Continuing with my series of posts reviewing the debate between Craig and Rosenberg, I'd like to comment in this post about Craig's novel argument for God's existence based on the applicability of mathematics. (As a matter of fact, this argument is not new at all; what is new is Craig's use of it in debating contexts. But in the history of thought, many scientists and philosophers have suspected that a strong connection exists between mathematics and God).
Before commenting on more detail on Craig's argument, let's to briefl clarify some questions:
Firstly, it is important to realize that Craig's argument is not based on the ontological existence of mathematical objects (like numbers or sets), but in the adequacy of mathematical formulations, laws, and theorems for the explanation and prediction of physical realities.
The argument for God from the ontological existence of mathematical objects is wholly another theistic argument. Roughly, this argument says that mathematical objects, if they exist objectively (and not just as a bunch of ideas in our minds), then they point out to a Cosmic, Infinite Mind in which such nonphysical, abstract objects are contained. Such cosmic mind would have created a world using such mathematical structures, which would explain why our mathematical theories match so beautifully the physical world. (Note that a certain similarity with Craig's argument does exist).
In my opinion, this is a good argument, but a very complex one, because it requires to prove that mathematical objects exist objectively, and such proof requires addresing complicated issues in the philosophy of mathematics.
In any case, the overwhelming majority of people would probably agree that if such mathematical objects exist objectively, then a cosmic, infinite, perfect mind in which such extraordinary nonphysical objects are contained would exist too, and this is (among other things) what God is supposed to be.
In my interview with mathematician Elliot Benjamin, who has a PhD in mathematics, when I asked him about this, he commented:
Well if it were the case that numbers and mathematics did exist in some kind of objective/ontological sense, then perhaps this would give us some evidence for some kind of intelligent being who designed the universe--I suppose you can call it God. For the astounding logic involved in higher mathematics is staggering virtually beyond comprehension, with a phenomenal level of mental acrobatics involved in the highest mathematical realms. But once again this is not an area that I can speak very knowledgably about, as I am both a pure mathematician and experiential philosoher (both very subjective worlds).
The naturalist, not believing in any "mind" whatsoever as a fundamental part of the fabric of reality, has not the mataphysical resources to explain the objective existence of mathematical objects. Like with the absolute beginning of the universe, the naturalist has to believe that such objects just exist "inexplicably", and that for "not reason at all" our purely contingent and finite material minds have evolved in a way in which we can grasp and manipulate such perfect non-physical (abstract) entities and their mysterious relations.
So, a good argument for God's existence can be developed from the objective existence of mathematical objects (if these objects do exist somehow beyond our finite minds).
Secondly, it is important to avoid confusing the existence (or non-existence) of mathematical objects with the truth-values of mathematical propositions, which are conceptual or formal truths.
For example, 2+2=4 is conceptually true (i.e. true given Peano's axioms and the rules of mathematical inference), but it tells us absolutely nothing about if such objects (like "2" or "+" or "4", or the propositions which include them) exist objectively or not.
Compare: The proposition "bachelors are unmarried men" is conceptually and formally true (i.e. true in virtue of form of the proposition and the concepts contained in it; in fact it is a tautology, an analytical truth). But the truth of such proposition tells us absolutely nothing about whether bachelors exist objectively or not. (In fact, suppose that God refrained from creating an universe. In this case, if God himself define in his own mind "bachelors" as "unmarried men", the proposition "bachelors are unmarried men" would be true, given such concepts, even if not such entities like bachelors do exist objectively).
Compare: God is omnipotent. This proposition is true given the classical theistic concept of God. But such truth tells us nothing about if such God exists or not.
Compare: Evil is the negation of the good. This meta-ethical proposition seems to be true (and necessarily so), but it tells us nothing about if evil or good exists objectively.
People unfamiliar with philosophy tend to think that the truth of conceptual propositions (like 2+2=4) imply the objective existence of the entities in question. They conflate the semantic and conceptual properties of propositions with the metaphysical status of the referents in question.
ON CRAIG'S ARGUMENT:
Craig's argument in the debate was this:
1-If God doesn't exist, the applicability of mathematics is a happy coincidence
2-The applicability of mathematics is not a happy coincidence
3-Therefore, God exists.
This argument is formulated in terms of Rosenberg's own published work. Clearly, Craig designed and formulated the arguments specifically to confront the arguments of Rosenberg's own version of naturalistic scientism. Since Rosenberg has argued that scientism cannot countenance "happy coincidences", it follows that either 1)He has to provide a scientistic explanation of the applicability of mathematics to the universe (in order to refute premise 1), or 2)Concede that naturalistic scientism is false (which was Craig's purpose).
Regarding 1, it is hard to see how Rosenberg's scientism, which is based on the fundamental principle that "physics fixes all the facts" can provide an explanation for the applicability of mathematics to the universe, since mathematics is conceptual and mathematical objects are nonphysical. As far I know, nothing in Roseneberg's work has provided an explanation of it. And it is hard to see how, given his own naturalistic premises, such account could be offered.
In fact, in the debate, Rosenberg's reply was to pose the existence of alternative mathematics, like non-Euclidean geometries. This is a very inept reply. Because the existence of non-Euclidean geometries don't refute the extraordinary applicability, power, uselfulness and beauty of other mathematical systems, and are the latter which suggests that the universe is constructed in a way which matches such the language of mathematics.
Even though Craig's argument is not based on the existence of mathematical objects, his argument seems assume that such objects, somehow, exist objectively, that is, the physical universe has intrinsic mathematical properties as part of its constitution which allows human beings to use the language of mathematics to describe it. This can be summarized in the phrase "Mathematics is the language of nature".
I think this is a good argument for God' existence, but it needs more elaboration in terms of alternative theories in the philosophy of mathematics which Craig didn't provided in the debate.
Perhaps I'll provide some suggestions in the future on how to develop this argument, since I'm convinced that it is a powerful argument for God's existence (and one which has persuaded some world's leading scientists).
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