#847 The Puzzle of Mathematics’ Applicability Once More
August 06, 2023Hello RF staff, greetings to Dr. Craig.
I've read various things that Dr. Craig has said about the logical necessity of the applicability of mathematics to the laws of physics, both in the Q&A and on podcasts.
I've also seen videos where string theorist Michio Kaku (who doesn't completely rule out a kind of "God of philosophers") explains that all alternatives to string theory are mathematically inconsistent, i.e. that in all alternatives 2 + 2 = 5, and that only in string theory 2 + 2 = 5. I have no idea what this means. Could string theory therefore perhaps give a scientific and not a philosophical or theological answer to the applicability of mathematics?
Moreover, from that argument:
1. If God does not exist, the applicability of mathematics to the physical world is just a happy coincidence.
2. The applicability of mathematics to the physical world is not just a happy coincidence.
3. Therefore, God exists.
Let me explain better: in the Kalam, the word "God" does not appear in the premises, but only in the conclusions one arrives at saying that the cause of the universe is out of space, out of time and immaterial, and so on, it is not said else, it is not even called God. Although I don't share the premises of the Kalam at all (this is another matter) I like this way of arguing better.
So my fear, while I like this argument, is that it's a circular argument or a false dichotomy (God or coincidence, while there could also be a logical necessity, or something else that I'm not even imagining).
However, I must admit that not being in agreement with non-theistic realism I find it hard to think how abstract entities can cause the mathematical structure of the cosmos, and according to anti-realism it would be a coincidence that requires a lot of faith in naturalist and scientistic atheism. ..
But since I'm not an expert, I'm asking for confirmation.
Thank you.
F.
Italy
Dr. craig’s response
A
Before we get to the meat of your question, let’s clear away the suggestion that string theory is the only logically consistent theory of fundamental physics. I don’t believe for a moment that Michio Kaku meant this, since it is just nonsense. In fact, on the contemporary scene physicists have become rather disillusioned with string theory and have turned away from it in increasing numbers. In any case, it could do nothing to explain the applicability of mathematics to the physical phenomena for the simple reason that it is itself a mathematically formulated theory of physics, so that if it is true, it would be a case of the applicability of mathematics crying out for explanation. String theory is not metaphysically necessary (there could have been different substances and different laws of nature), so its applicability would remain a mystery.
Now your question is whether the argument formulated above posits a false dichotomy between God and coincidence, whether there might not be other alternatives. Please understand that the argument above is my attempt to formulate in a simple, easily graspable way a much fuller seven-step argument explained elsewhere.[1] Nonetheless, the argument does not postulate a false dichotomy, since an adequate defense of the first premiss will include the rejection of any other proffered alternatives. I formulated this argument on the model of the moral argument:
1. If God does not exist, then objective moral values and duties do not exist.
2. Objective moral values and duties do exist.
3. Therefore, God exists.
The truth of the first premise entails rejecting other alternatives than God as a foundation for objective moral values and duties. The argument’s detractor is free to suggest any such alternative he wishes, and it shall be discussed in the defense of the first premise. So also, in the case of the argument from the applicability of mathematics, in order to defend that if God does not exist, then the applicability of mathematics is just a happy coincidence, one will need to refute any suggested alternatives to God which the argument’s detractor might care to suggest. I consider a number of these in my fuller discussion of the argument. Logical necessity is pretty clearly not a good explanation, since there could have been different laws of nature than there are. In the absence of a good explanation, the applicability of mathematics to the physical phenomena does seem to be a happy coincidence.
[1] “The Argument from the Applicability of Mathematics,” in Contemporary Arguments in Natural Theology: God and Rational Belief, ed. C. Ruloff and P. Horban (London: Bloomsbury, 2021), pp. 195-215. I develop the argument even more extensively in my projected Systematic Philosophical Theology.
- William Lane Craig