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Title needs a (2013) at the end. In my opinion, trying to settle the matter by adopting a new axiom is a bit like proving that blue is the best color for cars
by excalibur 9y ago
Title needs a (2013) at the end.
In my opinion, trying to settle the matter by adopting a new axiom is a bit like proving that blue is the best color for cars by requiring all cars to be painted blue.
- xamuel 9y agoA different viewpoint: "adding a new axiom" is synonymous with "further restricting the things under discussion". Imagine biologists decide that "DAG" is the correct abstraction for parent-child relationships. Then they spend years trying to prove the obviously-true fact that parents can't have infinitely many children. Of course, they never can, because DAG nodes can have infinitely many children. Finally they realize they chose the wrong abstraction, they should've chosen "DAGs where all nodes have finitely many children". To suggest adding a new axiom to ZFC is to suggest that ZFC was an over-broad abstraction for capturing what things are supposed to be "sets".