THEISTIC PROOF: MATHEMATICAL VERITIES ARE MIND DEPENDENT

What is the number 1? It is a concept, an idea. We don’t find the number 1 in nature apart from our conceptualizations of it. It is therefore mind dependent, unlike the rain, which doesn’t depend on what I think about it!

If this is true about the number 1, it is also true about the numbers 2, 3, 4…. And it must also be true about higher level mathematical constructs, like the Pythagorean Theorem, which depends on these numbers:

If the lengths of sides (a) and (b) of a right triangle are known, then the longest side (c) can always be determined in this manner: a² + b² = c². But from where does this precise symmetry arise, the consistent relationship between math and this physical world? And what gives the knowledge among the many fields of discovery its harmony? These questions speak to the larger question of design (ID). If knowledge is one consistent and harmonious whole, its source must also be one – the Mind of God, rather than unconnected and discordant human creations.

To illustrate a small part of the unity of knowledge, this same Pythagorean Theorem can be applied to many other phenomena, as one respondent pointed out:

·       A famous Pythagorean triple is 5-4-3, since 3 squared plus 4 squared is equal to 5 squared. But, this same theorem applies to more than just right triangles. It applies to circles. After all, a circle with radius 5 has the same area of two circles, one with radius 4 and the other with radius 3. That's because the formula for area has the same quadratic structure. It can also be used to compare kinetic energy of objects with the same mass. The formula for kinetic energy is 1/2 times mass times the square of the velocity. Given the same mass, we have a quadratic equation, so one bullet traveling at 500 meters per second has the same connected energy as two other bullets of the same mass, one traveling at 400 m/s, and the other at 300 m/s.

Clearly, we didn’t create this elegant, precise, and unifying theorem. Instead, we discovered it, as we also do with many other theorems! Although distinct from the material world, math seems to understand the material world and tell us much about it, as if it has intimate knowledge of this world. It is able to discover aspects of the physical world even before we’ve observed them. But why this correspondence? Design!

Likewise, the angles of every triangle contain exactly and invariably 180 degrees. If you were to add a fourth line or side to the triangle, this four-sided figure would contain angles equaling 180 + 180 = 360 degrees. If you would add a fifth line or side to this four-sided figure, it would contain angles equaling 180 + 360 = 540 degrees, ad infinitum.

How can we explain this uniformity, this elegance? Certainly, this isn’t an elegance that we created, but rather discovered. Besides, this uniformity seems to be immutable and universal – traits that transcend our individual, changing minds. However, if mathematics is conceptual and, therefore, mind-dependent, but doesn’t depend on our minds, then there must be a universal and immutable Mind that it does depend upon.

To state this another way:

1.    Mathematical truths are conceptual.

2.    They therefore require minds.

3.    Our human minds are not adequate to account for the uniformity, immutability, and elegance that we find in mathematical realities.

CONCLUSION: Therefore, a greater, immutable Mind must exist.