John Corcoran State University of New York, Buffalo
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  • Faculty, State University of New York, Buffalo
  • PhD, Johns Hopkins University, 1963.

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John Corcoran taught logic at Berkeley, Penn, Michigan, Santiago de Compostela, and, most recently, Buffalo--from 1970 to 2010. His writings are on history and philosophy of logic, mathematical logic, epistemology, and linguistics. His most important contributions to history of logic concern his reconstruction of Aristotle’s logic as a natural deduction system. His work in history of logic also treats the Stoics, Ockham, Saccheri,Boole,Lewis,Church,Quine,and Tarski. He has worked in several areas of mathematical logic including proof theory, model theory, string theory, and variable-binding term-operators. He edited the 1983 second edition of Tarski’s 1956 LOGIC, SEMANTICS, METAMATHEMATICS. He also edited the 1993 second edition of the 1934 Cohen-Nagel INTRODUCTION TO LOGIC. His signature 1989 article “Argumentations and Logic”, which appeared in ARGUMENTATION, has been translated into Spanish, Portuguese, and Farsi. Corcoran headed the committee that organized the 1990 Alonzo Church Symposium and that successfully petitioned the University of Buffalo to award the Doctor Honoris Causa to Alonzo Church.
My works
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  1. John Corcoran, A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.
    This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...)
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  2. John Corcoran, JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.
    JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...)
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  3. John Corcoran (forthcoming). Tarski’s Convention T: Condition Beta. SOUTH AMERICAN JOURNAL OF LOGIC 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  4. John Corcoran (2015). Review Of: Hodesdon, K. “Mathematica Representation: Playing a Role”. Philosophical Studies (2014) 168:769–782. Mathematical Reviews. MR 3176431. MATHEMATICAL REVIEWS 2015:3176431.
    This 4-page review-essay—which is entirely reportorial and philosophically neutral as are my other contributions to MATHEMATICAL REVIEWS—starts with a short introduction to the philosophy known as mathematical structuralism. The history of structuralism traces back to George Boole (1815–1864). By reference to a recent article various feature of structuralism are discussed with special attention to ambiguity and other terminological issues. The review-essay includes a description of the recent article. The article’s 4-sentence summary is quoted in full and then analyzed. The point (...)
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  5. John Corcoran & Gerald Rising (2015). Expressing Set-Size Equality. Bulletin of Symbolic Logic 21 (2):239.
    The word ‘equality’ often requires disambiguation, which is provided by context or by an explicit modifier. For each sort of magnitude, there is at least one sense of ‘equals’ with its correlated senses of ‘is greater than’ and ‘is less than’. Given any two magnitudes of the same sort—two line segments, two plane figures, two solids, two time intervals, two temperature intervals, two amounts of money in a single currency, and the like—the one equals the other or the one is (...)
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  6. John Corcoran (2014). ARISTOTELIAN LOGIC AND EUCLIDEAN GEOMETRY. Bulletin of Symbolic Logic 20 (1):131-2.
    John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the premises: (...)
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  7. John Corcoran (2014). Formalizing Euclid’s First Axiom. Bulletin of Symbolic Logic 20:404-405.
    Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...)
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  8. John Corcoran (2014). INVESTIGATING KNOWLEDGE AND OPINION. In A. Buchsbaum A. Koslow (ed.), The Road to Universal Logic. Vol. I. SPRINGER 95-126.
    This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is truth. Some but not all opinion is truth. Every proposition known to be true is believed to be true. Some but (...)
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  9. John Corcoran (2014). Meanings of Hypothesis. Bulletin of Symbolic Logic 20 (2):348-9.
    The primary sense of the word ‘hypothesis’ in modern colloquial English includes “proposition not yet settled” or “open question”. Its opposite is ‘fact’ in the sense of “proposition widely known to be true”. People are amazed that Plato [1, p. 1684] and Aristotle [Post. An. I.2 72a14–24, quoted below] used the Greek form of the word for indemonstrable first principles [sc. axioms] in general or for certain kinds of axioms. These two facts create the paradoxical situation that in many cases (...)
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  10. John Corcoran (2014). Review of Macbeth, D. Diagrammatic Reasoning in Frege's Begriffsschrift. Synthese 186 (2012), No. 1, 289–314. Mathematical Reviews MR 2935338. MATHEMATICAL REVIEWS 2014:2935338.
    A Mathematical Review by John Corcoran, SUNY/Buffalo -/- Macbeth, Danielle Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314. ABSTRACT This review begins with two quotations from the paper: its abstract and the first paragraph of the conclusion. The point of the quotations is to make clear by the “give-them-enough-rope” strategy how murky, incompetent, and badly written the paper is. I know I am asking a lot, but I have to ask you to read the quoted passages—aloud if (...)
