Straightening out the cladistic confusion

Cladists have obviously confused harnessing horses to the cart, putting the cart in front of instead of behind the horses. They obviously (see, for example, Mikael Härlin) think (and claim) that classification is posterior rather than prior to hypotheses.The fact that every hypothesis requires a prior classification has obviously escaped them. How on earth could a hypotheses originate without a prior classification. What on earth would it in that case specify?

This confusion has obviously led cladists into a search for a single True Classification of biological organisms, which they call the "natural" classification or The Tree of Life, USING prior classifications of biological organisms and logical reasoning, just as if there is a True Classification lurking beyond all possible prior classifications.

This irrational idea is easily falsified by considering the fact that every logical reasoning is orthogonal (ie, diametrically opposed) in a classificatory sense between its premises and conclusion. If, for example, the premises are that:

1. All men are mortal
2. Socrates is a man

(thus allocating Socrates to the class "men"), then the conclusion

3. Therefore, Socrates is mortal

allocates Socrates to the class "mortals", which is orthogonal to "men", because although all men are mortals, not all mortals are necessarily men. The two classes are orthogonal, ie, acting on orthogonal classificatory levels. Every logical conclusion is simply orthogonal in a classificatory sense to its premises. Logical reasoning can thus not retrieve its initial classification in conclusion, and if the number of possible logical reasonings are infinite, then the number of cladistic hypothesized True Classifications is either infinite or zero. There is thus no single "natural" classification, or True Tree of Life, lurking beyond all possible prior classifications.

This finding of, and investigation of, the cladistic confusion ought to be unnecessary. No knowledgeable researcher ought to fall into it. The question why cladists (beginning with Willi Hennig) obviously fell into it anyway remains to be answered. The reasons may be many, but only they themselves can answer it. A confusion is it in any case, actually a conceptual melt-down. And, a specific solution to the confusion is not to be found. The number of solutions are either infinite or zero, meaning, in practice, infinite.             

     

Is "clade" a class or an entity?

The approach called cladistics in biological systematics rests on the notion of "clades". This kind of "thing" is, however, confusing. The fundamental problem is that if "clade" (in indefinite form), analogous to "human", means both the class clade, analogous to the class human, and a single clade, analogous to a single human, then every single clade must consist of ONLY clades, and there must also be NEITHER anything else than clades NOR any clades at all, contrary to "human". "Clades" does thus, obviously, exclude everything, including itself. Accepting it does in practice mean denying everything, including itself.

What, then, is the reason for this confusion? Well, the reason is that "clade" is the opposite to "object". "Clade" is thus not a kind of "object", but actually the opposite to "object". It means that we have to think up-side-down and in-side-out when we discuss "clades". Thus,

- whereas there are different kinds of objects, there are different clades of kinds.
- whereas "object" is ambiguous between pattern and process, "clade" is instead contradictory between pattern and process.
- whereas objects are classified, classes are cladified.
- whereas objects are different from classes, clades are classes.
- whereas objects exclude clades, clades exclude objects.

"Clade" is simply using the ultimate conclusion if one starts with objects as axiom, that is, Russell's paradox, as axiom, thus landing in the opposite to object as ultimate conclusion (wherein the conclusion equals the axiom). It is a play with words landing in a paradox (i.e., Russell's paradox) as both axiom and conclusion.

The confusing property of "clade" does thus reside in that it turns assumption (actually axiom) and conclusion up-side-down and in-side-out. However, it is not the turning up-side-down and in-side-out itself that is confusing - it might just as well have been a normal development in science, a so-called "paradigm shift - but instead the fact that "clade" is a paradox, since it means that the axiom can't be real. Not even if all biological systematists would agree on this axiom could it be real, because it is contradictory, i.e., a paradox. "Clades" simply can't be real because they are contradictory, i.e., a paradox. The confusing property of "clade" is thus that it is contradictory (i.e., a paradox) and thus can't be used as an axiom because they are far from self-evident (as axioms ought to be). A contradiction may, of course, be self-evident to some of us, but not without contradiction.

The answer to the question "Is "clade" a class or an entity?" is thus "both". It is both a class and an entity. The problem is that class and entity are contradictory. The only difference between cladists and non-cladists is thus that cladists interpret this "both" erroneously as a confirmation (i.e., it is both at the same time), whereas non-cladists interpret it correctly as a contradiction (i.e., it is neither). This difference sends cladists on a vain search of a contradiction they call "clade", which currently seems to occupy a large part of the "research" in biological systematics. This search is thus correctly diagnosed as a mental desease - paranoia.
      

Den biologiska klassificeringens historia

Klassificering (egentligen begreppsbildning) är internt självmotsägande genom att splittra varje klass i (minst) två klasser. Varje klass är alltså både en klass och två eller flera klasser på samma gång. Denna inneboende självmotsägelse formulerades i logiska termer av Bertrand Russell 1901 och kallas idag Russels paradox.

Problemet med denna paradox kringrände (på engelska "bypassed") dock Aristoteles redan för 2350 år sedan genom att klassificera på två diametralt motsatta (kallade "ortogonala") nivåer, vilka han kallade "specificiteter" (dvs enskildheter) och "generaliteter" (dvs allmänheter), genom att särskilja det han kallade "specifika skillnader", dvs skillnader mellan specificiteter (enskildheter) av ett genus (dvs en allmänhet). Hans system "bröt" alltså upp verkligheten in i detta ortogonala system, dvs specificiter av olika generaliteter, istället för att helt platt klassificera objekt.

Aristoteles hade också en djup förståelse av vad han gjorde och varför, och förklarade det utförligt i många skrifter (i vilka han också skapade logiken som disciplin). Han förklarade bland annat att definitioner av begrepp är "en uppsättning ord som är ett, inte genom konjunktion [som logisk operator], såsom i Iliaden [det troligen äldsta bevarade Europeiska eposet], utan genom att referera till ett enskilt objekt". (Han avfärdade alltså uttryckligen den logiska konjunktionen som definitionsmetod, vilken kladistiken idag använder konsekvent (t ex "en klad är en monofyletisk grupp", dvs i en allmän mening: "en si är en så")).

Aristoteles löste alltså den "paradox" (dvs problemet med klassificeringens inneboende självmotsägelse) vi kan "känna" långt innan Russell kunde förklara den logiskt. Utvecklingen av detta problem tog dock ytterligare ett stort steg innan Russell kunde förklara det, i och med att Carl von Linné i början av 1700-talet konstruerade den hierarkiska sammansättningen av Aristoteles grundbult. Linné "flätade" alltså ihop Aristoteles specificiteter och generaliteter i mer omfattande specificiteter och generaliteter, i mer omfattande specificiteter och generaliteter, och så vidare... Detta system är alltså "Den enda konsekventa (dvs icke självmotsägande) klassificeringen" i en allmän mening, vilket är allt vi kan uppnå med Aristoteles system. Det utgör alltså en slutpunkt för denna startpunkt (vilken också är startpunkten för dagens traditionella vetenskap, dvs objektiv vetenskap, eller empirisk deduktion). (Linné är alltså VÄLDIGT stor, de facto oomkullrunkelig, faktiskt upphovet till dagens "appar".)

