Aristotle's “Logical Worldview”

2018

The author presents the idea of a “logical worldview” – an approach to understanding logic by examining philosophical positions in metaphysics, epistemology, and theories of cognition and perception, and exploring how philosophical and logical positions combine to form a complete logical system. Aristotle’s logical worldview is examined in some detail, and the logical systems of Francis Bacon and George Boole are examined by exploring how a new logic results when certain Aristotelian philosophical positions are abandoned. The logical worldview approach is also shown to help explain certain puzzles with Aristotle’s logic, such as existential import, the form of the syllogism, and Aristotle’s “missing” moods and figures from the list of valid moods.

Topoi-an International Review of Philosophy, 2004

I provide a survey of the contents of the works belonging to Aristotle's Organon in order to define their nature, in the light of his declared intentions and of other indications (mainly internal ones) about his purposes. No unifying conception of logic can be found in them, such as the traditional one, suggested by the very title Organon, of logic as a methodology of demonstration. Logic for him can also be formal logic (represented in the main by the De Interpretatione), axiomatized syllogistic (represented in the main by the Prior Analytics) and a methodology of dialectical and rhetorical discussion. The consequent lack of unity presented by those works does not exclude that both the set of works called Analytics and the set of works concerning dialectic (Topics and Sophistici Elenchi) form a unity, and that a certain priority is attributed to the analytics with respect to dialectic.

2018

This paper investigates a particular strategy for establishing the deep connection between metaphysics and logic using Aristotle's principle of non-contradiction and the theory of predication. The decisive move, according to this strategy, is to formulate and interpret the said principle as a metaphysical (or ontological) principle. In this paper, it is argued that: (1) despite the strategy's initial appeal, a successful argument still needs to be made in order to fully establish that metaphysics and logic are deeply connected, and (2) the theory of predication is more fundamental than the principle of non-contradiction. The main reason for (1) above is that the strategy is prone to a very powerful objection that Aris-totle's criterion of primary substance is inconsistent. The main reason for (2) above is that the principle of non-contradiction itself is best explained using the theory of predication. In addition, it is the theory of predication that does all the important explanatory work in the context of Aristotle's philosophical theory.

Corcoran, John. 1994. The Founding of Logic: Modern Interpretations of Aristotle's Logic. Ancient Philosophy, 14, 9–24. Since the time of Aristotle's students, interpreters have considered PRIOR ANALYTICS, hereafter PA, to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. More explicitly, PA was taken to be about “methods of logic” in Quine’s sense: methods for determining of a consequence of given premises that it indeed is a consequence of them and—which are quite different— methods for determining of a proposition not consequence of given premises that it indeed is not a consequence of them. PA took for granted the theses (1) that not ever valid argument is obviously valid and (2) that not ever invalid argument is obviously invalid. 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.

Bloomsbury, 2025

Aristotle's Organon in Old and New Logic 1800–1950 explores the reception and interpretation of Aristotle's logic over the last two centuries. The volume covers seminal works during this period by logicians, historians of logic, and historians of philosophy, including John Lloyd Akrill, Francesco Barone, Günther Patzig, Enrico Berti, and Mario Mignucci. Contributors consider the reception of the Organon in old logic and chart the appearance of formal approaches to logic beginning with Boole. This in-depth study of Aristotelianism also covers logic in Kant and Hegel, alongside the problems and projects of interpreting Aristotle in the new logic after Boole and Frege. The background of modern debates concerning induction and abduction provides further insight into Aristotelian logic during the period. By filling gaps in our understanding of Aristotelian logic, this book provides a fundamental missing link in 21st century studies of the history of Aristotelianism. It brings together scholars of both ancient and modern logic to understand the interpretation of ancient logic before and after the development of the modern, algebraic approach to logic.

The rediscovery of Aristotle's works on syllogisms in the Latin world, gave rise to sophisticated views on the nature of syllogistic form and syllogistic matter in the thirteenth century. It led to debates on the ontology of the syllogism with deep consequences on the definition of logic as a universal method for all sciences and as a science itself.

Prior Analytics by theGreek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematicianGeorge Boole (1815 – 1864) are the twomost important surviving original logical works frombefore the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort tomake his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of themain conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction— Boole became the founder of logic as formal ontology.

JOHN CORCORAN AND KEVIN TRACY A REVIEW OF: Rini, Adriane. Aristotle’s logic. The history of philosophical and formal logic, 29-49. Bloomsbury Academic, London, 2017. “Aristotle’s logic” is a 20-page essay intended to introduce Aristotle’s logic to undergraduates having studied one course in logic. It appears in “The history of philosophical and formal logic from Aristotle to Tarski”, a collection of similarly introductory essays all by different authors and all on different areas of history of logic.

Journal of the History of Philosophy, 2018