Mathematical realism must be true

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The quantity is not the things it quantifies.

We must not take our ability to perceive these totally distinct modes of existence for granted. The quantity is real, pure information. It exists as a real and objective feature of the world, completely independent of human brains and completely independent of the things quantified.

When five geese fly across the lake, five geese really fly across the lake. Not four or six. The quantity is nowhere to be found in the physical existence (or “extension”) of the geese themselves. Yet we can intuit the quantity, flying right there with them, just as plainly as we see and hear the geese. This intuition is a supernatural ability. The naturalist can observe the geese but has no explanation whatsoever for the existence of the quantity.

For this reason, naturalistic accounts of the origins of math must fail. They don’t explain anything.

The naturalist blithely assumes the existence of quantity. But he can provide no explanation for its existence. The hard binding of numbers to the physical world is forbidden by his worldview because his worldview excludes all immaterial objects.

His worldview commits him to confine numbers to human brains. But that just leads the naturalist down another blind alley of incoherence. If quantity doesn’t exist as an objective feature of the real world, then how could brains have evolved the capacity to count? It makes no sense.

The naturalistic story is nothing more than rhetorical sleight-of-hand, i.e., sophistry. Naturalistic accounts of origins are just-so stories and nothing more.