The Logiphro Dilemma

An Examination of the Relationship between God and Logic

McGlothlin

• Publisher: Pickwick Publications
• Year: 2017
• eBook ISBN: 9781498282246
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Is God above logic? If so, is he irrational? Is God subservient to logic? If so, is he really omnipotent? These questions are similar to Socrates' infamous challenge to explaining God's relation to morality, the so-called Euthyphro dilemma. In this book McGlothlin argues that the Euthyphro challenge can be extended to help explain the relationship between God and logic, what he call the Logiphro dilemma. Logic, on this account, depends on aspects of God's mind other than God's will. This is a nonstandard form of theistic logical dependence. It contrasts both with the standard form of theistic logical dependence, according to which logic depends on God's will, and with theistic logical independence, according to which logic is independent of God. These rival views can be seen as the horns of the Logiphro dilemma: either logic depends on God's will, in which case special revelation would no longer be communicable; or logic is independent of God, in which case core claims of classical theism--for example, that God is the only independent being--would be violated. The best way to escape both of these horns, according to McGlothlin, is to adopt the nonstandard form of theistic logical dependence.

1

PROLEGOMENA

My primary question in this book: 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. It should go without saying that a good explanation of this relationship, or any relationship, will be restricted by our understanding of the desiderata involved. Thus, in this first chapter, I will attempt to clarify what I mean be the terms “logic” and “God.” Once a clearer understanding of these notions is in place, we will then be in a better position to proceed towards seeing what the nature of the relationship between logic and God might be.

This chapter is divided into two main sections. In section 1.1 I will attempt to clarify the desideratum of “logic,” primarily by restricting it to what I take the primary focus of logic to be. 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 the second section, 1.2, I will attempt to clarify the desideratum of “God.” Since the divine is usually seen by most philosophers 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 philosophical claims concerning the being referenced as “God.” Even though this is strictly a philosophical investigation, I will also clarify the notion of the Western or Abrahamic religious tradition I’ll be assuming throughout this work.

I believe this 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.

1.1 Defining Logic

1.1.1 Logic’s Primary Focus

What do I mean by “logic” when I say I’m interested in the relationship between God and logic? 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. In this context, the word “argument” typically does not mean a shouting match between two or more people 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 business of distinguishing “good” arguments as deductively valid from “bad” arguments as deductively invalid. In this work I’ll simply call this relationship between a conclusion and its premises the logical consequence relation.

In our day, most logicians and philosophers of logic will agree that logic’s primary focus is the logical consequence relation. However, at one time logical truth was seen as the primary focus of logic.3 As philosopher Stephen Read briefly comments:

In the early twentieth century a number of authors (perhaps under the influence of the axiomatic method) seem to have concentrated on logical truth as the primary logical notion and logical consequence became an afterthought. This is a grave mistake, completely reversing the real situation.4

Why was this a “grave mistake”? Read goes on to give us two arguments to show why. First, Read claims that holding logical truth as the primary notion and logical consequence as “an afterthought” completely reverses the real situation. How so? Note that a logical truth is usually defined as the conclusion of a valid argument with no premises (i.e., [Ø]⊢Φ). Observe here that logical truth is being defined in terms of logical consequence. Read points out, the converse is not possible: logical consequence cannot be defined in terms of logical truth. This being the case, consequence seems like a more foundational notion than truth in logic and so consequence should indeed be recognized as the primary focus of logic.

Second, Read points out that logical truths, when counted among the premises of an argument, are unnecessary; or, put another way, premises that are logical truths may be suppressed. To see this point, take some argument where the conclusion Φ follows validly from a collection of premises Γ. Now suppose one of those premises in Γ is a logical truth. Logical validity is usually taken to mean that the conclusion follows from its premises alone. For if an argument is valid, then any interpretation that makes the conclusion false must make at least one of the other premises false too. But of course, the premise of an argument that is a logical truth cannot be made false. So the validity of this argument will not be affected by omitting the logical truth. Thus, the logical truth is redundant and so can be suppressed.

The conclusion that Read draws, along with the majority of logicians and philosophers of logic today, is that the notion of logical consequence is more central to logic than logical truth. Thus, in this book, I will also take the notion of logical consequence as the primary focus of logic as well.

1.1.2 Defining Logical Consequence

But how exactly should we understand this notion of logical consequence? If it is the primary focus of logic, it would also seem that logical consequence would probably be the primary focus of most any formal logical system.5 Indeed, this is usually the case. In such systems, which are typically about formal languages, consequence is often characterized in one or two closely related ways. Let L stand for any formal system of language, let Γ stand for a set of premise claims and let Φ be a single concluding claim. With this terminology in place, one formal notion of consequence that can be recognized is syntactic logical consequence and is usually defined in the following way:

(Γ⊢Φ) is syntactically valid in L just in case Φ is derivable from Γ, and the axioms of L, if any, by the rules of inference of L.

A second formal notion of consequence that can be recognized is semantic logical consequence and is usually defined this way:

(Γ⊢Φ) is semantically valid in L just in case Φ is true in all interpretations in which every member of Γ is true.6

Given that these are sharply defined notions on a formal language L, relations between them are a purely formal matter and so various formal results could be deduced from them. For instance, systems like L are considered sound if every syntactically valid argument in L is also a semantically valid argument in L; and L is considered complete if every semantically valid argument in L is also a syntactically valid argument in L. And since logical consequence is usually understood in these formal ways, like the above, distinguishing valid from invalid arguments is usually done by applying such a sharply defined formal interpretation of consequence within some strictly formal system L.

It thus makes sense then why logicians and philosophers of logic usually talk and think about logic, and logical consequence in particular, in terms of some specific formal system L. However, in pursuing the philosophical question about the relationship between God and logic, I need to be clear that I’m not interested in the relationship between God and some formal system L. (Though I’m sure there are interesting questions there.) Rather, I’m interested with the relationship between God and that which I believe such formal logical systems are usually attempting to model or capture—again, what I’m calling the primary focus of logic—the notion of logical consequence. It seems to me that just as formal grammatical rules for a natural language are attempts to capture the implicit rules of that natural language, in a similar way, I take it that formal logical notions for a formal language are attempts to capture the implicit notions of natural argumentation. If this is right, logical consequence is not primarily in the domain of formal logical systems, even if it is easier to talk about it in such systems.

But what exactly constitutes logical consequence then? If not formal notions, then what sorts of things make up logical consequence? I take this to be primarily a metaphysical question and historically there have been various suggested answers to it. Some candidates for what constitute logical consequence include mental entities (like thoughts, beliefs, etc.), or concrete objects in the world (such as sentence tokens), or abstract objects (propositions, possible worlds, sets, etc.).7 Since throughout this work I will be attempting to understand what relationship exists between God and logic, this will include attempting an answer to what sorts of entities constitute the logical consequence relationship. But, in order to not beg any questions at this point, I’ll remain neutral as to the exact sort of metaphysical nature that constitutes logical consequence. However, I will be returning to this question throughout this work, especially in chapters 4 and 5.

In order to attempt an answer to this metaphysical question later though, we still need to understand more clearly what sort of notion the logical consequence relation we are working with. I cl...

Table of contents

• Title Page
• Acknowledgments
• Introduction
• Chapter 1: Prolegomena
• Chapter 2: The Logical Euthyphro Dilemma
• Chapter 3: Logical Voluntarism
• Chapter 4: Logical Non-Voluntarism
• Chapter 5: A Viable Third Alternative
• Bibliography