Affiliation:
1. 1 Institute of Philosophy, Czech Academy of Sciences , Department of Logic , Jilská 1 , , Prague
Abstract
Abstract
Aristotle’s notion of deduction (syllogism) differs from the conception of logical consequence in classical logic in two essential features, which are required by Aristotle’s definition of syllogism and are incorporated into his formalisation of deduction: in addition to the standard necessary truth-preservation, Aristotle requires relevance of premises for the conclusion and non-repetition of premises in the conclusion. These requirements, together with Aristotle’s conception of simple propositions, lead to the result that valid deductive steps (syllogisms) must have very specific forms, namely the well-known syllogistic shape. All other kinds of deduction lacking this shape, such as “syllogisms based on a hypothesis”, can be considered “syllogisms” only in a relative sense: they are based on an assumption of the existence of genuine syllogistic deductions in the syllogistic shape. Aristotle’s demands should cover all kinds of deduction: all valid deduction must be relevant and non-repetitive. This brings Aristotle’s definition much closer to the intuition associated with the notion of logical consequence.
Reference24 articles.
1. Aristotle. The complete Works of Aristotle. The revised Oxford Translation, edited by Jonathan Barnes. Princeton: Princeton University Press, 1991. (Abbreviation for Aristotle’s Prior Analytics: ‘An. Pr.’; Topics: ‘Top.’)
2. Aristotle. Aristotle’s Prior Analytics Book I: Translated with an Introduction and Commentary. Translated by Gisela Striker. Oxford: Oxford University Press, 2009.
3. Alexander of Aphrodisias. Alexander of Aphrodisias: On Aristotle Prior Analytics 1.32–46 (Ancient Commentators on Aristotle). Translated by Ian Mueller. London: Bloomsburry Academic, 2006. (Abbreviation: ‘in An. Pr.’)
4. Barnes, Jonathan [1985]. “Theophrastus and hypothetical syllogistic”. In Aristoteles—Werk und Wirkung, Bd I, Aristoteles Und Seine Schule, edited by Jürgen Wiesner. Berlin: De Gruyter. DOI: 10.1515/9783110859720.557
5. Beall, J. C. & Restall, Greg & Sagi, Gil [2019]. “Logical consequence”. The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), edited by Edward N. Zalta. https://plato.stanford.edu/archives/spr2019/entries/logical-consequence/.