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Profile: John Corcoran (State University of New York, Buffalo)
  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. 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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  21. 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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  22. 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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  23. 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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  24. 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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  25. 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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  26. John Corcoran (2010). Argumentações e lógica. O Que Nos Faz Pensar:291-327.
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  27. 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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  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. 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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  34. 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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  35. John Corcoran (2008). From Peirce to Skolem. [REVIEW] Bulletin of Symbolic Logic 14 (4):541-543.
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  36. 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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  37. 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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  38. 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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  39. 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).
  40. John Corcoran, Timothy Madigan & Alexander Razin (2008). Remembering Peter Hare 1935-2008. Philosophy Now. 66 (March/April):50-2.
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  41. 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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  42. 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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  43. 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.
  44. 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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  45. 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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  46. 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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  47. 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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  48. John Corcoran (2006). Encyclopedia of Philosophy. 2nd Edition. Macmillan.
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  49. 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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  50. 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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