1 JOHN CORCORAN, Aristotle's Underlying Logics

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1 JOHN CORCORAN, Aristotle's Underlying Logics

JOHN CORCORAN, Aristotle’s Underlying Logics: A Three-hour Tutorial. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 E-mail: [email protected] This tutorial on Aristotle’s underlying logics begins with a treatment of his demonstrative logic, the principal motivation for his interest in the field. It ends with a faithful translation of Aristotle’s categorical syllogistic into a Hilbert-style many-sorted logic. Demonstrative logic, or apodictics, studies demonstration as opposed to persuasion. It presupposes the Socratic knowledge/opinion distinction—between knowledge (beliefs that are known) and opinion (those that are not known). Every demonstration produces (or confirms) knowledge of (the truth of) its conclusion for every person who comprehends the demonstration. Persuasion merely produces opinion. Aristotle was the first to see that every demonstrative science presupposes for its deductions what Church called an underlying logic. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations not just to those that are complete categorical syllogisms. According to him, a demonstration is an extended argumentation that begins with premises known to be truths and involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. For Aristotle, starting with premises known to be true and a conclusion not known to be true, the knower demonstrates the conclusion by deducing it from the premises. As Tarski emphasized, modern formal proof resulted from refinement and “formalization” of traditional Aristotelian demonstration. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions, not just to complete categorical syllogisms. For him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. 1.

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Publications of John Corcoran OCT 04
OCTOBER 2004 PUBLICATIONS OF JOHN CORCORAN I. Articles. MR indicates review in Mathematical Reviews. J indicates available at JSTOR. G indicates available at Google by entering John Corcoran plus the complete title. 1.J Three Logical Theories, Philosophy of Science 36 (1969) 153-77. 2. Logical Consequence in Modal Logic: Natural Deduction in S5 (co-author G. Weaver), Notre Dame Journal of Formal Logic 10 (1969) 370-84. 3. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and the Stratification of Language, Journal of Structural Learning 3 (1971) #1, 55-74. 4. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3 (1971) #2, 1-16. 5. Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof, Journal of Structural Learning 3 (1971) #3, 1-24. 6. Notes on a Semantic Analysis of Variable Binding Term Operators (co-author John Herring), Logique et Analyse 55 (1971) 646-57. MR46#6989. 7. Variable Binding Term Operators, (co-authors Wm. Hatcher, John Herring) Zeitschrift fu"r mathematische Logik und Grundlagen der Mathematik 18 (1972) 177-82. MR46#5098. 8.J Conceptual Structure of Classical Logic, Philosophy & Phenomenological Research 33 (1972) 25-47. 9. Logical Consequence in Modal Logic: Some Semantic Systems for S4 (co-author G. Weaver), Notre Dame Journal of Formal Logic 15 (1974) 370-78. MR50#4253. 10, 11, and 12. Revisions of 3, 4 and 5 in Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon and Breach Science Publishers, New York (1976).
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Sentence, Proposition, Judgment, Statement, and Fact: Speaking About the Written English Used in Logic John Corcoran
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Volume 12, Number 5 May 2018
Volume 12, Number 5 May 2018 thereasoner.org ISSN 1757-0522 matics and I realized that I had met his name some years earlier Contents when I had borrowed from the University Library of Patras his edition of George Boole’s “Laws of Thought”. Guest Editorial 37 Athanasios Christacopoulos Features 37 Hellenic Open University News 39 What’s Hot in . 41 Features Events 43 Courses and Programmes 43 Interview with John Corcoran Jobs and Studentships 44 Athanasios Christacopoulos: First of all I must say that it is an honour to have an interview with one of the leading personali- ties in logic. I would like to begin our conversation with your first scientific interests: those that shaped your way to research on logic –mathematical, historical, and philosophical– till the Guest Editorial moment you said to yourself “I have something new to say”. John Corcoran is an eminent John Corcoran: This sort of question would get different logician, philosopher, math- answers, all tentative, at different times. Today, I think back ematician, linguist, and his- to the late 1960s. My first published paper “Three logical the- torian of logic. He has ories”, offers rationales for logical-system properties such as been member of the IBM Re- weak completeness, strong completeness, deductive complete- search Center’s Linguistics ness, various forms of compactness, consistency, and sound- Group and teacher of logic ness, and the like. at the Universities of Cali- I wrote early drafts of what became “Three logical theories” fornia, Pennsylvania, Michi- for my graduate logic courses. One goal was to take the alien- gan, and Buffalo.
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Logic in the 21St Century: Advice for Young Logicians
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Bibliography of Ancient Logic in the Hellenistic Period
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[email protected] 052815 JUNE 2015 a BIBLIOGRAPHY
[email protected] 052815 JUNE 2015 A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran Indeed, one of the great strides forward in the modern study of Aristotle’s syllogistic was the realization that it is a system of natural deduction. —Kevin Flannery, SJ [2001, 219]. Corcoran […] has convincingly shown that the best formalization of Aristotle’s reductio ad impossibile is by means of a natural deduction system. —Mario Mignucci [1991, 12]. The most radical opponent of Lukasiewicz is J. Corcoran. —Tadeusz Kwiatkowski [1980, 188]. Contents Abstract I. Articles II. Abstracts III. Books IV. Reviews V. Discussions VI. Alternatives VII. Acknowledgements Abstract 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 and the Journal of Symbolic Logic article from his Buffalo period first reporting his original results; it ends with works published in 2015. A few of the items are annotated as listed or with endnotes connecting them with other work and pointing out passages that in- retrospect are seen to be misleading and in a few places erroneous. In addition, Section V, “Discussions”, is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 23 in the 1980s, 42 in the 1990s, 56 in the 2000s, and 69 in the current decade.
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Aristotle's Demonstrative Logic
HISTORY AND PHILOSOPHY OF LOGIC, 30 (February 2009), 1–20 Aristotle’s Demonstrative Logic JOHN CORCORAN Department of Philosophy, University at Buffalo, Buffalo, NY 14260-4150, USA Received 17 December 2007 Revised 29 April 2008 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 argumentation beginning with premises known to be truths and containing a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In particular, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction- chaining conception of deduction was meant to apply to all deductions. According to him, any deduction that is not immediately evident is an extended argumentation that involves a chaining of intermediate immediately evident steps that shows its final conclusion to follow logically from its premises. To illustrate his general theory of deduction, he presented an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. Introduction This expository paper on Aristotle’s demonstrative logic is intended for a broad audience that includes non-specialists. Demonstrative logic is the study of demonstration as opposed to persuasion.
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Aristotle's Logic: General Survey and Introductory Readings
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