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  11. John Corcoran (2014). Truth-Preserving and Consequence-Preserving Deduction Rules”,. Bulletin of Symbolic Logic 20:130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...)
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  12. John Corcoran & William Frank (2014). COSMIC JUSTICE HYPOTHESES. Bulletin of Symbolic Logic 20:247-248.
    Cosmic Justice Hypotheses. -/- This applied-logic lecture builds on [1] arguing that character traits fostered by logic serve clarity and understanding in ethics, confirming hopeful views of Alfred Tarski [2, Preface, and personal communication]. Hypotheses in one strict usage are propositions not known to be true and not known to be false or—more loosely—propositions so considered for discussion purposes [1, p. 38]. Logic studies hypotheses by determining their implications (propositions they imply) and their implicants (propositions that imply them). Logic also (...)
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  13. John Corcoran & Hassan Masoud (2014). The Tarskian Turn: Deflationism and Axiomatic Truth. [REVIEW] History and Philosophy of Logic 35 (3):308-313.
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  14. John Corcoran & Hassan Masoud (2014). Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions. History and Philosophy of Logic 36 (1):39-61.
    Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...)
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  15. John Corcoran & Sriram Nambiar (2014). De Morgan on Euclid’s Fourth Postulate. Journal of Symbolic Logic 20:250-1.
    This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...)
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  16. John Corcoran (2013). Aristotle’s “Whenever Three Terms”. Bulletin of Symbolic Logic 19:234-235.
    The premise-fact confusion in Aristotle’s PRIOR ANALYTICS. -/- The premise-fact fallacy is talking about premises when the facts are what matters or talking about facts when the premises are what matters. It is not useful to put too fine a point on this pencil. -/- In one form it is thinking that the truth-values of premises are relevant to what their consequences in fact are, or relevant to determining what their consequences are. Thus, e.g., someone commits the premise-fact fallacy if (...)
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  17. John Corcoran & William Frank (2013). SURPRISES IN LOGIC. Bulletin of Symbolic Logic 19:253.
    JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 (2013) 253. Some people, not just beginning students, are at first surprised to learn that the proposition “If zero is odd, then zero is not odd” is not self-contradictory. Some people are surprised to find out that there are logically equivalent false universal propositions that have no counterexamples in common, i. e., that no counterexample for one is a counterexample for the other. Some people would be surprised (...)
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  18. John Corcoran & Anthony Ramnauth (2013). Equality and Identity. Bulletin of Symbolic Logic 19:255-256.
    Equality and identity. Bulletin of Symbolic Logic. 19 (2013) 255-6. (Coauthor: Anthony Ramnauth) Also see https://www.academia.edu/s/a6bf02aaab This article uses ‘equals’ [‘is equal to’] and ‘is’ [‘is identical to’, ‘is one and the same as’] as they are used in ordinary exact English. In a logically perfect language the oxymoron ‘the numbers 3 and 2+1 are the same number’ could not be said. Likewise, ‘the number 3 and the number 2+1 are one number’ is just as bad from a logical point (...)
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  19. John Corcoran (2012). A Farewell Letter To My Students. Philosophy Now 92:18-18.
    I am saying farewell after more than forty happy years of teaching logic at the University of Buffalo. But this is only a partial farewell. I will no longer be at UB to teach classroom courses or seminars. But nothing else will change. I will continue to be available for independent study. I will continue to write abstracts and articles with people who have taken courses or seminars with me. And I will continue to honor the LogicLifetimeGuarantee™, which is earned (...)
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  20. J. Corcoran & G. Boger (2011). Protasis in Prior Analytics: Proposition or Premise. Bulletin of Symbolic Logic 17:151 - 2.
    The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) -/- A protasis is a sentence affirming or denying something of something…. -/- is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. This paper explores recent literature on these issues.
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  21. John Corcoran (2011). Contra-Argumento/Contraejemplo. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta 137--141.
    A universal proposition is shown false by a known counterexample. A premise-conclusion argument is shown invalid by a known counterargument. The failure to distinguish counterexample from counterargument is like the failure to distinguish falsehood from invalidity.
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  22. John Corcoran (2011). Deducción/Deducibilidad. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta 168--169.
