THE LOGICAL PROBLEM OF THE TRINITY A Dissertation Submitted to the Graduate School of the University of Notre Dame in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Beau Branson Richard Cross, Director Graduate Program in Philosophy Notre Dame, Indiana April, 2014 © 2014 Beau Branson Some Rights Reserved. cbnd Except where otherwise noted, this work is licensed under http://creativecommons.org/licenses/by-nc-nd/4.0/ You may copy and redistribute this work (but not create, copy or distribute any derivative work) in whole, and with proper attribution to the author, for non-commercial purposes only. For more information, see: http://creativecommons.org/licenses/by-nc-nd/4.0/ The Logical Problem of the Trinity Abstract by Beau Branson The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I argue that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.” iii Dedication To Kathleen Kaufman, for allowing me to think for myself. I thank you on behalf of all of us. For you touched the lives of so many, and in so many ways, “. the which, if they should be written every one, I suppose that even the world itself could not contain the books that should be written.” v Contents Page Abstract iii Contents vii Introduction 1 I Defining the Problem 7 1 Definitions 9 1.1 What is the Logical Problem of the Trinity? . 9 1.2 What Would Be a Solution? . 15 1.3 Proposed Solutions . 19 1.3.1 Contemporary Proposed Solutions . 19 Social Trinitarianism (ST) . 19 (“Pure”) Relative Identity Trinitarianism (Pure RI) . 23 “Impure” Relative Identity Trinitarianism (Impure RI) . 25 1.3.2 Classical Trinitarian Heresies . 28 Arianism . 28 (Naïve) Modalism . 33 2 Taxonomy of Possible Solutions 37 2.1 The LPT1 Family . 41 2.2 The Non-PLI (Pure RI) Family . 42 2.3 The Naïve Modalist Family (and Cousins) . 42 2.4 The Equivocation1 Family (Arian) . 44 2.5 The Equivocation2 Family (Social Trinitarian) . 45 2.6 The Non-Classical-Identity-Counting Family . 46 2.7 The LPT2 Family . 47 vii II Methodology 53 3 Methodology 55 3.1 The Puzzle Approach . 57 3.2 The Mysterian Approach . 80 3.3 The Historical Approach . 95 3.3.1 Objection 1: The Puzzler’s Tu Quoque . 95 3.3.2 Objection 2: The Mysterian’s Conundrum . 100 3.3.3 Objection 3: The Anti-Trinitarian’s Challenge . 109 III History 113 4 St. Gregory of Nyssa’s Account of the Trinity 115 4.1 Ad Ablabium: Its Structure and Purpose . 116 4.1.1 One Question, Three Answers . 116 4.1.2 The “Simple-Minded” Argument (SMA) . 118 4.2 The Unity of Nature Argument (UNA) . 123 4.2.1 Ousiai and Hypostases . 126 4.2.2 Gregory’s Semantics of Collective Nouns . 129 4.2.3 Did Gregory Really Believe in the UNA? . 134 Does “Is God” Really Predicate the Divine Nature? . 134 The Real Role of the UNA in Gregory’s Response . 139 4.3 Idiomata ................................151 4.3.1 Basil’s Epistles 214 and 236 . 152 4.3.2 Ad Petrum . 154 4.3.3 How “Peculiar” is an Idioma? . 161 4.3.4 Two Views of the Individuation of Hypostases . 165 4.3.5 Do Idiomata Really Individuate? . 169 4.3.6 Do Idiomata Really Exist? . 171 4.4 The Unity of Action Argument (UAA) . 174 4.4.1 Gregory’s Semantics for “is God” . 174 4.4.2 Gregory’s Metaphysics of Energeiai . 178 4.4.3 Gregory’s Theology of Synergy . 181 4.4.4 The Individuation of Ousiai . 184 The Individuation of Ousiai in Ad Xenodorum . 185 The Individuation of Ousiai in Ad Eustathium . 186 4.4.5 Conclusion . 189 IV Logic 195 5 Formalizing Gregory’s Account 197 Metaphysics, Theology, and Semantics . 198 5.1 Gregory’s Metaphysics . 200 5.1.1 Possible Object Types . 201 viii 5.1.2 Possible Relations Between Tokens of the Object Types . 202 5.1.3 Relations Possible for the Objects . 205 5.1.4 Identity Conditions for the Types of Objects . 207 5.2 Gregory’s Theology . 211 5.2.1 Postulated Token Objects . 211 5.2.2 Relations Posited Between the Token Objects . 223 5.2.3 Individuation of the Token Objects . 231 5.3 Gregory’s Semantics . 243 5.3.1 Gregory’s Semantics for S4 through S6 . 243 5.3.2 Gregory’s Semantics for S1 through S3 . 244 5.3.3 Gregory’s Semantics for S7 . 246 5.4 A Model for PGNT-F . 252 5.5 What is Essential? – GNT “Lite” . 258 5.5.1 MP-GNT-Lite . 258 5.5.2 GNTF-Lite . 260 V Evaluation 263 6 Defending Gregory’s Account 265 6.1 The Formal Adequacy of Gregory’s Account . 266 6.2 Semantic Objections . 273 6.3 Metaphysical Objections . 287 6.4 Theological Objections . 291 6.5 Final Conclusion . 307 Appendices 313 Appendix A: Appendix of Proofs 313 A.1 Ohomoousion ..............................315 A.2 NE*E . 316 A.3 E*Lemma ................................317 A.4 EUnique ................................318 A.5 Σ*8 ..................................320 A.6 P7GNT-EQ ...............................322 A.7 φGNTα 6j= α=t i for any t i such that t i 6= α . 323 Appendix B: Summary of GNTF 325 Bibliography 337 ix Acknowledgments I would like most especially to acknowledge my advisor, Richard Cross. Despite a bachelor’s in Classics and a strong interest in patristics, I originally came to Notre Dame thinking I would focus only on logic and contemporary analytic metaphysics. I knew that there was a lot of very serious philosophical thought going on in many of the church fathers, and I felt that it deserved careful attention from philosophers and that it was mostly obscured in bad (when even existent) English translations. But I couldn’t imagine how to bring them into conversation with current analytic philosophy and never thought I would be the man for that job in any case. That is, until reading Richard’s careful analysis of Gregory of Nyssa’s theory of universals several years ago showed me an example of how one might give the church fathers exactly the kind of careful philosophical analysis I felt they deserved. It was his work that originally inspired me to do my dissertation on the Trinity and to take it in the historical direction I’ve taken it in. It was only after I had already begun the dissertation that fate would bring him to Notre Dame and allow me to finish it under his direction. Even when critical, his advice and feedback along the way has been consistently helpful and encouraging, both of which qualities are absolutely essential when slogging through the difficult work of one’s dissertation. The dissertation was originally begun under Mike Rea, and although he was ultimately unable to be on my committee, I owe him a great deal of gratitude for his feedback during the initial stages of the dissertation. Much of the material that has ultimately made it in was originally written while he was director, and a great deal more was ultimately not incorporated into the final version. I thank him for his monumental efforts in reading through and commenting on this massive amount of material and for consistently forcing me to state my positions and arguments more clearly and precisely and to answer certain questions I had not considered. I really would not have had anything interesting to say about methodology at all were it not for him challenging me to clarify and distill my views on that issue. Finally, I thank him for ultimately being gracious enough to allow me to change advisors to Richard after he came to Notre Dame and it seemed to make more sense. I’m also extremely thankful to Fritz Warfield for taking Mike’s place as a reader at my defense at the last minute, when scheduling problems made it difficult for Mike, who was on leave. Peter van Inwagen was the main reason I wanted to come to Notre Dame in the first place.