Cladistics and Linnean systematics are merely the two possible classificatory solutions to "the problem of universals"

The "problem of universals" is an ancient problem in metaphysics about whether universals exist or not. This problem has two contradictory (orthogonal) solutions: Aristotelian essentialism and Plato's theory of forms, the former assuming that they do and the latter that they don't (at least not in the same reality as reality). Cladistics is consistent with the former and Linnean systematics is consistent with the latter, and they are mutually contradictory (ie, orthogonal). However, since classification of reality (for example into either clades or into genera, families, orders, etcetera) does not influence reality itself, Cladistics and Linnean systematics are merely the two possible (orthogonal) classificatory solutions to the problem of universals, Aristotelian essentialism and Plato's theory of forms, respectively.

This fact is, however, hidden behind the mutual contradiction between these two possible classificatory solutions by that it turns the difference between them into an existential problem for cladists and into an erroneous existential claim of cladistics to Linnean systematists. The mutual contradiction between them thus tilts the fact that they are merely the two possible (orthogonal) classificatory solutions to "the problem of universals" into a problem of cladistics' existential claim (ie, that universals exist). This claim was thus, as I have explained in recent posts on this blog, shown to be inconsistent by Betrand Russell in 1901 by what later became known as Russell's paradox (for those that hadn't understood this fact before, unlike Plato and many others).

It means that a biological systematist has to decide whether he/she believes that universals are real or not, ie, choose side between Aristotelian essentialism on the one hand and Plato's theory of forms/nominalism on the other, because the former leads to cladistic classification and the latter to Linnean systematics. However, if he/she chooses the former (ie, cladistic classification), then he/she has to be aware that it is inconsistent, ie, lacking consistent solution. None of them can thus reach the idea that cladistics calls "The Tree of Life".

Succumbing to cladistics is actually succumbing to a search for an illusion

The assumption that dichotomously branching processes can be consistently classified into only clades (ie, the axiom of cladistics), is also an assumption that all such processes (ie, dichotomously branching processes) of all involved kinds of entities are congruent. If this assumption is sensible, then reality is insensible, since it means that present does not exist, and that process is impossible.

This inconsistency of the cladistic axiom may be difficult to understand, but the meaning of it isn't. It simply means that the cladistic classification, ie, into only clades, is inconsistent, ie, lacking a consistent solution.

It is thus possible to assume that dichotomously branching processes can be consistently classified into only clades, but it is not possible to make dichotomously branching processes consistently classifiable into only clades. It is possible to wish they were, but it is not possible to make them be. Wish is wish, and reality is reality.

Succumbing to cladistics is thus actually succumbing to a search for an illusion.

On the impossibility of cladistics (and other such "natural" classifications)

The problem with the approach in biological systematics called "cladistics", ie, classifying bifurcating processes into so-called "clades" and "paraphyletic groups", is that this classification is inconsistent (actually paradoxically contradictory, see Russell's paradox), because this inconsistency means that the classification in practice is an infinite recursion, that is, a self-contradiction.

Such classification (ie, cladification) can thus search for a consistent solution forever without finding one, since there simply is none to be found. The fundamental error with the classification is that it confuses the concepts category (ie, finite class) and entity in an erroneous belief (thus actually axiom) that categories are consistent entities. This confusion is an occupational injury among people that deal too much with categorization (like biological systematists specifically and scientists generically), and is, unfortunately, shared with more simple-minded people just over-simplifying matters.

Those of us that don't confuse these concepts thus has an obligation to emphasize the difference between them, ie, that a single entity is not a category and that a category is not a single entity, because they simply can't be (see Russell's paradox), to help the confused out of this devastating confusion and hinder non-confused from falling into it. Category and entity are actually orthogonal concepts, ie, diametrically opposed, whereof category belongs to our minds, and entity belongs to reality. Never will nor can these two concepts thus meet. The difference between them is and will always be a pain in the ass for all extremist categorizers, but it will remain forever.  

The battle against cladistics is a matter of discarding belief in favor for skepticism

Cladistics only accepts a kind of group (ie, clades), which also includes the members of the group as groups. It thus only accepts groups that are also members of themselves. Such groups are thus not only groups, but also includes themselves as members of themselves. These groups are thus entities that include the groups themselves as entities.

If cladistics is not a paranoic circularity, then the question is what a paranoic circularity is. If cladists actually believe that they can partition reality into only such groups, then their mental statuses ought to be assessed. The question is thus whether cladists are in need of an assessment of their mental statuses or if they simply are confusing concepts for profit. Both of these are just as serious, since its paranoic approach is typological and thus supporting racism. If such groups actually would have been consistent, then racism would also have made sense, but since they aren't, it doesn't.

Cladistics is thus a reappearance of the same old oversimplified racism that dominated the beginning of the 20-ieth century. One would have hoped that it had stayed away longer, but the core of it was effectively transfered by the German entomologist Willi Hennig in the form of cladistics, and does today appear to have taken the power in biological systematics again, although it is clearly paranoic and thus not making sense. Making sense is thus, obviously, not a necessary prerequisite for an approach to be accepted, but instead belief, obviously, overrides making sense.

If we do not find a way to discard cladistics, then we're heading towards the same development as that in the beginning of the last century. And, if the description of cladistics above can't do this trick, then the question is what can. If the approach is immune to both being understood as paranoic and being falsified by facts, then nothing can stop it. Then, racism itself (ie, subjectivity) is bound to return over and over again, polarizing people and thus eradicating objectivity. Then, the question is: are you with us or with them, without any option to be objective in between.

The battle against cladistics is thus a battle for objectivity against subjectivity, and thus a battle against all subjective notions, such as racism. It is a battle for an objective approach between all opposite subjective approaches. It is a battle for gray between black and white, It is a battle for objective understanding between subjective notions. It is a battle for sensibility between beliefs. It is a battle for human rights between mine and your rights. It is a battle for the right to remain neutral between opposite subjective opinions (and skeptical to both of them). It is a battle for the freedom of both thoughts and talk. It is a battle for the freedom to explain that cladistics is both insensible and falsified by facts. It is a battle for the fact that the racism of cladistics is not supported by science, but instead by a belief in science, when science actually is not a matter of belief, but, on the contrary, of discarding belief.

The battle against cladistics is thus a matter of discarding belief in favor for skepticism (when cladistics instead is a battle of discarding skepticism in favor for belief).             

 
    

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 biological systematics and "True Trees of Life"

The "new" (actually pre-scientific) approach in biological systematics that is called "cladistics" rests on the idea, actually belief, that "there is a single True Tree of Life" (which thus is possible for us to find).

This belief may appear sensible in the light of Darwin's theory "on the origin of species", but is actually an illusion emerging from a combination of Darwin's theory and a generally typological approach. The illusion is, however, not easy to disclose.

The problem with the belief resides in that such "True Tree" in practice is a trace backwards in time from the situation today, and that the situation today in practice can be classified in several different, but just as "true" ways, because it means that there are several True Trees of Life per definition. The fact that the situation today thus in practice is ambiguous, moreover means that the possible "True Trees" in practice are contradictory. (The idea (ie, belief) that there should be a single unambiguous classification of the situation today is falsified by the fact that classification is inherently orthogonal and thus ultimately paradoxically contradictory, also shown by Russell's paradox).

The problem with the cladistic belief is thus not that there isn't a single True Tree of Life, but that there are several contradictory True Trees of Life. The problem with this fact for the belief is that the fact that these True Trees of Life are contradictory means that they can't be consistently summarized in a single True Tree of Life, but can instead only be consistently assembled in an orthogonal system of classification, like the Linnean systematics (and thus also evolutionary taxonomy).

It means that the founding idea (ie, belief) for cladistics, ie, that "there is a single True Tree of Life" (which thus is possible for us to find), is wrong. Fact is that there is no such thing to be found. Instead, there are several contradictory True Trees of Life which can only be consistently (coherently) assembled using an orthogonal system of classification, like the Linnean systematics (and thus also evolutionary taxonomy). Cladistics is thus an erroneous belief in a single True Tree of Life, whereas Linnean systematics is a consistent (coherent) assembly of the True Trees of Life.

