@kennethamy,
kennethamy wrote:
RexRed wrote:
kennethamy wrote:
RealEyes wrote:
RexRed wrote:Two things can be identical, zero is identical to zero...
Ah, but those aren't two things. They are two references to one thing. It goes into the idea of tautology.
But the question is about possibility, not about actuality. And why couldn't (say) two leaves on a tree have identical properties? We need not think of actual examples to show that two things could be identical. We need only think of possible examples. (But you are right about the zero example. To say that zero is zero is just to express a tautology).
Until it is proven wrong it is an axiom...
What, is an axiom (whatever that means) until it is proven wrong?
From my memory of geometry, an axiom is a mathematical statement that is always true until something proves it false.
For example, equals added to equals are equal.
Or... something with zero length, breath, depth and height is identical to something of zero length, breath, depth and height...