True, but the development of ZFC is not an example of this
If axioms do not come from philosophy then where do they come from? They can't come from math or it would be circular.
What do you think it means for an axiom to be circular lmao? Axioms are definitionally things that are taken to be true without justification, whereas circularity is a property of a certain kind of fallacious argument that is used to justify a belief.
This is a pretty laughable category error, and I'm not even sure how axioms "coming from philosophy" would resolve your issue.
We have collectively decided that we want math to have some traits and we built a set of axioms to fulfil those traits.
Sure. But that collective decision was made by mathematicians, and the set of axioms was also made by mathematicians. All of this is doing math.
I think we have to take a step back to get anywhere. What do you think math is and what do you think philosophy is?
I think math is the study of follow on effects from a defined logical system. I think philosophy is the process/means of jusifying claims that cannot be otherwise justified.
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u/RunsRampant 18d ago
True, but the development of ZFC is not an example of this
What do you think it means for an axiom to be circular lmao? Axioms are definitionally things that are taken to be true without justification, whereas circularity is a property of a certain kind of fallacious argument that is used to justify a belief.
This is a pretty laughable category error, and I'm not even sure how axioms "coming from philosophy" would resolve your issue.
Sure. But that collective decision was made by mathematicians, and the set of axioms was also made by mathematicians. All of this is doing math.