The error in cladistic reasoning

If we observe a dichotomously branching process, like an asexual propagation of cells, then we can classify this process in two different ways: (1) using an orthogonal system of classes as in the Linnean system, or (2) using a single class as in cladistics.

The difference between these kinds of classification is that an orthogonal system is internally consistent by avoiding the paradox of classification (ie, Russell's paradox), whereas a "single class" classification is inconsistent by encountering the paradox of classification (ie, Russell's paradox). It means that an orthogonal system is consistently consistent (ie, all possible classifications are consistent), whereas a single class classification is consistently inconsistent (ie, all possible classifications are inconsistent).

The cladistic idea (actually belief) that there is a single consistent "single class" classification to be found, which it calls "The True Tree of Life", is thus erroneous. A "single class" classification can in fact never reach consistency, because it requires that the class entity is inconsistent, which, in turn, would turn it inconsistent. Consistent inconsistency thus can't break even.

The error in cladistic reasoning resides in that it implicitly assumes as an axiom that the entities that are to be classified IS a class (for example cells) instead of IS CLASSIFIED as a class (for example cells). It thus rests on the erroneous axiom that classes are real, instead of being created by us. And, not unexpectedly, it leads to the erroneous conclusion that there is a single consistent "single class" classification to be found (which it calls "The True Tree of Life"). This hypothesized classification is thus actually a paradox that is inherent in classification (called Russell's paradox). This paradox can also be called "the impossibility of objective subjectivity". It tells us that subjectivity (ie, inconsistency) can never reach objectivity (ie, consistency), contrary to what cladistics claims, but does in this position instead encounter a paradox that we call Russell's paradox. Russell's paradox is thus actually the interface between subjectivity and objectivity - the impossibility of objective subjectivity.

This fact appears counter-intuitive to many of us, but it is just because we can't disclose subjectivity within subjectivity, since subjectivity "sees through" subjectivity. The fact thus appears more counter-intuitive the more subjective we are but less so the more objective we are. Our intuition thus depends on our preference for subjectivity (thinking in types) and objectivity (thinking in entities), respectively.   

No, no, reality isn't both continuous and particular at the same time (as cladistics wrongly has got it)

Cladistics has obviously understood that reality is both continuous and particular in our conceptualization of it, but wrongly thinks that it is both at the same time (ie, conflates class with entity). Turned this way, conceptualization is actually paradoxically contradictory, ie, in practice infinitely recursive, which also Russell's paradox shows.

No, continuity and particularity has to be comprehended as two aspects of reality (arising with our conceptualization of reality), whereof continuity logically is situated either between or extending over particularity, but definitely not simultaneous, since it is paradoxically contradictory (ie, in practice infinitely recursive). Moreover, if reality indeed should have been infinitely recursive, as cladists obviously think it is, then change, like the process of dichotomous propagation that cladists "only acknowledge", should actually have been impossible. Cladistics is thus not only a fundamental misunderstanding, but also fundamentally self-contradictory.  

Verkligheten är inte både kontinuerlig och partikulär samtidigt (vilket kladistiken felaktigt tror)

Verkligheten är kontinuerlig. Denna kontinuitet bryts dock när vi människor börjar prata om den, dvs begreppsbildar den, egentligen redan när vi tar emot den med våra sinnen, genom att vi då lägger till en artificiell skillnad mellan oss och det vi tar emot, vilken sönderdelar den kontinuerliga verkligheten i bitar (partikulariserar den). Den innebär att vi uppfattar verkligheten såsom varande både kontinuerlig och partikulär samtidigt.

Denna samtidiga kontinuitet och partikularitet handlar dock om två olika aspekter av vår uppfattning av verkligheten, inte om olika egenskaper hos verkligheten (vilket kladistiken felaktigt tror). Istället är den senare uppfattningen faktiskt paradoxalt motsägelsefull, vilket också Russells paradox visar. (Dvs, om vi missförstår verkligheten såsom varande både kontinuerlig och partikulär samtidigt, så är vi paradoxalt motsägelsefulla.

Verkligheten är således inte både kontinuerlig och partikulär samtidigt, utan verkar endast vara det för oss därför att vi har lagt till en artificiell skillnad mellan oss och det vi tar emot. Förståelse av detta faktum är grundläggande för behållande av fokus i vår diskussion om verkligheten på den verklighet vi tar emot istället för ett förlorande bland de ord vi använder för att diskutera den (vilket kladistiken alltså har råkat ut för). Ett sådant förlorande bland orden är dessvärre vanligt hos dem som betraktar sig som intellektuella. Det kan till och med betraktas som karaktäristiskt för dem.

Det är alltså detta förlorande bland orden som har fått många biologiska systematiker att tro att de kan hitta ett enda sant Livets Träd, och även fått många fysiker att tro att de kan hitta det de kallar Higgs partikel. De tror helt enkelt att deras uppfattning av verkligheten ÄR verkligheten. Det krävs alltså en viss intelligens för att kunna passera detta nålsöga från en konsekvent uppfattning av det vi kallar verkligheten till en paradoxalt motsägelsefull uppfattning av den. Det krävs en viss intelligens för att kunna passera nålsögat från vett till ovett.  

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? 

On discussions about process, and the excluded middle

When we discuss processes in general terms, we encounter a problem that originates from the division of process into entities consisting of "beginnings" and "ends". The problem is that this division means that there also must be middles between the beginnings and the ends although the division does not include such middles, because this discrepancy means that the middles are paradoxically contradictory between beginnings and ends per definition (ie, the class middle is paradoxically contradictory between the class beginning and the class end) - if one such middle is a beginning, then it both precedes and succeeds an end (at the same time) per definition, whereas if it is an end, then it both precedes and succeeds a beginning (at the same time) per definition, which is paradoxically contradictory.

This problem is tricky to interpret. The fundametal question is whether it is a property of reality or just a consequence of our conceptualization of reality (ie, of abstracting reality). The answer to this question is extremely far-fetched, but can be found if we first consider that the question implies (1) that there is a clearcut difference between the two (ie, between reality and our conceptualization of reality), and (2) that we can conceptualize this difference. It means that the answer must be a conceptualization that bridges reality and our conceptualization of reality, which we, maybe surprisingly, already have, since we traditionally call the former "reality" and the latter "the abstract". The answer to the question is thus, maybe sursprisingly, that the problem IS our division of reality and our conceptualization of reality into "reality" and "the abstract" itself. The paradoxical contradiction in middles between beginnings and ends is thus a consequence of our own division "reality" and "the abstract" itself, ie, our division "reality" and "the abstract" itself makes middles paradoxically contradictory between beginnings and ends.

It means that the problem neither is a property of reality nor a consequence of our conceptualization of reality, but instead a consequence of our division "reality" and "our conceptualization of reality" itself, that is, a consequence of the division itself rather than a property of reality or a consequence of our conceptualization of reality. The problem simply emerges with our division "reality" and "the abstract" itself when we conceptualize reality. It resides in the difference between reality and our concepts itself. It is actually the relation between reality and our conceptualization of it itself.

This is the reason why it has been called "the excluded middle". If we accept this class (ie, middles), as cladistics does, then we instead exclude the difference between reality and the abstract, and thus also between beginnings and ends. We then thus exclude the division of process into entities consisting of "beginnings" and "ends" that we started with. This contradiction can we, as humans, live with, but not make sense of. Instead, the contradiction is impossible to formulate consistently. It may appear very "natural" to some of us, but can't be formulated consistently, because it is inconsistent. It is thus something we have to adapt to (eg, with an orthogonal system of classification of the Linnean kind), instead of something we can solve. It is actually a corollary of conceptualization itself.

Accepting this class of middles (ie, cladistcs) thus leads into paradoxical contradiction, and paradoxical contradiction is infinite recursion when searching it. Cladistics is thus infinite recursion.