    Following Quine [] and others we take deductions to produce knowledge of implications: a person gains knowledge that a given premise-set implies a given conclusion by deducing—producing a deduction of—the conclusion from those premises. How does this happen? How does a person recognize their desire for that knowledge of a certain implication, or that they lack it? How do they produce a suitable deduction? And most importantly, how does their production of that deduction provide them with knowledge of the implication. (...)
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  23. John Corcoran (2011). Forma lógica/Formalización. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta 257--258.
    The logical form of a discourse—such as a proposition, a set of propositions, an argument, or an argumentation—is obtained by abstracting from the subject-matter of its content terms or by regarding the content terms as mere place-holders or blanks in a form. In a logically perfect language the logical form of a proposition, a set of propositions, an argument, or an argumentation is determined by the grammatical form of the sentence, the set of sentences, the argument-text, or the argumentation-text expressing (...)
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  24. John Corcoran (2011). Hare and Others on the Proposition. Principia 15 (1):51-76.
    History witnesses alternative approaches to “the proposition”. The proposition has been referred to as the object of belief, disbelief, and doubt: generally as the object of propositional attitudes, that which can be said to be believed, disbelieved, understood, etc. It has also been taken to be the object of grasping, judging, assuming, affirming, denying, and inquiring: generally as the object of propositional actions, that which can be said to be grasped, judged true or false, assumed for reasoning purposes, etc. The (...)
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  25. John Corcoran (2011). Valor de Verdad. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta 627--629.
    Down through the ages, logic has adopted many strange and awkward technical terms: assertoric, prove, proof, model, constant, variable, particular, major, minor, and so on. But truth-value is a not a typical example. Every proposition, even if false, no matter how worthless, has a truth-value:even “one plus two equals four” and “one is not one”. In fact, every two false propositions have the same truth-value—no matter how different they might be, even if one is self-contradictory and one is consistent. It (...)
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  26. John Corcoran & José Miguel Sagüillo (2011). The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper. History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
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  27. John Corcoran (2010). Argumentações e lógica. O Que Nos Faz Pensar:291-327.
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  28. John Corcoran (2010). Counterarguments and Counterexamples. In Luis Vega (ed.), Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta. 137-142.
    English translation of an entry on pages 137–42 of the Spanish-language dictionary of logic: Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta. -/- DEDICATION: To my friend and collaborator Kevin Tracy. -/- This short essay—containing careful definitions of ‘counterargument’ and ‘counterexample’—is not an easy read but it is one you’ll be glad you struggled through. It contains some carefully chosen examples suitable for classroom discussion. -/- Using the word ‘counterexample’ instead of ‘counterargument’ in connection with Aristotle’s invalidity (...)
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  29. John Corcoran (2010). Peter Hare on the Proposition. Transactions of the Charles S. Peirce Society 46 (1):21-34.
    Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent in the University of Buffalo's Philosophy Department in (...)
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  30. John Corcoran (2010). Review of Striker Translation of Aristotle's PRIOR ANALYTICS. [REVIEW] Notre Dame Philosophical Reviews:1-13.
    This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...)
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  31. John Corcoran (2009). Aristotle's Demonstrative Logic. History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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  32. John Corcoran (2009). Aristotle's Logic at the University of Buffalo's Department of Philosophy. Ideas Y Valores 140 (140):99-117.
    We begin with an introductory overview of contributions made by more than twenty scholars associated with the Philosophy Department at the University of Buffalo during the last half-century to our understanding and evaluation of Aristotle's logic. More well-known developments are merely mentioned in..
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  33. John Corcoran (2009). Aristotle's Logic at the Department of Philosophy of the University of Buffalo. Ideas Y Valores 58:99-117.
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  34. John Corcoran (2009). La lógica de Aristóteles en el departamento de filosofía de la Universidad de Búfalo. Ideas y Valores: Revista Colombiana de Filosofía 140:5.
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  35. John Corcoran (2009). Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic. In W. A. Carnielli (ed.), The Many Sides of Logic. College Publications 71-103.
    The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...)
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  36. J. Corcoran (2008). Aristotle's Many-Sorted Logic. Bulletin of Symbolic Logic 14:155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...)
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  37. John Corcoran (2008). From Peirce to Skolem. [REVIEW] Bulletin of Symbolic Logic 14 (4):541-543.
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  38. John Corcoran (2008). Meanings of Form. Manuscrito 31 (1):223-266.
    The expressions ‘form’, ‘structure’, ‘schema’, ‘shape’, ‘pattern’, ‘figure’, ‘mold’, and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of [FOR these PUT such] expressions by logicians. No [FOR such PUT similar] project has been attempted previously. After establishing general terminology, we present a variant of traditional usage of the expression ‘logical form’ followed by a discussion of the usage found in the two-volume Chateaubriand book Logical Forms (2001 and (...)
