there does exist a world (of universals or the form of the Good, which you can identify with God), which transcends the physical empirical world, and this world of intelligible forms is responsible for the “enforcement” of mathematical order in the physical world. Thus, intelligibility is responsible for the physical world.
The other theory of mathematics, the one which I happen to favour because it doesn’t require such icky occultic philosophical entities, is the idea that mathematics is a human creation. Just like how we invented chess, likewise did we humans invent mathematics. But even though chess and mathematics is our invention, but once invented it has a reality independent of our subjectivity. Thus, for example, it is an objectively true fact that one is able to checkmate in a number of moves, or one is forced to make a certain move to get out of a check, etc. The analogy which Karl Popper used is that of a spider spinning a web. The spider made the web, but once the web was made, it has an objective reality of its own, it is of a certain biochemistry, of a certain pattern, structure in order to retain its integrity, etc.
Thus, mathematics is a product of our minds, in exactly the same way that chess, fictional stories, myths, musical compositions, etc, are products of our minds. Thus, upon this conception, the miracle is that the universe happens to conform to our mind generated realities, that the universe is governed, structured, ordered by a mind generated reality. Therefore we can infer the universe is in fact ordered by a like mind upon the basis of the mind-resonating, that is, resonance and conformity to mind generated realities of mathematics, which the universe possesses.
The naturalistic explanation only explains how we came to create those mental constructs which are able to represent the universe, but it doesn’t explain why does nature itself possess those cognitive resonating and conformity to mind-like orders in the first place.
Perhaps the most convincing evidence that the world was expressly designed to conform to simple laws that man would readily discover is furnished by the universal law of gravitation: F= Gmm/r^2. Notice the exponent 2. Why is it not 1.9999999 . . ., or 4.3785264 . . ., or something else hard to use in computations? Yet research has been able to specify the exponent as far as the first six digits, giving 2.00000. Thus, so far as we can tell, the exponent is exactly 2. Coulomb's law of electric force is similar: F = kqq/r^2. In this case, research has established that the exponent is no different from exactly 2 as far as the first 17 digits. Would we find such laws in an accidental universe?
Matter-antimatter pair production ratio 1 in 10 billion of “leftover particles” happens to be the exact amount of mass necessary for the formation of stars, galaxies, and planets. The number of electrons (in the universe) is equivalent to the number of protons to an accuracy of one part in 10 to the 37th power. If it were not so, galaxies, stars, and planets would never form.
Upon the finetuning by a happy accident of the cosmological constant, the probability that our universe contains galaxies is akin to exactly 10^123. That is 1 possibility in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 .
During one orbit around the Sun, Earth actually rotates about its own axis 366.3 times. The Moon orbits the Earth in 27.3 days. Of course, a day is one Earth rotation on its own axis. 366.3 x 27.3 = 9999.99 At the same time, the Earth is 366.3% the diameter of the Moon and the Moon is 27.3% the diameter of Earth. 366.3% x 27.3% = .999999. The combined diameter of all the planets in our solar system is 10 times greater than the Earth’s circumference. This has astonishingly high accuracy at 99.99%. The distance between the moon and the sun is 400 times greater than the distance from the earth and the moon. The Sun happens to be 400 times the Moon’s diameter, and 400 times as far away. This means the Sun and Moon appear to be the same size when viewed from Earth. The circumference of the earth at the equator is 24,901.55 miles. The earth’s rotation speed is 1037.5646 mph. If you divide 24,901.55 by 1037.5646 you get 24. Which is the number of hours in a complete day. Just enough rotation speed compared to it’s size to equal a perfect exposure to both sun light and darkness so that life could exist here.
Scientist quotes about God, evolution, intelligent design