# John Corcoran (logician)

John Corcoran | |
---|---|

Born | 1937 Baltimore, USA |

Fields | Logic, History of logic, philosophy of logic, mathematical logic, philosophy of mathematics, epistemology, ontology, linguistics |

Institutions | 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, string theory, subregular polyhedra. |

**John Corcoran** (born 1937) is a 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. 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. A bibliography of Corcoran’s publications on Aristotle's logic is available at ResearchGate. https://www.researchgate.net/profile/John_Corcoran2/

Corcoran’s 2014 paper with Hassan Masoud – “Existential import today: New metatheorems; historical, philosophical, and pedagogical misconceptions” – is currently first on the “most-read” list at History and Philosophy of Logic.^{[4]} His mathematical results on definitional equivalence of formal string theories, sciences of strings of characters over finite alphabets, are foundational for logic, formal linguistics, and computer science.^{[5]} A current list of all of Corcoran’s publications is available at ResearchGate. https://www.researchgate.net/profile/John_Corcoran2/

## Contents

## Education

Corcoran studied engineering at the Baltimore Polytechnic Institute, Advanced Curriculum Engineering 1956, and the Johns Hopkins University, BES Mechanical Engineering 1959. After briefly working in engineering, he studied philosophy at the Johns Hopkins University: MA Philosophy 1962, PhD. Philosophy 1963. Post-doctoral study: Yeshiva University, Mathematics 1964 and University of California Berkeley, Mathematics 1965. Dissertation: Generative Structure of Two-valued Logics; Supervisor Robert McNaughton (PhD student of Willard Van Orman Quine).

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 held appointments both at The Johns Hopkins University and at its School of Medicine. His next two logic teachers were both accomplished and knowledgeable symbolic logicians: Joseph Ullian, a Quine PhD, and Richard Wiebe, a 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 made a name for himself in three fields: the metamathematics of number theory, the theory of formal languages, and the theory of automata. McNaughton encouraged Corcoran to do post-doctoral 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 his Berkeley colleagues. He was also instrumental in Corcoran’s move to his first tenure-track position, 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.

## Regular academic or research appointments

He has been Professor of Philosophy, University at Buffalo (SUNY), 1973–; Associate Professor of Philosophy, University at Buffalo, 1970–1973; Assistant Professor of Linguistics, University of Pennsylvania, 1965–1969; Member of Linguistics Group, IBM Research Center, 1963–1964.

## Visiting academic or research appointments

He is or 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; Visiting Lecturer 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.

## Research profile

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 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,^{[6]} 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^{[7]} 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 of 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^{[8]} led to publications on Tarski’s work^{[9]} 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.

## Scientific work

His work in philosophy of logic focuses on the nature of logic, the role of logic in inquiry, the conceptual structure of logic, the metaphysical and epistemological presuppositions of logic, the nature of mathematical logic and the gaps between logical theory and mathematical practice. 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 logic and 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 which strives to do justice to all aspects of mathematical and logical 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 recent 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 as mathematical archaeology. His philosophical papers often involve original historical research. He has been guided by the Aristotelian principle that the nature of modern thought is sometimes best understood in light of its historical development, a view that he attributes to Arthur Lovejoy’s History of Ideas Program at Johns Hopkins University and in which he has been encouraged by the American philosopher and historian Peter Hare.^{[10]}

## Collaboration

Many of Corcoran’s articles and reviews are co-authored and many of his single-author publications acknowledge involvement of colleagues and students. Corcoran emphasizes the intensely 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 can benefit 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 the University of Santiago de Compostela Press.^{[11]} 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 Logic volume 30, 2009, 21-48), which received the 2009 Ivor Grattan-Guinness Award for the History and Philosophy of Logic ( http://informaworld.com/thpl ).

