in the realm of foundations, Boole reduced Aristotle's four propositional forms to one form, that of equations—by itself a revolutionary idea.Second, in the realm of logic's problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving.Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle".
His collaboration with Alfred Tarski in the late 1970s and early 1980s[6] led to publications on Tarski's work[7] and to 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.
His work in philosophy of logic focuses on the nature of logic, the role of logic ininquiry, the conceptual structure of logic, the metaphysical and epistemological presuppositionsof logic, the nature of mathematical logic and the gaps between logical theory and mathematicalpractice. His mathematical logic treats propositional logics, modal logics, identity logics,syllogistic logics, the logic of first-order variable-binding term operators, second-order logics,model theory, and the theory of strings – a discipline which is foundational in all areas of logicand which provides essential background for all of his other mathematical work. In philosophy of mathematics Corcoran has been guided by a nuanced and inclusionary Platonism whichstrives to do justice to all aspects of mathematical and logical experience including those aspectsemphasized by competing philosophical perspectives such as logicism, constructivism,deductivism, and formalism. Although several of his philosophical papers presuppose littlehistory or mathematics, his historical papers often involve either original philosophy (e.g. hisrecent BSL article "Schemata") or original mathematics (e.g. his 1980 HPL article"Categoricity"). He has referred to the mathematical dimension of his approach to history asmathematical archaeology. His philosophical papers often involve original historical research. He has beenguided by the Aristotelian principle that the nature of modern thought is sometimes bestunderstood in light of its historical development, a view that he attributes to Arthur Lovejoy'sHistory of Ideas Program at Johns Hopkins University and in which he has been encouraged bythe American philosopher and historian Peter Hare.[8]
Many of Corcoran's articles and reviews are co-authored and many of his single-authorpublications acknowledge involvement of colleagues and students. Corcoran emphasizes theintensely and essentially personal nature of all genuine knowledge including logical knowledge.Nevertheless, he also stresses the importance of communities of knowers and how much each person canbenefit in the personal search for truth from critical cooperation with other objective researchers. For over 40 years he was the leader of the "Buffalo Syllogistic Group"—a community of philosophers, historians, linguists, logicians, and mathematicians dedicated to the study of the origin of logic. The achievements of this community are sketched in his 2009 paper "Aristotle's Logic at the University at Buffalo's Department of Philosophy", Ideas y Valores: Revista Colombiana de Filosofía 140 (August 2009) 99–117.A list of his publications, complete through 2000, appears in the 1999 volume of History and Philosophy of Logic, which also includes the expository article by M. Scanlan and S. Shapiro"The Work of John Corcoran: An Appreciation". Other articles about his work include"Corcoran the Mathematician" by S. Shapiro, "Corcoran the Philosopher" by J. M. Sagüillo, and"Corcoran in Spanish" by C. Martínez-Vidal; all appear in a 2007 volume published by theUniversity of Santiago de Compostela Press.[9] Corcoran's work in the 1990s on information-theoretic logic is discussed by José M. Sagüillo in the article "Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence" (History and Philosophy of Logicvolume 30, 2009, 21–48), which received the 2009 Ivor Grattan-Guinness Award for the History and Philosophy of Logic (informaworld.com).
History and Philosophy of Logic. Transactions of the C. S. Peirce Society. 42 (2006) 1–9.
For a complete list see John Corcoran's homepage.Some of his papers are available online: https://buffalo.academia.edu/JohnCorcoran
Corcoran died on January 8, 2021, at the age of 83.[11]