A STUDY IN EARLY MEDIEVAL MEREOLOGY: BOETHIUS, ABELARD, AND PSEUDO-JOSCELIN DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Andrew W. Arlig, M.A. The Ohio State University 2005 Dissertation Committee: Approved by Professor Tamar Rudavsky, Adviser Professor Peter O. King ______________________________ Professor Allan Silverman Adviser Graduate Program in Philosophy Copyright by Andrew W. Arlig 2005 ABSTRACT The study of parts and wholes, or mereology, occupies two of the best philosophical minds of twelfth-century Europe, Abelard and Pseudo-Joscelin. But the contributions of Abelard and Pseudo-Joscelin cannot be adequately assessed until we come to terms with the mereological doctrines of the sixth century philosopher Boethius. Apart from providing the general mereological background for the period, Boethius influences Abelard and Pseudo-Joscelin in two crucial respects. First, Boethius all but omits mention of the classical Aristotelian concept of form. Second, Boethius repeatedly highlights a rule which says that if a part is removed, the whole is removed as well. Abelard makes many improvements upon Boethius. His theory of static identity accounts for the relations of sameness and difference that hold between a thing and its part. His theory of identity also provides a solution to the problem of material constitution. With respect to the problem of persistence, Abelard assimilates Boethius’ rule and proposes that the loss of any part entails the annihilation of the whole. More precisely, Abelard thinks that the matter of things suffers annihilation upon the gain or loss of even one part. He also holds that many structured wholes, namely artifacts, are strictly dependent upon their parts. Yet Abelard insists that human beings survive a ii variety of mereological changes. Abelard is silent about objects which are neither artifacts nor persons. I argue that Abelard has the theoretical resources to provide an account of the persistence of these types of object, so long as some forms are ontologically robust. Pseudo-Joscelin rejects the thesis that the removal of any part entails the destruction of the whole. The annihilation of a whole follows only from the removal of essential parts. Pseudo-Joscelin employs two basic principles in his theory of persistence. First, forms and the functions encoded in them play a primary role in identity and persistence. He also makes use of a genetic criterion. Pseudo-Joscelin expands both principles and employs them when he vigorously defends the thesis that a universal is a concrete whole composed of particulars from Abelard’s criticisms. iii To Tri iv ACKNOWLEDGMENTS Many persons have helped to make the completion of this dissertation possible. Several deserve special mention. Professor Josef Stern introduced me to medieval philosophy. While advising me on my undergraduate thesis, he also taught me the virtues of precision in thought and expression. I hope that I have not failed him much in the subsequent years. Professor Peter King introduced me to Abelard and Pseudo-Joscelin, and to the pleasures of exploring twelfth-century metaphysics. Peter’s knowledge of Abelard and twelfth-century philosophy is profound, and I have learned much from our close collaboration on this project. Without him, this specific project could not have happened. Professor Tamar Rudavsky has been a tremendous source of support as my current adviser. The final stages of my work have benefited from her able guidance. Professor Allan Silverman has been a valuable resource, and a wonderful friend and colleague. To him I owe a greater appreciation of the Greek philosophy that underwrites twelfth-century metaphysics. Portions of chapter 4 have been read before audiences at the Cornell Summer Colloquium in Medieval Philosophy in May 2003, the Department of Philosophy at the Ohio State University in November 2003, and the annual meeting of the Ohio v Philosophical Association in April 2004. I benefited immensely from the comments and questions raised by these audiences. In particular, I must thank Kevin Guilfoy for his commentary at the OPA meeting, as well as his general enthusiasm for my project. I also want to thank Scott MacDonald for his generousity and encouragement, and for providing a relaxed but intellectually stimulating environment at Cornell in which medievalists can present their work. Carol Hay helped me with final-hour formatting issues. Her knowledge of Microsoft Word spared me uncountable hours of work, and perhaps even added several years to the life of my heart. My gratitude and affection are boundless. None of this would be possible without the love and sacrifice of my parents Douglas and Patricia Arlig. A long time ago they were forced to come to terms with the fact that their son was a humanist, and not a scientist. Their support has been unwaivering ever since. Finally, I must thank my wife Rajashree Datta. She above all has given me the means to bring this project to its end. She has sacrificed much in the process. With love and gratitude, I dedicate this work to her. vi VITA November 9, 1971 ……………….