laws of logic

Alex Malpass has offered one of the most thoughtful critiques of the argument for God from logic in his 2020 Sophia article, “Problems for the Argument from Logic: a Response to the Lord of Non-Contradiction.” Here’s the abstract:

James Anderson and Greg Welty have resurrected an argument for God’s existence (Anderson and Welty 2011), which we will call the argument from logic. We present three lines of response against the argument, involving the notion of necessity involved, the notion of intentionality involved, and then we pose a dilemma for divine conceptualism. We conclude that the argument faces substantial problems.

In this post I will share some thoughts on the third of these “three lines of response,” which I take to be the most interesting point of criticism.¹ (Note: I’m speaking only for myself in this post; Greg can speak for himself!)

The argument for God from logic involves defending a version of divine conceptualism (or better, “theistic conceptual realism,” to use Welty’s terminology) according to which the laws of logic, as necessarily true propositions, are ultimately just divine thoughts. Strictly speaking, the argument can be run from any necessary truths, not just the laws of logic, but the laws of logic serve as familiar and convenient examples of necessary truths.²

In the last major section of his article, Malpass presents a “dilemma for divine conceptualism.” Rather than quote him at length, I will try to summarize the thrust of his challenge. He begins by observing that parts of our argument appeal to a distinction between “thoughts and the content of those thoughts” (see, e.g., footnote 31 of our 2011 article). But then he points out that this seems to raise a problem for the claim that propositions are divine thoughts. In the first place, he argues, “a thought cannot be the content of itself” (p. 251). The idea that a thought can be its own content is either flat-out incoherent or leads to a “vicious infinite regress” (p. 252). To avoid this, the divine conceptualist has only two options:

1. A divine thought has no content.
2. A divine thought has content distinct from the thought itself.

Option 1 looks like a non-starter. If divine thoughts have no content, they can’t be about anything. Isn’t it obvious that God’s thought that 2+2=4 is contentful? Doesn’t it have some content that distinguishes it from other thoughts (e.g., God’s thought that Socrates is mortal)?

Option 2, however, doesn’t look any more promising. Recall our contention that the laws of logic, as necessarily true propositions, are a special category of divine thoughts. Let LL be some proposition that expresses a law of logic (e.g., the law of non-contradiction). LL is ultimately just a divine thought, so we argue. But according to option 2, the content of LL is something other than LL itself. So what could it be? Presumably that content would have to be propositional or intentional in nature. But it couldn’t be a proposition other than LL, for two reasons. First, that would mean LL has the wrong content; the divine thought would be about something other than what it’s supposed to be about. To use Malpass’s example, LL couldn’t have the Pythagorean theorem as its content; it’s supposed to be about the law of non-contradiction, not a geometrical theorem. The second reason is that if the content of LL is a proposition, but not LL itself, then it must be some other proposition, and therefore (given divine conceptualism) some other divine thought. Call that other divine thought LL*. But then the same considerations will apply to the content of LL*, in which case we’re on the road to a never-ending regress of divine thoughts containing divine thoughts, their content being endlessly deferred.

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