The difference in biological systematics between cladistics and Linnean systematics

The difference in biological systematics between cladistics and Linnean systematics is that cladistics is naive set theory, whereas Linnean systematics is axiomatic set theory. It means that cladistics is contradictory (actually paradoxically contradictory as Bertrand Russell demonstrated in 1901), whereas Linnean systematics is consistent.

As cladists claim, naive set theory is indeed simpler than axiomatic set theory is, but also contradictory in difference to axiomatic set theory. It is as Einstein stated: we shall simplify matters as much as possible, but not too much, because then we create impossibilities. The impossibility cladistics creates is "a true tree of life".

Cladists are thus actually just naive (ie, ignorant) biological systematists.

Cladistics - the science of infinite recursion

An infinite recursion (also known as an infinite loop, endless loop or unproductive loop) is a sequence of operations which loops endlessly, either due to the loop having no terminating condition, having one that can never be met, or having one that causes the loop to start over.

One example of an infinite recursion is the notion that commonly is called "the tree of life". This infinite recursion is of the kind that have a terminating condition that can never be met. The problem with the notion is thus not whether it is true or not, but that it lacks a consistent solution. This statement points at two different issues to be addressed:

1. the question whether a statement about history can be true at all, and

2. why the notion lacks a consistent solution.

These two issues do, however, meet in that the answer to the former explains the latter. The fundamental problem is that a statement about history can't be true at all, since all statements about history requires an aspect, and that there is no aspect of aspects. This lack of an aspect of aspects does, in turn, explain why there isn't any consistent solution of the notion: there simply isn't any aspect of aspects. It means that we can search forever for an aspect of aspects, because the only thing we will find are different aspects which all are inconsistent.

The approach in biological systematics called "cladistics" has, however, turned this fact up-side-down by instead claiming that there indeed is an aspect of aspects that we can find, ie, the notion of a "the tree of life", which, thus, actually is an infinite recursion. This claim cannot, of course, change the fact that the notion is an infinite recursion, but only our understanding of that we can't find an infinite recursion into a belief that we can find an infinite recursion. It cannot change the fact that the notion is an infinite recursion, but only distort our heads into believing that we can find an infinite recursion.

In the course that this approach (cladistics) has gained more influence and power in biological systematics, it has excluded biological systematists that understand the issue from positions in the academy in favor for cladists, and has thereby kidnapped biological systematics. Today, cladists not only claim that an infinite recursion like the notion of a "tree of life" can be found, but also that biological systematics equals cladistics. It aims at eradicating everything except its inconsistent belief in biological systematics.

Cladistics has thus turned facts into fiction and fiction into facts, thereby giving the impression that an infinite recursion, ie, the notion of a "tree of life", can be found, when the truth is that a search for it is endless per definition. This has helped cladists to academic careers (see for example Steve Farris, Kåre Bremer and Per Sundberg), for which the judgement remains. It seems suspiciously like fraud. We at least ought to ask them if they indeed think that a "tree of life" can be found. If they answer yes, then they are definitely wrong, but to be be held responsible for their actions, we have to prove that they understand that they are wrong, which is more difficult. However, they ought at least be detached from their positions.  

On two impossible scientific endeavours: Higg's particle-ism and cladism

There are two scientific endeavours that are vain per definition:

1. to find the smallest particle and
2. to find species,

which Bertrand Russell demonstrated about a hundred years ago.

These two endeavours do, however, share one property: being considered as self-evidently within reach by many physicists (Higg's particle-ists) and biologists (cladists), respectively.

The belief of these physicists and biologists is so strong that the former claim that they have found it with a certain probability and the latter simply turns matters up-side-down by considering it as found.

Don't accept their claims! Fact is that neither Higg's particle-ists nor cladists ever will find their respective dream, because it simply isn't to be found, as Bertrand Russell demonstrated. They need money and have to produce results, but their respective strives are actually vain. We can understand how reality functions, in several different ways, but not find out what it is. That's the fact of life we have to accept and live with.

On the concept "clade" and the belief "cladistics"

The now popular concept "clade" in biological systematics is actually an infinitely recursive concept, like "the list of all lists", by including itself as a member of itself. A belief that this concept indeed can break even, today called "Cladistics", and its corollary search for what it calls "the true tree of life", is actually in practice a belief that every clade is what cladistics calls a "sister-group" to itself and that the most inclusive clade also is a sister-group to the least inclusive clade. It is thus an absurd belief by believing in the obviously absurd.

