Cladistics is indeed consistent - consistently inconsistent

If cladistics ain't contradictory, then Russel's paradox is false. However, the fact that Russell's paradox can't be falsified thus instead means that cladistics IS contradictory. Russell's paradox simply falsifies cladistics (as a consistent approach).

Now, how can this fact be united with the fact that cladistics is consistent on the basis of its axiom (i.e., that classes are real)? The answer is that cladistics is consistently inconsistent. Cladistics is thus indeed consistent - consistently inconsistent.

On the paradox of the cladistic idea of a single True Tree of Life

Willi Hennig's (today cladistics') idea of a single True Tree of Life is possible ONLY IF the class clade is real, and thus if classes in general are real, because the idea hangs on the axiom that classes are real.

However, IF classes are real, then the idea of a single True Tree of Life is neither possible, since it then is contradictory between all other classes, and contradictions can't be real (at least not as singularities).

It means that Willi Hennig's (today cladistcs') idea of a single True Tree of Life is not possible even if it is possible. All gates to it are closed.

This is, actually, the destiny of all beliefs. Non-contradictory verification is simply an impossibility (as also both Wittgenstein and Popper, among others, have concluded). Understanding of this fact is actually not rocket science today, but just requires understanding of linear algebra, which cladists thus, obviously, haven't. "Cladistics" thus shows all signs of being just an outburst of over-simplification (i.e., populism) by an ignorant bunch of people. However, the fact that some of these people today have come to occupy professor's grades at universities appears to indicate a hidden scientific scandal. How could subjective populism sneak its way to professor's grade in scientific institutions? And, how can these people today be allowed to teach this populism in scientific institutions? What about the poor students that sign in on scientific universities just to have to listen to ignorant teachers teaching subjective populism?

The German entomologist Willi Hennig dived into between the barrels (today called cladistics)

The German entomologist Willi Hennig dived from objectivity to pure subjectivity, but found nothing but contradiction in accepting the idea of a single True Tree of Life (today called the class clade). Accepting this idea namely also means accepting paradoxes, when accepting paradoxes means denying a single True Tree of Life, and vice versa.The two simply can't make it up.

This fact ought not come as a surprise, since subjectivity, of course, can't be objective. Good old Willi thus dived into between the barrels, a dive that today is called cladistics.

Realism (like cladistics) simply can't be correct, since it contradicts itself

Humanity is since the dawn of conceptualization split into two approaches in our discussion about reality:

1. the belief (i.e., axiom) that classes are real, therefore called realism, first formulated by the ancient Greek Parmenides, and

2. the axiom that single objects are real (and thus that classes are only inventions of our mind), called nominalism, first formulated by the ancient Greek Heracleitos (although his writings are largely lost).

These two approaches are the only possible approaches in conceptualization, since we can only assume as an axiom that either classes or single objects are real. The difference in their entrances to conceptualization means that they talk past each other although using the same terminology, since assumption in one of them is conclusion in the other, and vice versa. Their relation is thus of the kind that is called orthogonal, that is diametrically opposed.

In their logically consistent versions, each of these approaches has its particular ultimate set of conclusions, which thus are orthogonal. One of the ultimate conclusions of realism is that there must be a single true dichotomously branching consensus origin of all objects, i.e., a single true origin of classes, which realists call The True Tree of Life (the class clade), but which in nominalism corresponds to the ultimate conclusion that classification is contradictory, called Russell's paradox. Interestingly, this is a meeting point of realism and nominalism, although realism views it as a reality whereas nominalism views it as a paradox. It thus has the potential to test the two approaches against each other. If this thing (i.e., class clade or Russell's paradox) is real, then realism is correct, whereas if it is not real, then nominalism is correct.

The issue thus melts down to the question whether paradoxes are real or not. If they are real, then realism is correct, whereas if they are not real, then nominalism is correct. This question can also be tested empirically, but in this post, I content myself to conclude that if paradoxes indeed are real, which realism thus concludes, then "real things" may be contradictory, a conclusion that is difficult to evaluate, but which does at least allow us to conclude that such "real things" cannot be found unambiguously like in the realistic idea of a single True Tree of Life. The conclusion thus allows us to conclude that realism is contradictory: if there is a single True Tree of Life, then paradoxes can't be real, whereas if paradoxes can be real, then there can't be a single True Tree of Life.

The meeting point of realism and nominalism thus allows us to shed light on the contradiction of realism. Realism simply can't be correct, since it contradicts itself. Nominalism, on the contrary, does not suffer of any such internal consistency problems. 

Karl R Popper om toleransens paradox

Även om Karl R Popper förespråkade tolerans, så hävdade han att intolerans (som den som till exempel hävdas i Sverigedemokraterna) inte ska tolereras.

För om tolerans skulle tillåta intoleransens totala framgång, så skulle den hota den toleransen i sig själv. Popper argumenterade att:

Obegränsad tolerans måste leda till utraderande av tolerans. Om vi utsträcker obegränsad tolerans även till de som är intoleranta, om vi inte är beredda att försvara ett tolerant samhälle mot slakt av de som är intoleranta, då kommer de toleranta att förgöras, och tolerans med dem.

Yttranden från intoleranta bör dock inte alltid undertryckas, så länge vi kan bemöta dem med rationella argument och hålla dem i schack med den allmänna opinionen. Emellertid,

vi bör hävda rätten att undertrycka de intoleranta, om nödvändigt även med våld; för det kan visa sig att de inte är beredda att möta oss på nivån av rationella argument, utan börja med att fastställa alla argument; de kan förbjuda deras följare att lyssna till rationella argument, därför att de är vilseledande, och lära dem att svara på argument genom användning av nävar eller pistoler.

Dessutom, till stöd för lagstiftningen om de mänskliga rättigheterna i senare delen av 1900-talet uttalade Popper:

Vi ska därför hävda, i toleransens namn, rätten att inte [min fetstil] tolerera de intoleranta. Vi ska hävda att varje rörelse som predikar intolerans placerar sig själv utanför lagen, och vi ska betrakta uppvigling till intolerans och förföljelse som kriminell, på samma sätt som vi betraktar uppvigling till mord, eller till kidnappning, eller återgång till slavhandeln, som kriminell.