On the difference between objectivity and subjectivity

Discussion between humans quickly splits into two principal lines of logical reasoning: one resting on the axiom that objects are real (ie, objectivity or object-realism, like traditional empirical science), and another resting on the axiom that classes are real (ie, subjectivity or class-realism, like cladistics and particle physics). (Particle physics may appear like a kind of objectivity by its method of observation, but it is actually a kind of subjectivity by its discovery of classes, not of objects).

These two lines of logical reasoning both lead to Russell’s paradox, as Bertrand Russell demonstrated in 1901, but from two different directions: objectivity arriving to it by arriving to the conclusion that classification, and thereby also subjectivity, ultimately ends in Russell’s paradox (like Bertrand Russell did), whereas subjectivity arriving to it by ending in an orthogonal logical rotation in Russell’s paradox without understanding that it is a paradox (ie, naive set theory, like cladistics and particle physics). Both lines thus leads to Russell’s paradox, but objectivity in the form of understanding that it is a pardox and subjectivity (ie, naive set theory) in the form of rotating in the paradox without understanding that it is a paradox.

Subjectivity can, however, avoid ending in this orthogonal logical rotation in Russell’s paradox by axiomatic set theory (eg, ZFC), like how computer science does, then instead ending in the question: does NP equal P (which can be analogized with the question: does “apple” equal “fruit”?).

It means that both objectivity and subjectivity are consistent iff (if and only if) subjectivity uses axiomatic set theory. The difference between them then is just that objectivity discusses process in light of pattern, whereas subjectivity discusses pattern in light of process. (Naive subjectivity, ie, naive set theory, like cladistics and particle physics is, however, inconsistent, actually paradoxically contradictory). But it also means that the subjective question whether NP equals P has the answer no. NP is actually an object if P is a class, and vice versa.

As a general principle, this relationship between objectivity and subjectivity can be stated as that “they are the two possible perspectives on reality:  classes in terms of objects and objects in terms of classes”, where classes have to be comprehended as change to avoid Russell’s paradox.

(Please, correct me if I’m wrong).