# John Corcoran (logician)

John Corcoran ( born 1937 in Baltimore ) is a major contemporary logician and philosopher. He is mainly concerned with the relationship between logic and epistemology and the significance of proof theory and model theory in logic.

His work on Aristotle's Analytica Priora logic is faithful to the spirit of the Greek text and the historical context. It is the basis of many other studies and was used for the translation of the Analytica Priora by Robin Smith in 1989.

## Training

Corcoran studied from 1956 to 1962 in engineering, mathematics and philosophy and received a PhD in 1963. in philosophy with the work of Generative Structure of Two -valued Logics. His supervisor was Robert McNaughton ( a student of Willard Van Orman Quine ). In 1964 he took a post-doctoral studies in mathematics.

## Academic career

From 1963 to 1964 he was a member of the Linguistics Group at the IBM Research Center. In 1965 he became Assistant Professor of Linguistics at the University of Pennsylvania in 1970 and finally Associate Professor of Philosophy at the University at Buffalo ( SUNY ). Since 1973 he is a professor of philosophy.

## Shorter research stays

- Visiting Professor of Logic, University of Santiago de Compostela 1994;
- Visiting Scholar, Linguistic Institute, University of Buffalo ( SUNY ) Oswego in 1976;
- NSF (National Science Foundation ) Seminar Project Director, Linguistic Institute, University of Buffalo in 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 Center in 1962;
- Mathematician, Aeronca Astro Mechanics Institute, 1961;
- Junior Instructor in Philosophy, Johns Hopkins University from 1960 to 1961.

## Research Profile

Corcoran's work in the field of the history of logic treat the majority of the most productive periods of the discipline. He has worked, among others, the following logicians: Aristotle, the Stoics, William of Ockham, Giovanni Girolamo Saccheri, George Boole, Richard Dedekind, Frege, Alfred Tarski and Willard Van Orman Quine.

His interpretation of 1972 Analytica Priora of Aristotle, which was proposed independently of him, also written by Timothy Smiley is considered to be more faithfully than any previous interpretations; this concerns both the Greek text and the historical context. This work provides the basis for later research work of Boger, Correia, Crivelli, Gasser, Martin, Mulhern, Scanlan, Smith, and others, and it was used by Robin Smith as the basis of his translation of the Analytica Priora.

His critical reconstruction of Boole's logic system from 1847 brought hitherto unnoticed gaps and errors in Boole's work for days and made the essentially Aristotelian basis of Boole's logic philosophy clearly. An article from 2003 provides a systematic comparison and a critical evaluation of the logic of Aristotle and Boole.

Corcoran's collaboration with Alfred Tarski in the late 70s and early 80s led to publications on Tarski's work and to the article Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski from the year 2007, which traces the ideas of Aristotle and followed Boole in Tarski's work and in the Tarski's status is confirmed as one of the founding fathers of logic - on a par with Aristotle and Boole.

## The work

John Corcoran's work on philosophy of logic concentrate on the essence of logic, the conceptual structure of the logic, the metaphysical and epistemological conditions of logic, the nature of mathematical logic and the differences between logical theory and mathematical practice. His mathematical logic deals with the propositional logic, modal logic, identity logic, syllogistic logic, predicate logic, second stage, model theory and the theory of strings - a discipline that is all areas of the underlying logic and provides the essential background for all other his mathematical work.

In the philosophy of mathematics Corcoran is headed by a nuanced enclosing Platonism that strives to meet all aspects of the mathematical and logical experience justice; this includes the aspects that are stressed by competing philosophical perspectives such as logicism, constructivism, and formalism deductivism.

Although some of his philosophical work require very few historical or mathematical knowledge, his historical works often affect original questions of philosophy (eg, his article schemes ) or mathematics (eg his 1980 published in the journal History and Philosophy of Logic article Categoricity ). He has described the mathematical dimension of his conception of history as a "mathematical archeology ". His philosophical works are often concerned with the science of history. He has always followed the Aristotelian principle that the essence of modern thought can sometimes be best understood in light of their historical development. This view he attributes to Arthur Lovejoy's "History of Ideas " program at Johns Hopkins University, for which he was encouraged by the American philosopher and historian Peter Hare.

## Further material about John Corcoran

Many of Corcoran's publications have co-authors, and many others recognize the involvement of colleagues and students explicitly. Corcoran emphasizes the essentially personal nature of all true knowledge, even of the logical. He also stressed the importance of knowledge communities and the advantage of each individual through critical collaboration with other researchers.. A list of publications, completely by the year 2000, published in the journal History and Philosophy of Logic, born 1999 This volume contains a review article by M. Scanlan and S. Shapiro, " The Work of John Corcoran: An Appreciation ." Three other articles about his work in the anthology Current Topics in Logic and Analytic Philosophy, edited in 2007, published by the University of Santiago de Compostela Press. These are the contributions

- " Corcoran the Mathematician " by S. Shapiro
- " Corcoran the Philosopher " by JM Sagüillo,
- " Corcoran in Spanish " by C. Martínez -Vidal

## Writings

- Three Logical Theories. Philosophy of Science 36:1969. 153-177.
- Completeness of an Ancient Logic. Journal of Symbolic Logic 37: 1972nd 696-702.
- Gaps Between Logical Theory and Mathematical Practice. In Bunge, M., Ed. Methodological Unity of Science. Dordrecht: Kluwer. In 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 JM 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. In 1996.
- Boole 's Criteria of Validity and Invalidity. Notre Dame Journal of Formal Logic 21 (1980 ) 609,639th 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. In 1983.
- Contemporary Relevance of Ancient Logical Theory. Philosophical Quarterly 32 (1982 ) 76-86. With M. Scanlan.
- Reasoning and Logic. Argument 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. 1986th In Mathematical Reviews 91h: 01101, 2, 3.4. In 1991.
- The Founding of Logic. Ancient Philosophy 14 (1994 ) 9-24.
- Information - theoretic logic, 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 CA Anderson., Kluwer Publishing Company, Dordrecht, Holland. In 1998.
- Aristotle's Prior Analytics and Boole 's Laws of Thought. . History and Philosophy of Logic 24 (2003) 261-288.
- Schemes: the Concept of Schema in the History of Logic. Bulletin of Symbolic Logic. 12 (2006) 219-40.
- CI Lewis: History and Philosophy of Logic. Transactions of the C. S. Peirce Society. 42 (2006) 1-9.

## Honors

- Festschrift: double issue of the journal History and Philosophy of Logic 1999 ( Eds. M. Scanlan and S. Shapiro );
- Exceptional Scholar Award from the University of Buffalo in 2002;
- Doctor H.C. the University of Santiago de Compostela (Spain ) 2003;
- Corcoran Symposium, University of Santiago de Compostela (Spain ) 2003.