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18Book Review:Foundations of Mathematics William S. Hatcher (review)Philosophy of Science 39 (1): 88-. 1972.
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1021Completeness of an ancient logicJournal of Symbolic Logic 37 (4): 696-702. 1972.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 deducib…Read more
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351Counterarguments and counterexamples.In Luis Vega (ed.), Luis Vega, Ed. Compendio de Lógica, Argumentación, y Retórica. Madrid: Trotta., . pp. 137-142. 2010.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’ …Read more
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51On definitional equivalence and related topicsHistory and Philosophy of Logic 1 (n/a): 231. 1980.
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248Review of: Garciadiego, A., "Emergence of...paradoxes...set theory", Historia Mathematica (1985), in Mathematical Reviews 87j:01035.MATHEMATICAL REVIEWS 87 (J): 01035. 1987.DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more commonly, from the hypothesi…Read more
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1582007-2008 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). 2008.
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Bernard Bolzano's "Theory of Science" (review)Philosophy and Phenomenological Research 34 (2): 282. 1973.
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12La lógica de Aristóteles en el departamento de filosofía de la Universidad de BúfaloIdeas y Valores: Revista Colombiana de Filosofía 140 5. 2009.
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918Meanings of ImplicationDiálogos. Revista de Filosofía de la Universidad de Puerto Rico 9 (24): 59-76. 1973.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 a…Read more
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262The principle of wholistic referenceManuscrito 27 (1): 159-171. 2004.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…Read more
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Axiomatic methodIn Audi Robert (ed.), The Cambridge Dictionary of Philosophy, Cambridge University Press. pp. 57--58. 1995.
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563This 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 anno…Read more
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300Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication.Bulletin of Symbolic Logic 14 (4): 435-6. 2008.Iffication, Preiffication, Qualiffication, Reiffication, and Deiffication. Roughly, iffication is the speech-act in which—by appending a suitable if-clause—the speaker qualifies a previous statement. The clause following if is called the qualiffication. In many cases, the intention is to retract part of the previous statement—called the preiffication. I can retract part of “I will buy three” by appending “if I have money”. This initial study focuses on logical relations among propositional cont…Read more
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773The 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 trea…Read more
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48Aristotle's Prior Analytics and Boole's Laws of ThoughtHistory and Philosophy of Logic 24 (4): 261-288. 2003.Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole 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 many othe…Read more
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133Deducción/DeducibilidadIn Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 168--169. 2011.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 knowled…Read more
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300Disbelief Logic Complements Belief Logic.Bulletin 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 follow…Read more
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441Semantic 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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267Subregular tetrahedraBulletin of Symbolic Logic 14 (3): 411-2. 2008.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; rat…Read more
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69Logical Consequence in Modal LogicNotre Dame Journal of Formal Logic 10 (4): 370-384. 1969.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 define…Read more
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218Complete 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 equiva…Read more
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28Review: Elliott Mendelson, Introduction to Mathematical Logic (review)Journal of Symbolic Logic 54 (2): 618-619. 1989.
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865REVIEW OF Alfred Tarski, Collected Papers, vols. 1-4 (1986) edited by Steven Givant and Ralph McKenzie (review)MATHEMATICAL REVIEWS 91 (h): 01101-4. 1991.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 virtually everythi…Read more
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3335C. I. Lewis: History and philosophy of logicTransactions of the Charles S. Peirce Society 42 (1): 1-9. 2006.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 bles…Read more
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335Aristotle’s semiotic triangles and pyramids.Bulletin 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 …Read more
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451Meanings 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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944Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08.Philosophy of Science 39 (1): 106-108. 1972.Reid, Constance. Hilbert (a Biography). Reviewed by Corcoran in Philosophy of Science 39 (1972), 106–08. Constance Reid was an insider of the Berkeley-Stanford logic circle. Her San Francisco home was in Ashbury Heights near the homes of logicians such as Dana Scott and John Corcoran. Her sister Julia Robinson was one of the top mathematical logicians of her generation, as was Julia’s husband Raphael Robinson for whom Robinson Arithmetic was named. Julia was a Tarski PhD and, in recognition of …Read more
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