•  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
  •  383
    Significados de la implicación
    Agora 5 279. 1985.
    John Corcoran ’s “Meanings of Implication” outlines and discusses 12 distinct uses of the term “implies” while also commenting on the ways in which these different notions of implication might be confused or conflated. Readers may take special note of Corcoran ’s analysis of Russell’s truth-functional account of “implication” and its historical function as logical consequence, as well as Corcoran ’s discussion of Bolzano’s previously obscure and rarely mentioned notion of “relative implication.”
  •  531
    This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo perio…Read more
  •  29
    Strange arguments
    Notre Dame Journal of Formal Logic 13 (2): 206-210. 1972.
  •  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
  •  5
  •  237
    Review 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
  •  48
    C. I. Lewis: History and Philosophy of Logic
    Transactions of the Charles S. Peirce Society 42 (1): 1-9. 2006.
  •  286
    COSMIC JUSTICE HYPOTHESES
    with William Frank
    Bulletin of Symbolic Logic 20 (2): 247-248. 2014.
    Cosmic Justice Hypotheses. This applied-logic lecture builds on [1] arguing that character traits fostered by logic serve clarity and understanding in ethics, confirming hopeful views of Alfred Tarski [2, Preface, and personal communication]. Hypotheses in one strict usage are propositions not known to be true and not known to be false or—more loosely—propositions so considered for discussion purposes [1, p. 38]. Logic studies hypotheses by determining their implications (propositions th…Read more
  •  265
    CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115
  •  107
    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
  •  262
    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
  •  825
    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
  •  638
    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
  •  351
    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..
  •  802
    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
  •  568
    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.
  •  242
    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
  •  512
    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.
  •  1211
    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.
  •  438
    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