X

So if a set X is identical with each of its aspects or parts or elements or whatever and X and any one of those are two and not one and the same, then what is X aside from all that? Is it the Whole? No, at least not in this ontology. There is no Whole. Or if there we say there is, then it is just one more element. So what is it? I have at times said it is the Form, the Platonic Form, the essence, even the thing itself. I have also called it a structure, which is an ordered set. 

 Still, there is an ontological mystery here. Indeed the very idea of identity, the not-different, is weird. It is a two-one thing. And is the nexus of identity a thing? I think it is, but Bergmann and others think it isn't. They thing the class and its members are one sans nexus. A strange sort of internal relation, a super-dependence. I think I see why they think that, but to me that fusion is confusion. Identity as a nexus is a thing. I say that knowing that paradox looms up ahead.


Most today would say that a set or a class is a mental construct. They have jumped into the Sun of philosophical Idealism. I cling as hard as I can to realism. There are no mental constructs. Sets or whatever they are exist external to thought. Psychologism will not do. Russell et al. wrestled with it for years and made little progress, if any. It's a bugger of a problem