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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.
Acknowledgements
I dedicate this article to my friend and colleague Professor Robin Smith in celebration of the twentieth anniversary of his definitive translation with commentary of Aristotle's Prior Analytics.
This essay is based on my lecture at the Coloquio Internacional de Historia de la Lógica dedicado a la Lógica de Aristóteles held in November 2007 in Santiago de Chile at PUC de Chile, the Pontifical Catholic University of Chile. The first speaker was the revered Prof. Roberto Torretti, acknowledged dean of Chilean philosophers. PUC/CL has a rich tradition of excellence in logic, both in mathematics and philosophy. Its distinguished logic faculty hosts the annual international logic conference named in honor of Rolando Chuaqui (1935–1994), the great Chilean logician. Under Chuaqui's leadership, PUC earned the distinction of being the first university to confer the honorary doctorate on Alfred Tarski (Feferman and Feferman 2004, 353). I am grateful to Prof. Manuel Correia for organising the colloquium and for his attentive and warm hospitality. I am also grateful to other santiaguino professors, especially to the mathematician Renato Lewin. I will always be grateful to Roberto Torretti for his warm and generous introduction and for his gracious hospitality. This essay owes much to informative discussions with Pierre Adler, George Boger, Elizabeth Compton, Manuel Correia, Newton da Costa, John Foran, Gabriela Fulugonio, James Gasser, Josiah Gould, Steven Halady, James Hankinson, David Hitchcock, Forest Hansen, Amanda Hicks, John Kearns, Daniel Merrill, Joaquin Miller, Mary Mulhern, Frango Nabrasa, Carlo Penco, Saci Pererê, Walther Prager, Anthony Preus, José Miguel Sagüillo, Michael Scanlan, Robin Smith, Thomas Sullivan, Roberto Torretti, Kevin Tracy, Jiyuan Yu, and others. The HPL Editor John Dawson and his two anonymous referees made many useful suggestions. The article borrows from my encyclopedia entries cited in the references, especially from ‘Demonstrative Logic’, ‘Knowledge and Belief’, and ‘Scientific Revolutions’. Parts of this paper were presented to Prof. Jiyuan Yu's University of Buffalo Aristotle Seminar, the Buffalo Logic Colloquium, the University of Buffalo Philosophy Colloquium, Evergreen State College, and Canisius College.