Linnés system (liksom Einsteins teoretiska upptäckt att tiden är relativ till rummet, vilken senare bekräftades empiriskt) skapade naturligtvis förstämning hos företrädare för den motsatta uppfattningen, dvs att klasser är reella och att definitioner således ska vara konjuktioner, kallad realism (åsyftande dess axiom att klasser är reella). På 1960-talet gick de dock till frontalangrepp på objektiviteten ledda av den Tyske entomologen Willi Hennig genom att helt frankt hävda att en klass, vilken han kallade "monofyletisk grupp" men vilken senare kom att kallas "klad", är vad han kallade "naturliga grupper". Angeppet återupplivade den för-Aristotelianska (och således för-vetenskapliga) uppfattningen som företräddes av Parmenides och representeras i Iliaden, att klasser är reella (med den ultimata logiska slutsatsen att världen "egentligen" är oföränderlig, dvs att förändring endast äger rum i våra huvuden). Hur Hennig kunde komma på idén att återuppliva denna förkastade uppfattning trots de brister som ledde till dess förkastande är obegripligt om man inte antar att Hennig var okunnig om såväl begreppsbildningens, vetenskapens, och filosofins utveckling de senaste 2500 åren. Den går endast att förstå genom att anta att Hennig (och därmed också hans efterföljare) helt enkelt är okunniga.

Problemet med realism är, naturligtvis, detsamma idag som det var för 2500 år sedan, dvs att den är inneboende självmotsägande (i.e., paradoxal), dvs praktiskt orealistisk, av den enkla anledningen att klasser är internt självmotsägande genom att splittra varje klass i (minst) två klasser. Om man, likt kladister, letar efter den så söker man alltså förgäves. Bättre vore att att de tänkte om själva från botten och upp, isället för att lura in unga studenter i denna fälla genom konsekvent begreppsförvirring.


       

Realism vs nominalism (or cladistics vs Linnean systematics)

Classification can only be contradictory or ambiguous: internally contradictory or ambiguous with regard to reality. It is internally contradictory when applied on a single level (like cladistics), and ambiguous with regard to reality when applied on two levels (then necessarily orthogonal, like Linnean systematics). Classification thus can't reach consistent unambiguity, for the simple reason it IS consistently ambiguous, that is, splits every class into two classes.

Now, there are fundamentally two opposite approaches to conceptualization of reality: realism (i.e., subjectivity) assuming as an axiom that classes are real (and thus that objects are abstract), and nominalism (i.e., objectivity) assuming as an axiom that objects are real (and thus that classes are abstract). Since realism assumes that classes are real, it tends towards classification on a single level, that is, towards internal contradiction, whereas since nominalism instead assumes that objects are real, it instead tends towards classification on two levels, that is, towards ambiguity with regard to reality.

In summary: there are fundamentally two opposite approaches to conceptualization: realism and nominalism, whereof realism is internally contradictory and nominalism is ambiguous with regard to reality. Between them resides the idea of a consistent and unambiguous classification (e.g., the True Tree of Life), thus totally impossible to reach.

The idea of a consistent and unambiguous classification is thus a running point, which realism tries to catch and nominalism tries to encircle. Neither of them will, of course, succeed to catch the impossible idea, but whereas nominalism (i.e., objectivity) ought to close up on it, realism instead drifts without a rudder. The realistic (cladistic) idea that parsimony might do the trick is a return alley, since it does not offer any criteria to distinguish between just as parsimonious hypotheses, which, thus, will always remain. A worse problem with realism is, however, that it is both consistently inconsistent and at odds with facts.

The sooner we get rid of realism in the form of cladism in biological systematics the better thus for biological systematics. How can anyone believe that biological systematics can defend consistent inconsistency and incongruence with facts in the long run?
     

What is a rabbit, really?

Human discussion about reality has forever been split between the two approaches nominalism (i.e., comprehending classes as artificial constructs, that is, resting on the axiom that only objects are real) and realism (i.e., resting on the axiom that classes are real). The two approaches can't be distinguished in discussions except by that when a nominalist for example says: "this is a rabbit", a realist asks: "how do you know?". The difference between them is that the nominalist views the classification as a provisional agreement to discuss common properties of objects of this kind, whereas the realist views it as a statement of a fact.

Neither of these two approaches is thus completely satisfactory concerning the question "what something really is", or "how the universe is constructed"; nominalism not considering the question and realism just asking the question (i.e., not providing the answer). Considering the great interest in this question, it is, however, important to straighten out if there possibly can be an answer to this question and what it, in that case, possibly can be.

The first question (i.e., super-question) is thus: can the question (i.e., sub-question) "what is a rabbit, really?" have an answer? It implies (i.e., assumes as an axiom) that there is an existential "True" class for every object, i.e., that every object basically IS a single something, that is, belongs to a single fundamental class. The super-question is thus if this axiom is sensible, that is, if there is there an existential "True" class for every object, if each object is a single something and if each object belongs to a single fundamental class? The answer to this question can be found in the fact that the axiom requires that every single object also is a single class, since every class that includes more than one object has to turn at least one object ambiguous between at least two classes. The answer to the super-question whether the sub-question  "what is a rabbit, really?" can have an answer is thus that it can, given that every object also is a single class.

This answer also gives the answer to the second question, that is, what this answer can possibly be. The answer is that the answer must be that every object is its own class. The sub-question is thus sensible ONLY IF each object is its own class.

The simple logical reasoning above thus discloses that realism is sensible ONLY IF each object is its own class. It means that the question "what is a rabbit, really" does not have an answer per definition, since it doesn't specify which rabbit, and that the more general question "what something really is" has the answer "what it is". The latter is thus a feedback-answer to the question. (For a more thorough understanding of this conclusion, please read Gödel, Escher and Bach by Douglas Hofstadter.)

The generic conclusion of this logical reasoning is thus that realism is a feedback-loop from answers to questions, that is, paranoia. It ports wherever the question leads it to end up, thus drifting with the question it poses, but always contradictory.

On clades and (the) Higgs boson - chasing paradoxes

The two facts that (1) logic is rational and has two entrances: the two axioms that objects respectively classes are real, and (2) that reality is irrational means that rationality meets reality as an orthogonality. Such meeting point means that reality is a passage (i.e., a process) in a rational sense - the passage between the two entrances to rationality. Reality thus can't be caught by rationality, because it actually IS the passage between the two entrances to rationality. This fact is expressed by Russell's paradox - neither of the two entrances to rationality can reach reality. This fact is more simply illustrated by Magritte's pipe - an illustration of a pipe is not, of course, a real pipe (can't be smoked).

