[QUOTE=Contrapuntal]
I’m not convinced that mathematics is a feature of the universe, or has any “laws.” Isn’t it all axiomatic?
At any rate, if God invented humans, and humans invented math, he can make math be anything he wants. He can make a world where triangles are impossible.
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Mathematics is a system of self-consistent rules that naturally follow from a small number of basic axioms. (The axioms are the “laws”.) Therefore, if you accept the axioms, then you must accept all the rest of mathematics, since they rely on nothing else (not on reality, not on god, not on anything besides the axioms). And, since the axioms are defined as being accepted within the mathematical system regardless of all external factors, they are not subject to reality or god either. They’re not dependent on man, either; 1+1=2 was true even before proto-man figured out how to count, sheerly as a side effect of what the concepts 1,+,=,and 2 are, even if those concepts are unknown, unexplored, or forgotten.
If God made a man that couldn’t think up mathematics, that doesn’t matter. Rocks can’t think up mathematics and it doesn’t stop mathematics from being as it is; changing humans into intellectual rocks would have no more effect on math than the rocks we already have do. It doesn’t change the fact that if we happened to think of the same set of axioms that support our current version of math, all the rest of math would develop naturally from those axioms, whether God likes it or not.
As for triangles, creating a reality where triangles-as-we-know-them couldn’t exist would just mean you’d created a reality where the axioms of math-with-triangles don’t apply to the existing universe. That’s not a problem, though. If I recall correctly, we actually have thought up forms of geometry that don’t have triangles as we know them; isn’t non-euclidian geometry one of these? But, if the universe operated on non-euclidian geometry, that wouldn’t stop regular euclidian geometry from working, just like our euclidean-geometry universe doesn’t stop us from doing non-euclidean geometry.