Quote:
Originally Posted by LesMts
Maths is self-contained and axiomatic.
I'm undecided as to whether maths is a science. Although that opens up a whole can of philosophical worms.
Can you prove that a mathematical principle will hold at all points, everywhere?
No.
But it probably will, at least as far as it's useful. Which is my point.
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Mathematics is the only truly untainted form of thought. Everything else to an extent is tainted by opinion. Biology, chemistry, physics, philosophy, religion, etc all to an extent are 'tainted' by opinions. Pure Mathematics isn't.
And yes mathematical principles hold at all points, everywhere. Thats the very nature of the proofs. Things aren't proved in 2D or 3D space only but over all spaces. I'm not talking about formals used by physics, which don't always hold true. I'm talking pure mathematics here: abstract algebra, topology, analysis... There are so many absolute truths in Mathematics which have been rigorously proven.
You should check out what Alain Badiou(most important living philosopher?) has to say on this or anything else for that matter.