What kind of reference you are using for your reference to sets if not the axioms? That reads to me as if “Are they just totally unrelated objects to red busses that just happen to be a bus and red?”
Some times I have seen people argue for example that the word “yellow” is grounded by the set of all yellow things. But usually that kind of definition suffers from the list being ambigious/insufficient. Like if a give a thing it either is or is not a member of that set. But listing all the members or otherwise giving some procedure to give out all the members seems like is not the most natural thing to do. Thus if you tried to take the cartesian product of yellow things and red things because you can’t exemplify a sample just from the concept you can’t build up the product from members. The collection of yellow things propbably is not a set but it has many set-like properties. By having a close inventory of sets properties they can be distinguished from confused or nearby notions.
Another possible imagination prompt would be a person faced with coordinates. Is there a real number that you can spesify that the human can point out on the x axis? No, they are always going to be off. In the same way if you present the axis and ask the human to point out their “favourite number” (that is supposed to keep stable) they will point out a slightly different real number each time they supposedly point that point out. Such a person can’t provide a choice function. It might still make sense to treat the person as being able to specify intervals, or refer to all of the points or being able to reference crossing points and others that have geometrical spesification. But in general a line is not guaranteed to have any referancale points falling within it.
What kind of reference you are using for your reference to sets if not the axioms? That reads to me as if “Are they just totally unrelated objects to red busses that just happen to be a bus and red?”
Some times I have seen people argue for example that the word “yellow” is grounded by the set of all yellow things. But usually that kind of definition suffers from the list being ambigious/insufficient. Like if a give a thing it either is or is not a member of that set. But listing all the members or otherwise giving some procedure to give out all the members seems like is not the most natural thing to do. Thus if you tried to take the cartesian product of yellow things and red things because you can’t exemplify a sample just from the concept you can’t build up the product from members. The collection of yellow things propbably is not a set but it has many set-like properties. By having a close inventory of sets properties they can be distinguished from confused or nearby notions.
Another possible imagination prompt would be a person faced with coordinates. Is there a real number that you can spesify that the human can point out on the x axis? No, they are always going to be off. In the same way if you present the axis and ask the human to point out their “favourite number” (that is supposed to keep stable) they will point out a slightly different real number each time they supposedly point that point out. Such a person can’t provide a choice function. It might still make sense to treat the person as being able to specify intervals, or refer to all of the points or being able to reference crossing points and others that have geometrical spesification. But in general a line is not guaranteed to have any referancale points falling within it.