>>13920157>you think some sets are infiniteI don't. "Set" is not a thing. It's meaningless gibberish.
Natural numbers are a thing. I can count, I can tell if something is a natural number or not, I can compute operations with them. I can also build many beautiful structures based on them, such as finite sets, finite functions, finite groups, polynomials, Gaussian integers, rational numbers, or computable infinite sets of natural numbers, or many other objects. However talking about "general sets" is nonsense. A fortiori, asking whether there is a general set satisfying such and such property is nonsense. It only because meaningful when you translate it as a statement about natural numbers.
You can also talk about uncountable sets if you specify what you mean by it in terms of natural numbers, so that our finite minds can understand what we're talking about. For example, you could talk about some type of transfinite classically-regarded-as-uncountable ordinals in terms of ordinal notations which are built in terms of natural numbers.
As expected, all the nontrivial (hence undecidable within ZFC) statements like CH or martin's axiom are ceased to be regarded as meaningful because objects and constructions used in stating them are not explained in basic terms, and are left largely undefined by extension of the notion of a general set being undefined.
Basically I regard mathematical objects as legitimate only if they are built from natural numbers(or any equivalents thereof, e.g. hereditarily finite sets).