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  39. John Corcoran, Schema. Stanford Encyclopedia of Philosophy.
    -/- A schema (plural: schemata, or schemas), also known as a scheme (plural: schemes), is a linguistic template or pattern together with a rule for using it to specify a potentially infinite multitude of phrases, sentences, or arguments, which are called instances of the schema. Schemas are used in logic to specify rules of inference, in mathematics to describe theories with infinitely many axioms, and in semantics to give adequacy conditions for definitions of truth. -/- 1. What is a Schema? (...)
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  40. John Corcoran (2008). Subregular Tetrahedra. Bulletin of Symbolic Logic 14:411-2.
    This largely expository lecture deals with aspects of traditional solid geometry suitable for applications in logic courses. Polygons are plane or two-dimensional; the simplest are triangles. Polyhedra [or polyhedrons] are solid or three-dimensional; the simplest are tetrahedra [or triangular pyramids, made of four triangles]. -/- A regular polygon has equal sides and equal angles. A polyhedron having congruent faces and congruent [polyhedral] angles is not called regular, as some might expect; rather they are said to be subregular—a word coined for (...)
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  41. John Corcoran (2008). 2007-2008 Winter Meeting of the Association for Symbolic Logic-San Diego Convention Center, San Diego, CA-January 8-9, 2008-Abstracts. [REVIEW] Bulletin of Symbolic Logic 14 (3).
  42. John Corcoran, Timothy Madigan & Alexander Razin (2008). Remembering Peter Hare 1935-2008. Philosophy Now. 66 (March/April):50-2.
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  43. John Corcoran & Wagner Sanz (2008). Disbelief Logic Complements Belief Logic. Bulletin of Symbolic Logic 14:436.
    JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: corcoran@buffalo.edu Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: sanz@fchf.ufg.br -/- Consider two doxastic states belief and disbelief. Belief is taking a proposition to be true and disbelief taking it to be false. Judging also dichotomizes: accepting a proposition results in belief and rejecting in disbelief. Stating follows suit: asserting a proposition conveys belief and denying conveys disbelief. Traditional logic (...)
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  44. John Corcoran (2007). AMERICAN PHILOSOPHY: AN ENCYCLOPEDIA.
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  45. John Corcoran (2007). CONDITIONS AND CONSEQUENCES. In Lachs And Talisse (ed.), AMERICAN PHILOSOPHY: AN ENCYCLOPEDIA. 124-7.
    This elementary 4-page paper is a preliminary survey of some of the most important uses of ‘condition’ and ‘consequence’ in American Philosophy. A more comprehensive treatment is being written. Your suggestions, questions, and objections are welcome. A statement of a conditional need not be a conditional statement and conditional statement need not be a statement of a conditional.
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  46. John Corcoran (2007). Logically Equivalent False Universal Propositions with Different Counterexample Sets. Bulletin of Symbolic Logic 11:554-5.
    This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...)
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  47. John Corcoran (2007). 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. In C. Martínez (ed.), Current Topics in Logic and Analytic Philosophy /. 145-178.
  48. John Corcoran (2007). SYNTACTICS. In AMERICAN PHILOSOPHY: AN ENCYCLOPEDIA. 746-7.
    Corcoran, J. 2007. Syntactics, American Philosophy: an Encyclopedia. 2007. Eds. John Lachs and Robert Talisse. New York: Routledge. pp.745-6. -/- Syntactics, semantics, and pragmatics are the three levels of investigation into semiotics, or the comprehensive study of systems of communication, as described in 1938 by the American philosopher Charles Morris (1903-1979). Syntactics studies signs themselves and their interrelations in abstraction from their meanings and from their uses and users. Semantics studies signs in relation to their meanings, but still in abstraction (...)
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  49. John Corcoran (2007). The principle of wholistic reference/o princípio da referência universalista. Manuscrito 30 (2):493-505.
    In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...)
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  50. John Corcoran (2006). An Essay on Knowledge and Belief. International Journal of Decision Ethics (2):125-144.
    This accessible essay treats knowledge and belief in a usable and applicable way. Many of its basic ideas have been developed recently in Corcoran-Hamid 2014: Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. http://www.springer.com/birkhauser/mathematics/book/978-3-319-10192-7 .
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  51. John Corcoran (2006). Complete Enumerative Inductions. Bulletin of Symbolic Logic 12:465-6.
    Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such. -/- Matthew, Mark, Luke, and John wrote Greek. ? Every evangelist wrote Greek. -/- Matthew, Mark, Luke, and John wrote Greek. Every evangelist is Matthew, Mark, Luke, or John. ? Every evangelist wrote Greek. -/- The above pair of premise-conclusion arguments is of a sort familiar to logicians and philosophers of science. In each case the first premise is (...)
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  52. John Corcoran (2006). C. I. Lewis: History and Philosophy of Logic. Transactions of the Charles S. Peirce Society 42 (1):1-9.
    C. I. Lewis (I883-I964) was the first major figure in history and philosophy of logic—-a field that has come to be recognized as a separate specialty after years of work by Ivor Grattan-Guinness and others (Dawson 2003, 257).Lewis was among the earliest to accept the challenges offered by this field; he was the first who had the philosophical and mathematical talent, the philosophical, logical, and historical background, and the patience and dedication to objectivity needed to excel. He was blessed with (...)
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  53. John Corcoran (2006). Encyclopedia of Philosophy. 2nd Edition. Macmillan.
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  54. John Corcoran (2006). George Boole. In Encyclopedia of Philosophy. 2nd edition. Macmillan
    2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and Sriram (...)
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  55. John Corcoran (2006). Schemata: The Concept of Schema in the History of Logic. Bulletin of Symbolic Logic 12 (2):219-240.
    The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...)
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  56. John Corcoran, Stephen F. Barker, Eric Dayton, John Greco, Naomi Zack, Richard S. Robin, Joel Isaac & Murray G. Murphey (2006). A Symposium on Murray G. Murphey, CI Lewis: The Last Great Pragmatist. Transactions of the Charles S. Peirce Society 42 (1):1-77.
     
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  57. J. Corcoran (2005). Counterexamples and Proexamples. Bulletin of Symbolic Logic 11:460.
    Corcoran, J. 2005. Counterexamples and proexamples. Bulletin of Symbolic Logic 11(2005) 460. -/- John Corcoran, Counterexamples and Proexamples. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: corcoran@buffalo.edu Every perfect number that is not even is a counterexample for the universal proposition that every perfect number is even. Conversely, every counterexample for the proposition “every perfect number is even” is a perfect number that is not even. Every perfect number that is odd is a proexample for the existential proposition that some (...)
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  58. John Corcoran (2005). Wholistic Reference, Truth-Values, Universes of Discourse, and Formal Ontology: Tréplica to Oswaldo Chateaubriand. Manuscrito 28 (1):143-167.
    ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, its history, (...)
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  59. John Corcoran (2004). Review of" Michael Dummett". [REVIEW] Essays in Philosophy 5 (2):7.
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  60. John Corcoran (2004). The Principle of Wholistic Reference. Manuscrito 27 (1):159-171.
    In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly (...)
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  61. John Corcoran (2003). Aristotle's Prior Analytics and Boole's Laws of Thought. History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  62. John Corcoran (2001). Second-Order Logic. In M. Zeleny (ed.), Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. KLUKER 61–76.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework and (...)
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  63. John Corcoran (1999). CORCORAN'S 27 ENTRIES IN THE 1999 SECOND EDITION. In Robert Audi (ed.), Cambridge Dictionary of Philosophy. CAMBRIDGE UP 65-941.
    Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...)
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  64. John Corcoran (1999). Critical Thinking and Pedagogical License. Manuscrito 22 (2):109.
    Critical thinking involves deliberate application of tests and standards to beliefs per se and to methods used to arrive at beliefs. Pedagogical license is authorization accorded to teachers permitting them to use otherwise illicit means in order to achieve pedagogical goals. Pedagogical license is thus analogous to poetic license or, more generally, to artistic license. Pedagogical license will be found to be pervasive in college teaching. This presentation suggests that critical thinking courses emphasize two topics: first, the nature and usefulness (...)
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  65. John Corcoran (1999). Information-Theoretic Logic and Transformation-Theoretic Logic,. In R. A. M. M. (ed.), Fragments in Science,. World Scientific Publishing Company, 25-35.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information beyond that of the premise-set. This (...)
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  66. John Corcoran (1999). The Logical Form of Quantifier Phrases: Quantifier-Sortalvariable. Bulletin of Symbolic Logic 5:418-419.
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  67. J. Corcoran (1996). Semantic Omega Properties and Mathematical Induction. Bulletin of Symbolic Logic 2:468.
     
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  68. John Corcoran (1995). Axiomatic Method. In Audi Robert (ed.), The Cambridge Dictionary of Philosophy. Cambridge University Press 57--58.
