John Corcoran (logician)
Encyclopedia
.

John Corcoran is a logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

ian, philosopher, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, and historian of logic. He is best known for his philosophical work, helping us to understand such central concepts as the nature of inference
Inference
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...

, the relationship between logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

 and epistemology, and the place of proof theory
Proof theory
Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed...

 and model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....

 in logic.

His work

on Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

’s logic of the Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....

 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
Robin Smith
Robin Smith may refer to:* Robin Smith , British comic book artist* Robin Smith , South African-born England international* Robin Smith , American seminarian and author* Robin Smith , American WWF performer...

 and for the 2009 translation of the Prior Analytics Book A by Gisela Striker
Gisela Striker
Gisela Striker holds a joint appointment in Philosophy and Classics at Harvard University.She was born and educated in Germany...

.

Education

Baltimore Polytechnic Institute
Baltimore Polytechnic Institute
Baltimore Polytechnic Institute is a US public high school founded in 1883. Though established as an all-male trade school,it now is a institution that emphasizes mathematics, the sciences, and engineering. It is located on a tract of land in North Baltimore at Falls Road and Cold Spring Lane,...


A Dipl Engineering 1956, Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...

 BES Mechanical Engineering 1959, MA
Philosophy 1962, PhD. Philosophy 1963, Post-doctoral study: Yeshiva University
Yeshiva University
Yeshiva University is a private university in New York City, with six campuses in New York and one in Israel. Founded in 1886, it is a research university ranked as 45th in the US among national universities by U.S. News & World Report in 2012...

 Mathematics
1964 and University of California Berkeley Mathematics 1965. Dissertation: Generative
Structure of Two-valued Logics; Supervisor Robert McNaughton (himself a pupil of Willard Van Orman Quine
Willard Van Orman Quine
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...

).

Regular academic or research appointments

Professor of Philosophy, University of Buffalo (SUNY), 1973–; Associate Professor of Philosophy, University of Buffalo, 1970–1973;
Assistant Professor of Linguistics, University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...

, 1965–1969; Member of
Linguistics Group, IBM Research Center, 1963–1964.

Visiting academic or research appointments

Visiting Professor of Logic, University of
Santiago de Compostela 1994; Visiting Scholar, Linguistic Institute, SUNY Oswego 1976; NSF
Seminar Project Director, Linguistic Institute, University of Buffalo 1971; Visiting Associate
Professor of Philosophy and Research Associate, University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...

 1969–1970; Visiting
Lecturer in Philosophy, University of California, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

 1964–1965; Mathematician, GE
Research Center 1962; Mathematician, Aeronca Astromechanics Institute, 1961; Junior
Instructor in Philosophy, Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...

 1960–1961.

Research profile

Corcoran’s work in history of logic
History of logic
The history of logic is the study of the development of the science of valid inference . Formal logic was developed in ancient times in China, India, and Greece...

 involves most of the discipline’s
productive periods. He has discussed Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

, the Stoics
Stoicism
Stoicism is a school of Hellenistic philosophy founded in Athens by Zeno of Citium in the early . The Stoics taught that destructive emotions resulted from errors in judgment, and that a sage, or person of "moral and intellectual perfection," would not suffer such emotions.Stoics were concerned...

, William of Ockham
William of Ockham
William of Ockham was an English Franciscan friar and scholastic philosopher, who is believed to have been born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of...

, Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri
Giovanni Girolamo Saccheri was an Italian Jesuit priest, scholastic philosopher, and mathematician....

, George Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...

, Richard Dedekind
Richard Dedekind
Julius Wilhelm Richard Dedekind was a German mathematician who did important work in abstract algebra , algebraic number theory and the foundations of the real numbers.-Life:...

, Gottlob Frege
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...

, the American Postulate Theorists, Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...

, and Willard Van Orman Quine
Willard Van Orman Quine
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...

. His 1972 interpretation of Aristotle’s Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....

, proposed independently by Timothy Smiley
Timothy Smiley
Timothy John Smiley FBA is Emeritus Knightbridge Professor of Philosophy at Clare College, Cambridge University.He has edited and contributed to numerous papers and publications including:...

 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
Newton da Costa
Newton Carneiro Affonso da Costa is a Brazilian mathematician, logician, and philosopher. He studied engineering and mathematics at the Federal University of Paraná in Curitiba and the title of his 1961 Ph.D...

, Catarina Dutilh, Paolo Fait, Nicolas Fillion, James Gasser, Klaus Glashoff, John Martin, Mary Mulhern, Michael Scanlan, Robin Smith 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
Gisela Striker
Gisela Striker holds a joint appointment in Philosophy and Classics at Harvard University.She was born and educated in Germany...