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.   

Kladistik är intressant i många avseenden

Den nya inriktningen i biologisk systematik som kallas "kladistik" (kladism) är verkligen intressant i många avseenden.

Den är egentligen en direkt cirkularitet vari man "rekonstruerar" en klassificering som man också börjar med. En sådan "rekonstruktion" leder alltså inte till någon överraskning, utan är endast den klassificering som ens egen initiala klassificering leder till när man minimerar dess interna motsägelser. Den optimerar alltså ens egen klassificering genom att minimera dess motsägelser.

Kladismens grundläggande idé är att det finns en enda klassificering som är sann, vilken kladistiken kallar Livets Träd, och tanken är att optimeringen av klassificeringen ultimat ska nå denna sanna klassificering. Argumentet är att "något Livets träd måste ju vara sant" och då spelar det ingen roll att vägen till det är en direkt cirkularitet.

Den kritiska frågan för kladismen är således om "något Livets träd" måste vara sant. För att besvara denna fråga måste man bena ut vad kladisterna menar med "Livets träd". För ett kritiskt sinne tycks det inte vara något annat än en klassificering. Kladismen börjar ju med klasser och klassificerar sedan dessa klasser. Att kladisterna själva anser att de initiala klasserna representerar "arter" spelar mindre roll, eftersom det för det första saknar betydelse och för det andra leder in i en annan komplicerad fråga om vad kladisterna menar med sådana "arter". Det viktiga är att vad kladismen egentligen gör är att klassificera klasser. Så, den kritiska frågan är om någon klassificering måste vara sann, dvs, om det finns en enda klassificering som är sann (i ljuset av evolutionsteorin förstås).

Problemet för kladismen är att Bertrand Russell visade 1901, alltså långt innan kladismens födelse, (med Russell's paradox) att klassificering ultimat är paradoxalt självmotsägande. Det innebär att en optimering såsom den kladistiska är förutbestämd att hamna i en paradoxal självmotsägelse. Detta motsäger alltså kladismens grundläggande idé att det finns en enda klassificering som är sann. Istället är klassificering tydligen inneboende inkonsekvent. Det innebär att inte "något Livets träd" måste vara sant, utan att själva idén "Livets träd" är paradoxalt självmotsägande. Den kritiska frågan för kladismen om huruvida "något Livets träd" måste vara sant har alltså svaret att nej, det måste det inte, dvs, att inget Livets träd måste vara sant.

Detta faktum är totalt obegripligt för kladister, eftersom de således utgår ifrån ett felaktigt grundantagande (axiom) och de inte kan begripa hur detta kan vara fel. Felet ligger (dock tydligen) i att kladisterna (likt Platon) antar att klasser är reella, dvs verkligen finns, eftersom klasser således är ultimat paradoxalt självmotsägande (vilket Bertrand Russell visade). Den konsekventa inriktningen är således tydligen att de objekt Platon föraktade såsom illusioner istället är reella, dvs verkliga  (vilket också Wilhelm af Occam hävdade). Platons tredelade uppdelning av verkligheten och vår uppfattning av den (ie, idévärlden) är konsekvent, men hans antagande att verkligheten ligger i "den perfekta" idévärlden är tydligen fel, vilket Russell's paradox visade genom att visa att idévärlden är paradoxalt självmotsägande. Detta faktum hade således varit totalt obegripligt också för Platon.

Vad detta faktum visar är att kontinuerlig förändring (och imperfektion) är vad vi har att förhålla oss till. I denna kontext finns det inget enda sant "Livets träd". Istället finns det flera lika sanna "Livets träd", dvs begreppet är relativt. Det beror på vad vi tittar på.

Det mest intressanta med kladistik är alltså att den har spetsat till motsättningen mellan realister (de som antar att klasser är reella) och nominalister (de som antar att objekt är reella), och därmed tvingat oss till en sammanfattning av var forskningen står idag, och där vinner nominalister över realister. (Realism i denna kontext ska inte sammanblandas med pragmatism. Den handlar enbart om att anta att klasser är reella).

Kanske visar kladistiken att realismen är förutbestämd att hamna i sin egen fälla, dvs Russells paradox. Väl där, måste den ju försöka "rädda skenet" genom att hålla fast vid den till det bittra slutet. Kanske kan allmänhetens bristande förmåga att förstå rädda den genom rått maktutövande, dvs utesluta och ignorera sanningssägare som mig. Förr eller senare måste dock en sak som nu kan skönjas framträda i all sin prakt. Då, om inte förr, kommer konsekvenserna av Russells paradox att styra skeendet.

Fundamental facts about classification and systematics (and cladistics)

Bertrand Russell showed 1901 that classification is paradoxically contradictory, ie, internally inconsistent, see Russell's paradox. This inconsistency is immediately due to that classes contain two kinds of classes: finite classes (ie, objects and categories) and infinite classes (ie, abstract types). The reason is that each finite class must correspond to an infinite class (ie, that each real class must correspond to an abstract class), that is, that there must be a one-to-one correspondance between finite classes and infinite classes, because it means that the total number of classes must be even, which, in turn, is impossible, since the relation between finite classes and infinite classes is orthogonal (ie, diametrically opposed), and that their numbers thus differs with one, because it means that their total number always is odd. It is thus impossible to obtain a one-to-one correspondance between finite classes and infinite classes in classification. The situation is like putting a puzzle where the last piece always is redundant.

However, using an orthogonal system of classification (ie, classifying objects into finite classes of infinite classes), like the Linnean system, transfers this internal inconsistency into a an ambiguity between classification and the classified. It means that such system, on the contrary, can't be inconsistent, ie, that every possible such system is consistent. The reason is that the numbers of finite classes and infinite classes in such system differs with one, because it makes their total number odd per definition, which neutralizes the paradoxical contradiction (ie, internal orthogonality) in classification.

These two kinds of classifications are the only kinds of classification there are. It means that the cladistic idea "a single true tree of life" is inconsistent per definition, since it requires that classification is consistent. If we, like cladists, don't acknowledge the fact that classification is inconsistent, but instead erroneously claim that classification can be consistent, then we actually just transfer the inconsistency of classification into our own heads (into our logical reasoning), thereby turning us, ourselves, inconsistent, (if we weren't before) like cladists are.

This internal inconsistency of classification can we not get rid of, but can only transfer into other positions, ie, to between classification and the classified or to our own heads, because it is fundamentally due to, or is the reason for, the ever-changing nature of reality. At this fundamental level it is impossible to distinguish cause from effect. (This, in turn, may be due to that cause and effect are orthogonal, and that a beginning actually is lacking. If so, change just follows the tracks it is bound to follow, but according to certain principles. Principles rule, but they continuously conflict, and the result is a compromise. A beginning is in any case impossible to invoke without transferring the inconsistency of classification into our own heads, ie, to our logical reasoning).

Conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory

Conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory. It is ambiguous in relation to the classified if it rests on the axiom that objects are real (ie, objectivity), and it is internally paradoxically contradictory if it rests on the axiom that concepts (classes) are real (ie, subjectivity).

It means that we can't say something that isn't ambiguous or paradoxically contradictory, ie, unambiguous, at all. The question whether there is a single truth to be found or not does thus have the answer no, simply because it is impossible using the only tool we have.

The reason for this answer is, however, not the tool itself, but that unambiguity is an impossibility (ie, a void) in a changing world. There's nothing wrong with conceptualization (classification) itself; it just can't create the single truth we want. It is still a very useful tool if we use it consistently, that is, resting on the axiom that objects, not classes, are real. Using it resting on the axiom that concepts (classes) are real, like cladistics, is actually a misuse of it. Science is, as also cladistics indeed claim, a practice to optimize the fit between our models of reality and reality itself, but we have to remember that optimization always is second to reality itself, on the contrary to what cladistics claim. There is no reason to assume that reality itself is optimized. Instead, optimization must always be a matter of optimizing the fit between our models and the facts of reality, as traditional science does, not optimizing the models themselves, as cladistics does.

