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).