Painting by Escher.[1] |
The so-called axioms of mathematics are the few thought
determinations which mathematics needs for its point of departure.
Mathematics is the science of magnitudes; its point of departure is the
concept of magnitude. It defines this lamely and then adds the other
elementary determinations of magnitude, not contained in the definition,
from outside as axioms, so that they appear as unproved, and naturally
also as mathematically unprovable. The analysis of magnitude
would yield all these axiom determinations as necessary determinations
of magnitude. Spencer is right in as much as what thus appears to us to
be the self-evidence of these axioms is inherited. They are provable dialectically, in so far as they are not pure tautologies.
Engels
Dialectics of nature
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