The reasoning above explains and illustrates how we can get lost among words, but, more importantly, points at the illusion that resides within words called Russell's paradox. This paradox is actually the orthogonal opposite to object, and is thus just as real as objects are in a rational sense (i.e. not distinguishing the two entrances to rationality: objectivity and subjectivity). It is thus both a paradox and a reality at the same time (although paradoxes are not real per definition) in a generic sense in both of the  rational approaches. It means that rational reasoning may acknowledge this kind of phenomenon independently of which entrance one takes into rationality, although it can't be real (i.e., can't exist). This kind of phenomenon is thus a lure for rationality. It displays all necessary properties of being real in a rational sense, although it isn't real per definition. Its existential problems is further emphasized by that it denies the existence of objects, which it rests on.

Two examples of this kind of phenomenon is the class clade and (the) Higgs boson. Much can thus be said about this kind of phenomenon, but most important is that it is contradictory (i.e., paradoxes). Although it thus is real in a rational sense, it can't be found in reality. If this fact means that paradoxes are real and empirical realities (like objects) are not real, or not, is a matter of words, but the fact that paradoxes are contradictory is a fact. It means that acknowledging such paradoxes leads into contradiction, independently of whether they are considered real. Contradiction comes with the acknowledgement. Ironically, the "acknowledgement" is actually a confession to (rational) belief instead of rationality. Generic agreement between the two entrances to rationality - subjectivity and objectivity - is thus actually an entrance to their contradiction, that is, belief. The passage that rationality tries to catch does in practice lead to belief.

A much simpler explanation of the problem complex described above is that conceptual contradiction, what we normally call contradiction, is contradictory. It may be comprehended as The Truth by some rationalists, but it is actually an elevator to belief. It ought to be a no-no for all rationalists, but in the battle of the formulation privilege, some of them (us) just can't resist the temptation of diving into it, although it is their own end. Fact is that neither clades nor (the) Higgs boson can be found in reality. Both of them are just varieties of Russell's paradox.

 

  

Why (the) Higgs boson will never be found

(The) Higgs boson will, of course, never be found, for the simple reason that kinds do not exist (i.e., are not real), as theoretically shown by Russell's paradox and empirically evidenced by the fact that time is relative to space. This fact (i.e., that kinds do not exist) does, of course, also apply on the class "Higgs boson" (given that it does not consist of a single object - "The True Higgs boson". Physicists' attempt to "prove the existence" of this class (or of any class) is nothing but ridiculous. even if performed in the high-tech context at Cern. It is, none-the-less, nothing but a case of what I would like to call "blinding by belief" - a turning of deduction into induction under influence of a subjective belief that reality must be rational, although both theory and facts contradict this belief. Reality is, on the contrary, obviously, irrational, although following some basic principles that allows us to discuss it rationally. Reality isn't rational, only we are (at least some of us). (The) Higgs boson is thus, of course, just a tool that we (objectivists) use to be able to talk about reality both consistently and rationally. Without it, not only we (objectivists), but all of us are totally lost. The only alternative is the subjective (i.e., believing) contradiction (see Cladistics) that presently lead some physicists into a vain chase for (the) Higgs boson.

When will subjectivists stop chasing their own classification (i.e., "what really is")? I can give them the answer: reality is, and it is irrational. That's why it can't stop. We can only discuss it, not find out what it "really is". (If we could prove it to be something else than what it is, then we could also prove this something to be something else, and so on in an endless transformation between representations of representations.)

These physicists are like donkeys chasing the carrot in front of their eyes (just like cladists). The subject for their chase is their own assumption, and their own assumption is contradictory as a conclusion. They are simply contradictory from the beginning to the end.

Cladistics is the fundamentalism of science, ie the belief that concepts are real

Conceptualization began mankind's intellectual development. Today, cladistics is trying to end this development with reverse conceptualization. Unfortunately for cladistics, reverse conceptualization is contradictory, i.e., has no definite solution. Cladistics will thus never be able to finish mankind's intellectual development (luckily), but will instead continue its vain search for the solution that could forever. Meanwhile, cladistics is the fundamentalism of science, ie the belief that concepts are real.

Biological systematics - the vain quest for The Consistent Classification

Biological systematics has been chasing the idea "The Consistent Classification" since at least the ancient Greeks, that is, for at least 2500 years. The goal is a classification that breaks even, ie, is free from contradictions.

Today, we have, however, obtained the knowledge to figure out that this goal is actually an interface between subjectivity and objectivity (traditionally called realism and nominalism, respectively) and thus not a "thing", but a passage between two things, ie, between subjectivity and objectivity. The goal is the difference between subjectivity (realism) and objectivity (nominalism). If we analogize subjectivity and objectivity with railway stations, the goal is the rails between them. It is possible to pass, but it is not possible to transform to a single station (or several stations) in both approaches, because it in one view (subjectivity) has to be transformed into types of stations (ie, into several stations of the same kind) whereas it in the other has to be transformed into single stations. The two approaches thus can't see (or can't recognize) the same thing (s). The passage between them, that is, the goal for biological systematics, will thus remain an unattainable idea as long as the two approaches exist. This passage was in the early 1900's named Russell's paradox in objectivity, and about 50 years later named "clade" in subjectivity.

Biological systematics is thus closing up on understanding of the context, but right now too much of it (perhaps most) is too busy trying to find the ultimate clade, ie, Russell's paradox, which it calls the Tree of Life, to be able to think clearly. These biological systematists think they are so close to the goal that thinking is finished and only the practical chase remains. They can almost see the goal.

Biological systematics is thus approaching understanding of the context, but right now it is too occupied with the vain chase for "The consistent classification" to be able to think clearly. Ironically, the approach called evolutionary taxonomy has already formulated the solution (although not the explanation).  

On the relation between "clade" and "Russell's paradox"

The term (i.e., class) clade is contradictory: if clades can be unambiguously distinguished, then entities (like organisms or biological species) can't, because clades are incompatible with entities. If, thus, clades are entities, then they are contradictory entities, which, thus, can't be unambiguously distinguished. Clades thus can't be unambiguously distinguished if they are entities (and, of course, neither if they are not entities).

This contradiction is defined in Wikipedia in terms of Russell's paradox as (slightly modified by replacing set with clade):
(The axiomatic definitions are that any definable collection is a set (i.e., naive set theory) and that clade is a set). So, let R be the clade of all clades that are not members of themselves (i.e., the ultimate clade of clades, or the True Tree of Life). Now, if R qualifies as a member of itself, it contradicts its own definition as a clade containing all clades that are not members of themselves. On the other hand, if R does not qualify as a member of itself, it qualifies as a member of itself by the same definition. R does thus neither qualify as a member of itself nor as not a member of itself. This contradiction is a true paradox (i.e., with two impossible and contradictory states) called Russell's paradox.

Symbolically:

The term clade thus denotes the same "thing" (i.e., contradiction) as Russell's paradox, that is, the interface between objectivity and subjectivity, An entity of this kind is thus just a passage between objectivity and subjectivity. The difference between it and an entity is analogous to the difference between a passage through a door and the door. Never can they fuse, and the door is, obviously, a paradox. .    

