Platonic Division and the Origins of Aristotelian Logic

Dissertation, University of California, Berkeley (2017)


Aristotle's syllogistic theory, as developed in his Prior Analytics, is often regarded as the birth of logic in Western philosophy. Over the past century, scholars have tried to identify important precursors to this theory. I argue that Platonic division, a method which aims to give accounts of essences of natural kinds by progressively narrowing down from a genus, influenced Aristotle's logical theory in a number of crucial respects. To see exactly how, I analyze the method of division as it was originally conceived by Plato and received by Aristotle. I argue that, while Plato allowed that some divisions fail to rigorously investigate the essence, he began a program continued by Aristotle (and others in antiquity and the middle ages) of seeking norms for division that would apply in any domain whatsoever. This idea of a rigorous, general method was taken up and developed by Aristotle in his syllogistic. Aristotle also used Plato's conception of predication as parthood in his semantics for syllogistic propositions. As part of my argument, I prove that a semantics based on Platonic divisional structures is sound and complete for the deduction system used in the literature to model Aristotle's syllogistic.

Download options


External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

1,182 (#5,149)

6 months
121 (#5,101)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Justin Vlasits
University of Illinois, Chicago

References found in this work

No references found.

Add more references

Citations of this work

A Bitstring Semantics for Calculus CL.Fabien Schang & Jens Lemanski - 2022 - In Ioannis M. Vandoulakis & Jean-Yves Beziau (eds.), The Exoteric Square of Opposition. Cham: Springer. pp. 171–193.

Add more citations

Similar books and articles

Platonic Epogoge and the “Purification” of the Method of Collection in Advance.Holly G. Moore - forthcoming - Epoché: A Journal for the History of Philosophy.
A Reconstruction of Aristotle's Modal Syllogistic.Marko Malink - 2006 - History and Philosophy of Logic 27 (2):95-141.
Platonic Epogōgē and the “Purification” of the Method of Collection.Holly G. Moore - 2019 - Epoché: A Journal for the History of Philosophy 23 (2):353-364.
A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
Remarks on Axiomatic Rejection in Aristotle’s Syllogistic.Piotr Kulicki - 2002 - Studies in Logic and Theory of Knowledge 5:231-236.
Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
A Sharp Eye for Kinds: Collection and Division in Plato's Late Dialogues.Devin Henry - 2011 - In Michael Frede, James V. Allen, Eyjólfur Kjalar Emilsson, Wolfgang-Rainer Mann & Benjamin Morison (eds.), Oxford Studies in Ancient Philosophy. Oxford University Press. pp. 229-55.
Is Aristotle's Syllogistic a Logic?Phil Corkum - forthcoming - History and Philosophy of Logic.
Aristotle's Platonic Response to the Problem of First Principles.Evan Rodriguez - 2020 - Journal of the History of Philosophy 58 (3):449-469.