God, Santa, and The Tooth Fairy

[polymath257]

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, i. e. In all possible worlds...includeing the alternative physical universes of a speculative multiverse. That is why I do not find your conviction that everything supervenes on the physical persuasive. A universe with different physical laws seems conceivable but not a universe in which true logic systems or maths yield different results. As such, those are metaphysically prior preconditions for a physical universe.

I can see you haven't done much with the foundations of mathematics, Nor, I would guess of its history.

There *are* in fact different sets of logical axioms (paraconsistent logic, for example) and different mathematics that we know about. Kant made the mistake of thinking geometry to be synthetic a priori just before the discovery of non-Euclidean geometries. We know there are many different ways to set up set theory and to 'ground' the natural numbers.

So, no, I do NOT think that there is only one 'reasonable' math and that aliens would be forced to have anything like the same mathematical assumptions that we do.

I am a formalist and not a platonist when it comes to mathematics precisely for this reason. We choose the axioms of math to satisfy our intuitions, but those intuitions are far from being mutually consistent or determinative of a single foundation for math.

BTW I have to hand it to you for reading Hart. May I ask, because I assume you can see that Hart is a serious and intelligent thinker even if you think he is wrong...do you feel it is right and proper to compare his sincerely held conviction in God with believing in Tooth Fairies?

Yes, I do. I think he gives a good argument for equating tooth fairies and a demiurge (would you agree with this?)

But I would go further. His metaphysics is so poor that, if anything, I would consider the evidence for the existence of the tooth fairy far more persuasive. Poor logic and bad ontology doesn't show the existence of anything. He comes across as someone who is trying desperately to believe in the tooth fairy by saying it has the special property of necessary existence.

Arguing for the 'necessary being' seems to me to be trying to define something into existence without any real evidence. Trying to define a 'source of existence' seems to be a category error of the type that you like to accuse others of when arguing that the tooth fairy and God are equivalent. And, frankly. I find the whole 'contingent existence' concept to be a horrid philosophical obfuscation.

But then, I find most of classical metaphysics to be severely lacking. It assumes *way* too much about how things 'must be' without looking at how they actually are (as revealed by quantum mechanics, for example). This is in essence, the same mistake that Aristotle made when saying heavy things much fall faster than light things or that motion requires a force.

I am frankly surprised that a serious modern philosopher still accepts these types of arguments.