Russell’s paradox is an interface -the interface between nominalism and realism. It is what I call a paradox passage between the conceptual “neither nor” and “both and” states. In the nominalistic aspect, this passage appears as “neither nor“, whereas it in the realistic aspect appears as “both and“.
A concrete example is the fact that particles have both particle and wave properties. To a nominalist, this fact means that particles are neither particle nor waves, whereas it to a realist means that particles are both particles and waves. To a nominalist, the fact that the statement “neither nor” leaves things hanging in emptiness as “nothings” means nothing, since he/she views concepts as mere abstractions, whereas to a realist, this statement is instead absurd, since he/she views concepts as realities and thereby comprehends this state as meaning that things are nothings, thus instead concluding that they must be “both and“. To a nominalist, this conclusion is instead a conflation of the concepts “particle” and “wave”.
The difference between “nominalism” and “realism” is thus merely a fundamental difference in approach between the two alternatives that conceptualization offers us, ie, assuming that things or concepts are real, without any bearing on the reality they discuss what-so-ever, and the connection between them is the paradox passage that is called Russell’s paradox.
This paradox passage is, however, a generic thing, ie, a conceptual abstraction of second degree, since it occurs in many different disguises in conceptualization itself (ie, in the first degree), eg, the cladistic idea of a “true tree of life” and particle physics’ idea of a “Higgs particle”. Such “things” are thus actually paradox passages viewed in the realist aspect of “both and“, which in the nominalist aspect instead are conceptual conflations of “neither nor“. They are thus just as absurd in the nominalistic approach as the statement that “particles are neither particles nor waves” is in the realistic approach. Both are thus absurd in each others eyes.
So, which is right? Well, this million dollar question unfortunately lacks an answer. Nominalism is consistent in avoiding conflation of concepts, and is also represented by mathematics, whereas realism is consistently inconsistent, but unfortunately none of them can be “right”, because the relation between conceptualization and reality is the same kind of relation as the relation between nominalism and realism, ie, fundamentally absurd in each others eyes. Reality is thus absurd in our eyes, independently of whether we adopt a nominalistic or realistic approach, whereas conceptualization is absurd in the eyes of reality. The best we can do is thus to be consistent, as nominalism is.
It means that both cladistics and particle physics are looking for things that do not exist. “Not exist” does in this statement mean “not belonging to reality”, where “reality” means “what statements can¨t create”. (Statements can create things, but this statement refers to the things that statements can’t create. The difference is between reality and dream, or between the concrete and the abstract.)
We can thus not find out what reality is, but merely model its behavior consistently. Unfortunately, this leaves realists like cladists and particle physicists as donkeys trying to reach the carrot in front of their eyes.