Could there be more axioms out there we haven't found out yet?

I'm just curious.

1 Answer
SCooke
Jan 3, 2018

Yes.

Explanation:

Remember that an "axiom" is by definition an ASSUMPTION to begin a logic sequence, NOT an observable "law" or rule!

The axioms we have depend on the study we are doing - there are different forms of mathematics from geometry that necessarily have completely different sets of axioms.

Now, in Euclidean Geometry specifically, it may yet be possible to conceive of more axioms ( never say "never"!). However, given the centuries of the use of geometry in various forms, it may be reasonable to assume that the axioms needed (so far) for its development and use are complete.

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