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70Logical 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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134Deducción/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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302Disbelief 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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446Semantic 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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270Subregular 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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3348C. 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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220Complete 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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870REVIEW 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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2958Aristotle'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 (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 arti…Read more
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337Aristotle’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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454Meanings 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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946Reid, 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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1707Ancient logic and its modern interpretations (edited book)Reidel. 1974.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 logic stud…Read more
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696INVESTIGATING 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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493We 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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19The Logical Form of Quantifier Phrases: Quantifier-sortalvariableBulletin of Symbolic Logic 5 418-419. 1999.
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10Freddoso Alfred J.. Ockham's theory of truth conditions. Ockham's theory of propositions, Part II of the Summa logicae, by William of Ockham, translated by Freddoso Alfred J. and Schuurman Henry with an introduction by Freddoso Alfred J., University of Notre Dame Press, Notre Dame and London 1980, pp. 1–76 (review)Journal of Symbolic Logic 49 (1): 306-308. 1984.
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325Formalizing Euclid’s first axiom.Bulletin of Symbolic Logic 20 (3): 404-405. 2014.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…Read more
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1937Schemata: The concept of schema in the history of logicBulletin of Symbolic Logic 12 (2): 219-240. 2006.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…Read more
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1657The Founding of Logic: Modern Interpretations of Aristotle’s LogicAncient Philosophy 14 (S1): 9-24. 1994.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 conc…Read more
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34Book Review:The Theory of Logical Types Irving M. Copi (review)Philosophy of Science 40 (2): 319-. 1973.
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803Conceptual structure of classical logicPhilosophy and Phenomenological Research 33 (1): 25-47. 1972.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…Read more
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238Critical thinking and pedagogical license. Manuscrito XXII, 109–116. Persian translation by Hassan Masoud.Manuscrito: 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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320Review of Striker translation of Aristotle's PRIOR ANALYTICS (review)Notre Dame Philosophical Reviews 1-13. 2010.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 infl…Read more
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265Surprises in logicBulletin of Symbolic Logic 19 (3): 253. 2013.JOHN CORCORAN AND WILIAM FRANK. Surprises in logic. Bulletin of Symbolic Logic. 19 253. 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 to f…Read more
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30The 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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429CONDITIONS AND CONSEQUENCESIn Lachs And Talisse (ed.), AMERICAN PHILOSOPHY: AN ENCYCLOPEDIA, . 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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