In his November 17, 2016, post on Siris, “Implying Bottom,”* Brandon Watson casts a critical eye on a paragraph contained in an article by Stephen Maitzen, “The Problem of Magic.”** The two then, in the Comments section, engage in nicely intelligent discussion of a few of the issues at hand; I’m not quite sure that they have wrapped that discussion up.
The present post will be primarily concerned with the opening lines of the paragraph to which Watson draws our attention. They read:
Instead, any theistic explanation of the operation of the laws of logic must say at least this: If God didn’t exist, then the laws of logic wouldn’t hold. But no sense at all can be attached to the consequent of that conditional.
Important though they are, I’m not concerned in this post with either “any theistic explanation” of what Maitzen calls “the operation of the laws of logic” or with the conditional, “If God didn’t exist, then the laws of logic wouldn’t hold,” as a whole. Rather, I will be concerned, first, with offering what I consider a friendly amendment to the wording, and the thought behind the wording, of “the operation of the laws of logic.” Then I will offer a critique of Maitzen’s assertion that “no sense at all can be attached to the consequent of that conditional,” i.e., a critique of the position that “no sense at all can be attached” to the proposition that “laws of logic wouldn’t hold.”
1. First, then, “the operation of the laws of logic”: There is an equivocation pervasive in philosophical thought involving two quite different meanings of the word “logic.” According to the one meaning, logic is a theory of concepts, propositions, and arguments composed of propositions. Or, according to those less comfortable with a theory entailing the existence of conceptual entities, or “beings of reason,” logic is a theory of linguistic entities, terms, sentences or statements, and, again, arguments, but arguments composed of sentences or statements.
The logic with which Maitzen appears to be concerned, however, is a theory of real entities, i.e., extra-conceptual and extra-linguistic entities. That this is so is evident in, among several places, the first half of the second paragraph of his article, in which he treats the thesis that “the universe is intelligible” as sufficiently equivalent for his purposes to that of Bernard Lonergan that “the real is completely intelligible.”
Various philosophers and theologians – including Aquinas, Leibniz, Bernard Lonergan, and Hugo Meynell – see evidence for the existence of God in the fact that the universe is intelligible to us, i.e., the fact that we can understand to an impressive degree how the universe works. As Lonergan says, “If the real is completely intelligible, God exists. But the real is completely intelligible. Therefore, God exists” (2004: 5).***
Maitzen is not, of course, endorsing Lonergan’s argument.
I think it clear that the logic of which Maitzen speaks would be better identified as onto-logic, and better again as ontology, the theory of (real) beings.
2. Maitzen’s laws of logic then are, as I see things, laws of ontology. In what follows I’ll speak only of the law or, as I along with others would have it, the principle of non-contradiction, that, in its traditional formulation:
No being can both be and not be, in the same respect and at the same time.
or, in a more contemporary formulation:
For any existent, x, and any predicable, φ, x cannot both be a φ and not be a φ.
I’ll take it that Maitzen’s assertion that “no sense at all can be attached to the consequent of that conditional,” i.e., of the position that “no sense at all can be attached” to the proposition that “laws of logic wouldn’t hold,” would entail in particular that “no sense at all can be attached” to the proposition that the law or principle of non-contradiction wouldn’t hold. I’ll further take it that to say that the law of or principle of non-contradiction wouldn’t hold is to say that it is not true and that that in turn is to say that its contradiction would be true.
And to this sense can be perfectly well be attached, for we now have what I will dub the thesis of particular contradiction, that:
Some being can both be and not be, in the same respect and at the same time.
or, in a more contemporary formulation:
For some existent, x, and some predicable, φ, x can both be a φ and not be a φ.
Of course that proposition is false, and indeed irrational, even as sense can perfectly well be attached to it. The same can be said for the more radical thesis that is, not the contradiction of the law of contradiction, but its contrary, the thesis of universal contradiction, that:
All beings can both be and not be, in the same respect and at the same time.
or, in a more contemporary formulation:
For any existent, x, and any predicable, φ, x can both be a φ and not be a φ.
While I am in the process of taking note of versions, false but having sense, of what begs to be called ontological irrationalism, I might just as well add a yet more radical one, that:
All beings must both be and not be, in the same respect and at the same time.
or, in a more contemporary formulation:
For any existent, x, and any predicable, φ, x must both be a φ and not be a φ.
A closing note: similar things could be said, mutatis mutandis, of the law or principle of excluded middle, that:
All beings must be or not be, but not both, in the same respect and at the same time.
or, in a more contemporary formulation:
For any existent, x, and any predicable, φ, x must either be a φ or not be a φ, but not both.
I’ll leave the working out of the expressions of the opposed theses to the reader as an optional exercise.
Until next time.
Richard
After Aristotle 
Thank you for blogging about part of the passage of mine that was quoted at Siris. The context of the passage is whether it makes sense to say that (D) “All of the laws of logic depend on God,” much as traditional theism says that all of the laws of physics depend on God. (I don’t know of any position that says that some but not all of the laws of physics depend on God.) Now, D, if it makes any sense, implies (N) “If God didn’t exist, then none of the laws of logic would hold.” It’s the consequent of N that I think is senseless.
You listed a few principles that violate the law of noncontradiction or the law of excluded middle. In order to make any sense of the listed principles, however, we need to presuppose other laws of logic not (directly) challenged by the listed principles, such as “Any proposition implies itself” and “Any conjunction implies each of its conjuncts.” I don’t see how anyone can suppose that *none* of the laws of logic (whatever those may be) hold.
And thank you for your comment.
I have understood that that it is “the consequent of N that [you] think is senseless.” I would have agreed with you were you to have said simply that any proposition claiming that the laws of logic (I prefer “ontologic” or “ontology” here) do not or would not hold is false, utterly false. But not senseless, in what I take to be the most obvious sense of “senseless.” Heraclitus, at least arguably if at most arguably, held that the laws in question do not hold: “we are and we are not.” His followers, up to and including the present day, at least arguably if at most arguably, have also so held.
If anyone were to say to me, “If there is no god, then the law of non-contradiction does not hold,” I would tell him or her, not that the consequent is senseless, but that it is, again, false, utterly false.
Thank you for your reply. I say that, in order to assign any sense to (H) “We are and we are not” and (L) “The law of noncontradiction does not hold” (including enough sense to see that H and L are false),we must presuppose at least the following instances of the laws of logic: H implies H, L implies L, H implies “We are,” and H implies “We are not.” Do you agree?
I agree heartily. Sorry to keep you waiting. Family stuff (and stuffing).