(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.
He who desires to worship God must harbor no childish illusions about the matter but bravely renounce his liberty and humanity.
Mikhail Bakunin
A casual stroll through the lunatic asylum shows that faith does not prove anything
Friedrich Nietzsche
Mikhail Bakunin
A casual stroll through the lunatic asylum shows that faith does not prove anything
Friedrich Nietzsche