The Logiphro Dilemma: An Examination of the Relationship between God and Logic Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By James C. McGlothlin, M.A. Graduate Program in Philosophy The Ohio State University 2014 Dissertation Committee: Stewart Shapiro, Advisor Tamar Rudavsky Chris Pincock Copyright James C. McGlothlin 2014 Abstract In this dissertation I set out to answer the following main question: What is the relationship between God and logic? I argue for an answer to this question by first examining two possible options and then give my own philosophical explanation that I believe overcomes the problems associated with the prior investigated options. In Chapter 1 I first define and clarify the desiderata of my main question. I understand God to be the divine being of classical theism shared by Jews, Christians and Muslims. I understand logic as primarily about the logical consequence relation. I characterize this relation in terms of necessity and universal applicability (or form), which captures various popular intuitions. Therefore, my main question is refined to: What is the relationship between the God of classical theism and logical consequence? In Chapter 2 I investigate an ancient question and dilemma presented by Plato in his Euthyphro dialogue, known popularly as the Euthyphro Dilemma. I suggest that the structure of this question naturally lends itself to the investigation of my question—what I call the Logiphro Dilemma, or the Logical Euthyphro Dilemma. As the name suggests, this dilemma gives us at least two options for thinking about the relationship between God and logic: (1) logical voluntarism: the view that claims the logical consequence relation is the result of God’s commands or will; and (2) logical non-voluntarism: the view that the logical consequence relation is completely independent of God’s commands ii or will in the sense of being independent of his creating or sustaining power. I then investigate both of these positions each in turn. In Chapter 3 I investigate logical voluntarism. I clarify what the position amounts to and then investigate a few possible historical proponents to see what might motivate this view. I then investigate various objections to this view, especially focusing on one of these and the negative results for accepting the consequences of this objection. I conclude that logical voluntarism cannot provide an answer to my main question. In Chapter 4 I investigate logical non-voluntarism. I clarify what the position of logical non-voluntarism amounts to and note its advantages over logical voluntarism. I clarify that it can be construed either platonistically (i.e. explicitly appealing to abstract objects) or nominalistically (i.e. explicitly not appealing to abstract objects). I investigate the platonist version first noting several objections to it from classical theism. I then investigate the nominalist version showing that it is a poor account of logic. I conclude that logical non-voluntarism (both versions) cannot provide an answer to my main question. In Chapter 5 I give my positive account to explain the relationship between God and logic. I first re-investigate the original Euthyphro Dilemma and find that the literature discussing this dilemma suggests a third alternative. I suggest that an analogous third alternative is available to the Logiphro Dilemma as well. Borrowing from Greg Welty’s account of modality and God, I argue for a model of logical consequence constituted by mental objects within the mind of God. I conclude that this model explains the relationship between God and logic while overcoming the problems associated with both logical voluntarism and logical non-voluntarism. iii Dedication To W. Wiley Richards My first philosophy professor iv Acknowledgments Thanks of course go to my dissertation committee: Stewart Shapiro, Tamar Rudavsky, and Chris Pincock for all of their advisement, criticisms, and help throughout this dissertation process. I would like to especially thank Stewart Shapiro who patiently guided me throughout my graduate career, particularly when I wanted to quit. Thanks also to all of the professors in the philosophy department of The Ohio State University (both current and now elsewhere) who have helped me at every step. Much thanks to my wife Cynthia—the one person who really knows how difficult this whole process has been for me. Finally, all thanks to Him who undoubtedly has kept me and blessed me (Numbers 6:24-6). v Vita May 1988.……………………………………Eau Gallie High 1998………………………………………….B.A. Theology, The Baptist College of Florida 2004………………………………………….M.Div. The Southern Baptist Theological Seminary 2006………………………………………….M.A. Philosophy, Western Michigan University 2006 to present……………………………….Graduate Teaching Associate, Department of Philosophy, The Ohio State University Publications 1. Review of Vern Poythress’ Logic: A God-Centered Approach to the Foundation of Western Thought. Themelios 28:2 (2013): 320-321. 2. Review of Paul Copan’s True For You But Not For Me. Areopagus Journal, Nov/Dec (2009): 34-5. 