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Essence and Necessity, and the Aristotelian Modal Syllogistic: a Historical and Analytical Study Daniel James Vecchio Marquette University

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Essence and Necessity, and the Aristotelian Modal Syllogistic: a Historical and Analytical Study Daniel James Vecchio Marquette University Marquette University e-Publications@Marquette Dissertations (2009 -) Dissertations, Theses, and Professional Projects Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study Daniel James Vecchio Marquette University Recommended Citation Vecchio, Daniel James, "Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study" (2016). Dissertations (2009 -). 686. http://epublications.marquette.edu/dissertations_mu/686 ESSENCE AND NECESSITY, AND THE ARISTOTELIAN MODAL SYLLOGISTIC: A HISTORICAL AND ANALYTICAL STUDY by Daniel James Vecchio, B.A., M.A. A Dissertation submitted to the Faculty of the Graduate School, Marquette University, in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Milwaukee, Wisconsin December 2016 ABSTRACT ESSENCE AND NECESSITY, AND THE ARISTOTELIAN MODAL SYLLOGISTIC: A HISTORICAL AND ANALYTICAL STUDY Daniel James Vecchio, B.A., M.A. Marquette University, 2016 The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. Chapter Three explores how Aristotle’s syllogistic fits within Aristotle’s philosophy of science and demonstration, particularly within the context of the Posterior Analytics. Consideration is given to the Aristotelian understanding of the relationship among necessity, explanation, definition, and essence. Chapter Four applies Aristotelian modal logic in contemporary contexts. I contrast Aristotelian modality and essentialism with contemporary modalism based upon the semantics of possible worlds, e.g. Kripke and Putnam. I also develop an account of how Aristotelian modal logic can ground a sortal dependent theory of identity, as discussed by Wiggins. i ACKNOWLEDGEMENTS Daniel James Vecchio, B.A., M.A. I am grateful Dr. Owen Goldin, who first proposed at a Philosophy Department social that I take a look at Aristotle’s modal syllogistic to see if I could make any sense of it. As director of my dissertation project, Dr. Goldin has provided an enormous amount of support— meeting with me remotely, at all hours, while I wrote the bulk of this dissertation in Madrid, Spain. I am also thankful for the support and helpful comments of my other committee members: Dr. Michael Wreen, Dr. Noel Adams, and Dr. Marko Malink. Dr. Wreen has guided me in becoming a better writer, and a more rigorous and logical thinker. Without the tools he taught me in the Philosophy of Logic, this dissertation would never have gotten off the ground. Dr. Adams has also been an extraordinary mentor and friend, who has provided insightful comments at the outset of my project. Dr. Malink has been of central importance to me for the past few years, both in terms of his brilliant work on Aristotle’s modal syllogistic, and in terms of meeting with me to guide and teach me so much about this topic. Finally, I would like to acknowledge the loving support of my family. In particular, I should mention the tireless efforts of my father, James, who often served as a second set of eyes, in reviewing my writing. I would like to thanks my mother, Kathleen who did not live to see this project through to its completion, but whose love gave me the foundation to believe that I could complete my dissertation. I would like to thank my mother-in-law, Graciela, who is always praying for me and our family, and has provided so much to me and my family as I complete this dissertation. Also, I would like to thank my beautiful daughter, Vivian, whose recent birth gave me a special impetus to complete the dissertation, though the demands of the dissertation often called me away from her. I ii dedicate this work to my darling wife, Gabriela, who has believed in me and supported me through this challenging period. Without you, Gabriela, I could not have done this. I love you. Finally, I am grateful to God, who is the source of all good things. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS………………………………………………………………………………………… i LIST OF FIGURES………………………………………………………………………………………………….. v ABBREVIATIONS OF THE WORKS OF ARISTOTLE…………………………………………………. vi CHAPTER ONE…………………………………………………………………………………………………………… 1 1.0 Introduction………………………………………………………………………….. 1 1.1 Symbolization……………………………………………………………………….. 