So, what does this paradox tell us? Existentially that history is inherently contradictory, theoretically that our distinctions can't be found, and practically that theorists can screw matters up all the way to contradiction. What it definitely does not tell us is The Truth. On the contrary.   
 

Cladistics is the practical search for Russell's paradox

The class clade is the subjective aspect of Russell's paradox (link to Wikipedia).

The (subjective) approach called "cladistics" is thus the practical search for Russell's paradox (per definition).

Strangely enough, Wikipedia doesn't accept that this is the proper definition of "cladistics" (link to Wikipedia). Doesn't Wikipedia understand what it explains?

On the third alternative approach to the question of the origin of Life (i.e., evolutionary taxonomy)

Cladistics claim to BE phylogenetics. However, if cladistics (i.e., classification of biodiversity into only clades) would be possible, then evolution would be impossible, and thus also a Tree of Life, and much more the single True Tree of Life cladistics acknowledges. Cladistics is thus contradicted by denying, in turn, evolution, Trees of Life and a single Tree of Life, that is, itself.

Cladistics thus makes phylogenetics appear ridiculous. If its self-contradiction would be the only alternative to creationism, then humanity would be doomed to self-contradiction - either as a self-contradictory belief in a single True Tree of Life (i.e., cladistics) or as a self-contradictory belief in that a God created Life.

Luckily, there is a third alternative - belief in a single origin of Life combined with understanding that this origin can't be described unambiguously, that is, understanding that there is no single True Tree of Life to be found (i.e.,the scientific approach called evolutionary taxonomy). The scientific alternative thus bypasses the contradiction between the self-contradictions of cladistics and creationism by acknowledging Darwin's idea of a single origin of Life combined with understanding that a description of the origin of Life has to be either ambiguous (which it acknowledges) or contradictory (which it does not acknowledge, but which cladistics only acknowledges). The scientific alternative thus distinguishes itself from cladistics by denying cladistics' idea "a single True Tree of Life". It understands that this idea is practically impossible.

Evolutionary taxonomy is thus the preferable approach for people that acknowledge Darwin's idea of a single origin of Life, but which at the same time understand that such origin can't be unambiguously described. They understand that the fundamental obstacle for an unambiguous description of reality is that reality is distinct from descriptions of it. They do not fall into the cladistic trap of confusing reality with descriptions of it.

Evolutionary taxonomy is thus the only approach that combines belief in Darwin's idea with practical possibility. The system it uses for classification is the orthogonal Linnean systematics. It is thus not revolutionary, but inclusive. It includes Darwin's idea in Linnean systematics.

Cladistics is the denial that reality has two aspects, pattern and process

Cladistics is the denial that reality has two aspects, pattern and process, and the corollary claim that not every description of history thus is self-contradictory per definition, but that there instead is a single True description of history to be found, manifested in its idea "a single True tree of Life".

Fact is, however, that reality has two aspects, pattern and process, and thus that cladistics' both denial and claim are plain wrong. Instead, fact is that every description of history is self-contradictory per definition, and thus that cladistics' idea of a non-contradictory "True" description of history is an illusion, a "pie in the sky". It would not help if all historians agreed on this idea, it would still remain an illusion. Facts is not a matter of popularity contest, but of undeniable conditions. Cladistics does thus deny undeniable conditions to instead claim self-contradictory conditions. Much can be said about this proactive "move", but most important is that it is self-contradictory.  

How long can this go on?

Isn't allowing cladists to preach their belief in scientific institutions letting the fox into the hen-house?

It is impossible to find a non-contradictory dichotomous classification, because every dichotomous classification is contradictory.

The approach called cladistics is a belief in the contrary, but it is both internally and externally contradictory, and also falsified by facts.

So, how can science allow cladists to preach their contradictory belief in their institutions? Isn't it letting the fox into the hen-house?  

Cladistics is the ultimate paranoic trap for theorists that begin with the axiom that classes (instead of objects) are real

What cladists don't understand is that their idea "the class clade" is contradictory, due to that the class object and the class class contradicts each other. The reason is that objects participate in one orthogonal system with its two aspects pattern and process, whereas classes participate in another orthogonal system with its classes in classes, and that these two orthogonal systems are orthogonal to each other.Such orthogonal relation between two orthogonal systems is actually a double ambiguity between the two kinds of entities of the two systems, which, in turn, actually is a contradiction (i.e., a paradox). The class object does thus contradict the class class, and vice versa, making up a paradoxical relation.

Such double ambiguity (i.e., paradoxical relation) between classes (i.e., objects and classes) may be comprehended as an unambiguity, following the principle that "two wrongs may be comprehended as one right", but it is a (practical) illusion. The problem is that every possible specific solution of one of them is contradictory with all specific solutions of the other. There is thus no specific solution that is not contradictory between them (i.e., the two orthogonal systems); but the illusionary unambiguity is restricted to a generic level. The relation thus appears unambiguous in a theoretical sense, but is contradictory (i.e., paradoxical) in a practical sense.

Cladistics is thus the ultimate paranoic trap for theorists that begin with the axiom that classes (instead of objects) are real, like many biological systematists do. Sooner or later they are bound to arrive to the class clade, which then has to be real (i.e., unambiguous), although it factually is contradictory (i.e., paradoxical). At this point, these theorists have only two options: to reconsider their approach, or to go all the way (that is, to argue contradictory for a contradiction). I can see examples of one of them (e.g., Malte Ebach), but guess that there are examples of the other too although I don't see them. My aim is not, however, to convert cladists, but to protect young students from cladistics.

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.

Ceci, n'est pas une phylogénie

Inspired by Magritte's example, I would like to present the problem with the class clade in phylogenetic systematics as: 

Ceci, n'est pas une phylogénie.

Compare:

The statements accompanying the illustrations appear contradictory (to some of us), but, try to smoke the pipe...

What the contrast between the illustrations and the statements actually does, is that it reveals a confusion of the abstract with reality that some of us are prone to. This is, perhaps less obvious in the upper example than in the lower, because most of us can understand the difference between a pipe and an illustration of a pipe.

So, what is the difference between a phylogeny and illustrations of this phylogeny? Well, the difference is that a phylogeny is unambiguous, whereas illustrations of this phylogeny are contradictory. This difference means that the phylogeny is indecisive between itself and its contradictory illustrations. We simply can't distinguish between the phylogeny itself and its contradictory illustrations. 

This difference means that we practically have to choose between chasing a non-existing True Illustration of The True Phylogeny or accept The Set of Illustrations that contradictory illustrate The True Phylogeny. The option of finding The True Illustration of The True Phylogeny simlply is not given.

Cladistics "denies" this fact and instead "claims" that it is the other way around, that is, that the phylogeny is a phylogeny, and thus that the pipe is a pipe. This "denial" and "claim" do not, of course, turn the phylogeny into a phylogeny nor the pipe into a pipe, but just claims the confusion the illustrations reveals. It simply boldly denies the difference between the abstract and reality that the illustrations reveal.