Linnean systematics and Evolutionary taxonomy avoid this sink hole by arranging concepts orthogonally as categories of classes (of organisms).

The question whether there is such a "single true tree of life" or not thus has a negative answer - there isn't. Instead, there are actually several equally true graph illustrations of a hypothesized evolutionary origin of biological organisms. Large scale change (ie, evolution) actually can't be unambiguous if small scale change is, because only entities are unambiguous and they are physically nested as INDEPENDENT entities in other entities. Unambiguity in change at different scales at the same time actually requires total dependency between entities on different scales, which, in turn, makes change impossible. The cladistic belief in a single true tree of life does thus contradict its own assumption of the underlying process (ie, evolution) itself. Cladistics does thus believe in something it at the same time denies.

Giddy, this siding in biological systematics, isn't it?

On distinction of species

We can only partition biological organisms into species by distinguishing (ie, defining) the class (ie, the concept) species. Now, distinguishing classes, like species, do we, however, perform by distinguishing both some similarity between the entities in the class and some difference between this class and other classes of such entities at the same time. By this, we contrast the new class against its opposite class as being both dissimilar and different.

The problem concerning the class species is what the opposite class possibly can be? Which class can we contrast species against? The answer is that we can only contrast it against the class entity, meaning that one of them excludes the other per definition, ie, that we can't acknowledge both of them at the same time, because they are not just dissimilar, but moreover different. The class species is thus consistent only if the class entity isn't, and vice versa.

This fact explains our extreme problems to define the class species. These classificatory (ie, conceptual) problems may we confuse with the (then apparently factual) problem that reality consists of a vast variety of life forms, but these two kinds of problems (ie, conceptual and real) are actually just two facets of one and the same problem, that is, that not both species and entity can be consistent at the same time. Solution of these problems does thus not hinge on whether they are abstract or real; we can't distinguish both species and entity consistently at the same time independently of which.

The distinction of species is thus doomed to fail by being inconsistent per definition. The problem of distinguishing species, which cladistics thinks it has overcomed, thus still remains. Cladistics thus still lacks the fundament it needs to turn rational to irrational, and vice versa.The concept species still lacks a consistent definition.

On the fundamental error of cladistics

Those biological systematists that are called cladists conflate entity (or object) with class. It means that they also conflate monophyletic groups of entities with monophyletic groups of classes.

This conflation makes cladists erroneously believe that monophyletic groups of entities can be consistently distinguished as monophyletic groups of classes with what they call "apomorphies", and picks up that thread in a practical search for such groups.

Their conflated kind of monophyletic group is, however, what biological systematists searched for for about 2,000 years before Linné, and failed. The problem with such groups is that entities consist of classes in that every entity belongs to several classes, and that the relation between entities and classes thus is not 1-1, but 1-many, and that the relation between classes and entities thus is many-1, The latter part of this relation, ie, many-1, between classes and entities, means that there are several classes that fit one entity, and thus that there also are several monophyletic groups of classes that fit one monophyletic group of entities. There simply isn't a 1-1 relation between monophyletic groups of entities and monophyletic groups of classes which cladists erroneously believe there is.

This fundamental error of cladists´means that they search for something that isn't to be found (ie, the true tree of life). Their conflation of entity (or object) with class has lured them into the belief that there is a 1-1 relation between monophyletic groups of entities and monophyletic groups of classes, which simply is wrong. Instead, their search for this singularity is in practice an infinite recursion. It is, actually, the same search for an infinite recursion as it was before Linné. This reinvented (cladistic) approach is thus just as vain as it was before Linné, but adherents of it appears to have difficulties abandoning it. Demonstration that it is inconsistent does obviously not suffice to make them abandon it.

This fundamental error of cladistics is thus obviously larger than facts. It appears to be what we tend to believe in contradiction to facts. In the case of cladistics, it has led some of us (ie, cladists) into a vain search for something that isn't to be found, but which they believe in, ie, the true tree of life. Not even the fact that there isn't any such thing to be found suffices to make them stop searching it. Somewhere here something is fundamentally stupid.         

Doesn't cladistics represent science going nuts?

