Cladistics and Higgs particle-ism are simply just annoying conceptual conflations of "object" and "class"

Things like "the true tree of life" of cladistics and "the Higgs particle" of particle physics are logical end paradoxes of conflation of "object" with "class", ie, actually assuming that classes are real instead of objects, as in the cases of the class "species" of cladistics and all classes of "elementary particles" of particle physics, which also Bertrand Russell demonstrated in 1901 with his "Russell's paradox". The simple reason for this fate of such conflations is that classification is orthogonal and therefore leads to paradox in logical reasoning if we conflate the direction of the orthogonality of classification.

Exactly how it leads to paradox is, however, more difficult to explain, because it only concerns conceptualization and logic themselves, not the reality they refer to, that is, the relation between the concepts "objects" (or "particles") and "classes" together with the relation between "premises" and "deductions" of logic, and thus is confusing.

The fundamental problem is that whereas few of us would ever conflate "premises" with "deduction", many of us have a tendency to conflate "objects" with "class" (notice that the former in these two pairs is in plural whereas the latter is in singular), although the relation between the former of the pairs to the latter of the pairs is the same in both pairs: a deduction can't exist without presumed premises just as a class can't exist without presumed objects. This problem (ie, that many of us have a tendency to conflate "objects" with "class") thus means that those (many of us) start their logical reasoning from assumed classes instead of from assumed objects, meaning that they get the relation between the two pairs "objects and class" and "premises and deduction" as orthogonal, meaning that they actually conflate "plural" with "singular" by conflating "class" with ""premises" and "objects" with "deduction". This conflation leads to some kind of Russell's paradox because a single single object thereby is "a half" deduction. Such "a half" deduction (ie, Russell's paradox) are thus both "the true tree of life" of cladistics and "the Higgs particle" of particle physics. Typical for such figments of the imagination is that they are singular, ie, "THE true tree of life" and "THE Higgs particle", in difference from, for example, "species", "leptones" and "bosons". As "half deductions" they are paradoxically contradictory between pattern and process, as the Barber in Barbers paradox.

Belief in such paradoxes is either devastating or irrelevant. It is devastating if it induces a practical search for the paradox, because a paradox can't, of course, be found, and irrelevant if it claims to have found the paradox (like particle physics). It is simply just an annoying conceptual conflation in science.             

Class-realism, as cladistics and particle physics, and Russell's paradox

Class-realism, as cladistics and particle physics, rests on the axiom that classes are real. This assumption did Bertrand Russell falsify in 1901 by demonstrating that it leads to paradox, ie, Russell's paradox, in logical reasoning.

Russell's paradox can be understood fairly simple as that a class consisting of two classes, for example class "A" consisting of class "B" and class "C", is BOTH neither class "B" nor class "C" AND both class "B" and class "C". Class "A" is thus BOTH neither nor AND both and class "B" and class "C". This relationship makes the question: "Which of "B" and "C" is "A"?" indeterminable - it is neither any of them nor both of them.

This paradox do the opposite to class-realism, nominalism - resting on the axiom that particles are real, not have to encounter, since a corresponding particle "A" consisting of the particles "B" and "C" can be allocated to another and orthogonal class to "B" and "C" (like the genera of Linnean systematics). Particles that are physically nested can be consistently allocated to different (and orthogonal) classes.

The fact that class-realism leads to paradox do class-realists themselves, however, not comprehend as a falsification of their axiom, but instead as that paradoxes are real, eg, cladistics' belief in "a single true tree of life" and particle physics' belief in "Higgs particle". This comprehension is, however, inconsistent with Heisenberg's uncertainty principle and falsified by the fact that time is relative with speed in space. It is thus falsified empirically by the only empirical fact we have to test it. There thus simply can't be such "things". Instead, belief in them is in practice an infinite recursion, ie, endless orthogonal loop.

On the impossibility to find a consistent and unambiguous model of reality

The impossibility for us to find a consistent and unambiguous model of reality, such as the ideas of "a single true tree of life" (cladistics) and of "a single Grand Unifying Theory" (particle physics), is obviously not due to reality, but to our conceptualization itself (see Russell's paradox), although reality itself obviously has the same problem, since it can't stop. It means that a search for such ideas actually mimics reality instead of modeling it. Ironic, isn't it?

On the vain battle for cladistics

The fact that our conceptualization of reality separates reality from our conceptualization of reality means that conceptualization creates an artificial rift between reality and our conceptualization of it, which we call Russell's paradox. This rift (ie, Russell's paradox), in turn, is actually an orthogonal cube interface between reality and our conceptualization of it having two facets (or aspects): subjectivity and objectivity, whereof subjectivity is paradoxically contradictory and thus ultimately the inverse of a paradoxical contradiction, that is, an infinite recursion, and objectivity is consistently ambiguous. It means that our conceptualization of reality leaves us with two options: (1) paradoxical contradiction ultimately ending up in infinite recursion (ie, subjectivity), or (2) consistent ambiguity (ie, objectivity). This is the setting of conceptualization that we have to relate to.

Cladists are trying to make this fundamental choice between subjectivity and objectivity into an existential question, ie, concerning whether a particular kind of group (ie, clades, or genera with their species) "are natural groups" or not, but this focus is actually just a diversion. The problem is, instead, that such "natural groups" in fact are ultimately paradoxically contradictory. This problem does not, however, reside in the "natural groups" themselves, but in that they are inconsistent, ie, that they don't break even. Our fundamental choice is thus not an existential question between whether a particular kind of group "are natural groups" or not, but instead the much less dramatical choice of whether we prefer subjectivity or objectivity (ie, paradoxical contradiction or consistent ambiguity). Those that choose subjectivity just have a tendency to fall into existential arguments.

Biological systematics perceives itself as having the task of finding the natural classification of biological organisms. Given Russell's paradox, this task is  however, indeed mission impossible, since this paradox shows that there is no such natural classification to be found, ie, that the idea itself is practically void. The question whether biological systematics will ever accept this fact is, however, written in the stars. Presently, it is doing all it can to deny it. It battles for its existential aim, although Russell (among others) already has discarded it. Cladists are thus fighting a vain battle for the idea that there is a consistent meeting point between subjectivity and objectivity, ie, a "natural" classification, although Russell's paradox has already shown that this idea is practically void. Why continue this hopeless battle?