Cladistics thus "claims" that the abstract equals reality, and "denies" any difference between them. Unfortunately, this "claim" and "denial" is contradictory, actually the contradiction that is called Russell's paradox, and thus wrong per definition.The claim and denial are actually a conceptual confusion  which cladists "claim" instead of acknowledging that it is a conceptual confusion. Cladistics thus can't be objected to per definition, since the objections are the facts that cladistics "deny". Cladistics is thus an orthogonal circularity (i.e. a paranoia) which can't be objected to, since all objections are denied by cladistics. Cladistics is thus a sect by all definitions of a "sect".     

On the problem with the concepts monophyletic group and clade

The problem with the concept monophyletic group is that it is ambiguous between specifics (i.e., in time) and generics (i.e., over time) - whereof the concept specific monophyletic group is synonymous with what cladists call paraphyletic group, and generic monophyletic group is synonymous with holophyletic group. This conceptual ambiguity means that specific and generic monophyletic groups can't be practically distinguished unambiguously, because an ambiguity can't be distinguished unambiguously.

The problem with the concept clade is that it confuses the concept monophyletic group with holophyletic group, and thus also generic with specific. It means that clades can't be practically distinguished without contradiction, because generic is orthogonal (i.e., diametrically opposed) to specific.

Unambiguous "natural groups" is an impossibility

Biological systematists have been searching for unambiguous so-called "natural groups" since the dawn of Man. Today, scientific discoveries have, however, paved the way for an understanding that unambiguous (i.e., neither ambiguous nor contradictory) such "natural groups" is a both theoretical and practical impossibility.

The fundamental problem is that a logical discussion about finite classes, that is, set theory, ends in contradiction (i.e., Russell's paradox) in the objective perspective, because it means that the opposite, that is, the subjective perspective, also ends in contradiction (concerning which class a particular object belongs to). Russell's paradox simply reveals that the opposite to the concept object, that is, the concept finite class is fundamentally contradictory, a contradiction that can be changed into an ambiguity if we classify classes in categories, but which can never be turned into an unambiguity. A fusion (i.e., equalization) of the concept classification with the concept class is simply contradictory, but the concepts can be consistently, although ambiguously, kept apart using the concept category.

The discovery of Russell's paradox thus revealed that the ancient idea of unambiguous so-called "natural groups" is a both theoretical and practical impossibility. The idea is actually just as impossible as objects are possible (i.e., given). Instead, the closest we can come (i.e., the best we can get) is ambiguous "natural groups" (like in the orthogonal Linnean system of classification). Such "natural groups" can't be unambiguous, but are at least not contradictory.

Cladistics claims “the contrary”

Biological systematics developed from about 350 BC to about 1700 AC in an objective scientific context from Aristotle’s first steps using generics, specifics and specific differences into Linné’s ingenious, orthogonal hierarchical classificatory system.

About 300 years later, the German entomologist Willi Hennig turned this 2000-year scientific development up-side-down and in-side-out into the purely subjective context of the pre-Aristotelian, ancient Greek Parmenides, which has since then (during the last 50 years) developed into the approach called “cladistics”. Cladistics has thus during the last 50 years diverted from an objective scientific context. At the same time as the Linnean system in science has developed into consistent object-oriented programming (OOP) in IT and also provided the foundation for consistent CAD (and thus CAM), cladistics in biological systematics has instead taken the orthogonal route "denying" the Linnean system and instead only "acknowledging" consistent contradiction. Cladistics has thus initiated an orthogonal battle against objective science (hitherto only in biological systematics).

The reason for cladistics' obviously insensible, orthogonal line of reasoning appears to be that cladists considers this route to be simpler (“more parsimonious”, as they express it) than consistent objectivity is, thereby obviously dismissing the consideration of sensibility. Cladists obviously don’t care about whether they contradict both facts and themselves consistently, as long as they are principally simple-minded. Instead, they are actually guided by simplemindedness itself (which they call “being parsimonious”). And, the most parsimonious you can be is, of course, to believe whatever you may believe (and "deny" other beliefs).

It means that cladistics claims “the contrary” (to both other beliefs, objective scientific thinking and itself). It actually claims contradiction itself. It is an eternal merry-go-round of orthogonal conceptual triangulation, wherein everthing is contradicted (because the approach is founded on contradiction). It does neither actually try to find something, but instead tries to get rid of the factual contradiction to it, that is, what it calls “paraphyletic groups”. It actually believes it can make one brain-ghost come true by getting rid of another brain-ghost. And, since it denies facts, nothing can stop it from trying (forever). It can actually run around its eternal merry-go-round driven by its claim of "the contrary" forever, because it is disconnected from sense.

If cladistics isn’t a historical record of misunderstanding and confusion, then Einstein is, and the reverse. One of them has to be. The fact that classification is orthogonal means that it is cladistics that is the historical record of misunderstanding and confusion. It actually believes that there is an objective subjectivity to be found, although a such can only be what one says it is, that is, a subjectivity.

The correct definition of "cladistics", per definition

The correct definition of cladistics is "the confusion of object with class, by confusion of the specific (in the form of holophyletic group) with the generic (in the form of monophyletic group", that is, "the confusion of empirical science (i.e., nominalism) with belief in classes (i.e., realism)". Or, put simpler, "generic subjectivity", or "objective subjectivity". It is the old idea that subjectivity can find a single objective solution by optimizing facts. It is the idea that truth can be revealed by simply optimizing the fit between "observations", in this case, classifications. This belief in a single true classification is so strong that it blinds the believers from the obvious fact that classification is orthogonal, i.e., that it lacks an unambiguous middle, and thus can't be unambiguous per definition, that is, can't be single. The believers fail to understand the fact that there can't be a single true classification to be found per definition, because they so strongly believe that there is a single true classification to be found. Their wish has turned their minds into belief instead of understanding to the degree that they deny an obvious definitional fact (actually contradict themselves definitionally). They choose definitional contradiction instead of definitional consistency to acknowledge their belief that classes are real. They voluntarily dive into contradiction, although it, in itself, proves them wrong, because they are so convinced (i.e., believe) that it can't be wrong (given that classes are real). They thus refuse to arrive to the consistent conclusion that classes are not real (that is, nominalism), because their whole reasoning rests on the axiom that classes are real. They thus refuse to acknowledge that they are simply wrong - totally wrong.       

The confused definition of cladistics you can find in Wikipedia is written by cladists, that is, of persons that confuse object with class. Unfortunately, I haven't been able to correct the definition in Wikipedia, because I have consistently been hindered to do so by cladists. When belief rules, then facts are surpressed.

A single Tree of Life is not to be found

Cladists are simply searching their own comprehensions of reality. The fact that they can't produce a single subjective classification forces them to argue in a generic sense that there is a single true classification to be found. This argumementation is, however, vain. Such thing is simply not to be found. If it had been, then Russell's paradox would have been wrong.