We must, however, abandon our paradoxically contradictory idea that there is a single truth, like The Tree of Life, to be found, and instead acknowledge the fact that there isn't. Understanding is superior to belief in painting reality, because it does in any case close up on the most accurate painting of reality. Painting reality is moreover not only a matter of black and white, but of Plato's three-folded division in his geometrical (or mathematical) atomism, wherein perfection is ultimately reduced to geometry (ie, to the world of ideas), which we today know is paradoxically contradictory (ie, Russell's paradox). However, this world is thus not a perfect reality of forms, as Plato claimed and cladists claim, since it is paradoxically contradictory, but instead a paradoxically contradictory mind construction which ultimately depends on the real, but changing, objects.

Conceptualization (classification) is thus a tool that can help us understand reality, but it can't produce a single truth. The belief that it can, ie, cladism, is indeed visionary, but wrong. It does thus not lead to a single truth, but only to a conceptual mess. If we want to keep thoughts clear, we have to abandon vision and accept facts, for example that conceptualization (classification) is a tool that can only be ambiguous or paradoxically contradictory. It is perhaps sad, but a fact. 

Cladistics is both contradictory and falsified by facts

The ancient Greeks quarreled about two orthogonal approaches to discussing reality, Heracleitus' and Parmanides' approaches, until Plato solved the contradictions both between and within them with his geometrical (or mathematical) atomism. This approach provided the foundation for the theories of modern physics, Linnean systematics and Object-Oriented Programming.

Recently, about 50 years ago, the German entomologist Willi Hennig challenged Plato's geometrical atomism by simply conflating Plato's "world of ides" with his "forms", claiming that they are equal. Hennig's claim transferred the approach in biological systematics from Plato's geometrical atomism back into Parmenides' approach, thereby denying the existence of change.

Now, if Hennig indeed is right, and if Plato's "world of ides" thus equals his "forms", then infinity equals finity and time is not relative to space. Then contradictions are thus real and facts are fiction. This kind of being right can actually not be falsified by anything, but is, instead, hard-core belief. It will search the treasure at the foot of the rainbow forever, independently of its goallessness.

Cladistics is the search for your own classification

The approach in biological systematics called "cladistics" is the search for your own classification, and since classification is paradoxically contradictory (see Russell's paradox), it is infinite (ie, an infinite recursion) per definition. Every specific solution contains paradoxical contradictions (ie, single entities that possess mutually exclusive properties) per definition.

Don't let cladists fool you into this eternal merry-go-round. 

On the war between nominalism (ie, Linnean systematists) and realism (ie, cladists) in biological systematics

Biological systematics is a battlefield for the eternal war between the two fundamental orthogonal approaches in conceptualization: (1) "objectivity" (ie, "nominalism") and (2) "subjectivity" (ie, "realism"), that is, between assuming as an axiom (1) that objects and (2) subjects (ie, classes) are real, respectively. The difference between them resides in that the former (1) understands that an unambiguous classification is an imposibility (by Russell's paradox), whereas the latter (2) not understands that an unambiguous classification is an impossibility (by not understanding Russell's paradox). Understanding of why an unambiguous classification is an impossibility is, however, extremely complicated, but at the most fundamental level, the reason is that reality is in a constant process of change and thus is impossible to nail.

In this war in biological systematics between objectivity and subjectivity, the approach called "cladistics" is an elevator (or bridge) from objectivity to subjectivity. It functions by first conflating object (ie, organisms) with class (ie, biological species), and then by treating groups of such classes as real entities (ie, objects), called "clades", although classes can't be objects, since they are orthogonal to them, and that classes thus can't be real entities (ie, objects). It thus creates an impression that classes indeed can be objects although they actually can't. By this, it not just conflates the concept object with the concept class, but moreover turns these concepts up-side-down, thereby creating a mess of all other concepts.

Cladistics is, however, not a new approach, but actually the same old realism that the ancient Greek Parmenides formulated about 2,500 years ago, although dressed in new clothes. The problems cladistics encounters are thus the same as Parmenides' approach encountered, which have been thoroughly discussed in the history of philosophy. However, the worst blow to this approach was delivered quite recently by Einstein's discovery (actually objective conclusion) that time is relative to space (which later was empirically verified), since realism claims that change is an impossibility (and thus an illusion), because an impossibility (illusion) can't contain factual differences (like the difference in the pace of time at different paces of time). An illusion can't contain factual differences. This discovery (actually objective conclusion) did thus actually falsify Parmenides realism and with it cladistics, thus before cladistics was born. Cladistics was thus falsified before it was born.

Cladistics is thus actually only a desperate attempt by realists to escape the fact that an unambiguous classification is an impossibility (ie, Russell's paradox). Before it emerged, some objective biological systematists had proposed that biological systematics should try to agree about a certain systematization of biological organisms (based on the Linnean systematics), but pre-cladists reacted aggressively against this proposal claiming that there indeed is a single true classification to be found (based on Willi Hennig's conflation of object with class). These pre-cladists thus simply refused to acknowledge the fact that an unambiguous classification is an impossibility. They moreover won supporters (ie, cladists) so that this fact (ie, that an unambiguous classification is an impossibility) is still not acknowledged in biological systematics.

If biological systematics could reach a consensus to acknowledge this fact, then it could make a difference in future for humanity. It actually could contribute to the development of thinking. But its refusal to acknowledge this fact instead turns itself into a mess, actually the worst possible mess. Which way it will go in the future is determined by its participants. Clear thinking participants lead it towards clearly formulated conclusions, while confused participants lead it towards confused conclusions, and confused conclusions are those conclusions that contradict facts.    

Cladistics is a fraud

Cladistics is a fraud. It does not have a consistent solution per definition. It is an infinite recursion per definition.

Can cladistics be more discarded than proven paradoxically contradictory and empirically wrong?

The German entomologist Willi Hennig conflated entities (ie, entity) with classes (ie, class) and did thereby enter consistent inconsistency. The conflation also conflates infinite classes (ie, class) with finite classes (ie, category), and thereby also entities (ie, entity) with finite classes (ie, category), and thus also singularities (ie, single) with groups (ie, group), It thus conflates everything that possibly can be conflated, leaving us with the paradoxical class (category?, entity?) that originally erroneously was called "monophyletic group", but which today is called clade.

This conflation led biological systematics into an irrational and insensible chase for "the True Clade", called "the True Tree of Life", which actually is a paradox called Russell's paradox. The conflation made some biological systematists (notably Steve Farris and Gareth Nelson) believe that this paradox actually can be found, instead of understanding that it is a paradox (although the paradox had been revealed logically about 50 years before Hennig's conceptual conflation).

Unfortunately, this conflation still holds the ideas of biological systematists in a firm grip. The notion of clades, which was abandonded by the introduction of the consistent Linnean systematics, does once again rule, as it did before the introduction of Linnean systematics. The paradoxically contradictory idea of a fusion of time and space is obviously difficult to get rid of, although it has been shown to be paradoxically contradictory by Bertrand Russell and also contradicts (ie, is falsified by) the fairly recently discovered fact that time is relative to space. This toughness of this insensible and irrational idea makes one wonder what it takes to discard it. Can it be more than proven paradoxically contradictory and empirically wrong?   

     

On classification and the cladistic idea of a "true tree of life"

1,a Classification of objects (ie, entities, like you, me, a cell and a mitochondrion) is ambiguous, because every object can be assigned to at least two classes of objects.

1.b Classification of classes of objects (like classes of biological organisms, eg, humans, cells and mitochondria) is contradictory, because every object of a class is contradictory between at least two classes of objects.

2,a Classification of classes of classes of objects (like Linnean genera) is ambiguous, because every class of class of objects can be assigned to at least two classes of classes of objects.

2.b Classification of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of objects is contradictory between at least two classes of classes of objects.

