-
627Philosophy of Logic. Hilary Putnam (review)Philosophy of Science 40 (1): 131-133. 1973.Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book 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 ph…Read more
-
5An Introduction to Logic (edited book)Hackett Publishing Company. 1993.Written for independent study and suitable for an introductory course in logic, this classic text combines a sound presentation of logic with effective pedagogy and illustrates the role of logic in many areas of humanistic and scientific thought. Cohen and Nagel's elegant integration of the history of philosophy, natural science, and mathematics helps earn this work its distinguished reputation.
-
14Logic, Semantics, Metamathematics: Papers from 1923 to 1938Journal of Symbolic Logic 54 (1): 281-282. 1956.
-
18Information Recovery ProblemsTheoria: 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
-
12Future Research on Ancient Theories of Communication and ReasoningIn Ancient logic and its modern interpretations, Reidel. pp. 185--187. 1974.
-
Dept. of Philosophy University of California at San Diego La Jolla, CA 92093 USALinguistics and Philosophy 13 423-475. 1990.
-
992A Mathematical Model of Aristotle’s SyllogisticArchiv 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
-
2340A 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
-
30Logical Structures of Ockham's Theory of SuppositionFranciscan 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
-
587Meanings 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
-
720Variable Binding Term OperatorsZeitschrift 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
-
4Gottlob Frege's "On the Foundations of Geometry and Formal Theories of Arithmetic" (review)Philosophy and Phenomenological Research 34 (2): 283-286. 1973.
-
283Logically Equivalent False Universal Propositions with Different Counterexample Sets.Bulletin of Symbolic Logic 11 554-5. 2007.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
-
108Logic, 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.
-
43Existential-Import MathematicsBulletin of Symbolic Logic 21 (1): 1-14. 2015.First-order logic haslimitedexistential import: the universalized conditional ∀x[S(x) → P(x)] implies its corresponding existentialized conjunction ∃x[S(x) & P(x)] insome but not allcases. We prove theExistential-Import Equivalence:∀x[S(x) → P(x)] implies ∃x[S(x) & P(x)] iff ∃xS(x) is logically true.The antecedent S(x) of the universalized conditional alone determines whether the universalized conditionalhas existential import: implies its corresponding existentialized conjunction.Apredicateis a…Read more
-
381Equality and identityBulletin 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
-
330“Truth-preserving and consequence-preserving deduction rules”,Bulletin of Symbolic Logic 20 (1): 130-1. 2014.A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dis…Read more
-
35Book Review:Conceptual Notation and Related Articles Gottlob Frege, Terrell Ward Bynum (review)Philosophy of Science 40 (3): 454-. 1973.
-
Critical Notice: Contemporary Relevance of Ancient Logical TheoryPhilosophical Quarterly 32 (1): 76-86. 1982.
-
338Corcoran recommends Hambourger on the Frege-Russell number definitionMATHEMATICAL REVIEWS 56. 1978.It is widely agreed by philosophers that the so-called “Frege-Russell definition of natural number” is actually an assertion concerning the nature of the numbers and that it cannot be regarded as a definition in the ordinary mathematical sense. On the basis of the reasoning in this paper it is clear that the Frege-Russell definition contradicts the following three principles (taken together): (1) each number is the same entity in each possible world, (2) each number exists in each possible world…Read more
-
18Review: Nino B. Cocchiarella, Logical Investigations of Predication Theory and the Problem of Universals (review)Journal of Symbolic Logic 53 (3): 991-993. 1988.
-
859Argumentaciones y lógicaAgora 13 (1): 27. 1994.Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstrac…Read more
-
837CategoricityHistory and Philosophy of Logic 1 (1): 187-207. 1980.After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences…Read more
Buffalo, New York, United States of America
Areas of Specialization
Epistemology |
Logic and Philosophy of Logic |