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  69. John Corcoran (1995). Information Recovery Problems. Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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  70. John Corcoran (1995). Semantic Arithmetic: A Preface. Agora 14 (1):149-156.
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  71. John Corcoran (1995). Tarski, Alfred.”. In Audi Robert (ed.), The Cambridge Dictionary of Philosophy. Cambridge University Press
     
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  72. Morris R. Cohen, Ernest Nagel & John Corcoran (1994). An Introduction to Logic. Transactions of the Charles S. Peirce Society 30 (4):1064-1068.
     
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  73. J. Corcoran (1994). Argumentaciones y lógica. Agora 13 (1):27.
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  74. John Corcoran (1994). The Founding of Logic. Ancient Philosophy 14 (1):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  75. J. Corcoran (1992). Logical Methodology: Aristotle and Tarski. Journal of Symbolic Logic 57:374.
     
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  76. John Corcoran (1992). El nacimiento de la lógica. La concepción de la prueba en términos de Verdad y Consecuencia. Agora 11 (2):67.
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  77. John Corcoran (1991). REVIEW OF Alfred Tarski, Collected Papers, Vols. 1-4 (1986) Edited by Steven Givant and Ralph McKenzie. [REVIEW] MATHEMATICAL REVIEWS 91 (h):01101-4.
    Alfred Tarski (1901--1983) is widely regarded as one of the two giants of twentieth-century logic and also as one of the four greatest logicians of all time (Aristotle, Frege and Gödel being the other three). Of the four, Tarski was the most prolific as a logician. The four volumes of his collected papers, which exclude most of his 19 monographs, span over 2500 pages. Aristotle's writings are comparable in volume, but most of the Aristotelian corpus is not about logic, whereas (...)
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  78. J. Corcoran, A. Tarski, Waikoe W. J. Jr & D. Westerstahl (1990). Dept. Of Philosophy University of California at San Diego La Jolla, CA 92093 USA. Linguistics and Philosophy 13:423-475.
     
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  79. John Corcoran (1989). Argumentations and Logic. ARGUMENTAION 3 (1):17-43.
    Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial philosophic (...)
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  80. John Corcoran (1989). The Inseparability of Logic and Ethics. Free Inquiry 9 (2):37-40.
    This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion; ethics is pointless without rigor and objectivity. The logician urging us to be dispassionate is in resonance and harmony with the ethicist urging us to be compassionate.
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  81. John Corcoran & Woosuk Park (1989). Review: Elliott Mendelson, Introduction to Mathematical Logic. [REVIEW] Journal of Symbolic Logic 54 (2):618-619.
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  82. John Corcoran (1988). REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), Edited and Translated by G. B. Halsted, 2nd Ed. (1986), in Mathematical Reviews MR0862448. 88j:01013. MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
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  83. John Corcoran & Woosuk Park (1988). Review: Nino B. Cocchiarella, Logical Investigations of Predication Theory and the Problem of Universals. [REVIEW] Journal of Symbolic Logic 53 (3):991-993.
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  84. John Corcoran (1987). Three Rules of Distribution: One Counterexample. Journal of Symbolic Logic 52:886-887.
    This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does (...)
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  85. John Corcoran (1986). Essay Review. History and Philosophy of Logic 7 (1):65-75.
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  86. John Corcoran & Alfred Tarski (1986). What Are Logical Notions? History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  87. J. Corcoran (1985). Significados de la implicación. Agora 5:279.
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  88. John Corcoran (1984). Review: Alfred J. Freddoso, William of Ockham, Henry Schuurman, Ockham's Theory of Truth Conditions. [REVIEW] Journal of Symbolic Logic 49 (1):306-308.
  89. Roderick M. Chisholm, John Corcoran, Jorge Gracia, L. S. Carrier, T. N. Pelegrinis, Alfred L. Ivry, D. S. Clarke, Leo Rauch, Robert Young, Michael J. Loux, Rita Nolan, Gerald Vision, E. D. Klemke, Ruth Anna Putnam, Edward S. Reed, Maurice Mandelbaum, John Wettersten & Rachel Shihor (1983). Book Reviews. [REVIEW] Philosophia 13 (1-2):359-362.
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  90. Alfred Tarski & John Corcoran (1983). Logic, Semantics, Metamathematics Papers From 1923 to 1938. Hackett.
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  91. John Corcoran & Michael Scanlan (1982). Review: The Contemporary Relevance of Ancient Logical Theory. [REVIEW] Philosophical Quarterly 32 (126):76 - 86.
    This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...)