3a Classification of classes of classes of classes of classes of objects (like Linnean families) is ambiguous, because every class of class of class of objects can be assigned to at least two classes of classes of objects.

3.b Classification of classes of classes of classes of classes of objects (like the different Linnean genera) is contradictory, because every class of class of class of class of objects is contradictory between at least two classes of classes of classes of objects.

And so on ...

In this scheme, we can see that there are two principally different components of classification: objects and classes. We can also see that each of these components occurs at every second level of a classification into more inclusive classes (ie, objects in 1.a, 2.a and 3.a, and classes in 1.b, 2.b and 3.b), and that objects consistently are ambiguous between their classes, whereas classes consistently are contradictory between their classes, and that the classes of objects are the same as the classes of the classes (ie, 1.a and 1.b, 2.a and 2.b and 3.a and 3.b). This fact is just a consequence of the two facts that every object can be assigned to at least two classes, and that every class is contradictory between at least two classes, whereof "can be assigned to" ultimately equals "is contradictory between", because the relation between object and class is orthogonal. The relation between object and class is simply both ambiguous and contradictory at the same time.

The scheme thus paints the practical picture of the orthogonality of classification. This orthogonality means that classification itself neither can be "true" nor can contain the "truth", because it is fundamentally orthogonally circular. Its output totally depends on its input. There is a saying that "shit in", "shit out", but in this case it is rather "anything in", "the same thing out", but always contradictory. Every particular solution simply points at another solution. Consistency (ie, not pointing to another solution) can only be found using an orthogonal system of classification (like the Linnean systematics), consistently keeping objects and classes apart.

The question whether this means that there isn't a single true tree of life (to be found) has the answer that it depends on whether this hypothetical tree is orthogonally consistent or not. If it isn't, then there isn't, whereas if it is, then there is. If the classes that every object "can be assigned to" actually equals the classes that every object "is contradictory between", then there is indeed a true tree of life, but if thy don't, then there is not a true tree of life. The existence of a true tree of life does thus depend on the actual history of life: if the history of all included classes are congruent, then there is a true tree of life, but if they aren't, then there isn't. The probability that there isn't is, however, vastly larger than the probability that there is. A true tree of life actually requires a multiple of two entities, which have a totally symmetrical origin, and wherein all properties also are totally consistently distributed. The probability of such a tree is almost zero.

The probability that there is a single true tree of life is thus almost zero. Moreover, if there indeed should be one, then our fundamental partitioning of reality into objects and classes, and thus the foundation for this tree, should be wrong. If cladistics should be right, then all of us, including the cladists, thus should be wrong.

Cladistics is thus a huge problem for science. How do we get rid of it? How can we explain that it is impossible, ie, a vain serch to define the indefinable, as Darwin called it?

  

  

The contradiction of cladistics

Cladistics is the idea that we can acknowledge continuity instead of entities. The problem with this idea is that lineages are conflated. The end point of this acknowledgement is actually the same as acknowledging entities; the only difference being that the latter acknowledges both single and several, whereas the former only acknowledges several. This difference means that cladistics is contradictory between one and many, because one is, of course, true. . 

Om livets träd

En dikotom förgreningsprocess, såsom en asexuell cellinje (eller Darwins modell av evolution), går inte att klassificera konsekvent. Anledningen är att processen i sig själv då måste vara både en enhet (dvs ett objekt) och en klass, vilket i sig själv innebär att den är en paradox (Russell's paradox), vilken är inkonsekvent per definition. En sådan process går alltså inte att klassificera konsekvent därför att klassificeringen i så fall skulle vara inkonsekvent. Idén om en sådan klassificering, dvs kladistik, ger alltså ett ansikte åt begreppet omöjlighet. Kladistiken strävar efter att finna den omöjliga klassificeringen av process i sig själv.Denna strävan är alltså en oändlig rekursion, dvs oändlig loop, per definition. Varje möjlig lösning innehåller motsägelser som pekar på andra lösningar.

Detta faktum är svårt att förstå i sig självt, men speciellt när det gäller Darwins modell av evolution, eftersom den tycks förutsätta att omöjligheten är möjlig. Denna tolkning bygger dock på den felaktiga fördomen att Darwin med modellen hävdar att det finns ett enda sant livets träd, vilket han inte gör. Han hävdar endast att evolution kan beskrivas med ett träd. Det utesluter inte att evolution kan beskrivas lika korrekt med flera olika träd. Istället sliter han just med denna fråga i de 20 år det tar innan han (under stark press) publicerar sin teori. Både han och hans vapendragare (t ex Huxley) insåg att modellen kan missförstås, men åtminstone Huxley ansåg att detta problem fick man ta itu med senare. Den första prioriteten var att vinna över kreationisterna.

Tråkigt nog är det just denna möjlighet till missförstånd som Willi Hennig utnyttjade för att skapa kladismen (också kallad kladistiken). Detta gjorde han genom att särskilja den paradoxala klass som idag kallas "klader" och vilken egentligen är Russell's paradox (genom att peka på holofyletiska grupper och kalla dem för monofyletiska grupper). Genom detta öppnade han en möjlighet för fylogenetiken att attrahera trosinriktade personer, dvs att vara opportunistisk, men sänkte samtidigt dess vetenskapliga värde, eftersom denna öppning är lika inkonsekvent som, och på samma sätt som, kreationismen. Dvs, om Gud skapade världen, vem skapade då Gud? jämfört med: om om alla klasser har en enda ursprungsklass, vilken ursprungsklass har då denna klass? Dvs, var börjar klasser?

Istället borde fylogenetiken ha konfronterat det faktum att ett "livets träd" måste vara en approximation, dvs att det måste finnas flera lika korrekta approximationer, innan Hennig presenterade missförståndet. Den borde ha insett att Linnés system faktiskt samlar grupper av sådana lika korrekta approximationer under ett enda paraply. Den borde ha förstått att entydighet i denna fråga är omöjlig. Om den hade gjort det, så hade Hennigs missförstånd varit omöjligt. Emellertid, när den nu inte gjorde det, så står vi här med kladistiken, vilket gör problemet mycket svårare. I detta läge har vi endast två alternativ: att fortsätta kladistikens fåfänga försök att uppnå en omöjlighet (och samtidigt förvirra unga studenters sinnen) eller att förkasta kladistiken, vilket är mycket svårare än ens någon kladist kunnat föreställa sig. När vi väl har släppt ut vargarna så styr vi inte längre deras beteende. Det enda hållbara alternativet (dvs det senare) är alltså mycket svårare än ens någon kladist kunnat föreställa sig.

Hur detta drama kommer att utveckla sig är svårt att spå, men det faktum att dumheten oftast vinner över klokskapet bådar sannerligen inte gott för fylogenetiken. Kanske kommer Darwins teori att förkastas som en teorins villfarelse, dvs tron på Russell's paradox.

Why do cladists claim an impossibility?

I understand that the two facts that:

1. classification is ultimately contradictory (ie, Russell's paradox), and

2. cladistics believes in classification

means that cladistics is ultimately contradictory.

I'm just surprised that this fact has such a hard time to be acknowledged.

Why are there so few biological systematists out there willing to admit this fact? Why is this ancient belief in classification so hard to get rid of?

Is it because one third of all people assumes that classes are real, ie, are realists? If so, exactly what do they expect to gain by this resistance to acknowledge facts? Personal benefits?

Independently of cladists claim, fact is that classification (including "cladification") is paradoxically contradictory. It doesn't matter that all cladists agree about the approach, it is still inconsistent. Hundreds of billions of flies can't make eating shit tastefully, but can only lure people into eating shit. 

   

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.

Idén om en otvetydig sanning (t ex kladistik) kan inte realiseras

Begreppsbildning är självmotsägande
Vår begreppsbildning av verkligheten är i grunden en klassificering av verkligheten. Problemet med detta är att klassificering är ultimat självmotsägande, vilket Bertrand Russell visade 1901 med det som senare kom att kallas Russell's paradox. Russell's paradox visar alltså att begreppsbildning är ultimat självmotsägande.