On biological systematics - its eternal rift between subjectivity and objectivity

Biological systematics is traditionally a battle between realists (i.e., subjectivists) and nominalists (i.e., objectivists), the former assuming as an axiom that classes are real, whereas the latter assuming as an axiom that objects are real, undulating back and forth between these entrances to reasoning. Realists created the mess in biological systematics before Linné, and Linné as a nominalist straightened out the mess. However, recently (around the 1950-ies), realists had gained new strength reappearing on the scene by the German entomologist Willi Hennig introducing a new kind of realist approach, called cladistics, which is best described as "consistent subjectivity".

Hennig's idea is basically that a consistent dichotomous confusion of classes will ultimately (i.e., by optimization of the number of included properties) lead to a single consistent classification, which is "True" with regard to the origin of classes (called "The Tree of Life"). The idea does thus not only rest on the axiom that classes are real, but also on the axiom that classes have originated in a dichotomous fashion, that is, opposite to the consistent confusion of them by which their True origin is found.

Much can be said about this idea. The first is that it is able to rotate around any classification, given that it finds the "True" origin of classes by confusion of any particular classification. This method is indeed paranoic, but not necessarily inconsistent, since its consistency is ultimately decided by whether there are several different possible classifications of the True origin of classes to be found or not, and thus ultimately of whether classes are real or not. If classes are real, and if they have originated according to the model, then this paranoic reconstruction of their origin is consistent, because it actually reconstructs their origin. The question whether this paranoic method is rational or not is thus transferred to whether classes are real or not.

This question, i.e., whether classes are real or not, can be answered only if it can be tested empirically. If it can't, then the two entrances to reasoning (i.e., subjectivity and objectivity) are indecisive, in which case cladistics is ultimately correct by the scientific parsimony criterion. The problem is thus to find facts that can decide between the two (orthogonal, i.e., diametrically opposed) approaches empirically. This search has only a single finding, namely the only fact that distinguishes reality from abstraction, that is, that time is relative to space. This fact namely falsifies subjectivity by that subjectivity equalizes space with time, thereby leaving no possibility for time to be relative to space, whereas objectivity leaves the relation between time and space open. This fact thus falsifies subjectivity in favor for objectivity. It thus reveals that subjectivity is inconsistent, and thereby that objectivity is consistent, and thus that cladistics is consistently inconsistent. This fact is thus, no matter how far-fetched it may appear, the decisive fact for the choice between subjectivity and objectivity, It actually falsifies subjectivity in a specific sense, and cladistics in a generic sense, by denying subjectivity's axiom that classes are real. It thus answers the question whether classes are real or not with a NO. Classes are not real.

Subjectivists (i.e., cladists) are thus merely a pain in the ass for biological systematics. Their approach is a paranoic, and this paranoia is falsified by empirical facts. Subjectivity can actually not find neither a specific nor a generic classification that is consistent and unambiguous, because consistent can't be consistently combined with unambiguous, no matter how much we wish it could have.
    

 

On Willi Hennig's fundamental conceptual triangulation from objectivity to subjectivity (called cladistics)

In the middle of the 1950-ies, the German entomologist Willi Hennig performed a conceptual triangulation (in the context of biological systematics) leading from an objective approach to subjective approach, accompanied by a claim that subjectivity can be objective (i.e., that there is a single True Tree of Life to be found). The triangulation slided on a confusion of monophyly with holophyly (later called clade), landing in a rejection of what Hennig called paraphyly, whereof clade terms every possible class of classes, whereas paraphyly terms single classes. Hennig's approach appeared sensible in that it appeared to acknowledge Darwin's "theory on the origin of species", but insensible in that a clade thus joins "entities" that the approach rejects (i.e., paraphyletic entities). The insensibility can be counterattacked by envisioning that paraphyletic entities actually are clades internally, but it does at the same time deny Hennig's rejection of paraphyly. Hennig's triangulation thus ended in an approach that appeared sensible by "acknowledging" Darwin's theory "on the origin of species", but insensible by rejecting itself.       

Hennig's conceptual triangulation was never accepted by any scientific journal, but instead published in a book. From there, it was, however, picked up by Steve Farris and Gareth Nelson, won supporters, and was then enforced on biological systematics by brute force. Protesters against its insensibility were either silenced by all possible means or simply ignored (like me). The insensible conceptual triangulation thus took the power in biological systematics by brute force alone.

The problem with Hennig's triangulation is that the fact that subjectivity can't be objective means that it merely confuses subjectivity with objectivity, which, joined by the claim that subjectivity can be objective, leads into the belief that if there are disagreements between subjectivity and reality (which there always are), then subjectivity can be more true than reality is. It thus leads into the belief that if there are disagreements between the map and reality, then the map is more true than reality is. One can thus be right even if facts contradict one's opinion. This belief can't be questioned, like no belief can, but its claim that it can be consistent and unambiguous can. Fact is that subjectivity can't be objective, which is evidenced by the approach's fundamental problem with paraphyly. This fact means that subjectivity not only can't be objective, but moreover can't be non-contradictory, but, instead, always are contradictory.

It means that Hennig's triangulation leads into consistent contradiction, as evidenced by the contradiction of its paraphyly. Luckily, no scientific journal accepted it.  

On the orthogonal merry-go-round called "Cladistics" - the meaning of its "clade" and "paraphyly"

Cladistics is the fundamental confusion of the generic with the specific, or of class with object, by confusion of the generic concept monophyly with its specific concept holophyly into the confusing concept clade. It means that the concept clade terms both classes and objects at the same time, whereas the opposed concept paraphyly terms neither classes nor objects at the same time. The concept clade thus terms everything, whereas the concept paraphyly terms nothing. In light of this understanding, it is not surprising that cladists strive so hard to get rid of paraphyletic groups - nothing is, of course, nothing, whereas everything is, just as of course, everything. The insoluble problem with this quest is to find everything without finding nothing.

This approach is what one falls into when one bites oneself in one's own tail by confusing class with object. Cladistics has thus given this orthogonal merry-go-round a name - that is, Cladistics. Cladistics is thus in practice "the vain search for a consistent and unambiguous classification of classification". 

Cladistics is The Fundamental Conceptual Circularity

Searching for truth by conceptualization presumes that statements can be true, and they are true if they agree with reality.

Truth must, as such, be split between reality and our comprehension of reality. Of these, the truth in reality (i.e., the objective truth) is hidden in reality as the ambiguity of the objective approach, that is, that we can discuss every real phenomenon in at least two aspects, whereas the truth in our comprehension of reality (i.e., the subjective truth) is hidden in our minds as the contradiction between and within subjective approaches, that is, that subjective approaches are both externally and internally contradictory.

This split of truth is thus merely a property of conceptualization itself, and thereby also a property of the conceptual search for a truth itself. Such search simply leads to a choice between ambiguity (objectivity) and contradiction (subjectivity): truth being relative as an ambiguity in an objective approach and unreachable as a contradiction in a subjective approach.

The preferable choice of these two is ambiguity (i.e., objectivity) by that it agrees with facts in reality (fundamentally the fact that time is relative to space), because contradiction (subjectivity) instead is falsified by facts in reality (fundamentally the same fact). This choice does thus not find or decide the truth, but merely agrees with facts in reality. This is, as far as we know, the closest we can come to the truth. The choice leads to a search for the truth by comparing competing hypotheses about reality with reality, that is, empirical science.