6 1.2 Basic Modal Syllogisms………………………………………………………... 6 1.3 The Two Barbaras……………………………………………………………….. 13 1.4 The Modal Copula………………………………………………………………….. 22 1.5 Malink on the Metaphysics of Aristotelian Modality………………... 28 1.6 Malink’s Heterodox Interpretation of Aristotelian Semantics….. 29 1.7 An Adjustment to Malink’s Heterodox Interpretation……………... 40 1.8 Conclusion…………………………………………………………………………… 62 TWO…………………………………………………………………………………………………………. 65 2.0 Explication of Argument Forms along with Venn Diagrams……. 65 2.1 The First Figure……………………………………………………………………. 68 2.2 The Second Figure………………………………………………………………… 76 2.3 The Third Figure…………………………………………………………………… 89 2.4 Conclusion………………………………………………………………………….... 101 THREE……………………………………………………………………………………………………….. 105 3.0 Introduction………………………………………………………………………… 105 iv 3.1 Transcending the De Re/De Dicto Distinction……………………….. 106 3.2 The Modality of Definition, Explanation, and Essence…………….. 109 3.3 Towards an Aristotelian Demonstrative Science……………………. 133 3.4 Knowledge of Essences………………………………………………………… 151 3.5 Aristotelian Essentialism and Aristotelian Science………………… 166 3.6 Conclusion…………………………………………………………………………… 170 FOUR………………………………………………………………………………………………………… 173 4.0 Introduction…………………………………………………………………………. 173 4.1 The Circularity Problem………………………………………………………... 184 4.2 Actualism…………………………………………………………………………….. 186 4.3 Possible Worlds and Essences………………………………………………. 192 4.4 Transworld Individuals and Counterpart Theory………………….. 195 4.5 Identity and Essence……………………………………………………………… 204 4.5.1 Leibniz’s Laws and Regulating Identity Relations…………. 205 4.5.2 Relative Theory of Identity…………………………………………. 209 4.5.3 Sortal Dependency Theory of Identity………………………… 213 4.5.4 Identity Grounded on Aristotelian Essentialism and Modality……………………………………………………………… 222 4.6 Conclusion, or Counteracting Indispensability………………………… 232 BIBLIOGRAPHY…………………………………………………………………………………………………….. 236 APPENDIX……………………………………………………………………………………………………………. 245 v LIST OF FIGURES Fig. 1: Assertoric Categorical Propositions…………………………………………………………… 66 Fig. 2: Apodictic Categorical Propositions…………………………………………………………….. 67 Fig. 3: Comparison of Barbara-LXL to Barbara-XLL……………………………………………… 69 Fig. 4: Comparison of Celarent-LXL to Celarent-XLL……………………………………………… 71 Fig. 5: Comparison of Darii-LXL to Darii-XLL………………………………………………………… 73 Fig. 6: Comparison of Ferio-LXL to Ferio-XLL………………………………………………………… 75 Fig. 7: Comparison of Cesare-LXL to Cesare-XLL……………………………………………………. 77 Fig 8: Comparison of Camestres-XLL to Camestres-LXL…………………………………………. 78 Fig. 9: Comparison of Festino-LXL to Festino-XLL………………………………………………….. 80 Fig. 10: Comparison of Baroco-LLL to Baroco-XLL………………………………………………... 83 Fig. 11: Comparison of Baroco-LLL to Baroco-LXL………………………………………………... 87 Fig. 12: Comparison of Baroco-LXX to Baroco-XLX………………………………………………… 88 Fig. 13: Comparison of Darapti-LXL to Darapti-XLL……………………………………………….. 90 Fig. 14: Comparison of Felapton-LXL to Felapton-XLL…………………………………………… 92 Fig. 15: Comparison of Disamis-XLL to Disamis-LXL……………………………………………… 94 Fig. 16: Comparison of Datisi-LXL to Datisi-XLL…………………………………………………….. 95 Fig. 17: Comparison of Bocardo-LLL to Bocardo-LXL…………………………………………… 97 Fig. 18: Comparison of Bocardo-LLL to Bocardo-XLL…………………………………………… 98 Fig. 19: Comparison of Ferison-LXL to Ferison-XLL……………………………………………… 100 vi ABBREVIATIONS OF THE WORKS OF ARISTOTLE APo. Posterior Analytics APr. Prior Analytics Cat. Categories De An. de Anima De In. de Interpretatione Meta. Metaphysics PA de Partibus Animalium Phys. Physics Top. Topics 1 CHAPTER ONE 1.0 Introduction Aristotle’s modal logic is considered by many commentators to be a murky mess. The oft repeated phrase on this subject, coined by Günther Patzig, is that the modal syllogistic is “a realm of darkness” (1968, 86 fn.21). Patzig was specifically referencing the attempt by Albrect Becker to interpret Aristotle’s use of “modal operators” in the “traditional way”. This is, by no means, a recent condemnation. Alexander of Aphrodisias reports that Aristotle’s earliest commentators disagreed with many of his supposed valid forms of argument. Theophrastus and Eudemus thought that no valid mixed apodictic syllogism, a syllogism with one apodictic premise and one non-apodictic premise, could have an apodictic conclusion. Rather, they insisted that the weaker modality of the premises should rule over the conclusion.
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