….…. Born – Phoenix, AZ, USA 1994 ………….………………………… B.A. with Honors, The University of Chicago. 2002 ………………………………….… M.A. Philosophy, The Ohio State University. 1998 -1999 ………………………….….. Distinguished University Fellow, The Ohio State University 1999 - 2003 …………………………….. Graduate Teaching Associate, The Ohio State University 2003 - 2004 ………………………….…. Distinguished University Fellow, The Ohio State University 2004 - present ………………….……….. Graduate Teaching Associate, The Ohio State University FIELDS OF STUDY Major Field: Philosophy vii TABLE OF CONTENTS Page Abstract . .ii Dedication . iv Acknowledgments . .v Vita. vii List of abbreviations. .xi Chapters: 1. Introduction . .1 2. Introduction to mereology and the metaphysics of mereology . .12 2.1 Formal mereology and the metaphysics of mereology . 13 2.2 Mereological sums, and the problem of what things are wholes . .15 2.3 When is something a part? . .27 2.4 Dependence . 35 2.4.1 Varieties of ontological dependence . .35 2.4.2 Dependence of the whole upon its parts . .36 2.4.3 Dependence of the part on the whole . 39 2.5 Synchronic and diachronic identity . .49 2.6 Conclusion to chapter 2 . .60 3. Boethius and the early mereological tradition . 62 3.1 Parts, wholes, and division . .65 3.1.1 The science of division. 66 3.1.2 Universal wholes are not integral wholes. 75 3.2 The four-fold distinction between the genus and the whole . 84 3.2.1 The genus is divided with respect to quality. 85 3.2.2 The genus is naturally prior. .89 viii 3.2.3 The genus is matter. 97 3.2.4 The species is the same thing as its genus. .101 3.2.5 Conclusion to the four differences. .109 3.3 Boethius’ metaphysics of mereology. 113 3.3.1 The problem with quantity . 113 3.3.2 On when something is a part of an integral whole. .121 3.3.3 On static identity . .127 3.3.4 The ontological dependence of wholes upon their parts. .132 3.4 Conclusion to chapter 3 . .139 4. Abelard’s mereology and its role in metaphysics . 141 4.1 Abelard’s metaphysics. 141 4.1.1 Ontology. 142 4.1.2 Hylomorphism and the constitution of things . .144 4.1.3 Integral wholes . 153 4.1.4 States and states-of-affairs . 159 4.2 Identity . .165 4.2.1 Abelard on numerical sameness . .. .165 4.2.2 Identity and material constitution . .180 4.2.3 Segue to problems of persistence and change . .195 4.3 Persistence and change . 197 4.3.1 The Growing Argument . 198 4.3.2 No temporal parts . 214 4.3.3 Substantial persistence . 227 4.3.4 The persistence of persons . 234 4.4 Conclusion to chapter 4 . .242 5. Pseudo-Joscelin and the Moderate critique of Abelard . .243 5.1 The Moderate theory of identity and persistence . .245 5.1.1 The Mereological Sorites. .246 5.1.2 Moderate responses to the Sorites . .250 5.2 The collection theory of universals . 271 5.2.1 Abelard on the collection theory . .272 5.2.2 An Abelardian critique of collective realism . 277 5.2.3 A new version of the collection theory. 283 ix 5.3 Conclusion to chapter 5. 302 6. Conclusion . .304 List of references . .316 x LIST OF ABBREVIATIONS Abelard Dial. Abelard Dialectica. (1954a) Abelard Hex. Abelard Expositio in Hexaemeron. (1855) Abelard In de Div. Abelard De divisionibus incipit. (1954b) Abelard LNPS Logica ‘nostrorum petitioni sociorum’. (1933) Abelard Log. Ingr. 1 Logica ‘ingredientibus’, pt. 1: glossae super Porphyrium. (1919) Abelard Log. Ingr. 2 Logica ‘ingredientibus’, pt. 2: glossae super Praedicamenta Aristotelis. (1921) Abelard Sent. Abelard Sententiae secundum M. Petrum. (1958) Abelard Theol. Chr. Abelard Theologia Christiana. (1969) Abelard Theol. Sch. Abelard Theologia Scholarium. (1987a) Abelard TSB Abelard Theologia ‘summi boni’. (1987b) Alexander in Metaph. Alexander of Aphrodisias In Aristotelis Metaphysica commentaria. (1891) Ammonius In Cat. Ammonius In Aristotelis Categorias commentarius. (1905) Ammonius In Isag. Ammonius In Porphyrii Isagogen sive V voces. (1891) Arethas Sch. Arethas of Caesarea Scholia on Porphyry’s Isagoge and Aristotle’s Categories. (1994) xi Asclepius In Metaph. In Aristotelis Metaphysicorum libros A-Z commentaria. (1888) Boethius Contra Eut. Boethius Contra Eutychen. In Boethius 2000. Boethius De Div. Boethius De Divisione. (1998) Boethius De top. diff. Boethius De topicis differentiis. (1990) Boethius De Trin. Boethius De Sancta Trinitate. In Boethius 2000. Boethius In Cat. Boethius In Categorias Aristotelis libri quatuor. (1891) Boethius In de Int. II Boethius In librum Aristotelis Peri Hermenias pars posterior. (1880) Boethius In Isag. I Boethius In Isagogen Porphyrii Commentorum editionis primae. (1906) Boethius In Isag. II Boethius In Isagogen Porphyrii Commentorum editionis secundae. (1906) Boethius In Cic. Top. Boethius In Topica Ciceronis Commentaria.