•  18
    Information Recovery Problems
    Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (3): 55-78. 1995.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and pr…Read more
  •  52
    Conceptual Notation and Related Articles (review)
    with David Levin
    Philosophy of Science 36 (1): 454-455. 1972.
  •  323
    Formalizing 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
  •  1932
    Schemata: The concept of schema in the history of logic
    Bulletin 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
  •  1649
    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
  •  237
    Critical 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
  •  318
    Review 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
  •  263
    Surprises in logic
    with William Frank
    Bulletin 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
  •  34
    Book Review:The Theory of Logical Types Irving M. Copi (review)
    with John Richards
    Philosophy of Science 40 (2): 319-. 1973.
  •  797
    Conceptual structure of classical logic
    Philosophy 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
  •  427
    CONDITIONS AND CONSEQUENCES
    In 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.
  •  526
    Peter Hare on the proposition
    Transactions of the Charles S. Peirce Society 46 (1): 21-34. 2010.
    Peter H. Hare (1935-2008) developed informed, original views about the proposition: some published (Hare 1969 and Hare-Madden 1975); some expressed in conversations at scores of meetings of the Buffalo Logic Colloquium and at dinners following. The published views were expository and critical responses to publications by Curt J. Ducasse (1881-1969), a well-known presence in American logic, a founder of the Association for Symbolic Logic and its President for one term.1Hare was already prominent …Read more
  •  331
    This 4-page review-essay—which is entirely reportorial and philosophically neutral as are my other contributions to MATHEMATICAL REVIEWS—starts with a short introduction to the philosophy known as mathematical structuralism. The history of structuralism traces back to George Boole (1815–1864). By reference to a recent article various feature of structuralism are discussed with special attention to ambiguity and other terminological issues. The review-essay includes a description of the recent ar…Read more
  •  1463
    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
  •  30
    The 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...
  •  314
    Contrary to dictionaries, a non sequitur isn’t “any statement that doesn’t follow logically from previous statements”. Otherwise, every opening statement would be a non sequitur: a non sequitur is a statement claimed to follow from previous statements but that doesn’t follow. If the sentence making a given statement doesn’t contain ‘thus’, ‘so’, ‘hence’, ‘therefore’, or something else indicating an implication claim, the statement isn’t a non sequitur in this sense. But this is only one of sever…Read more
  •  85
    The switches "paradox" and the limits of propositional logic
    with Susan B. Wood
    Philosophy and Phenomenological Research 34 (1): 102-108. 1973.
  •  280
    Aristotle's Many-sorted Logic
    Bulletin of Symbolic Logic 14 (1): 155-156. 2008.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved us…Read more
  •  7610
    An Essay on Knowledge and Belief
    International Journal of Decision Ethics (2): 125-144. 2006.
    This accessible essay treats knowledge and belief in a usable and applicable way. Many of its basic ideas have been developed recently in Corcoran-Hamid 2014: Investigating knowledge and opinion. The Road to Universal Logic. Vol. I. Arthur Buchsbaum and Arnold Koslow, Editors. Springer. Pp. 95-126. http://www.springer.com/birkhauser/mathematics/book/978-3-319-10192-7
  •  950
    JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies …Read more
  •  705
    Tarski’s Convention T: condition beta
    South American Journal of Logic 1 (1). forthcoming.
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In…Read more
  •  1907
    Aristotle's demonstrative logic
    History and Philosophy of Logic 30 (1): 1-20. 2009.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argume…Read more
  •  2824
    Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjuncti…Read more
  •  325
    De Morgan on Euclid’s fourth postulate
    with Sriram Nambiar
    Bulletin of Symbolic Logic 20 (2): 250-1. 2014.
    This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact …Read more