Platonic Division and the Origins of Aristotelian Logic By Justin Joseph Vlasits A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Timothy Clarke, Co-Chair Professor Klaus Corcilius, Co-Chair Professor John MacFarlane Professor GRF Ferrari Summer 2017 Abstract Platonic Division and the Origins of Aristotelian Logic by Justin Joseph Vlasits Doctor of Philosophy in Philosophy University of California, Berkeley Professor Timothy Clarke, Co-Chair Professor Klaus Corcilius, Co-Chair 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. 1 Contents 1 Introduction 1 2 The Puzzle of the Sophist 11 2.1 The Traditional View of Division and the Puzzle of the Sophist. 12 2.2 MinimalView: PredicationandTransitivity . ..... 19 2.3 AgainsttheTraditionalView . 22 2.3.1 Dichotomy.............................. 23 2.3.2 Exclusivity.............................. 25 2.3.3 EssentialPredication . 34 2.4 ThePuzzleAgain .............................. 36 3 The Goal and Norms of Platonic Division 39 3.1 Goal...................................... 40 3.2 TwoNorms ................................. 42 3.2.1 TheTortoiseNorm . .. .. .. .. .. .. .. 42 3.2.2 TheMinimizationNorm. 49 3.3 Conclusion:Plato’sProgram. 52 4 The (Ab)use of Division in the Analytics 56 4.1 APr I.31:Divisiondoesnotsyllogize . 57 4.2 APo II.5:Divisionanddemonstration . 65 4.3 APo II.13:Definingwithdivision . 68 4.3.1 EssenceandGenus . .. .. .. .. .. .. .. 70 4.3.2 Theorderofinquiry . 73 4.3.3 Definingthesimplespecies . 76 4.3.4 Theaccountofthesummumgenus . 93 4.4 Conclusion.................................. 94 5 Division, Syllogistic Method, and Science in Prior Analytics I.31 99 5.1 The Puzzle of APr I.31 ...........................100 5.1.1 Division ...............................100 5.1.2 Syllogistic ..............................101 5.1.3 ThePuzzle..............................102 5.1.4 Previousresolutionsofthepuzzle . 105 i CONTENTS 5.2 DivisionandSyllogisticasscientificmethods . .. ..108 5.2.1 EpistemicGenerality . .108 5.2.2 Rigor.................................110 5.3 InvestigatingMereologicalRelations . .112 5.4 ResolvingthePuzzle . .. .. .. .. .. .. .. ..115 6 The Influence of Platonic Division on Aristotelian Syllogistic 119 6.1 The Question of Division and the Syllogistic . .121 6.2 LogicandMethod..............................125 A Mereology in Aristotle’s Assertoric Syllogistic 129 A.1 The Mereological Interpretation of Predication . .......131 A.2 AlgebraicSemantics . .. .. .. .. .. .. .. ..133 A.2.1 Soundness..............................134 A.2.2 Completeness . .. .. .. .. .. .. .. ..135 A.2.3 ASemanticHierarchy . .137 A.3 TheMereological InterpretationVindicated . .. ..137 Bibliography 139 ii Acknowledgements The initial impetus for this dissertation came from Alan Code’s seminar “Aristotle on Definition” at Stanford in Winter 2012. There I was struck by the importance of the method of division for Aristotle’s account of essence and definition. In Fall 2012, Tim Clarke taught a seminar on Plato’s Sophist where I began to develop the ideas of Chapter 2 and realized that an interesting story could be told relating Plato and Aristotle on these issues. Discussions with Marko Malink since 2013 further spurred me to connect this work with Aristotle’s syllogistic. Philosophy in the Socratic tradition was always fundamentally a conversation. This dissertation itself is a product of many, many such conversations. I’m grateful to everyone who suggested new paths, pointed out my frequent missteps, and encouraged me to dig deeper. Your words have made an impression on every page. While I have been working on this project, I’ve had the benefit of incredibly helpful audiences at UC Berkeley, UC Davis, LMU-Munich, Marquette University, Northwestern University, and the West Coast Plato Workshop. For stimulating conversations and comments on papers, I am indebted to Andreas Anagnostopou- los, Michael Arsenault, Joseph Bjelde, Robert Bolton, Adam Bradley, David Bron- stein, Lara Buchak, Chris Buckels, Agnes Callard, John Campbell, Nicola Carraro, Alan Code, Michel Crubellier, Shamik Dasgupta, Huw Duffy, David Ebrey, Dan Esses, Emily Fletcher, Mary Louise Gill, Owen Goldin, Laura Grams, Mark Griffith, Verity Harte, George Harvey, Dhananjay Jagannathan, Sarah Jansen, Ethan Jerzak, Jeff Kaplan, Sean Kelsey, Alex Kerr, Elaine Landry, Richard Lawrence, Tony Long, Paolo Mancosu, Sara Magrin, Marko Malink, Richard McKirahan, Katy