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  92. John Corcoran & Micheal Scanlan (1982). Critical Notice: Contemporary Relevance of Ancient Logical Theory. Philosophical Quarterly 32 (1):76-86.
  93. J. Corcoran (1981). From Categoricity to Completeness. History and Philosophy of Logic 2:113.
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  94. John Corcoran (1981). Review: Michael J. Loux, The Ontology of William of Ockham. [REVIEW] Journal of Symbolic Logic 46 (3):667-668.
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  95. John Corcoran & Michael Scanlon (1981). Jonathan Lear, Aristotle and Logical Theory Reviewed By. Philosophy in Review 1 (2/3):85-91.
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  96. John Corcoran & Michael Scanlon (1981). Jonathan Lear, Aristotle and Logical Theory. [REVIEW] Philosophy in Review 1:85-91.
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  97. J. Corcoran (1980). On Definitional Equivalence and Related Topics. History and Philosophy of Logic 1:231.
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  98. John Corcoran (1980). Categoricity. History and Philosophy of Logic 1 (1):187-207.
    After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...)
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  99. John Corcoran & Susan Wood (1980). Boole's Criteria for Validity and Invalidity. Notre Dame Journal of Formal Logic 21 (4):609-638.
    It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...)
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  100. John Corcoran & Stanley Ziewacz (1979). Identity Logics. Notre Dame Journal of Formal Logic 20 (4):777-784.
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  101. John Corcoran & Stewart Shapiro (1978). What is Mathematical Logic? Philosophia 8 (1):79-94.
    This review concludes that if the authors know what mathematical logic is they have not shared their knowledge with the readers. This highly praised book is replete with errors and incoherency.
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  102. John Corcoran & John Swiniarski (1978). Logical Structures of Ockham's Theory of Supposition. Franciscan Studies 38 (1):161-183.
    This exposition of ockham's theory of (common, Personal) supposition involves the logical form of the four descent/ascent conditions and the logical relations of these with the three main modes of supposition. Central theses: each condition is a one-Way entailment, Each mode is a truth-Functional combination of conditions, Two of the three modes are not even coextensive with the two-Way entailments commonly taken as their definitions. Ockham's idea of "the singulars" of a general proposition is vague and problematic and the entailment (...)
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  103. John Corcoran & Stewart Shapiro (1976). Review of J. N. Crossley Et Al., What Is Mathematical Logic?. [REVIEW] Philosophy of Science 43 (2):301-.
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  104. John Corcoran (ed.) (1974). Ancient Logic and its Modern Interpretations. Boston,Reidel.
    This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...)
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  105. John Corcoran (1974). Ancient Logic and its Modern Interpretations Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972. [REVIEW]
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  106. John Corcoran (1974). Aristotle's Natural Deduction System. In Ancient Logic and its Modern Interpretations. Boston,Reidel 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  107. John Corcoran (1974). Aristotelian Syllogisms: Valid Arguments or True Universalized Conditionals? Mind 83 (330):278-281.
    Corcoran, John. 1974. Aristotelian Syllogisms: Valid arguments or true generalized conditionals?, Mind 83, 278–81. MR0532928 (58 #27178) This tightly-written and self-contained four-page paper must be studied and not just skimmed. It meticulously analyses quotations from Aristotle and Lukasiewicz to establish that Aristotle was using indirect deductions—as required by the natural-deduction interpretation—and not indirect proofs—as required by the axiomatic interpretation. Lukasiewicz was explicit and clear about the subtle fact that Aristotle’s practice could not be construed as correctly performed indirect proof. Lukasiewicz (...)
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  108. John Corcoran (1974). Future Research on Ancient Theories of Communication and Reasoning. In Ancient Logic and its Modern Interpretations. Boston,Reidel 185--187.
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  109. John Corcoran (1974). Remarks on Stoic Deduction. In Ancient Logic and its Modern Interpretations. Boston,Reidel 169--181.
    This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.
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  110. John Corcoran, William Frank & Michael Maloney (1974). String Theory. Journal of Symbolic Logic 39 (4):625-637.
    For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...)
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  111. George Weaver & John Corcoran (1974). Logical Consequence in Modal Logic. II. Some Semantic Systems for ${\Rm S}4$. Notre Dame Journal of Formal Logic 15 (3):370-378.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  112. John Corcoran (1973). A Mathematical Model of Aristotle's Syllogistic. Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...)
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  113. John Corcoran (1973). Bernard Bolzano's "Theory of Science". [REVIEW] Philosophy and Phenomenological Research 34 (2):282.