Biological systematists that are called "cladists" believe that there is a true "tree of life" to be found, and spend their time and our money searching for it. Now, if there really is such a true "tree of life" to be found, how can cladists then know when they have found it?

If this true "tree", as cladists themselves claim, is the "tree" that requires the fewest number of explanations on the origin of traits among organisms, then there isn't any such tree at all, since classification is ultimately paradoxically contradictory, which we can figure out ourselves but which Bertrand Russell also demonstrated already in 1901 (that is, before the origin of cladistics), because it means that there are at least two such "trees". If so, then cladists will thus search forever for their true "tree of life", because there simply isn't any single such thing to be found.

So, can there possibly be another true "tree of life" (ie, one that doesn't minimize the number of explanations on the origin of traits among organisms) to be found? If so, then there will also be a mirror image of this "tree" actually representing the other side of the same real "tree" (ie, the true "tree" seen from the other side). How can cladists then distinguish which of these two true "trees" that represent the true "tree" (when both actually do)?

The existence of such a true "tree of life" does thus appear to be a practical impossibility. Instead, the belief in it appears to be a conflation of representation with the represented (ie, class with object). It gives rise to the questions: how can we pay cladists for a search for a practically impossible belief? Doesn't cladistics actually represent science (in this case biological systematics) going nuts into its own classification?

Cladistics (Willi Hennig) got off the problem for biological systematics on the wrong foot

Cladistics (Willi Hennig) got off the problem for biological systematics on the wrong foot. The problem isn't which dichotomously branching illustration of the origin of life that is "true", but that there can't be a single "true" dichotomously branching illustration of the origin of life.

This problem is due to that classification is orthogonal and thus ultimately paradoxically contradictory, which also Bertrand Russell demonstrated in 1901, and is actually the reason for Linné's invention of his orthogonal classification, which avoids the paradox. Cladistics' (actually Hennig's) belief there is a single "true" dichotomously branching illustration of the origin of life does not change the fact that there isn't. Belief can overcome many problems, but not change facts. 

Explanation of what a "species" is

Biological systematists (and others) have long wondered what a "species" is. Well, I can tell them that a "species" is the opposite to an "object" (or "entity"). I can also tell them that the problem to find out what a "species" is, is that whereas an "object" has two different aspects: pattern and process, these two different aspects are in a species instead orthogonal properties. It means that a "species" is different from itself by having orthogonal properties (per definition).

This property of a "species" (ie, being different from itself by having orthogonal properties ) is difficult to understand, but Bertrand Russell (1901) gave the explanation by the paradox that became known as Russell's paradox. The explanation is simply that classification is inherently paradoxically contradictory by being orthogonal, and that species is the paradox itself.

A "species" is thus the opposite to an "object" (or "entity"), that is, a paradox. It is the paradox that emerges in the moment we distinguish "objects" of different "species". One of "objects" and "species" has to be a paradox, we can just choose which. (Whereof the approach for typologists, cladistics, chooses "objects". To a cladist the problem is thus not what a "species" is, but what an "object" is. A representative for a species, like the cladist Steve Farris for Homo sapiens, is not a representative for the species Homo sapiens, but the species Homo sapiens. As an object, he is a paradox, And, although this may be true for Steve Farris, it is not true for all representatives for all species).

Linnean systematics and cladistics are just two different kinds of classifications of dichotomously propagating processes

Linnean systematics and cladistics are just two different kinds of classifications of dichotomously propagating processes: Linnean systematics accepting the fact that the classification of such processes can't be unambiguous, and cladistics instead searching for unambiguous classifications of such processes (ie, not accepting the fact that classification of such processes can't be unambiguous).

These two kinds of classifications are thus just different (orthogonal) opinions on whether classification of dichotomously propagating processes can be unambiguous or not, whereof cladistics is wrong.

On the choice between Linnean systematics and cladistics

When we conceptualize reality, we implicitly distinguish reality from our conceptualization of it. This distinction is thus not a real difference, but an arbitrary (artificial) distinction in a continuity consisting of reality and our distinction of it. This distinction creates an orthogonal (ie, diametrically opposed) relation between reality and our conceptualization of it, which, in turn, leaves us with two orthogonal approaches to conceptualize reality: subjectivity and objectivity. These two approaches are thus the only two facets (or aspects) of the thus created interface between us and reality that it offers us to look at (and thus conceptualize) reality.

