Abstract
In A 4–6 Aristotle discusses fourteen syllogisms belonging to the first, second and third of the traditional figures. The four syllogisms of the first figure he calls perfect, that is self-evident, arguments. The remaining syllogisms are valid, but their validity is not evident. Aristotle therefore shows that they are valid if the first figure syllogisms are valid, that is, true logical theorems. We might describe this procedure in modern terms as a proof of the imperfect syllogisms from certain accepted but unproven axioms — here the perfect syllogisms. Aristotle was the first to state the properties of such an axiomatic system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1968 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Patzig, G. (1968). Reduction and Deduction. In: Aristotle’s Theory of the Syllogism. Synthese Library, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0787-9_5
Download citation
DOI: https://doi.org/10.1007/978-94-017-0787-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8322-7
Online ISBN: 978-94-017-0787-9
eBook Packages: Springer Book Archive