Aristotle: the Theory of Categorical Syllogism

N.B.: For the references, please see Selected Bibliography on Aristotle's Theory of Categorical Syllogism "When modem logicians in the 1920s and 1930s first turned their attention to the problem of understanding Aristotle’s contribution to logic in modern terms, they were guided both by the Frege-Russell conception of logic as formal ontology and at the same time by a desire to protect Aristotle from possible charges of psychologism. They thought they saw Aristotle applying the informal axiomatic method to formal ontology, not as making the first steps into formal epistemology. They did not notice Aristotle’s description of deductive reasoning. Ironically, the formal axiomatic method (in which one explicitly presents not merely the substantive axioms but also the deductive processes used to derive theorems from the axioms) is incipient in Aristotle’s presentation. Partly in opposition to the axiomatic, ontically-oriented approach to Aristotle’s logic and partly as a result of attempting to increase the degree of fit between interpretation and text, logicians in the 1970s working independently came to remarkably similar conclusions to the effect that Aristotle indeed had produced the first system of formal deductions. They concluded that Aristotle had analyzed the process of deduction and that his achievement included a system of natural deductions including both direct and indirect deductions which, though simple and rudimentary, was semantically complete. Where the interpretations of the 1920s and 1930s attribute to Aristotle a system of propositions organized deductively, the interpretations of the 1970s attribute to Aristotle a system of deductions, extended deductive discourses, concatenations of propositions, organized epistemically. The logicians of the 1920s and 1930s take Aristotle to be deducing laws of logic from axiomatic origins; the logicians of the 1970s take Aristotle to be describing the process of deduction and in particular to be describing deductions themselves, both those deductions that are proofs based on axiomatic premises and those deductions that, though deductively cogent, do not establish the truth of the conclusion but only that the conclusion is implied by the premise-set. Thus, two very different and opposed interpretations had emerged, interestingly both products of modern logicians equipped with the theoretical apparatus of mathematical logic. The issue at stake between these two interpretations is the historical question of Aristotle’s place in the history of logic and of his orientation in philosophy of logic. This paper affirms Aristotle’s place as the founder of logic taken as formal epistemology, including the study of deductive reasoning. A by-product of this study of Aristotle’s accomplishments in logic is a clarification of a distinction implicit in discourses among logicians—that between logic as formal ontology and logic as formal epistemology. Aristotle’s Logic: New Goals, New Results Our understanding of Aristotle’s logic has increased enormously in the last sixty years. It is gratifying to review the cascade of progress beginning with the independently achieved but remarkably similar advances reported in 1929 by Jan Lukasiewicz and in 1938 by James Wilkinson Miller. Penetrating examination and critical evaluation of the Lukasiewicz-Miller viewpoint in the 1950s and 1960s set the stage for work in the early 1970s by Timothy Smiley and myself. Subsequent work in the late 1970s and early 1980s by various people including Timothy Smiley, Robin Smith, Michael Scanlan and myself can be seen as culminating, at least for the moment, in the 1989 translation and commentary on Prior Analytics by Robin Smith." (pp. 9-10)