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The pythagorean theorem could easily be tested empirically. In fact it was probably discovered through empirical observation as many ancient mathematical facts were.

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Where do you put that test, though? The theory itself is not empirical, nor is the proof, nor is anything used in the theorem.

Even if the idea came through empirical means, the theory itself isn't empirical.

The pythagorean theorem predicts how long the hypotenuse of a right triangle will be, based on it's sides. That's quite easy to test empirically. You take a ruler out and draw a right triangle. It's nice that we have a solid mathematical proof for it. But if the axioms of geometry were somehow thrown into question, no one would question pythagoreans theorem because we know it works and have tested it countless times. It has more evidence than entirely scientific matters like the law of gravity.

And all that empirical stuff doesn't matter when it comes to the actual theorem. The proof does. As is the case with tons of math that don't have empirical evidence.

That's why it's math and not science.

My original point was that calling a philosophical problem unscientific is like saying this ice cream is nonelectronic. It wasn't meant to be, it doesn't mean it's not good. Or in the case of mathematical theorems or philosophical problems, insightful.

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