God, Santa, and The Tooth Fairy

[LadyForCamus]

Do you really expect that aliens will have the same mathematics as us? That the Peano axioms for the natural numbers are universal?  That Euclidean geometry is a priori? Do you really think that they will use the same trigonometric functions that we do? Or have the same set theory or even logic?

I don't. There are simply too many ways to construct math.

Math is, ultimately, a board game. It has rules of deduction (of play) and axioms (starting positions) and gets results from those.

On the other hand, I would suspect that their math and ours would be mutually comprehensible and that they arrive at equivalent laws of physics as we (given equivalent technology).

I would also be very, very surprised if they have anything close to the same metaphysics.

Thank you for putting that in bold because the key issue is in fact an intelligibility that transcends circumstances. If their maths are true, they will be true in the same way ours is and for the same reasons.

But only if we share the same physical reality. A universe with different physical laws may necessitate different tools to describe and understand it. Is there a way to show that can’t be a possibility?