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There are such reachable truths, but every mathematical system has a non empty set of axioms - or assumptions- which are 'given'.

• jojobas 4y ago
  These axioms are not given in course of socialization and generally are observations of nature rather than human.
  • roywiggins 4y ago
    There are multiple set theories using different axioms. Is the Axiom of Choice based on an observation of nature or do mathematicians keep it around because it's useful? It's a statement about infinities that absolutely have no physical reality. You can do mathematics without it, and the question of whether to do math relying on it is a matter of opinion. (Yes, proofs relying on AC are arguably true even if you don't accept AC, but as a social reality some sets of axioms are considered valid bases for work and some aren't, you can keep adding stronger axioms to ZFC to prove more things more easily, but how far you go with that before it stops being interesting is a matter of opinion)
  • pencilguin 4y ago
    ... of what people can and also choose to observe about nature.