Re:Opinions of Doron Zeilberger
by epgui on Friday January 19, 2024 @04:26PM
(#39061414)
> No, axioms are hypotheses
IMO they're neither "faith" nor "hypotheses", although "whether a set of axioms is self-consistent" is probably a hypothesis.
Axioms are just building blocks. They don't even need to be "true" in any real sense. They're just arbitrary determinations or rules that we make up, and then we figure out what the consequences of these choices are.
In practice we often try to come up with axioms that have some practical value in the real world, but this is not necessarily or always how we go about doing maths.
IMO they're neither "faith" nor "hypotheses", although "whether a set of axioms is self-consistent" is probably a hypothesis.
Axioms are just building blocks. They don't even need to be "true" in any real sense. They're just arbitrary determinations or rules that we make up, and then we figure out what the consequences of these choices are.
In practice we often try to come up with axioms that have some practical value in the real world, but this is not necessarily or always how we go about doing maths.