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19The Logical Form of Quantifier Phrases: Quantifier-sortalvariableBulletin of Symbolic Logic 5 418-419. 1999.
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726“Truth-preserving and consequence-preserving deduction rules”Bulletin of Symbolic Logic 20 (1): 130-1. 2014.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 dis…Read more
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655Disbelief Logic Complements Belief LogicBulletin of Symbolic Logic 14 (3): 436. 2008.JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: [email protected] Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: [email protected] 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…Read more
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929Critical thinking and pedagogical licenseManuscrito 22 (2): 109. 1999.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 cours…Read more
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609Complete Enumerative InductionsBulletin of Symbolic Logic 12 465-6. 2006.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 logically equivale…Read more
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2511String theoryJournal of Symbolic Logic 39 (4): 625-637. 1974.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 syno…Read more
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1216Girolamo 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…Read more
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106Book Review:The Theory of Logical Types Irving M. Copi (review)Philosophy of Science 40 (2): 319-. 1973.
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135The Tarskian Turn: Deflationism and Axiomatic Truth (review)History and Philosophy of Logic 35 (3): 308-313. 2014.This brief, largely expository book—hereafter TT—blends history and philosophy of logic with contemporary mathematical logic. Page 3 says it “is about the relation between formal theories of truth...
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796Aristotle’s semiotic triangles and pyramidsBulletin of Symbolic Logic 21 (1): 198-9. 2015.Imagine an equilateral triangle “pointing upward”—its horizontal base under its apex angle. A semiotic triangle has the following three “vertexes”: (apex) an expression, (lower-left) one of the expression’s conceptual meanings or senses, and (lower-right) the referent or denotation determined by the sense [1, pp. 88ff]. One example: the eight-letter string ‘coleslaw’ (apex), the concept “coleslaw” (lower-left), and the salad coleslaw (lower-right) [1, p. 84f]. Using Church’s terminology [2, pp. …Read more
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2053Wholistic reference, truth-values, universes of discourse, and formal ontology: tréplica to Oswaldo ChateaubriandManuscrito 28 (1): 143-167. 2005.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, and i…Read more
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Axiomatic methodIn Robert Audi (ed.), The Cambridge Dictionary of Philosophy, Cambridge University Press. pp. 57--58. 1995.
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796Meanings of formManuscrito 31 (1): 223-266. 2008.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 …Read more
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1546Logic Teaching in the 21St CenturyQuadripartita Ratio: Revista de Argumentación y Retórica 1 (1): 1-34. 2016.We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, contextualism…Read more
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156The switches "paradox" and the limits of propositional logicPhilosophy and Phenomenological Research 34 (1): 102-108. 1973.
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1441Investigating Knowledge and OpinionIn A. Buchsbaum A. Koslow (ed.), The Road to Universal Logic. Vol. I, Springer. pp. 95-126. 2014.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 not every proposition believed to be true i…Read more
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1183George BooleIn Encyclopedia of Philosophy. 2nd edition, Macmillan. 2006.2006. 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 s…Read more
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1570The Contemporary Relevance of Ancient Logical TheoryPhilosophical Quarterly 32 (126): 76. 1982.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 treat…Read more
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2730Sentence, Proposition, Judgment, Statement, and Fact: Speaking about the Written English Used in LogicIn W. A. Carnielli (ed.), The Many Sides of Logic, College Publications. pp. 71-103. 2009.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 rec…Read more
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138Existential-Import MathematicsBulletin of Symbolic Logic 21 (1): 1-14. 2015.First-order logic haslimitedexistential import: the universalized conditional ∀x[S(x) → P(x)] implies its corresponding existentialized conjunction ∃x[S(x) & P(x)] insome but not allcases. We prove theExistential-Import Equivalence:∀x[S(x) → P(x)] implies ∃x[S(x) & P(x)] iff ∃xS(x) is logically true.The antecedent S(x) of the universalized conditional alone determines whether the universalized conditionalhas existential import: implies its corresponding existentialized conjunction.Apredicateis a…Read more
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443Critical thinking and pedagogical license. Manuscrito XXII, 109–116. Persian translation by Hassan MasoudManuscrito: Revista Internacional de Filosofía 22 (2): 109-116. 1999.CRITICAL THINKING AND PEDAGOGICAL LICENSE https://www.academia.edu/9273154/CRITICAL_THINKING_AND_PEDAGOGICAL_LICENSE JOHN CORCORAN.1999. Critical thinking and pedagogical license. Manuscrito XXII, 109–116. Persian translation by Hassan Masoud. Please post your suggestions for corrections and alternative translations. -/- 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 accorde…Read more
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881Review of Macbeth, D. Diagrammatic reasoning in Frege's Begriffsschrift. Synthese 186 (2012), no. 1, 289–314MATHEMATICAL REVIEWS 2014 2935338. 2014.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—alou…Read more
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Critical Notice: Contemporary Relevance of Ancient Logical TheoryPhilosophical Quarterly 32 (1): 76-86. 1982.
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933Conditions and ConsequencesIn Lachs And Talisse (ed.), AMERICAN PHILOSOPHY: AN ENCYCLOPEDIA, Psychology Press. pp. 124-7. 2007.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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1286Semantic Arithmetic: A PrefaceAgora 14 (1): 149-156. 1995.SEMANTIC ARITHMETIC: A PREFACE John Corcoran Abstract Number theory, or pure arithmetic, concerns the natural numbers themselves, not the notation used, and in particular not the numerals. String theory, or pure syntax, concems the numerals as strings of «uninterpreted» characters without regard to the numbe~s they may be used to denote. Number theory is purely arithmetic; string theory is purely syntactical... in so far as the universe of discourse alone is considered. Semantic arithmetic is a …Read more
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Areas of Specialization
| Epistemology |
| Logic and Philosophy of Logic |