Anledningen till självmotsägelsen
Anledningen till denna ultimata självmotsägelse är att klassificering är inneboende ortogonal (dvs diametralt) självmotsägande genom att alla klasser innehåller andra klasser. Alla klasser är alltså både en och flera klasser samtidigt, vilket är självmotsägande.

Följdverkningar av självmotsägelsen
Denna begreppsbildningens inneboende självmotsägelsel har många följdverkningar, varav en är viktigare än alla andra. Den är att vi måste dela upp vår uppfattning av verkligheten i två aspekter: mönster och process, och sedan hålla dessa isär konsekvent, dvs för alltid, för att undvika att flytta över självmotsägelsen till våra egna resonemang om verkligheten. Om vi sammanblandar mönster och process (vilket kan ge intrycket av att vara "naturligt" för personer som inte förstår vetenskap), så likställer vi istället en motsägelse mellan ändliga klasser (dvs "kategorier") och oändliga klasser (dvs det vi vanligen endast kallar "klasser"), vilka är ortogonala, dvs diametralt motsatta, och således inte kan likställas, utan är motsägande per definition  Då flyttar vi således över begreppsbildningens självmotsägelse ifrån verkligheten till våra egna resonemang om den.

Denna följdverkning innebär att idén om en otvetydig sanning är en utopi, dvs en omöjlighet, fundamentalt beroende på att en otvetydig klassificering av verkligheten är en utopi. Det innebär, bland annat, att "partikelfysikernas" strävan att hitta "Higgs boson" är en utopi, och att paleontologernas strävan att hitta "Livets Träd" är en utopi. Istället är faktiskt Linnés klassificeringssystem ett exempel på den konsekventa kompromissen mellan mönster och process. De ortogonala storheterna "mönster" och "process" kan förenas endast med en kompromiss, och den konsekventa kompromissen är ett ortogonalt system, dvs klassificerande enskilda enheter (t ex organismer) i kategorier av klasser, vilket Linnés klassificeringssystem är ett exempel på. "Den otvetydiga sanningen" är ultimat endast en idé, likt Gud, som omöjligen kan realiseras, därför att den är självmotsägande.

Summa summarium
Slutsatsen av dessa förhållanden är att idén om en otvetydig sanning är klämd emellan verkligheten och vår uppfattning av verkligheten, där ingen plats finns. Istället kommer denna idé för alltid att vara klämd mellan "strukturalister" och "funktionalister" (vilka också har många andra benämningar, såsom "objektivister" och "subjektivister"), där segraren alltid kommer att vara kompromissen mellan dem, men således aldrig den otvetydiga sanningen. Ultimat måste vi alltså acceptera kompromissen och överge idén om den otvetydiga sanningen. Det kan kännas tungt för extremister som hävdar idén om den otvetydiga sanningen, såsom kladister, men är icke desto mindre den påtvingade verkligheten. Dröm kommer alltid att förbli dröm, och verklighet kommer alltid att förbli verklighet, och mötet mellan de två kommer alltid att förbli en kompromiss. Higgs boson kommer aldrig att hittas (om nu inte partikelfysikerna lyckas lura i oss att sannolikhet är lika med sanning), och "Livets Träd" kommer inte heller att hittas, därför att de är omöjliga per definition. Det är omöjligt att realisera en begreppsmässig motaägelse.     

Cladistics is the extremism of empirical science

Cladistics is the extremism of classification, ie, classificationism, or typology (resting on the same idea as racism, ie, that the biological diversity consists of definable collections of organisms, that is, sets. It does not realize that Russell's paradox actually falsifies this idea by demonstrating that the set of all sets that does not include themselves is paradoxically contradictory. Its corollary set of sets is thus falsified by Russell's paradox. 

On the basis of its erroneous idea, cladistics first allocates objects (ie, organisms) into classes, and then conflates the obtained classes back towards the singular objects it started with, asserting that there indeed is a single True Classification (ie, The Tree of Life) to be found at the end of this paranoic procedure.

There of course isn't. The procedure is nothing but a classificatory circularity that actually is an infinite recursion (infinite loop), since it can't return to the singular objects (ie, organisms) it started with. Instead, it will, of course, always end up with the same classes as it started with, but always contradictory.

Extremists are always contradictory, independently of what the extremism focuses on. It doesn't matter if they appear to be scientific by claiming that classes are real. Empirical science does not claim that classes are real, but merely classifies to be able to discuss reality in a generic sense. The idea that classes are real is not scientific, but actually a misunderstanding of science. Unfortunately, this misunderstanding leads into a racism that appears to be supported by science. For this, I, as a scientist, have to apologize. It was never my meaning to give the impression that the classes I distinguish are real. This weird off-shot of science is a no-go that neither I nor all other empirical scientists can take responsability for. There is always a possibility to misunderstand everything. Strict objectivity, ie, empirical science, can unfortunately not provide the simple truths that extremism can, but is, on the other hand, not paradoxically contradictory, as extremism is.

Cladistics is, however, an extremism that all empirical scientists ought to apologize for. It leads right into the racism that Willi Hennig was a child of.     

On the barrier between us and a single truth

The fundamental problem for classification is that it is paradoxically contradictory between in time (ie, class) and over time (ie, continuity), just like entity (object) displays two different aspects: pattern and process. It means that the two different aspects of entity (object) correspond to the paradoxical contradiction for classification. The two aspects and the paradoxical contradiction are thus actually two aspects of the same paradox, ie, an interface between them, which is called Russell's paradox.

This paradox is thus the core of classification. It is what we end up in when we search the truth in classification (like cladistics does). It is also the barrier between us and a single truth, because without a single non-contradictory classification we cannot, of course, find a single truth.

The idea of a single truth (ie, a single True Tree of Life, or single consistent system) will thus forever be hidden behind a fundamental paradoxical contradiction in classification. If this means that the idea is wrong depends on how we define "wrong". A more suitable word appears to be "impossible". A single True Tree of Life, or single consistent system, is simply impossible. It is, actually, an unreachable state between reality and our classification of it, which is consistently classified using an orthogonal system like the Linnean classification. Such system thus touches a single Truth, but, unfortunately, just as one aspect of it. The single Truth remains hidden behind the fundamental paradoxical contradiction in classification, called Russell's paradox.

Cladistics may claim that matters are the other way around, that is, that the idea of a single truth (ie, a single True Tree of Life, or single consistent system) is within reach, but it can't change the fact that it isn't. It can only lure people into a vain search for it. An unwanted understanding can be suppressed by an irrational wish, but can't be conjured away. In the long run, we must accept also unwanted facts, because striving for impossibilities is vain.   

The problem with cladistics is that it denies what it aims at

The basic idea of cladistics is that:

if you comprehend an entity (eg, yourself) yesterday as the ancestor of the same entity today, then the ancestor and the entity today can be said to form a group, which cladistics calls a "natural group", or a "clade". Cladistics ONLY acknowledges such groups.

As a corollary, cladistics does not acknowledge niether single entities nor categories.

The fundamental problem with this idea is that:

the facts that "clade" in practice is a category (ie, as the set of clades), and that cladistics denies all categories, mean that cladistics can't find a consistent set of "clades" (ie, a consistent category of clades) simply because it actually denies it (by denying categories).

The fundamental problem with cladistics is thus that it denies what it aims at (or aims at something it denies).

Isn't it a brilliant spin? (A pseudo-scientific approach that can't find a consistent solution per definition. Guaranteed life-long support and career in the academy).

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.

On classification of dichotomously propagating (bifurcating) processes

Dichotomously propagating  (bifurcating) processes can't be classified unambiguously. This does not, however, only concern this kind of process, but moreover all kinds of processes (ie, processes in some generic sense). The reason is that kinds of processes actually are classes (of processes), and classification of classes is ultimately contradictory, since classification is orthogonal. 

