A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with other work. 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, 22 in the 1980s, 39 in the 1990s, 56 in the 2000s, and 65 in the current decade. The secondary bibliography is annotated with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. As is evident from the Acknowledgements sections, all of Corcoran’s publications benefited from correspondence with other scholars, most notably Timothy Smiley, Michael Scanlan, and Kevin Tracy. All of Corcoran’s Greek translations were done in consultation with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications

The Founding of Logic: Modern Interpretations of Aristotle’s Logic

Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the epistemic process of extracting information implicit in explicitly given information) and, second, the process of establishing knowledge that a conclusion does not follow. Despite the overwhelming tendency to interpret the syllogistic as formal epistemology, it was not until the early 1970s that it occurred to anyone to think that Aristotle may have developed a theory of deductive reasoning with a well worked-out system of deductions comparable in rigor and precision with systems such as propositional logic or equational logic familiar from mathematical logic. When modern 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 semantically complete system of natural deductions including both direct and indirect deductions. 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, or extended deductive discourses, 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

Deductions and Reductions Decoding Syllogistic Mnemonics

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally irrelevant to the post-Łukasiewicz paradigm established in the 1970s and 1980s by John Corcoran, Timothy Smiley, Robin Smith, and others. Robin Smith’s comprehensive 1989 treatment of syllogistic does not even quote the mnemonic’s four verses. Smith’s work devotes only 2 of its 262 pages to the mnemonic. The most recent translation of Prior Analytics by Gisela Striker in 2009 continues the post-Łukasiewicz paradigm and accordingly does not quote the mnemonic or even refer to the code—although it does use the terminology. Full mastery of modern understandings of syllogistic does not require and is not facilitated by ability to decode the mnemonic. Nevertheless, an understanding of the history of logic requires detailed mastery of the syllogistic mnemonic, of the logical theories it spawned, and of the conflicting interpretations of it that have been offered over the years by respected logicians such as De Morgan, Jevons, Keynes, and Peirce. More importantly, an understanding of the issues involved in decoding the mnemonic might lead to an enrichment of the current paradigm—an enrichment so profound as to constitute a new paradigm. After presenting useful expository, bibliographic, hermeneutic, historical, and logical background, this paper gives a critical exposition of Smith’s interpretation

A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic

International audienceIn this paper we first show that Robin Smith's ecthetic system SE for Aristotle's assertoric syllogistic is not complete, despite what is claimed by Smith. SE is then not adequate to establish that ecthesis allows one to dispense with indirect or per impossibile deductions in Aristotle's assertoric logic. As an alternative to SE, we then present a stronger system EC which is adequate for this purpose. EC is a nonexplosive ecthetic system which is shown to be sound and complete with respect to all valid syllogistic arguments with a consistent set of premises

A Completed System for Robin Smith's Incomplete Ecthetic Syllogistic

International audienceIn this paper we first show that Robin Smith's ecthetic system SE for Aristotle's assertoric syllogistic is not complete, despite what is claimed by Smith. SE is then not adequate to establish that ecthesis allows one to dispense with indirect or per impossibile deductions in Aristotle's assertoric logic. As an alternative to SE, we then present a stronger system EC which is adequate for this purpose. EC is a nonexplosive ecthetic system which is shown to be sound and complete with respect to all valid syllogistic arguments with a consistent set of premises