Chris Humphries’ Blog

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Here is another way of looking at things

Recently, a Festschrift meeting was held in my honour.  I presented some new findings on the origin of reasoning within systematics and was surprised to find that the triadic process so well described by Darwin, Hennig and Nelson and Platnick according to Peirce had its origin in medeival thinking.  There is no doubt that the origin of parsimony has its origins in the 14th century as so clearly stated by William of Ockham, but, to find that the three taxon statement has similar origins was a surprise to me.  From the works of Saussure and Peirce it is obvious that systematics has a long track record.  I will develop these ideas further with readings of Whitehead and other philosophers interested in the workings of triadic relations. The papers for the published volume are now coming in and it is hope to be sent to press early in the New Year.

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  1. This is my own contribution to “Beyond Cladistics” edited by David M. Williams and Sandra Knapp. California Press (yet to be published)

    The history of systematics goes back deeper than you think

    By Christopher J. Humphries,

    Associate Researcher, The Department of Botany, The Natural History Museum, London SW7 5BD, UK.

    The origin of modern systematics is generally thought to have emerged since Linnaeus, especially during the Darwinian revolution in evolutionary biology, but the general principles are part of medieval science that became elaborated in the 18th and 19th centuries into the subject we know today. It is clear that systematics, as currently practiced, owes as much to semiotics as it does to empirical investigation. The revitalization of Peirce’s work during the latter part of the 19th century shows that systematics is as much about ideas of triadic relations, as part of general science, to understand the theory of evolution as interpreted by modern practitioners. Here, will be presented a brief review of the literature to show that the thinking behind systematics runs deeper than most people think.

    Having worked through the sixties, seventies and eighties I have experienced the principal developments that have occurred in contemporary systematics. The dominant paradigms during that time have been cladistics and phenetics. We think of modern cladistics as being a development from Darwin’s theory of evolution (Hennig 1966) but the connection between systematics and evolution has seen some difficult times in determining exactly how. Charles Darwin (1859) is one of my greatest heroes, in the sense that although evolution was in vogue before he came along, he did provide a mechanism for evolution, natural selection, to explain the pattern of descent, and thus provide an explanation of biological diversity in the world. He was also deeply involved in systematics, writing a comprehensive monograph on Barnacles (Darwin, 1851, 1854) as perhaps his most important systematic contribution. He was deeply committed to the idea that evolution was dependent on systematics and in fact he said that one could not talk about the evolution by common descent without having a classification at the outset .
    His notion of relationships, can be seen easily in his transmutation notebook B. Here we see that among 25 taxa, four are labelled A-D (Figure 1). Darwin noted relationship in terms of the four taxa could be as follows: (((B,C)D)A). In other words, B and C are the most closely related relative to D or A, D is more related to A and B than it is to A, and so on. “1” indicates the root of the tree. Hence, it might be said that Darwin understood the principle of triadic relations. In logic and mathematics a triadic relation is an important special case of a polyadic or finitry relation, one in which the number of places in the relation is three, and discussed in greater detail later in this paper.
    Triadic relations
    The adjectives 3-adic, 3-ary, 3-dim, or 3-place are used to describe these relations. Just as a binary relation is a set of pairs, forming a subset of some cartesian product A × B of a pair of sets A and B, so a triadic or ternary relation is a set of triplets, forming a subset of the cartesian product A × B × C of three sets A, B and C (Peirce, 1958-60). Thus, in Darwin’s transmutation notebook diagram (Figure 1) there are 4 taxa, A, B, C and D. Triadic relations amount to A(BC) and A(BD), A(DB), A(DC) and thus logically add together to give A(D(BC). Note that the root is designated as 1. So it seems to me that Darwin was already stating systematic questions in terms of triadic or three-taxon relations. Furthermore, it was clear that Darwin was thinking in phylogenetic patterns to be explained by the process of natural selection. The only diagram in the Origin of Species (1859; reproduced in Figure 2 below), shows that he had created a model for evolution by common descent. This model included speciation events, stasis, and fossil lineages through time, succeeding to the present day or dying out.
    Evolutionary ideas
    It was not long that after the Origin that attempts to show phylogenies and evolutionary scenarios emerged. Among the best known in the literature were those of Huxley (1858-1862), Haeckel (1866) and others. Haeckel, for example used Darwin’s tree metaphor rather literally when depicting the evolution of life as a European oak (reproduced in Figure 3 below). Haeckel invented the word phylogeny to describe the tree which now finds itself rampant through evolution parlance. There were many efforts to produce phylogenies, but it was during the 20th century with the work of Willi Hennig (1950, 1965, 1966) that the best method for determining phylogenies was developed. So, instead of saying such statements as hoofed animals are ancestral to whales’ the relation became rephrased into statements of relationships, ‘Mesonychids are more closely related to whales than they are to other hoofed animals.’ Similarly, rather than using Huxley’s approach that suggested ‘Great apes are ancestral to humans’, this became transformed into the statement ‘Chimpanzees are more closely related to humans than to other great apes’ (Wood 2007).
    This is the substance of the revolution in thought that Hennig brought about. Hennig himself still used evolutionary language to justify the triadic relation (Wood, 2008). Hennig provided the means of changing phenetics into phylogenetic relationships, making the recognition of groups by breaking up the concept of similarity into three parts: Synapomorphy to designate monophyletic groups, Autapomorphy to recognise taxa whether terminals or groups and, Plesiomorphy for paraphyletic and polyphyletic groups. As we have already stated Darwin noted the relationships in terms of four taxa in his notebook diagram could be as follows: (((B,C)D)A). In other words, C and D are the most closely related relative to D or A, D is more related to A and B than it is to A, and so on. So in Hennig’s terms ABC, ADC, ADB, BCD, BC would be monophyletic groups. Assemblages of taxa such as AD, ADC, ADB, CD, BD would be paraphyletic and AB and AC polyphyletic and hence not real groups at all. It follows too, that three is the minimum number of taxa, (hence triadic group) to express the simplest monophyletic relation.
    It is debatable to consider whether Hennig (1966) ever considered Peirce’s work as there are no citations in any of his references. However, since Hennig’s initial writings there have been a massive increase in the number of papers written on cladistics, ranging from small problems such as the relationships of a few species right through to the tree of life as originally diversity was considered by Darwin in the epigraph at beginning of this paper. More recent systematic work on the Tree of Life is summarized in D.R. Maddison et al. (2007). The Tree of Life Web Project is a collection of information about biodiversity compiled collaboratively by many different specialists, both professional and amateur. Its aim is to contain a page with pictures, text, and other information for every species and for each group of organisms, living or extinct. Connections between Tree of Life web pages use cladograms for each group of organisms, so anyone can browse the hierarchy of life and learn about systematics and evolution as well as the features of individual groups.