It means that kinds of processes are inconsistent (ie, contradictory) entities, and thus that classification into such entities is infinitely recursive. There simply is no consistent solution to any such classification.

This fact may appear counter-intuitive to some of us, but this appearance is only due to that those of us are not aware of that typification is classification. Those of us simply classify (ie, typify) without being aware of that it is what they do. Also illustrating a dichotomously propagating (bifurcating) process with a line graph is typification, since such graphs is a class. Understanding such illustrations consistently is a science on its own (ie, graph theory in mathematics), see "Are node-based and stem-based clades equivalent? Insights from graph theory" by Jeremy Martin et al. 2011.     

On the limits for classification (and the practical impossibility of cladistic classification)

The fact that classification is orthogonal, ie, that every single class contains several classes within every single set of entities (eg, the class "primates" and all different classes of primates), and that finite class thus is orthogonal to infinite class, means that classification is fundamentally contradictory between single and several, since orthogonalities are contradictory between single and several per definition. Cladistic classification accepts this contradiction, ie, accepts being contradictory, by equalizing the concepts finite class and infinite class.

The only way to avoid this orthogonal contradiction, ie, to achieve consistency, in practical classification is to use an orthogonal system of classification, classifying entities into categories of classes, like the Linnean system, in order to thereby keep finite classes and infinite classes (ie, the orthogonal concepts finite class and infinite class) consistently apart. Such orthogonal system of classification is, however, ambiguous in relation to reality per definition, simply by keeping the orthogonal concepts finite class and infinite class) consistently apart.

It means that classification can only be either internally contradictory or ambiguous in relation to reality. The fundamental reason for this impossibility to achieve unambiguity is that classes can't be (and thus aren't) real per definition, but can only be (and thus are) an artificial invention.

How to cure a cladist

If you believe that your classification is true (as cladists do), then you is contradictory, because classification is contradictory, which Bertrand Russell also demonstrated in 1901 with Russell's paradox.

It is thus not your belief (ie, that your classification is true) that is wrong, but what you believe in (ie, classification) that is. Your error does thus not reside in your conclusion (ie, that your classification is correct), but in your assumption (ie, that classification can be true).

If you end up in this belief (ie, cladistics), you thus have to scrutinize your assumptions.

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?   

An old cladist woman does indeed try to shoot the bear with the broom handle

Instead of understanding Russell's paradox, cladistics believes that it can find it.

Instead of understanding that Russell's paradox means that classification is ultimately contradictory, cladistics claims that classification is ultimately consistent.

It means that instead of being consistent, cladistics is consistently inconsistent. It leads cladistics into a vain search for an infinite recursion, that is, the subjective side of Russell's paradox.

Cladistics is thus actually the up-side-down approach, or the belief that "if" does not exist, exemplified with the expression that "if if did not exist, so had the old woman shot the bear with a broom handle". An old cladist woman does indeed try to shoot the bear with the broom handle. She not only believes, but also claims and defines, that the broom handle is a gun, and then she shoots.

On the black hole for classification called "cladistics"

The class clade is an infinite recursion that you enter when you conflate infinite class with finite class, ie, type with set, that is, when you don't "see" your own typification and subsequent categorization, and thereby can't distinguish them.

Conflation of these for conceptualization so fundamental concepts makes you turn Russell's paradox, ie, the fact that set theory leads to contradiction, up-side-down into the comprehension that contradiction instead is consistent, ie, forming a consistent class, that is, the class clade.

This comprehension is ambiguous between being correct in that clade is a consistent infinite class, but wrong in that clade is a consistent finite class, thus forming an infinite recursion between consistent and inconsistent, ie, a consistently inconsistent infinite loop, which you can't see because you're in it. Instead, you're convinced that there is a consistent solution at the end of this infinite recursion, which there thus isn't per definition.

Cladistics is thus a black hole in conceptualization that you enter when you conflate infinite class with finite class, ie, when you don't "see" your own typification and subsequent categorization, and thereby can't distinguish them. You simply don't know what you're doing.

The correct understanding of Russell's paradox is that classification is ultimately contradictory. This fact also means that process can't be classified consistently, ie, that there are always more than one consistent classification of a single process, because continuity is indistinguishable from class. Consistent classifications, in turn, can we only produce using an orthogonal system of classification, like the Linnean system. Instead ignoring Russell's paradox leads into an eternal orthogonal merry-go-round between inconsistent (contradictory) classifications, because it is infinitely recursive (per definition). Russell's paradox is thus a fact we need to relate to, not something we can ignore or a solvable problem. It is fundamentally due to the unavoidable fact that classification is orthogonal.

Cladists promise to deliver the "natural groups" tomorrow

Cladistics reminds me about when I once asked for the recipe for a good meal at a restaurant. The chef replied that you get it tomorrow. Similarly, cladists promise to deliver the "natural groups" tomorrow.

The most surprising in this issue is not cladists' belief in illusion itself, but that there indeed is someone out there willing to pay them for this illusionary delivery. It must be due to that they don't need it anyway.

The idea of a single "True Tree of Life" (ie, the foundation of cladistics) is both a definitional contradiction and a practical impossibility

The assumption that there is a single "True Tree of Life" to be found (ie, the foundation for cladistics)may appear intuitively self-evident (ie, axiomatically correct) to some of us, but it does in fact lead to Russell's paradox, meaning that it is a practical contradiction by being an infinite recursion (ie, lacking consistent solution). This fact forces a choice to discard either the assumption or the contradiction. Discarding the contradiction may then appear as the intuitively self-evident (ie, axiomatically correct) choice to some of us, but it instead meets the contradiction that nested "trees" in such hypothetical "True Tree of Life" (eg, of mitochondria or genes) may well be incongruent with the hypothetical "True Tree of Life" in that entities of nested trees (ie, holophyletic groups, or "clades") may well be incompatible with entities of the "True Tree of Life", and thus that entities (in a generic sense) may well be contradictory. This fact, however, together with the fact the assumption leads to Russell's paradox, actually mean that entities not just "may well" be contradictory, but that they are contradictory per definition, ie, lacking a consistent solution by being infinitely recursive.

The assumption that there is a single "True Tree of Life" (ie, the foundation for cladistics) may thus appear intuitively self-evident (ie, axiomatically correct) to some of us, but is actually contradictory with regard to both classes (ie, concepts) and entities. It is thus actually both a definitional contradiction and a practical impossibility.

Cladists have defended cladistics by that it is logically correct given its premises, but its premises (ie, resting on the axiom that there is a single "True Tree of Life" to be found) do thus prove to be both a definitional contradiction and a practical impossibility. Where does this fact place cladistics? Is it logically correct, but wrong? Can formulation of contradictory definitions that acknowledge a practical impossibility be logically correct? I would rather say that formulation of contradictory definitions is illogical in the first place.

Russell's paradox and Hennig's spin of it (ie, cladistics)

Bertrand Russell demonstrated in 1901 that classification leads to contradiction (called Russell's paradox), which can be exemplified with Barber's paradox.

Barber's paradox read (from Wikipedia):
Suppose there is a town with just one barber, who is male. In this town, every man keeps himself clean-shaven by doing exactly one of two things:

1. Shaving himself, or
2. going to the barber.

Another way to state this is:

The barber shaves only those men in town who do not shave themselves.

All this seems perfectly logical, until we pose the paradoxical question:

Who shaves the barber?

This question results in a paradox because, according to the statement above, he can either be shaven by:

1. himself, or
2. the barber (which happens to be himself).

However, none of these possibilities are valid. This is because:

• If the barber does shave himself, then the barber (himself) must not shave himself.
• If the barber does not shave himself, then he (the barber) must shave himself.

(end of the citation from Wikipedia).

All men in this town thus keep themselves clean-shaven, but whereas some shave themselves, the rest goes to the Barber, and the Barber himself consistently belongs to the other of these two groups if he behaves as defined for any of them. The Barber is thus consistently contradictory between the definitions of the two groups. This is an example of an infinite recursion. Every categorization of the Barber points to the alternative categorization in an infinite loop.

