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256The 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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255Subregular 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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253Surprises 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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246Counterexamples and ProexamplesBulletin of Symbolic Logic 11 460. 2005.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: [email protected] 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 th…Read more
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243Valor de verdadIn Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 627--629. 2011.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 co…Read more
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241Aristotle’s “whenever three terms”.Bulletin of Symbolic Logic 19 (3): 234-235. 2013.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 they think that …Read more
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237Review 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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234Three rules of distribution: one counterexample.Journal of Symbolic Logic 52 886-887. 1987.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 havin…Read more
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225Identity logicsNotre Dame Journal of Formal Logic 20 (4): 777-784. 1979.In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both the direct and the indirect deductions constructed with the three traditional rules. IL3 is …Read more
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224Critical 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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219Review of WILLARD QUINE, Philosophy of logic, Harvard, 1970/1986. (review)Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 39 37-39. 1972.This book is best regarded as a concise essay developing the personal views of a major philosopher of logic and as such it is to be welcomed by scholars in the field. It is not (and does not purport to be) a treatment of a significant portion of those philosophical problems generally thought to be germane to logic. It would be easy to list many popular topics in philosophy of logic which it does not mention. Even its "definition" of logic-"the systematic study of logical truth"-is peculiar to th…Read more
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212Complete 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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210CORCORAN’S THUMBNAIL REVIEWS OF OPPOSING PHILOSOPHY OF LOGIC BOOKSMATHEMATICAL REVIEWS 56 98-9. 1978-9.PUTNAM 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 far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary sci…Read more
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1492007-2008 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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130Deducción/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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104Aristotelian syllogisms: Valid arguments or true universalized conditionals?Mind 83 (330): 278-281. 1974.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 explici…Read more
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100Logic, Semantics, Metamathematics: Papers from 1923 to 1938 (edited book)Hackett Publishing Company. 1983.Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.
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82SchemaStanford Encyclopedia of Philosophy. 2008.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? 2.…Read more
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80The switches "paradox" and the limits of propositional logicPhilosophy and Phenomenological Research 34 (1): 102-108. 1973.
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61Logical 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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60Existential-import mathematicsBulletin of Symbolic Logic 21 (1): 1-14. 2015.First-order logic has limited existential import: the universalized conditional ∀x [S → P] implies its corresponding existentialized conjunction ∃x [S & P] in some but not all cases. We prove the Existential-Import Equivalence:∀x [S → P] implies ∃x [S & P] iff ∃x S is logically true.The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import: implies its corresponding existentialized conjunction.A predicate is a formula having o…Read more
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54Heinz-Dieter Ebbinghaus. Über eine Prädikatenlogik mit partiell definierten Prädikaten und Funktionen. Archie für mathematische Logik und Grundlagenforschung, vol. 12 , pp. 39–53 (review)Journal of Symbolic Logic 37 (3): 617-618. 1972.
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53Review of J. N. Crossley et al., What Is Mathematical Logic? (review)Philosophy of Science 43 (2): 301-. 1976.
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52Gaps between logical theory and mathematical practiceIn Mario Augusto Bunge (ed.), The Methodological Unity of Science, Reidel. pp. 23--50. 1973.
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50Logical Investigations of Predication Theory and the Problem of UniversalsNoûs 25 (2): 221-230. 1991.
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49Murray Murphey's Work and C. I. Lewis's Epistemology: Problems with Realism and the Context of Logical PositivismTransactions of the Charles S. Peirce Society 42 (1): 32-44. 2006.
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48C. I. Lewis: History and Philosophy of LogicTransactions of the Charles S. Peirce Society 42 (1): 1-9. 2006.
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48On definitional equivalence and related topicsHistory and Philosophy of Logic 1 (n/a): 231. 1980.
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Logic and Philosophy of Logic |