## Publications

- Three Logical Theories. Philosophy of Science 36:1969. 153–177.
- Completeness of an Ancient Logic. Journal of Symbolic Logic 37: 1972. 696–702.
- Gaps Between Logical Theory and Mathematical practice. In Bunge, M., Ed. Methodological Unity of Science. Dordrecht: Kluwer. 1973. 23–50.
- Meanings of Implication, Dialogos 9 (1973) 59–76. Reprinted in R. Hughes, Ed., Philosophical companion to first order logic. Indianapolis: Hackett. 1993. Spanish translation by J. M. Saguillo Agora 5(1985) 279–294.
- Aristotle’s Natural Deduction System. In Ancient Logic and its Modern Interpretations. Ed. J. Corcoran, Dordrecht: Kluwer, 1974. 85–131.
- Remarks on Stoic Deduction. Ibid., 169–181.
- String Theory. Journal of Symbolic Logic 39 (1974) 625–37. With W. Frank, and M. Maloney.
- Logical Structures of Ockham's Theory of Supposition. Franciscan Studies 38(1978) 161–83. With J. Swiniarski.
- Crossley on Mathematical Logic. Philosophia 8(1978) 79–94. Spanish translation by A. Garciadiego Mathesis X (1988) 133–150. With S. Shapiro.
- Categoricity. History and Philosophy of Logic 1(1980) 187–208.Reprinted in S. Shapiro, Ed., The Limits of Logic, Aldershot, England: Dartmouth Publishing Company. 1996.
- Boole’s Criteria of Validity and Invalidity. Notre Dame Journal of Formal Logic 21(1980) 609–639. With S. Wood. Reprinted in J. Gasser, Ed. Boole Anthology. Dordrecht: Kluwer.2000.
- Introduction and analytical index. In Tarski, A. Logic, Semantics, Metamathematics. Second ed. Edited by J. Corcoran. Trans. J. H. Woodger. Indianapolis: Hackett. 1983.
- Contemporary Relevance of Ancient Logical Theory. Philosophical Quarterly 32(1982) 76–86. With M. Scanlan.
- Argumentations and Logic. Argumentation 3(1989) 17–43., Spanish translation by R. Fernandez and J. Sagüillo Agora 13/1 (1994) 27–55.
- Review of Alfred Tarski: Collected Papers. 4 Vols. Edited by S. Givant and R. McKenzie. Basel: Birkhäuser. 1986. Mathematical Reviews 91h:01101, 2, 3,4. 1991.
- The Founding of Logic. Ancient Philosophy 14(1994) 9–24.
- Information-theoretic logic, in Truth in Perspective edited by C. Martínez, U. Rivas, L. Villegas-Forero, Ashgate Publishing Limited, Aldershot, England (1998) 113–135.
- Second-Order Logic. In the “Church Memorial Volume”, Logic, Meaning, and Computation: Essays in Memory of Alonzo Church edited by M. Zeleny and C.A. Anderson., Kluwer Publishing Company, Dordrecht, Holland. 1998.
- Aristotle’s Prior Analytics and Boole’s Laws of Thought. . History and Philosophy of Logic 24(2003) 261–288.
- Schemata: the Concept of Schema in the History of Logic. Bulletin of Symbolic Logic. 12 (2006) 219–40.
- C. I. Lewis: History and Philosophy of Logic. Transactions of the C. S. Peirce Society. 42 (2006)1–9.
- John Corcoran (2008-09-21). "Schema".
*Stanford Encyclopedia of Philosophy*.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk), ISBN 978-0-19-925041-7." in the
*Notre Dame Philosophical Reviews*, 2010.02.02. - “The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper”,
*History and Philosophy of Logic 32 (2011)*: 359–80. Co-author José Miguel Sagüillo. http://www.tandfonline.com/doi/abs/10.1080/01445340.2011.577145#.UksmOD_-kQs - “Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions”,
*History and Philosophy of Logic 36 (2014)*: 39–61. Co-author Hassan Masoud. http://www.tandfonline.com/doi/full/10.1080/01445340.2014.952947

For a complete list see John Corcoran's homepage. Some of his papers are available online: http://buffalo.academia.edu/JohnCorcoran

## Service to the profession

- Co-founder with George Weaver of Philadelphia Logic Colloquium 1966
- Founder of Buffalo Logic Colloquium [1] 1970.
- Chair of Buffalo Logic Colloquium 1970 to present with interruptions.
- Founding member of the Editorial Board, History and Philosophy of Logic 1980–present.
- Regular reviewer for Mathematical Reviews 1969–present.
- Occasional reviewer for Philosophy of Science, Bulletin of Symbolic Logic, and Journal of Symbolic Logic.
- Occasional referee for various logic journals.
- Organizer of four conferences:
- Ancient Logic (Corcoran, Kretzmann, Mueller, et al.) 1972
- Nature of Logic (Tarski, Putnam, Friedman, Jech, Vesley, Goodman, et al.) 1973
- Church Symposium (Church, Davis, Henkin, Rogers) 1990
- Conference on Gaps between Logical Theory and Mathematical Practice (Shapiro, Scanlan, McLarty, Weaver, Tiezsen, Kearns, et al.) 2001.