. 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 provides a systematic comparison and critical evaluation of Aristotelian logic and Boolean logic
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...

. His collaboration with Alfred Tarski in the late 1970s and early 1980s led to publications on Tarski’s work 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.

The work

His work in philosophy of logic
Philosophy of logic
Following the developments in Formal logic with symbolic logic in the late nineteenth century and mathematical logic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be termed either philosophy of logic or philosophical logic if no longer simply...

 focuses on the nature of logic, the role of logic in
inquiry, the conceptual structure of logic, the metaphysical
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

 and epistemological presuppositions
of logic, the nature of mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

 and the gaps between logical theory and mathematical
practice. His mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

 treats propositional logics, modal logic
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...

s, identity logics,
syllogistic logics, the logic of first-order variable-binding term operators, second-order logic
Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory....

s,
model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....

, 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
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...

 Corcoran has been guided by a nuanced and inclusionary Platonism
Platonism
Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism...

 which
strives to do justice to all aspects of mathematical and logical experience including those aspects
emphasized by competing philosophical perspectives such as logicism
Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory fathered by Richard Dedekind...

, constructivism
Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption, one still has not found the object and therefore not proved its...

,
deductivism, and formalism
Formalism (mathematics)
In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules....

. 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.

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 of 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
Stewart Shapiro
Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...


“The Work of John Corcoran: An Appreciation”. Other articles about his work include
“Corcoran the Mathematician” by S. Shapiro
Stewart Shapiro
Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

 , “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
University of Santiago de Compostela
The Royal University of Santiago de Compostela - USC is a public university located in the city of Santiago de Compostela, Galicia, Spain. A second campus is located in Lugo, Galicia....

 Press.
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 ).

Key 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
    Stewart Shapiro
    Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

    .
  • Categoricity. History and Philosophy of Logic 1(1980) 187–208.Reprinted in S. Shapiro
    Stewart Shapiro
    Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

     , 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. In 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.
  • 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.


For a complete list see John Corcoran's homepage.

Service to the profession

  • Co-founder with George Weaver of Philadelphia Logic Colloquium 1966
  • Founder of Buffalo Logic Colloquium http://philosophy.buffalo.edu/events/colloquia/buffalo_logic 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
    Mathematical Reviews
    Mathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...

     1969–present;
  • occasional reviewer for Philosophy of Science
    Philosophy of science
    The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...

    , Bulletin of Symbolic Logic, and Journal of Symbolic Logic
    Journal of Symbolic Logic
    The Journal of Symbolic Logic is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic.Founded in 1936, the journal publishes articles on mathematical 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
      Stewart Shapiro
      Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

       , Scanlan, McLarty, Weaver, Tiezsen, Kearns, et al.) 2001.
  • Sponsor of Alonzo Church for Doctor Honoris Causa at the University of Buffalo 1990.

Teaching

Corcoran’s courses are all introductory, having no prerequisites and presupposing no
previous knowledge. 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. His former students teach at Bryn Mawr, Canisius College,
Colorado State, Dordt College, Ohio State, Oregon State, Pontifical University of Rio de Janeiro,
St. John’s College, UCLA, University of Lausanne
University of Lausanne
The University of Lausanne in Lausanne, Switzerland was founded in 1537 as a school of theology, before being made a university in 1890. Today about 12,000 students and 2200 researchers study and work at the university...

, University of Santiago de Compostela
University of Santiago de Compostela
The Royal University of Santiago de Compostela - USC is a public university located in the city of Santiago de Compostela, Galicia, Spain. A second campus is located in Lugo, Galicia....

, and
elsewhere. His best-known students include George Boger, James Gasser, Calvin Jongsma,
Edward Keenan
Edward Keenan
Edward Louis Keenan is a Professor of Linguistics at UCLA. He specializes in the areas of Mathematical Linguistics, Linguistic Typology and Semantics. He has also done extensive work on Malagasy, an Austronesian language spoken in Madagascar.-External links:*...

, José Miguel Sagüillo, Michael Scanlan, Stewart Shapiro
Stewart Shapiro
Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

, and George Weaver.

Honors and awards

  • Festschrift special double issue of History and Philosophy of Logic 1999 (Eds. M. Scanlan and S. Shapiro
    Stewart Shapiro
    Stewart Shapiro is O'Donnell Professor of Philosophy at the Ohio State University and a regular visiting professor at the University of St Andrews in Scotland. He is an important contemporary figure in the philosophy of mathematics where he defends a version of structuralism. He studied...

    );
  • Exceptional Scholar Award from the University of Buffalo 2002;
  • Doctor Honoris Causa from University of Santiago de Compostela (Spain) 2003;
  • Corcoran Symposium, University of Santiago de Compostela (Spain) 2003.
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