Archiv für Geschichte der Philosophie 55 (2):191-219 (1973)
In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible.
|Keywords||SYLLOGISTIC PREMISE-CONCLUSION ARGUMENT PREMISE-CHAIN-CONCLUSION DEDUCTION IMPLICATION/DEDUCTIBILITY COMPLETENESS UNDERLYING LOGIC ARISTOTLE LUKASIEWICZ TIMOTHY SMILEY DIRECT/INDIRECT DEDUCTIONS|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
Aristotle on Universal Quantification: A Study From the Point of View of Game Semantics.M. Marion & H. Rückert - 2015 - History and Philosophy of Logic 37 (3):201-229.
A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
Similar books and articles
Establishing Connections Between Aristotle's Natural Deduction and First-Order Logic.Edgar Jose Andrade & Edward Samuel Becerra - 2008 - History and Philosophy of Logic 29 (4):309-325.
A Reconstruction of Aristotle's Modal Syllogistic.Marko Malink - 2006 - History and Philosophy of Logic 27 (2):95-141.
Aristotle's Syllogistic Model of Knowledge and the Biological Sciences: Demonstrating Natural Processes.Mariska Leunissen - 2010 - Apeiron 43 (2-3):31-60.
Alexander of Aphrodisias' on Aristotle's Prior Analytics 1.1-7.Jonathan Barnes & Susanne Bobzien - 1991 - Duckworth.
Computation of Aristotle's and Gergonne's Syllogisms.S. N. Furs - 1987 - Studia Logica 46 (3):209 - 225.
Three-Membered Domains for Aristotle's Syllogistic.Fred Johnson - 1991 - Studia Logica 50 (2):181 - 187.
From Aristotle's Syllogistic to Stoic Conditionals: Holzwege or Detectable Paths?Mauro Nasti De Vincentis - 2004 - Topoi 23 (1):113-137.
Polarity and Inseparability: The Foundation of the Apodictic Portion of Aristotle's Modal Logic.Dwayne Raymond - 2010 - History and Philosophy of Logic 31 (3):193-218.
Conversion Principles and the Basis of Aristotle's Modal Logic.Richard Patterson - 1990 - History and Philosophy of Logic 11 (2):151-172.
Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
Aristotle's Syllogisms Lynn E. Rose: Aristotle's Syllogistic. Pp. Vii+149. Springfield, Ill.: Charles C. Thomas, 1968. Cloth. [REVIEW]W. Charlton - 1969 - The Classical Review 19 (03):283-284.
The Nature of Mathematics – an Interview with Professor Karlis Podnieks.Karlis Podnieks & John Tabak - 2011 - In John Tabak (ed.), Numbers: Computers, Philosophers, and the Search for Meaning. Revised Edition. Facts on File. pp. 188–197.
Added to index2010-09-14
Total downloads219 ( #17,255 of 2,164,598 )
Recent downloads (6 months)56 ( #3,877 of 2,164,598 )
How can I increase my downloads?