Meadows, Connie Meinwald, Josh Mendelsohn, Mitchell Miller, Georgia Mouroutsou, Emily Perry, Christian Pfeiffer, Kristin Primus, Christof Rapp, Jeremy Reid, Jason Rheins, George Rudebusch, David Sedley, Jan Szaif, Richard Taylor, Voula Tsouna, Daniel Warren, and John Wynne. I have been incredibly fortunate to have so many thoughtful and inspiring ad- visors. In many ways Klaus Corcilius and Tim Clarke were ideal committee chairs. They managed to simultaneously give me room to try out my latest bizarre ideas and managing to bring me back to earth. John MacFarlane and John Ferrari went above and beyond in giving feedback on work and always challenging me to con- nect my work to broader philosophical issues. Katja Vogt, while not officially on my committee, has been a mentor in so many ways since I took my first course on iii CONTENTS ancient philosophy with her in 2009. This dissertation would not have been possible without Anna Vlasits. I don’t know what I would be without her. Every day I am indebted to her energy, com- mitment, and encouragement. Her intellect and good sense have challenged me to improve myself both in my work and in our marriage. iv Chapter 1 Introduction What is Plato’s method of division? Plato himself takes the trouble to show us, at least superficially. In the dialogue Sophist, the Eleatic Visitor is trying to explain to his interlocutors how he will pursue his investigation of sophistry. While this is probably not the earliest dialogue in which the method appears,1 it is the one where we get the most thorough example of someone self-consciously carrying it out in order to show someone how it is to be done: Visitor: Well then, let’s go after the angler from this starting point. Tell me, shall we take him to be an expert at something, or a nonexpert with another sort of capacity? Theaetetus: He’s definitely not a nonexpert. V: But expertise as a whole falls pretty much into two types. T: How? V: There’s farming, or any sort of caring for any mortal body; and there’s also caring for things that are put together or fabricated, which we call equipment; and there’s imitation. The right thing would be to call all those things by a single name. T: How? What name? V: When you bring anything into being that wasn’t in being before, we say you’re a producer and that the thing you’ve brought into being is produced. T: That’s right. 1See Lukas (1888) for discussion of division in nine Platonic dialogues. However, he does not discuss the Euthyphro (see below, also Meinwald (2002)) or Cratylus (Ademollo, 2011). While the method arguably appears frequently, it is only emphasized and thoroughly described in the Phae- drus, Sophist, Statesman, and Philebus. Although I don’t need to argue for it here, the pervasiveness of division throughout the Platonic corpus puts pressure on the idea that there is some sort of de- velopment in Plato’s thinking from Socratic elenchus to the method of hypothesis to the method of collection and division. Robinson (1953) goes so far as to delimit his subject by the absence of this final stage. 1 Chapter 1. Introduction V: And all the things we went through just now have their own capacity for that. T: Yes. V: Let’s put them under the heading of production. T: All right. V: Next, consider the whole type that has to do with learning, recogni- tion, commerce, combat, and hunting. None of these creates anything. They take things that are or have come into being, and they take pos- session of some of them with words and actions, and they keep other things from being taken possession of. For that reason it would be ap- propriate to call all the parts of this type acquisition. T: Yes, that would be appropriate. V: If every expertise falls under acquisition or production, Theaetetus, which one shall we put angling in? T: Acquisition, obviously. V: Aren’t there two types of expertise in acquisition? ...... V: So now we’re in agreement about the angler’s expertise, not just as to its name; in addition we’ve also sufficiently grasped a verbal expla- nation concerning the thing itself. Within expertise as a whole one half was acquisitive; half of the acquisitive was taking possession; half of possession-taking was hunting; half of hunting was animal hunting; half of animal hunting was aquatic hunting; all of the lower portion of aquatic hunting was fishing; half of fishing was hunting by strik- ing; and half of striking was hooking.