Analysis in Prior Analytics I.45

History and Philosophy of Logic 43 (3):207-231 (2022)
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Abstract

I reconstruct Aristotle’s analytical procedure in Prior Analytics I.45 and its metalogical implications. Aristotle’s analysis unfolds three groups of syllogisms: symmetrically analysable, asymmetrically analysable, and non-analysable syllogisms. From the first and the third group could be extracted 27 combinations of the two mutually non-derivable deductive rules. Aristotle’s reduced deductive system in APr. I.7 with the two moods in the first figure (traditionally called Barbara and Celarent) follows this pattern. I demonstrate that the deductive system with Barbara and Celarent is just one of 27 possible complete deductive systems with the two mutually non-derivable syllogistic rules. On top of that, given the fact that there are two combinations of mutually non-derivable conversion rules, I conclude that Prior Analytics hides in itself 54 complete deductive systems with a minimal number of mutually non-derivable rules. Finally, it is commented what might be the role of analysis; to what extent Aristotle could be aware of possibilities presented here; why he still prefers only one deductive system to many others with the same deductive power.

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Igor Martinjak
University of Zagreb (PhD)

References found in this work

Introduction to logic.Patrick Suppes - 1957 - Mineola, N.Y.: Dover Publications.
Aristotle's Modal Syllogistic.Marko Malink - 2013 - Cambridge, MA and London: Harvard University Press.
Aristotle's Prior and Posterior Analytics.W. D. Ross - 1949 - Philosophy 25 (95):380-382.
What is a syllogism?Timothy J. Smiley - 1973 - Journal of Philosophical Logic 2 (1):136 - 154.
Completeness of an ancient logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.

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