3. Review (co-authored with John DePoe) of Angus Menuge’s Agents Under Fire: Materialism and the Rationality of Science and Victor Reppert’s C. S. Lewis’s Dangerous Idea: In Defense of the Argument from Reason. Faith and Philosophy, 26:3 (2009): 339- 346. 4. Review of William Lane Craig and Charles Taliaferro’s Is God Real? Areopagus Journal Jan/Feb (2008): 39-41. vi 5. Review of Mikael Stenmark’s How to Relate Science and Religion: A Multidimensional Model. Philosophia Christi 8:1 (2006): 194-8. 6. Review of To Everyone an Answer edited by Francis J. Beckwith, William Lane Craig, and J. P. Moreland. The Southern Baptist Journal of Theology 10:3 (2006): 86-8. Fields of Study Major Field: Philosophy vii Table of Contents Abstract…………………………………………………………………………………... ii Dedication…………………………………………………………………………..….... iv Acknowledgments……………………………………………………………………...… v Vita………………………………………………………………………………………. vi Chapter 1: Prolegomena ……………………………………………………………….… 1 Chapter 2: The Logical Euthyphro Dilemma ………………...……………………...…. 33 Chapter 3: Logical Voluntarism ………………………………………………….…….. 54 Chapter 4: Logical Non-voluntarism ………………………………………….……… 108 Chapter 5: A Viable Third Alternative ………………………………..…...…………. 165 References …………………………………………………………………..………… 216 viii CHAPTER 1: PROLEGOMENA My primary question in this work is: What is the relationship between logic and God? In the whole of the following I will investigate and attempt to explain the nature of this relationship. I believe a good explanation of this relationship will be restricted by our understanding of the desiderata of logic and God. Once a clear understanding of these notions is in place, we should then be in a better position to see what sort of explanation of the relationship between these two notions will count as an acceptable or unacceptable explanation. Therefore, in this present chapter I will clarify what I mean when using the terms “logic” and God.” In §1 I will clarify the desideratum of logic, what I take to be the primary focus of logic. Though I believe I won’t be saying much that is controversial in this section, I’ll argue for a certain way to understand logic’s primary focus. In §2 I will clarify the desideratum of God. Since the divine is usually seen as an epistemologically challenging subject for exploration, I will investigate the two broad theological methodologies that are usually appealed to in making claims about God. I’ll address some challenges with the methodology I will be mainly siding with and then explain the particular way I take myself to be epistemically justified in making claims concerning God. Even though this is strictly a philosophical investigation, I will also identify the notion of the western or Abrahamic religious tradition I’ll be assuming throughout this work. I believe this 1 chapter will sufficiently define our desiderata of logic and God in order that we may go forward with our investigation as to what sort of relationship exists between the two. 1. Defining Logic 1.1 Logic’s Primary Focus What do I mean by “logic” when I say I’m interested in the relationship between God and logic? What does “logic” represent here? Generally, logic is taken to be the study of correct reasoning.1 More particularly, it is often characterized as the study of assessing good arguments from bad arguments in a particular (i.e. logical) way. By “argument” here, we typically do not mean a shouting match but a stretch of indicative discourse where at least one claim is intended to be supported by one or more other claims. The claim that is intended to be supported is often called a “conclusion” while the claim, or claims, intended to do the supporting are often called “premises.” So, the technical term “argument” in logic refers to a collection of claims that includes one or more premises and a single conclusion with this sort of supporting relationship between them.2 It is usually claimed that logic’s particular means of assessment—what I’ll call its primary focus—is the supporting logical relation between the premises and conclusion. This sort of relationship goes by various names such as deductive (or logical): validity, entailment, or consequence. Thus logic seems to be primarily about the 1 As with most things in philosophy, the “general” view has its respectable detractors. Gil Harman challenges the straightforward connection between reasoning and logic. See his (1973) and (1986). 2 A couple of caveats to this description: (1) some conclusions need no support from other claims (|- Φ), i.e. the set of premises may be empty; and (2) it is trivially true that a claim can support (imply) itself (Φ |- Φ), at least on most accounts of logic. 2 business of distinguishing “good” arguments as deductively valid from “bad” arguments as deductively invalid. In this work I’ll simply call this relationship logical consequence. In our day, most logicians and philosophers of logic will agree that logic’s primary focus is the notion of logical consequence.