The generic reason for this kind of contradiction (ie, Russell's paradox in a generic sense) is that classification functions by distinction of difference in a similarity, since difference and similarity are diametrically opposed, ie, orthogonal, per definition, because orthogonality is contradictory per definition (in this case between the differences of the similarity). This inherent contradiction of classification is, however, invisible for us as long as it is restricted to only one of the two sides of the fundamental distinction, that is, to either process or pattern, since we then comprehend it as a similarity (rather than a difference and thus a contradiction), but becomes visible as soon as it bridges this fundamental distinction by that it then is not similar (as we intuitively expect), but instead opposite - ie, there is indeed a difference between process and pattern, but this difference is not in a similarity, but in an opposition, ie, what the Barber does is in opposition to each of the definitions of what the Barber can do.

This fundamental orthogonality of classification is also the driving force for the never-ending change in biological systematics. It is the obstacle that hinders it from reaching an unambiguous classification. However, about 50 years ago the German entomologist Willi Hennig escaped this fundamental contradiction by turning the orthogonality up-side-down. He simply asserted that only groups such as the Barber and the categories "those men in town who do not shave themselves" and "those men in town who do shave themselves" are "natural groups". He thus "acknowledged" the "difference part" (ie, contradiction) of the orthogonality and only it (ie, "denied" the "similarity part" of it). By this, he also "acknowledged" the paradoxical applications of this contradiction.

Hennig's irrational move was never accepted for publication by any scientific journal, but was instead published as a book in the 1950-ies, from which it was dragged into biological systematics in a joint effort by Steve Farris and Gareth Nelson in the 1970-ies, then won a popularity contest against consistent traditional science in the 1980-ies, and does today penetrate the thinking in biological systematics (under the name "cladistics") to the degree that the discipline is actually searching for such paradoxes (called clades) in a shared belief in the existence of a single "True Tree of Life". This imaginary "True Tree of Life" is thus actually Russell's paradox in disguise.

So, how does Hennig's move work? The answer emerges when we consider the fact that the Barber in the paradox represents the abstract similarity of a classification, whereas the two categories represent the real different parts of the classification. This consideration allows us understand that Hennig's grouping of the two categories into the Barber folds the difference itself between the real (different) parts of a classification back into its similarity, thus merely running the process of classification backwards, ie, canceling it. By this, it merely legitimates a comprehension that any classification is a "natural group". It thus does not solve the problem (ie, fact) that classification is fundamentally contradictory (and that every classification thus is contradictory per definition), but merely legitimates a comprehension that any classification is a "natural group". It does not change the fact that classification is fundamentally contradictory, but merely acknowledges contradiction, and only contradiction, as "natural groups".

The problem with this approach is that the fact that classification is orthogonal (and thus ultimately leading to Russell's paradox) means that it ultimately leads to infinite recursion of the same kind as that of Barber's paradox, today called clades, wherein every specific classification thus points to another classification in an infinite loop. (This ought not come as a surprise, since only acknowledging contradiction can't, of course, find a non-contradictory solution). The approach is thus merely a spin of classification into infinite recursion, although presently a mass-spin in biological systematics, which in practice is analogous to that like the hamster enter the running around in his wheel instead of using it as a wheel.
A consistent system of classification using an orthogonal arrangement of classes, like the Linnean system, avoids its fundamental contradiction and thus also infinite recursion, although neither it can reach unambiguity in relation to reality. Russell's paradox is namely, unfortunately, a fact we can't change.

The class clade is an infinite recursion, ie, an infinite loop

The class clade is a set that includes itself as a member, meaning that it is an infinite recursion. It is actually the same process as a single clade illustrates, that is, a dichotomous propagation, run backwards. As such it is infinitely contradictory, ie, loops in an infinite contradiction.

It means that cladistics can only produce an infinite sequence of contradictory clades. Its search for clades just goes around, and around, and around....all possible contradictions.

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.    

On the contradiction in the idea of a single "True Tree of Life"

The (today cladistic) idea of a single "True Tree of Life" is contradictory between being a single entity or many entities, ie, between being one or many (independently of what).

This contradiction is, however, ambiguous in that it can be consistently folded backwards until ending in a single entitity, thus making the idea appear as a "natural" (and thereby axiomatically consistent) idea of the origin of many entities from a single entity (thus at the same time as it is contradictory between one or many).

Now, if this "folding backwards" indeed is consistent, and the idea thus is a consistent idea of the origin of many entities from a single entity, then the idea is obviously contradictory between being consistent or inconsistent.

Understanding of this contradiction (actually Russell's paradox) resides in that the idea is contradictory in terms of being one or many entities of the same kind, but consistent in terms of being of the same kind, because a class (ie, kind) is both infinite and finite per definition, and is thus contradictory between being inconsistent or consistent per definition. The idea is thus contradictory between being consistent or inconsistent simply because classes are contradictory between being inconsistent or consistent. The idea is thus a practical impossibility, ie, an illusion, that emerges when we believe that kinds (ie, classes) are real (ie, form consistent entities), because such "entities" are contradictory between being one or many, and are thus incompatible with (actually orthogonal to) real entities (eg, organisms).

The (today cladistic) idea of a single "True Tree of Life" is thus a practical impossibility, ie, an illusion, that emerges when we believe that kinds (ie, classes) are real (ie, form consistent entities), because classes are fundamentally contradictory between one and many (as Bertrand Russell also showed in 1901 with Russell's paradox).

Had we all been aware of human progress, cladistics should thus not have emerged.
  

Om Livets Träd (och kladistik)

Sedan slutet av 1960-talet har den biologiska systematiken alltmer börjat överge den Linneanska systematiken för att istället tala om "naturliga grupper" och det man kallar "Livets träd" företrätt av en åsiktsinriktning som kallas kladistik. Denna idé är inte ny, utan fanns bevisligen redan hos Taoismens grundare, de antika grekerna, vikingarna och en massa andra kulturer och har levt parallella liv hela tiden sedan dess, för att nu återigen dyka upp i den moderna biologiska systematiken. 

Exempel är:

All she requested was that the painting should depict a Tree of Life.

Amnioternas "fylogeni".

För massor av ytterligare illustrationer, se Livets träd).

Idag kallas sådana släktträd dock "kladogram", varav det allomfattande kladogrammet alltså är livets träd.

Ett exempel är:

ITOL Tree of life (Wikipedia)

Problemet med denna idé är dock att den är inkonsekvent, dvs självmotsägande, som en singularitet (dvs ett enda Livets Träd) genom att innebära att enheterna det består av måste vara både åtskilda och överlappande samtidigt. Idén är helt enkelt i praktiken en direkt sammanblandning av vår särskiljning av enheterna det består av, oavsett vilka enheter vi än särskiljer för att konstruera det. Den är alltså i praktiken en självmotsägande cirkularitet, trots att många av oss tvärtom uppfattar den som "naturlig". Denna egenskap innebär att Livets Träd kan vara precis vad som helst, men alltid innehållande motsägelser. Idén är helt enkelt konsekvent inkonsekvent. (Egentligen representerar idén den subjektiva aspekten av Russell's paradox, men tar ett tag att reda ut).

Det enda sätt vi har att undvika denna paranoida cirkularitet är att dela upp enheterna trädet består av i kategorier av klasser, liksom i den Linneanska systematiken, genom att på så sätt konsekvent hålla isär begreppen klass och enhet (dvs oändlig och ändlig), då kategorierna representerar (ändliga) enheter och klasserna är oändliga.

Detta innebär att det inte finns något enda sant Livets Träd, utan endast flera lika sanna beskrivningar av Livets uppkomst. Livets uppkomst går helt enkelt att betrakta ur olika aspekter som är lika sanna. Idén om ett enda sant Livets Träd är i en vetenskaplig mening mer av en psykisk sjukdom än en realistisk idé, även om den för konsten erbjuder ett intressant uppslag (se ovan och på Livets träd).