The fact that the relation between reality and our conceptualiztion thus is orthogonal means, however, that neither of the offered approaches (ie, subjectivity and objectivity) can be unambiguous, since an orthogonal relation can't be unambiguous, but that one is paradoxically contradictory (ie, subjectivity), see also Russell's paradox, whereas the other is consistently ambiguous (ie, objectivity). Our choice in conceptualization of reality is thus between being paradoxically contradictory or consistently ambiguous. Subjectivity is also called realism, ie, assuming that classes are real, whereas objectivity also is called nominalism, ie, assuming that objects are real.

These two approaches (ie, realism and nominalism) have been battling each other since the dawn of conceptualization. The fundamental disagreement between them is which of them that can reach the ultimate truth that both of them search. This battle is thus a battle of the Pope's beard, since none of them can reach the ultimate truth, because the ultimate truth can't be reached at all, since none of the to us offered facets (or aspects) of reality is unambiguous. None of these two approaches can thus reach an ultimate truth, since one of them is paradoxically contradictory (ie, subjectivity) whereas the other is consistently ambiguous (ie, objectivity). Instead, we have to choose one of them by its pros and cons. We have to abandon the idea of a single "true" conceptualization and instead evaluate them by their respective pros and cons. The question we have to pose ourselves is thus: do we prefer to enter a vain search for a non-existing "True Tree of Life" (ie, cladistics) or produce a consistent classification (ie, an orthogonal system of classification like the Linnean system)? There is no other option given to us.

Another question is whether the sponsors of biological systematics prefer to pay for a vain search for a non-existing "True Tree of Life" or for the production of a consistent classification. This is a choice they have to contemplate.                     

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? 

Cladistics looses itself in the fogs of simplicity

When we classify reality, there are only two aspects we have to keep consistently apart: reality and the abstract (ie, object and class), to keep reality and our perception of it consistently apart. In doing so, there is one aspect we misses, the middle. There simply is no place for a middle between reality and our perception of it. It means that classification can't pinpoint reality unambiguously.

If we, like cladists, instead claim that classification indeed can pinpoint reality consistently, then we actually claim that there is no difference between reality and the abstract, and thus that there is a middle between reality and the abstract.

If there indeed is a middle between reality and the abstract, then there is no reason to partition our perception of reality into reality and our perception of reality, and thus that reality is what we think it is.

If reality is what we think it is, then the question is: what who thinks it is? We can, obviously, disagree about both what reality is and what history is, so which comprehension is correct? If the answer is the most parsimonious comprehension, then the most generalizing perception is right. The notion thus turns simplicity into a virtue. Knowledge is in this approach only a burden. The boldest painting of reality in only black and white wins. The approach thus looses itself in the fogs of simplicity.   

Cladistics tries to both distinguish and confound shared ancestry and apomorphy at the same time

On the talk page for Wikipedia's definition of the term cladistics, E O Wiley begins by stating that:

"As it stands, this article confounds "cladistic" and Linnaean classification. What is being contrasted is not "cladistics versus Linnaean" but "Phylocode versus Linnaean."

Wiley is a little careless with words, but he appears to mean that the definition of cladistics confounds cladistic [classification] and Linnean classification by contrasting [the] PhyloCode versus Linnean classification instead of "cladistics versus Linnean".

Apart from his inconsistent (realistic) method of defining by either contrasting or equalizing, instead of circumscribing, this statement boils down to the term Linnean in his expression "cladistics versus Linnean". Wiley obviously distinguishes cladistic classification (ie, PhyloCode) from cladistics, but what is his corresponding distinction of Linnean classification from Linnean? What does he mean with Linnean (if not Linnean classification)?

This question redirects to what Wiley means with cladistics (if not cladistic classification). He does not clarify this point further, but it is addressed in the first post on the talk page titled "Definition of cladistics" in the second comment by "The Braz":

"Cladistic classifications are not based on shared ancestry, rather inferences of shared ancestry are based on cladistic classifications. I don't think this [difference] is semantic, I think it matters because one [ie, the former] approach is purely circular and the other [ie, the latter] is not."

To The Braz, cladistics does thus obviously mean "inferences of shared ancestry", and he points at that it must succeed cladistic classification to avoid pure circularity.

