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

Ancient Philosophy 14 (S1):9-24 (1994)
  Copy   BIBTEX


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.

Similar books and articles

The logic of the moral sciences.John Stuart Mill - 1872 - La Salle, Ill.: Open Court. Edited by Henry Meyer Magid.
Papers on time and tense.Arthur Norman Prior - 2003 - New York: Oxford University Press. Edited by Per F. V. Hasle.
Aristotle's Prior Analytics and Boole's Laws of thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
Sets, classes, and categories.F. A. Muller - 2001 - British Journal for the Philosophy of Science 52 (3):539-573.
G. W. Leibniz and Scientific Societies.Markku Roinila - 2009 - Journal of Technology Management 46 (1-2):165-179.
Current topics in logic and analytic philosophy =.Concha Martínez, José L. Falguera & José M. Sagüillo (eds.) - 2007 - Santiago de Compostela: Universidade de Santiago de Compostela.


Added to PP

1,622 (#6,340)

6 months
153 (#22,065)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

John Corcoran
PhD: Johns Hopkins University; Last affiliation: University at Buffalo

Citations of this work

Aristotle's Prior Analytics and Boole's Laws of thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
Aristotle's demonstrative logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
Extensionalism: The Revolution in Logic.Nimrod Bar-Am - 2008 - Dordrecht, Netherland: Springer.
Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic 24 (4):261-288.

View all 20 citations / Add more citations

References found in this work

Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
Introduction to mathematical logic..Alonzo Church - 1944 - Princeton,: Princeton university press: London, H. Milford, Oxford university press. Edited by C. Truesdell.
Philosophy of Logic.W. V. Quine - 2005-01-01 - In José Medina & David Wood (eds.), Truth. Blackwell.
Introduction to mathematical philosophy.Bertrand Russell - 1920 - Revue de Métaphysique et de Morale 27 (2):4-5.
Aristotle's Prior Analytics.Robin Smith - 1989 - Hackett Publishing Company.

View all 24 references / Add more references