(June 10, 2010 at 5:48 am)Caecilian Wrote:(June 9, 2010 at 9:33 pm)The_Flying_Skeptic Wrote: [hide](June 9, 2010 at 7:58 pm)Caecilian Wrote: @Rhamsin.Kh
All this stuff about axioms being 'self-evident'. Of course they are. But why? Surely its because thats the way our universe works. If the axioms that applied to our universe were different, then they'd be 'self-evident'.
In other words: that our particular set of axioms is 'self-evident' is a consequence of them being our particular set of axioms.
can you think of a universe where (x=x) wouldn't be an axiom? To me saying that x=x wouldn't serve as an axiom in other universes is like saying that in other universes there are edged circles or triangles with angle sums greater than 180 degrees.[hide]
No, I can't think of a universe where (x=x) is not an axiom. But the fact that I can't conceive of it is totally irrelevant to whether or not it is possible. Which is the point that I've been trying to make.
I think that you'll find that in spherical trigonometry the sum of the angles of a triangle is always greater than 180 degrees.
@Ramsin.Kh
Yeah, in an important sense every universe is logical in terms of its own logic, bearing in mind that 'its own logic' may be a sort of empty set, or may be incomprehensible or inconceivable to us.
Its important not to conflate this with a universe being logical in our terms.
spherical triangles... ugh. why did you even bring that up? it's a tangent that there is a group of shapes called spherical triangles. You can't think of a universe were x = x would not be a starting point because it's illogical. it's like saying God can do the logically impossible or the illogical like make edged circles... Sure you can say it but it's senseless. this discussion parallels arguments against a deity that doesn't need to be created, and you're the one saying 'God exists outside of our universe, he doesn't need to be created.' You're reasoning looks the same: "just because you can't imagine it or find reason in it, doesn't mean it's not true"