However, we can also note that Wiley and The Braz disagree in their meanings of cladistic classification. Wiley appears to mean that cladistic classification equals the PhyloCode, whereas The Braz clearly states that it is "the grouping of things according to shared apomorphy (synapomorphy)". Wiley thus means that cladistic classification is by ancestry, whereas The Braz means that it is by apomorphy. However, the fact that cladistics axiomatically assumes that every clade also is distinguishable by an apomorphy, these two meanings of cladistic classification are actually perfectly synonymous under this axiom (ie, that ancestry corresponds to both clade and apomorphy). Under this axiom, none of shared ancestry and apomorphy is thus based on the other, as The Braz axiomatically assumes, but are instead the same things.

However, if shared ancestry and apomorphy indeed are the same things, as cladistics thus axiomatically assumes, then the confounding of cladistic classification and Linnean classification that Wiley points at in his introductory statement is actually a corollary to the cladistic axiomatic synonymization of ancestry and apomorphy, ie, if ancestry indeed corresponds to both clade and apomorphy, then cladistic classification also equals Linnean classification.

We can thus understand that the confounding of cladistic classification and Linnean classification in the article about cladistics that Wiley points at in his introductory statement actually is a corollary of cladistics' axiom that ancestry corresponds to both clade and apomorphy. That is, this axiom actually means that there is no difference between cladistic classification and Linnean classification. This fact explains both the inconsistency of cladistics (in its founding axiom) and the rationale for Linnean classification at the same time.

It isn't easy to both distinguish and confound shared ancestry and apomorphy at the same time, as cladistics tries to do, especially not when they actually are orthogonal. This fact is the rationale for the orthogonal Linnean classification.

Cladistics is what you end up in if you conflate (confound) pattern with process, ie, object with class, that is, Russell's paradox.

Cladists have really stuck in an infinite loop

The fact that classification is orthogonal, ie, that every single class contains at least two classes, means that it has to be arranged orthogonally, ie, classifying entities into categories of classes, as in the Linnean system, to avoid the inherent contradiction of an orthogonality (see Russell's paradox).

However, such orthogonal system of classification is ambiguous in relation to the classified per definition, since it actually consists of two orthogonal classifications.

The approach in biological systematics called "cladistics" simply ignores this fact (ie, that classification is orthogonal) instead entering the inherent contradiction of an orthogonality (see Russell's paradox) while asserting (actually defining) that it, ie, the contradiction, indeed is real (ie, can be found). In this approach, ie, assuming that the contradiction is real, it is actually an infinite recursion, ie, an infinite loop. But, how can cladists possibly understand that they have entered an infinite loop when they don't understand that classification is orthogonal in the first place (actually not even that they classify)? No, they have indeed stuck in this infinite loop.

Why should biological systematics accept a premise that is impossible?

If the class clade indeed is consistent, then there must be single entities (ie, single biological species) that can be divided into clades. Exactly how cladists mean that such division is possible remains to be explained. Until cladists provide an explanation of this impossibility, their approach thus ought to be discarded. Why should biological systematics accept a premise that is impossible?   

Cladistics is in practice nothing but a way to cheat your money

Cladistics is the approach in biological systematics that only acknowledges "clades", ie, the class clade. The class clade is a set that includes itself as a member, and is thus an infinitely recursive set. An infinitely recursive set is a set that lacks a consistent solution per definition, since it is infinitely contradictory. It means that cladistics is "The Approach that Only Acknowledges Infinite Contradiction".

What this approach possibly can be good for is thus hidden in the fog of biological systematics, but cladists obtain apparently nonetheless pay for their "work". This pay can thus only be for an infinite production of contradictory clades. This money could do much more good for humanity if they were invested in something else than cladistics. Cladistics is in practice nothing but a way to cheat your money.    

Is not cladistics rather paradoxical?

The British philosopher, logician, mathematician and historian Bertrand Russell showed 1901 that naive set theory leads to paradox.

The German entomologist Willi Hennig asserted (claimed) 1955 that only clades (ie, historical sets) are "natural" groups and that there is a single clade of clades (ie, historical set of all historical sets, or a true tree of life) to be found.

Since Russell's paradox no doubt is true, Hennig must thus assert (claim) that paradoxes can be found.