     
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  114. John Corcoran (1973). Gaps Between Logical Theory and Mathematical Practice. In Mario Augusto Bunge (ed.), The Methodological Unity of Science. Boston,Reidel 23--50.
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  115. John Corcoran (1973). Gottlob Frege's "On the Foundations of Geometry and Formal Theories of Arithmetic". [REVIEW] Philosophy and Phenomenological Research 34 (2):283.
     
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  116. John Corcoran (1973). Meanings of Implication. Dialogos 9 (1):59-76.
    Thirteen meanings of 'implication' are described and compared. Among them are relations that have been called: logical implication, material implication,deductive implication, formal implication, enthymemic implication, and factual implication. In a given context, implication is the homogeneous two-place relation expressed by the relation verb 'implies'. For heuristic and expository reasons this article skirts many crucial issues including use-mention, the nature of the entities that imply and are implied, and the processes by which knowledge of these relations are achieved. This paper is (...)
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  117. John Corcoran (1973). Book Review:Philosophy of Logic Hilary Putnam. [REVIEW] Philosophy of Science 40 (1):131-.
    Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as (...)
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  118. John Corcoran & David Levin (1973). Book Review:Conceptual Notation and Related Articles Gottlob Frege, Terrell Ward Bynum. [REVIEW] Philosophy of Science 40 (3):454-.
  119. John Corcoran & John Richards (1973). Book Review:The Theory of Logical Types Irving M. Copi. [REVIEW] Philosophy of Science 40 (2):319-.
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  120. John Corcoran & Susan B. Wood (1973). The Switches "Paradox" and the Limits of Propositional Logic. Philosophy and Phenomenological Research 34 (1):102-108.
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  121. John Corcoran (1972). Completeness of an Ancient Logic. Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system is deducible (...)
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  122. John Corcoran (1972). Conceptual Structure of Classical Logic. Philosophy and Phenomenological Research 33 (1):25-47.
    One innovation in this paper is its identification, analysis, and description of a troubling ambiguity in the word ‘argument’. In one sense ‘argument’ denotes a premise-conclusion argument: a two-part system composed of a set of sentences—the premises—and a single sentence—the conclusion. In another sense it denotes a premise-conclusion-mediation argument—later called an argumentation: a three-part system composed of a set of sentences—the premises—a single sentence—the conclusion—and complex of sentences—the mediation. The latter is often intended to show that the conclusion follows from (...)
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  123. John Corcoran (1972). Weak and Strong Completeness in Sentential Logics. Logique Et Analyse 15:429.
     
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  124. John Corcoran (1972). Book Review:Hilbert Constance Reid. [REVIEW] Philosophy of Science 39 (1):106-.
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  125. John Corcoran (1972). Book Review:Foundations of Mathematics William S. Hatcher. [REVIEW] Philosophy of Science 39 (1):88-.
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  126. John Corcoran (1972). Book Review:Philosophy of Logic Willard Van Orman Quine. [REVIEW] Philosophy of Science 39 (1):97-.
  127. John Corcoran (1972). Strange Arguments. Notre Dame Journal of Formal Logic 13 (2):206-210.
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  128. John Corcoran, William Hatcher & John Herring (1972). Variable Binding Term Operators. Mathematical Logic Quarterly 18 (12):177-182.
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  129. John Corcoran & John Herring (1972). Review: Heinz-Dieter Ebbinghaus, Uber eine Pradikatenlogik mit Partiell Definierten Pradikaten und Funktionen. [REVIEW] Journal of Symbolic Logic 37 (3):617-618.
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  130. John Corcoran & John Herring (1972). Review: Hao Wang, The Calculus of Partial Predicates and its Extension to Set Theory I. [REVIEW] Journal of Symbolic Logic 37 (3):617-617.
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  131. J. Corcoran & John Herring (1971). Notes on a Semantic Analysis of Variable Binding Term Operators. Logique Et Analyse 55:644-657.
     
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  132. John Corcoran (1969). Three Logical Theories. Philosophy of Science 36 (2):153-177.
    This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logical truth and logical (...)
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  133. John Corcoran & George Weaver (1969). Logical Consequence in Modal Logic. Notre Dame Journal of Formal Logic 10 (4):370-384.
    This paper develops a modal, Sentential logic having "not", "if...Then" and necessity as logical constants. The semantics (system of meanings) of the logic is the most obvious generalization of the usual truth-Functional semantics for sentential logic and its deductive system (system of demonstrations) is an obvious generalization of a suitable (jaskowski-Type) natural deductive system for sentential logic. Let a be a set of sentences and p a sentence. "p is a logical consequence of a" is defined relative to the semantics (...)
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