- Sponsor of Alonzo Church for Doctor Honoris Causa at the University at Buffalo 1990.
^{[12]} - Board of Editorial Advisors, Cambridge Dictionary of Philosophy 2012–present.

## Teaching

Corcoran’s courses are all introductory, having no prerequisites and presupposing no previous knowledge.^{[13]} In each course he reconstructs its subject-matter from the ground up and never covers the same material twice. Stressing the priority of education over indoctrination and the superiority of learning how to think over learning what to think, he strives to assist his students in connecting with the reality logic is about so that they may become autonomous judges of the adequacy of the field.^{[14]}

His former students teach at the Autonomous University of Mexico City, Bryn Mawr, Canisius College,Colorado State, Dordt College, Franciscan University, Fredonia State, Ohio State, Oregon State, Pontifical University of Rio de Janeiro, St. John Fisher College, St. John’s College, UCLA, University of Lausanne, University of Santiago de Compostela, and elsewhere.

His best-known students include George Boger, James Gasser, Calvin Jongsma, Idris Samawi Hamid, Edward Keenan,Timothy Madigan, Sriram Nambiar, José Miguel Sagüillo, Michael Scanlan, Stewart Shapiro, and George Weaver.

## Honors and awards

- Festschrift special double issue of History and Philosophy of Logic 1999 (Eds. M. Scanlan and S. Shapiro);
- Exceptional Scholar Award from the University at Buffalo 2002;
- Doctor Honoris Causa from University of Santiago de Compostela (Spain) 2003;
- Corcoran Symposium, University of Santiago de Compostela (Spain) 2003.
- Corcoran Colloquium, University at Buffalo, October 2010.

## Bibliography

- Corcoran, John (2009). “Aristotle's Demonstrative Logic”.
*History and Philosophy of Logic*,**30**: 1–20. - Corcoran, John (2009). “Aristotle's Logic at the University of Buffalo’s Department of Philosophy”.
*Ideas y Valores: Revista Colombiana de Filosofía*,**140**(August 2009) 99–117. http://www.revistas.unal.edu.co/index.php/idval/article/viewFile/12581/13183

## References

- ↑ Argumentations and Logic. Argumentation ‘’’3’’’(1989) 17–43., 1994 Spanish translation by R. Fernandez and J. Sagüillo;2010 Portuguese translation by W. Sanz; 2011 Persian translation by H. Masoud.
- ↑ Corcoran, John (1972). "Completeness of an Ancient Logic".
*J. of Symbolic Logic*. ASL.**37**(4): 696–702. doi:10.2307/2272415. JSTOR 2272415.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑ Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.
- ↑ http://www.tandfonline.com/action/showMostReadArticles?journalCode=thpl20&
- ↑ String Theory. Journal of Symbolic Logic
**39**(1974) 625–37. Co-authored by two of his doctoral students W. Frank (UPenn, Linguistics) and M. Maloney (UPenn, Computer Science). - ↑ Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.
- ↑ Corcoran, John (2003). “Aristotle's Prior Analytics and Boole's Laws of Thought”.
*History and Philosophy of Logic*,**24**: 261–288. Reviewed by Risto Vilkko.*Bulletin of Symbolic Logic*,**11**(2005) 89–91. Also by Marcel Guillaume,*Mathematical Reviews*2033867 (2004m:03006). - ↑ See pp. 361–368 in Feferman, Anita Burdman; Feferman, Solomon (2004).
*Alfred Tarski: Life and Logic*. Cambridge University Press. ISBN 978-0-521-80240-6. OCLC 54691904.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. - ↑ Corcoran, John, and Sagüillo, José Miguel, 2011. “The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper”,
*History and Philosophy of Logic***32**: 359–80. http://www.tandfonline.com/doi/pdf/10.1080/01445340.2011.577145 - ↑ Corcoran, John, (2009). Remembering My Life with Peter Hare. Remembering Peter Hare 1935–2008. Ed. J. Campbell. Society for the Advancement of American Philosophy. pp. 9–16. http://american-philosophy.org/documents/RememberingPeterHare_final.pdf .
- ↑ https://books.google.com/books?id=9IMEm4dYQXUC .
- ↑ Finding Aid for The Honorary Degree Conferral of Doctor of Science to Alonzo Church, 1990
- ↑ http://www.ratemyprofessors.com/ShowRatings.jsp?tid=1091372
- ↑ Corcoran, John, 2012. ‘’Farewell letter to my students”. ‘‘Philosophy Now’’. Issue ‘’’97’’’ September/October 2012.http://www.pdcnet.org/philnow/content/philnow_2012_0092_0018_0018