The above reasoning is a concentrated version of the foundation for empirical science. Cladistics is the opposite to empirical science. It agrees about the presumption that only statements can be true (except the cladist Mikael Härlin, as far as I know), but it claims that there is no split between reality and our comprehension of reality. On the contrary, it claims that the truth (i.e., The True Tree of Life) resides in a fusion of the two. It thus claims that there is an objective subjectivity, or subjective objectivity, to be found (at the same time explicitly denying the opposite, that is, the foundation for empirical science).

This cladistic claim is tricky to counter. The first problem is what the claim actually means? Does it claim that reality is the same as our comprehension of reality is, or that reality does not exist, or that our comprehension of reality is prior to reality? However, in practice, these three possibilities melts down into the simple claim of the choice of subjectivity instead of objectivity (that is, subjectivity instead of empirical science). It actually claims that subjectivity HAS TO BE preferred because IT CAN find The Truth (i.e., The True Tree of Life), and thus that subjectivity is not contradictory, DENYING the opposite, that is, the truth itself.

Now, if this claim should be true, then time thus would not be relative to space, which it obviously is.The claim is thus OBVIOUSLY contradictory to facts, that is, falsified by facts, that is, wrong. Truth is thus, instead, that subjectivity is contradictory, in spite of cladistics' claim of the opposite. The claim can't change the fact that the preferable choice is objectivity (which cladistics denies). Objectivity remains the preferable choice although it is denied by cladistics.

Cladistics is simply subjectivity that on a generic level claims that subjectivity on a specific level is correct. It is an orthogonal paranoia that leaves reality as a magic dragon by the claim that it itself is correct independently of what it says and of reality. It is THE bolt (spin-off) of subjectivity when it finds its way back to nothing in conceptualization. Cladists believe they can find the Truth (i.e., The True Tree of Life) by confirmation of their preconceived ideas, although this belief is a definitional contradiction .Cladistics is The Fundamental Conceptual Circularity, and its idea of a Single True Tree of Life is a hallucination in this circularity. The Single True Tree of Life cladists hallucinate is, in practice, their own subjectivity. It is classificatory monoteism, that is, typology.

On the paranoic idea that is called "cladistics"

Cladistics is actually a direct circular confirmation of one's own classification of biological organisms into species, and classification of species into classes of species, by repeating the classification backwards. It ends with whatever one assumes at the beginning.

The cladistic idea that this paranoic procedure can end in a single True Tree of Life is just as impossible as that subjectivity would equal objectivity. If this would have been possible, then there would have been no difference between subjectivity and objectivity, and thus no difference between right and wrong. It would actually have meant that everything is true, like what Kuhn appears to be saying. If this would have been true, then Kuhn and cladistics would have been both right and wrong at the same time. Luckily, both Kuhn and cladistics are ONLY wrong. Their error resides in that they equal difference with similarity, when difference is real whereas similarity is abstract, and thus that ONLY difference is real. Subjectivity thus can't equal objectivity, because subjectivity acknowledges similarity, which is artificial, whereas objectivity acknowledges difference, which is real.

The cladistic axiom that subjectivity can equal objectivity (i.e., that there is a single Tree of Life to be found) is thus ONLY wrong. This idea is actually a direct circular confirmation of one's own classification of biological organisms into species, and classification of species into classes of species, by repeating the classification backwards. The axiom is actually a paranoic (i.e., circular) typological reasoning in tself, and wrong. 

The problem with oversimplifications like Cladistics

The problem with oversimplifications like Cladistics is that they have several equally correct solutions between which they are contradictory, because oversimplification in itself is actually leaving objectivity in preference for subjectivity, and subjectivity is contradictory per definition. Oversimplification is both the act of leaving objectivity in preference for subjectivity and subjectivity itself, like how Fourier transformation is both a transformation and a transform. Independently of objectivity and subjectivity, fact is that there are at least two aspects of every real phenomenon in an objective sense, and that these aspects are contradictory "solutions" of this phenomenon in a subjective sense. Objectivity and subjectivity are merely two orthogonal approaches to reality, objectivity being ambiguous and subjectivity being contradictory.

What Hennig actually does when he confuses object with class is thus that he leaves ambiguous objectivity in preference for contradictory subjectivity. Instead of acknowledging reality's fundamentally ambiguous nature, he claims that reality (i.e., the historical "reality") is unambiguous, thereby instead being contradictory. He thus returns to the same subjectivity that dominated biological systematics before Linné invented his objective (orthogonal) classificatory system, although dressed in new clothes. Its subjectivity is easily recognized by the Golden Rule of Biological systematics: if it looks like a duck, walks like a duck and sounds like a duck, then it is a duck.
 

On the choice between the Linnean system of classification and Cladistic classification in Biological systematics

The difference between the Linnean system of classification (like Evolutionary taxonomy) and Cladistic classification in Biological systematics is actually fairly simple to understand. It resides in that classification as an orthogonal system, i.e., wherein each class consists of two orthogonal classes, has two logically consistent, but orthogonal lines of reasonings starting from either the bottom level (i.e., objects, therefore called Objectivity) or one level up (i.e., classes of objects, therefore called Subjectivity). Objectivity is ambiguous with respect to the classified (i.e., objects) and ends in a paradox (in this case called Russell’s paradox), whereas Subjectivity is consistently contradictory (i.e., with respect to both objects, classes and facts, and between assumption and deduction) and likewise ends in a paradox (here called the class clade). The two end points for the two lines of reasoning are actually one and the same point, namely the opposite to their orthogonal starting point, arriving to it from their respective orthogonal line of reasoning.

The problem for us to understand this difference is due to that an orthogonal system also is orthogonally 2-dimensional, that is, an orthogonal series (or orthogonal stack) of 2-dimensional planes, which is infinite. Such orthogonally nested dimensional structure can be simplified into a single 2-dimensional system in two different ways, which are consistent with each of the two orthogonal lines of reasoning respectively: orthogonally as in the Linnean system, which is consistent with Objectivity, and "flat" as in Cladistic classification, which is consistent with Subjectivity.

It means that the choice between the Linnean system of classification and Cladistic classification actually is a choice between being ambiguous with respect to objects (i.e., the Linnean system of classification) or being contradictory with respect to both objects, classes and facts, and between assumption and deduction (i.e., Cladistic classification). In this light, the choice between the Linnean system of classification and Cladistic classification appears fairly given.

Cladistic classification is different from a simple "flat" classification only in applying a consistently contradictory classification of classes. Its reference for this kind of classification to be "natural" is nothing but an appeal to the subjectivity in us all. Unfortunately, subjectivity in this version only leads to the Wonderland (i.e., where everything is up-side-down). Also unfortunately, cladists can’t understand this fact because they presume that classes are real.

