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Within a given inference system, one can define concepts. This doesn’t add any axioms. It is, in essence, just a way to abbreviate things.
by drdeca 29d ago
Within a given inference system, one can define concepts. This doesn’t add any axioms. It is, in essence, just a way to abbreviate things.
- andriy_koval 29d agook, you now added some unknown inference system in addition to zfc
- drdeca 28d agoNo, it is the same inference system. They are just abbreviations.
- andriy_koval 28d agoand what is that system?
- drdeca 27d agoZFC
- andriy_koval 27d agozfc is a bunch of axioms and not inference system. It is commonly assumed that it is built on top of some unspecified first order logic which commonly assumed to include bunch of inference rules. There is no ground truth in my understanding where this all is formally defined.
- drdeca 26d agoIf you want to use “ZFC” to refer to the axioms without any rules of inference, I guess you can do that, but when someone refers to “ZFC” when they are filling a slot that needs a (axioms + rules of inference), the obvious interpretation is that they are referring to the usual system of ZFC.
- andriy_koval 26d ago> when someone refers to “ZFC” when they are filling a slot that needs a (axioms + rules of inference), the obvious interpretation is that they are referring to the usual system of ZFC. its bro-math. In formal math you need to be specific what inference system you use. There are many of them. Then you need to have formal proof that in that system you can derive concept of function and then think about question if it won't make paradoxes and contradictions with ZFC.