"Finding" a paradox can only mean finding a solution of the paradox. Russell's paradox is stated as:

According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves. On the other hand, if it is not a member of itself, it qualifies as a member of itself by the same definition (slightly modified from Wikipedia).

The paradox thus means that R (ie, the set of all sets that are not members of themselves), corresponding to Hennig's "historical set of all historical sets (that are not members of themselves)" is inconsistent.

So, did Hennig find a consistent solution of this paradox? No, he merely asserted (claimed) that only such paradoxes (ie, sets) are "natural" groups and that there is a single solution to them.

Hennig's assertion (claim) gave rise to the new branch of biological systematics called cladistics and looking for the solution to Russell's paradox.

This leads unsought to the question: is not this new branch (ie, cladistics) rather paradoxical?

The "true tree of life" must be a fuzzy set

Biological systematists have been searching for the "true" classification since the dawn of man. They are convinced that every biological organism belongs to one and only one "true class" (or "true set of classes"), which is also the "natural group" (or "natural groups") for the organism. For them, classes are not something we allocate organisms to, but something organisms are. They just try to find out which classes every organism is (or which "natural groups" it belongs to). The approach is strictly typological, and has also been practically applied as "race cleansing" from time to time.

Never has it struck these biological systematists that the classes reside in their own eyes, although they have changed their minds about the specifics of these "natural groups" for about two and a half millenia by now. On the contrary, the post-war German entomologist Willi Hennig asserted (claimed, defined) that such "natural groups" are to be found practically by reversing our own classification !!! His suggestion led these biological systematists to assert (claim, define) that they have found "the natural groups" every time they have classified and reversed the classification (whichever classification it is) over and over again. The only difference to before Hennig is that they now also reverse their classification arriving to what they started with. That is, they think they have derived the "natural groups" instead of simply classified them, although they derive exactly what they classify.

One wonders how long they can continue with these stupid practices resting on the erroneous axiom that classes are real? Bertrand Russell showed that this axiom is paradoxically contradictory already 1901 and Einstein revealed some years later that time is relative to space, which falsifies this axiom, so when will these biological systematists acknowledge these facts and discard their erroneous axiom? When will they give up for facts and discard their erroneous idea of a single true tree of life?

I said it before and I say it again: there is no "true" classification of biological organisms to be found. None of us (organisms) can be pidgeon-holed into a single set of "natural groups". Instead, all of us are a little bit of this and a little bit of that, and can thus be pidgeon-holed into many different sets of "natural groups". It isn't that "natural groups" do not exist, but that every single set of "natural groups" is contradictory. If "natural groups" actually do exist, they they must thus be fuzzy sets.

It means that the idea of a "single "true tree of life" must be a fuzzy set.

   



 

On the paradoxical contradiction of the class "clade"

The concept "clade" terms a class of entities (ie, "ancestors including all their descendants"). This class of entities appear "natural" to some biological systematists, but is none the less paradoxically contradictory (ie, the subjective aspect of Russell's paradox).

This fact can be understood by considering that the fact that every class can be a member of another class (like how humans is a member of primates) means that every clade also can be a member of another clade (ie, that every clade contains member clades). Now, if there among all clades should be a single clade that is not a member of any other clade (like the idea "a true tree of life"), then this clade of clades must also equal (be the same as) each and every of its member clades, and thus exclude the possibility of any other clade of clades besides It (ie, exclude the existence of more than one clade of clades), thereby contradicting the fact that there are several clades per definition. Ie, if there are several clades, then there is no single clade, and vice versa.   

The class "clade" thus actually excludes the possibility of single instances of itself by excluding the possibility of clades that are not members of other clades.

The same explanation can be given in terms of entities: the fact that every entity can be a member of another entity (like how a cell in my body is a member of me) means that every clade of entities also can be a member of another clade of entities (ie, that every clade of entities contains member clades of entities). Now, if there among all those clades of entities should be a single clade that is not a member of any other clade (like the idea "a true tree of life"), then this clade of clades must equal (be the same as) each and every of its member clades and thus exclude any other clade of clades besides It (ie, exclude the existence of more than one clade of clades), thereby contradicting the fact that there are several clades per definition.

The class "clade" is thus actually just a mental circularity inside of Russell's paradox, that is, the subjective aspect of Russell's paradox. It actually lacks a single unambiguous solution (but has several ambiguous solutions in orthogonal systems of classification like the Linnean systematics).