I'm home on Google - discussing cladistics as a special case of fanatism

Now, I'm home at Google blogspot. Google really understands the problems in painting reality. It understands that reality can't be painted unambiguously in present, and thus much less so in past. It would never even consider falling into the double ambiguity, that is, contradiction, cladistics has fallen into. It may fail to realize that this contradiction actually is Russell's paradox seen from the subjective side, but it would definitely not fall into it.

So, in this blog I plan to develop my, which I think is extremely interesting, dissection of cladistics. For me, cladistics was a shock when I first encountered it - a totally stupid (i.e., simple-minded erroneous) simplification which for me appeared more like a joke than a serious approach - but I have gradually attained understanding of the underlying approach (i.e., realism) and the motives in this approach for this totally stupid (i.e., simpleminded erroneous) simplification. When I first questioned the consistency of the approach among cladists, I was surprised by that my points didn't seem to penetrate into their minds. It was just as if they couldn't see them just because they didn't want to see them. They refused to acknowledge them even when I put them in front of their eyes excluding all alternatives. They obviously had a blind spot for their inconsistencies in their belief. They couldn't even see how their own assumptions consistently contradict the conclusions they derive from them. They obviously had no sense what-so-ever for overall consistency (i.e., that everything have to fit together).

I realized that this issue in a larger perspective is a discusion about fanatism. Cladists are neither interested in finding out how reality works in a generic sense nor of how we can reconstruct history, but just of how history is best reconstructed in their perspective. They have lost (or have never had?) openness for different generic approaches in describing reality, but instead claim that they have The Correct Approach (denying all others). And, they simply presume that there is a Single True Approach in describing reality and it is, of course, their approach. And, their approach is that there is A Single True Description of the history of biological organisms to be found, although there are loads of both considerations and facts that contradict this approach, because, in their own terminology, it is "the most parsimonious" approach. They thus prefer an inconsistent and erroneous approach because it is "the most parsimonious", in practice meaning pure subjectivity. They thus seriously claim that pure subjectivity should be preferred because it is "the most parsimonious" approach. It indeed, is, but is this really a sensible reason to prefer contradiction? Or to start chasing the rainbow? Doesn't it matter that the approach is both consistently inconsistent and empirically erroneous?

The fanatism of the cladistic approach resides in that it is only open specifically, that is, within the boundaries of the approach (thus, pure subjectivity). It explicitly denies all other approaches (among them, specifically the scientific approach "objectivity"). It thus denies the fact that there are several ways to look at one and the same thing. This is the hall mark of fanatism. The problem for those outside of a fanatism is how they shall handle fanatics (like cladists). Amos Oz recently discussed this issue. Unfortunately, neither he nor anyone else has found a solution to this problem. Their consistent refusal to acknowledge anything else than one own's subjective opinion, or in the case of cladistics, subjectivity in general, is difficult to handle. Such conviction does not yield to anything, because for the convinced, there simply are no alternatives.                      

On the relativity of evolutionary entities

Hennig's dichotomous distinction of properties into apo- and plesiomorphies is inconsistent. Properties simply can''t be consistently partitioned into these two classes, because if they could, then they would not be ambiguous between these classes, which they are. This ambiguity actually shows that the classes are inconsistent, thus telling us that there is no non-contradictory solution to be found. A chase for a consistent solution is thus vain. Never can it be found.

The truth is instead that classes are relative by being orthogonal. It means that classes simply can't be arranged consistently and unambiguously, but only either consistently contradictory (in a non-orthogonal system like cladistics) or consistently and ambiguously (in an orthogonal system like the Linnean systematics).

It means that evolutionary entities (including biological species if they are evolutionary entities) have to be ambiguous to the extent that they can be said to exist, because they are both intermediate and overlapping the single objects over time. This property, i.e., being both intermediate and overlapping at the same time, is actually the definition of relativity.   

Conceptualization and cladistics

Our discussion about reality is limited by what conceptualization can accomplish. A fundamental limitation is that conceptualization can't be both consistent and unambiguous with regard to both class (concepts, or kinds) and quantity at the same time, but that consistency in class is ambiguus between different consistencies and makes quantity contradictory between infinite and finite, whereas consistency in quantity (i.e., in finite and infinite) is ambiguous with regard to class (i.e., there are several different, consistent solutions). The reason for this limitation is that the relation between class and quantity is orthogonal (i.e., diametrically opposed).

This fact does not impress on cladists, since they comprehend the situation as that every dichotomously branching process instead can (self-evidently) be partitioned into clades. The problem with this comprehension does, however, reside in that it comprehends a dichotomously branching process as a class (a concept, or a kind), because this comprehension is doubly ambiguous - both in time and over time - thus being contradictory between the concept and the conceptualized. It means that although every dichotomously branching process can be partitioned into clades, not any dichotomously branching process can be consistently and unambiguously partitioned into clades, that is, no dichotomously branching process can be non-contradictory partitioned into clades.

The question for cladists is whether this means that True Clades can be found or not. The answer is no. Such "things" cannot be found. They are actually nothing but brain-ghosts. The problem with them is that history is not frozen, but continues in this day. And, history is not superior to present, but present is instead superior to history. The only thing we know for sure is that single objects exist now. Everything else are either ambiguous or contradictory brain-ghosts. The idea of "True Clades" is a contradictory brain-ghost. This kind of thing simply can't be found consistently and unambiguously, because classes that extends over time can't be found consistently and unambiguously.

On the history of biological systematics

Biological systematics started off with the ancient Greek Parmenides claiming that reality is frozen. All change we percieve only occur in our own minds. Classes are thus nailed once and for all. All single objects are born into their respective class without possibility to escape it. An elephant is an elephant and a printer is a printer from the beginning and forever. This approach is called "realism".

Biological systematics continued with Heracleitos claiming that it is the other way around, that is, that reality is continously changing. That a single entity just appears to be the same over time like the flame on a candle appears to be the same, although it is continously changing. This approach is called "nominalism".

Aristotle united these two orthogonal (i.e., diametrically opposed) approaches into a system of specifics, generics and specific differences. The system united the contradiction of realism with the relativism of nominalism into a conceptual tool that can be used consistently to discuss reality. He thus invented the notion of a genus with its species. The problem that remained was how to combine genera consistently into something else.

This problem was solved by Linné by his orthogonal classificatory system uniting classes hierarchically by intervening categories (like species, genera, families, classes, etcetera).

When Linné had solved this problem, it took about 300 years until a biological systematist (i.e., the German entomologist Willi Hennig) found the way back through these conceptual developments again raising Parmenides´claim that reality is frozen and thus that classes are nailed once and for all. Hennig thus confused everything to the degree that it is difficult to get out of the confusion. The question is what the question is for Hennig's answer. Clear is, however, that Hennig's answer is wrong, independently of what the question is, because it is contradictory, just as contradictory as it was about 2,500 years ago.

Biological systematics thus appears to rotate in an eternal orthogonal carousel searching for a reality that fits its classification. Biological systematists do not appear to be interested in understanding of reality, but just in an unambiguous classification of it that can't be reached. The question is if biological systematics will ever acknowledge the fact that it can't be unambiguous (per definition).