Aristotle's Logic Department of Philosophy This tutorial on Aristotle’s logic begins with a treatment of his demonstrative logic, the principal motivation for his interest in the field. [Corcoran 2009b] Demonstrative logic is the study of demonstration as opposed to persuasion. It presupposes the Socratic knowledge/opinion distinction—between knowledge (beliefs that are known) and opinion (beliefs that are not known). [Corcoran-Hamid 2014] Demonstrative logic is the focal subject of Aristotle’s two-volume Analytics, as stated in its first sentence. [Smith, 1989] Many of Aristotle’s examples are geometrical. Every demonstration produces (or confirms) knowledge of (the truth of) its conclusion for every person who comprehends the demonstration. Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to this conception, a demonstration is an extended argumentation [Corcoran 1989] that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. For Aristotle, starting with premises known to be true, the knower demonstrates a conclusion by deducing it from the premises. As Tarski emphasized, formal proof in the modern sense results from refinement and “formalization” of traditional Aristotelian demonstration. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in Prior Analytics and embodied in his natural-deduction underlying logics. His general immediate-deduction-chaining conception of deduction was meant to apply to all deductions. According to this general conception, 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. His theory of deduction recognizes both direct and indirect reasoning, an achievement not equaled before Jaskowski’s 1934 masterpiece. [Corcoran 2003] To illustrate his general theory of deduction, Aristotle presented an ingeniously simple and mathematically precise specialized system traditionally known as the categorical syllogistic. With attention limited to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained. In his specialized theory, Aristotle explained how to deduce from any given categorical premise set, no matter how large, any categorical conclusion implied by the given set. [Corcoran, 1972] He did not extend this specialized treatment in general to cover non-categorical deductions, for example, those involving equations or proportionalities. Thus Aristotle set a program for future logicians, a program that continues to be pursued and that may never be completed. We will also treat several metatheorems about his basic systems and about various extensions and subsystems. In particular, we show that one-one translation of Aristotle’s syllogistic into a certain fragment of modern Hilbertian many-sorted symbolic logic yields a complete match in the following sense. In order for a conclusion to be a consequence of given premises according to Aristotle it is necessary and sufficient for the many-sorted translation of the conclusion to be a consequence of the many-sorted translation of the premises according to Hilbert. [Corcoran 2008] If time permits we will review the highpoints of the vast literature [Corcoran, 2010] responding to the ground-breaking scholarship produced in the 1970s in Buffalo, NY and Cambridge, UK. [Corcoran, 2009a; Smiley, 1973] Time will be set aside for student interaction. Students are encouraged to send questions in advance to the tutor. No prerequisites: knowledge of Greek and symbolic logic will not be needed.
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Bibliography Publications of John Corcoran on Aristotle
Corcoran, John, and Idris Samawi Hamid. 2014. Investigating knowledge and opinion. In The Road to Universal Logic . Arthur Buchsbaum and Arnold Koslow, Editors. Springer: Berlin. Corcoran, John. 2010. Essay-Review of: Striker, G., trans. 2009. Aristotle’s Prior Analytics: Book I. Trans. with Intro. and Comm. Oxford: Oxford University Press. 2005. Notre Dame Philosophical Reviews Corcoran, John. 2009a. Aristotle’s Logic at the University of Buffalo’s Department of Philosophy.Ideas y Valores: Revista Colombiana de Filosofía, 140 (August 2009) 99–117. Corcoran, John. 2009b. Aristotle's Demonstrative Logic. History and Philosophy of Logic,30 1–20. Corcoran, John. 2008. Aristotle’s Many-sorted Logic. Bulletin of Symbolic Logic, 14, 155–6. Corcoran, John. 2003. Aristotle's Prior Analytics and Boole's Laws of Thought. History and Philosophy of Logic,24, 261–288. Corcoran, John. 1989. Argumentations and Logic, Argumentation 3, 17–43. Robin Smith, 1989. Aristotle’s Prior Analytics, Indianapolis: Hackett. Smiley, Timothy. 1973. What is a Syllogism? J. of Philosophical Logic, 2: 136–154. Corcoran, John. 1972. Completeness of an ancient logic, J. of Sym. Logic, 37, 696–702.
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