•  108
    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
  •  274
    Aristotle’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
  •  805
    Information-theoretic logic and transformation-theoretic logic,
    In R. A. M. M. (ed.), Fragments in Science,, World Scientific Publishing Company,. pp. 25-35. 1999.
    Information-theoretic approaches to formal logic analyze the "common intuitive" concepts of implication, consequence, and validity in terms of information content of propositions and sets of propositions: one given proposition implies a second if the former contains all of the information contained by the latter; one given proposition is a consequence of a second if the latter contains all of the information contained by the former; an argument is valid if the conclusion contains no information …Read more
  •  832
    LOGIC TEACHING IN THE 21ST CENTURY
    Quadripartita 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
  •  644
    Three logical theories
    Philosophy of Science 36 (2): 153-177. 1969.
    This study concerns logical systems considered as theories. By searching for the problems which the traditionally given systems may reasonably be intended to solve, we clarify the rationales for the adequacy criteria commonly applied to logical systems. From this point of view there appear to be three basic types of logical systems: those concerned with logical truth; those concerned with logical truth and with logical consequence; and those concerned with deduction per se as well as with logica…Read more
  •  353
    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..
  •  570
    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 …Read more
  • Tarski, Alfred.”
    In Audi Robert (ed.), The Cambridge Dictionary of Philosophy, Cambridge University Press. 1995.
  •  244
    Three 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
  •  221
    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
  •  519
    This paper raises obvious questions undermining any residual confidence in Mates work and revealing our embarrassing ignorance of true nature of Stoic deduction. It was inspired by the challenging exploratory work of JOSIAH GOULD.
  •  1216
    Second-order Logic
    In Alonzo Church, C. Anthony Anderson & Michael Zelëny (eds.), Logic, meaning, and computation: essays in memory of Alonzo Church, Kluwer Academic Publishers. 2001.
    “Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a …Read more
  •  23
    Essay Review
    History and Philosophy of Logic 7 (1): 65-75. 1986.
  •  440
    Critical thinking and pedagogical license
    Manuscrito 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 cour…Read more
  •  311
    Protasis in Prior Analytics: Proposition or Premise
    with G. Boger
    Bulletin of Symbolic Logic 17 (1). 2011.
    The word pro-tasis is etymologically a near equivalent of pre-mise, pro-position, and ante-cedent—all having positional, relational connotations now totally absent in contemporary use of proposition. Taking protasis for premise, Aristotle’s statement (24a16) A protasis is a sentence affirming or denying something of something…. is not a definition of premise—intensionally: the relational feature is absent. Likewise, it is not a general definition of proposition—extensionally: it is too narrow. T…Read more
  •  277
    John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important …Read more
  •  9
    Hare and Others on the Proposition DOI: 10.5007/1808-1711.2011v15n1p51
    Principia: An International Journal of Epistemology 15 (1). 2011.
  •  289
    Counterexamples and Proexamples
    Bulletin 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
  •  456
    CORCORAN'S 27 ENTRIES IN THE 1999 SECOND EDITION
    In Robert Audi (ed.), The Cambridge Dictionary of Philosophy, Cambridge Up. pp. 65-941. 1999.
    Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, …Read more
  •  30
    Logical Structures of Ockham's Theory of Supposition
    with John Swiniarski
    Franciscan Studies 38 (1): 161-183. 1978.
    This exposition of ockham's theory of (common, Personal) supposition involves the logical form of the four descent/ascent conditions and the logical relations of these with the three main modes of supposition. Central theses: each condition is a one-Way entailment, Each mode is a truth-Functional combination of conditions, Two of the three modes are not even coextensive with the two-Way entailments commonly taken as their definitions. Ockham's idea of "the singulars" of a general proposition is …Read more
  •  585
    Meanings of word: type-occurrence-token.
    Bulletin of Symbolic Logic 11 (1): 117. 2005.
    Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token…Read more
  •  842
    Variable Binding Term Operators
    with William Hatcher and John Herring
    Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12): 177-182. 1972.
    Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes o…Read more
  •  978
    A Mathematical Model of Aristotle’s Syllogistic
    Archiv für Geschichte der Philosophie 55 (2): 191-219. 1973.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consu…Read more
  •  2322
    A Inseparabilidade entre Lógica e a Ética.
    Philósophos - Revista de Filosofia 18 (1): 245-259. 2013.
    A Inseparabilidade entre Lógica e a Ética. Philósophos. 18 (2013) 245–259. Portuguese translation by Décio Krause and Pedro Merlussi: The Inseparability of Logic and Ethics, Free Inquiry, Spring 1989, 37–40. This essay takes logic and ethics in broad senses: logic as the science of evidence; ethics as the science of justice. One of its main conclusions is that neither science can be fruitfully pursued without the virtues fostered by the other: logic is pointless without fairness and compassion…Read more
  •  283
    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 numbers satisfying “not od…Read more
  •  32
    The Founding of Logic
    Ancient Philosophy 14 (S1): 9-24. 1994.
  • Argumentações e lógica
    O Que Nos Faz Pensar 291-327. 2010.
  •  4
    Gottlob Frege's "On the Foundations of Geometry and Formal Theories of Arithmetic" (review)
    Philosophy and Phenomenological Research 34 (2): 283-286. 1973.
  •  380
    Equality and identity
    with Anthony Ramnauth
    Bulletin of Symbolic Logic 19 (3): 255-256. 2013.
    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 of view. …Read more