Russell’s paradox and its implications on cladistics and particle physics

Russell’s paradox demonstrates that if we believe in kinds, ie, adopt (class-)realism, then we will ultimately end up in paradox.

One example of this fact is biological systematics’ recently upcoming problem to understand what it calls “paraphyletic groups” is. It is biological systematics itself that distinguishes this kind of group, but it does anyway not understand what this kind of goup is, because it thinks it has found it. The problem is that it indeed has found it, but that this kind of group actually is inconsistent (ie, an inconsistent abstraction) consisting of “the rest” except holophyletic groups (which it calls “clades”), and if this kind of group is real, then holophyletic groups (ie, “clades”) is not real. Biological systematics has thus ended up in Russell’s paradox between recognizing holophyletic groups (ie, “clades”) or “paraphyletic groups” by joining (class-)realism. Not both of them can be real at the same time.

Another example of this fact is particle physics’ recently upcoming problem to find what it calls “Higgs particle”. If “Higgs particle” indeed  is real, then time isn’t relative to speed in space, and the probability of quantum mechanics is wrong. Particle physics has thus ended up in Russell’s paradox between recognizing “Higgs particle” or facts by joining (class-)realism. Not both of them can be real at the same time.

Russell’s paradox thus demonstrates that our attempts to reach a single ultimate truth are vain. We can manipulate reality, but we can’t find out what reality is. The fundamental problem is that reality obviously is continuous (since it can’t be classified both unambiguously and consistently), but has to be discrete (since classification can’t be both unambiguous and consistent), both of which it can’t be at the same time. The problem is thus that reality is impossible, although it is self-evident to us.