    Triadic Relations
    The reason I became interested in Peirce’s work and triadic relations was because I was intrigued by the suggestion of Wood (1996, 2007) that Peirce’s triadic philosophy holds the key to systematic theory. Specifically, Peirce’s theory of signs and his triad of object, sign and system of interpretance is, it seems, the very basis of systematics. Wood (1996) notes that the stages to classification have three founding relations – features, similarities and homologies (Wood, 1996: 43-44). The categories of first, second and third, while finding expression in his semiotics, have much wider implications. It was to his metaphysical categories that Peirce turned when describing the key ideas of biology and each of the sciences, Following Wood (1966) I show how Peirce’s triadic philosophy – present in his categories of first, second and third and in his semiotics of “sign”, “object” and “interpretant” – illuminates the study of living things, connecting Peirce’s philosophy to the three levels of species, homologies, taxa (groups) and hierarchies. In classification, I discuss the preference for different kinds of relation, monadic, dyadic or triadic. Peirce described the triadic logic (pertaining to cladistics) almost a hundred years before Hennig (1966) and Nelson and Platnick (1981), and even more intriguingly relates the development of such ideas to medieval scholars, such William of Ockham and several others.

    Representing the three stages of cladistic classification in semiotic terms, shows that each involves the discovery of a particular kind of sign when, say, we consider the steps in cladistic logic. As Hennig’s ideas were being were being picked up by systematists in the various branches of biology, zoology, botany etc., Nelson and Platnick, when applying the principles of cladistics at the American Museum of Natural History during the 1960s and 70s, came to realise that they had no need of Hennig’s evolutionary ontology (Nelson and Platnick, 1981), a notion they developed further in transformed cladistics with three-item analysis (Platnick, 1979). The necessity of triadic relations to classification was implicit in the logic of branching diagrams itself. They dispensed with ideas of perfection and ancestry and pared the science of classification down to the simple relations (Table 1).

    I have described single, dual and triple facts and how they express monadic, dyadic and triadic relations respectively. There are a number of different schools of classification. Each school shows a preference for a particular kind of relation. Monadic relations in classification are merely differences, or strangeness: For example, ‘Look at that parrot’. For another example, consider the classification of gorillas, chimpanzees and humans. Johann Friedrich Blumenbach, in his Manual of Natural History of 1779, placed humans in a separate order, Bimana, an arrangement that was followed by Georges Cuvier. Richard Owen, the great adversary of Charles Darwin elevated us to a separate subclass, the Archencephala (Owen, 1858). For Blumenbach, it was our opposable thumbs that set us apart; for Owen, our enlarged brains. This taste for the monad has influenced the classification of other groups, for example, the whales and the birds. Linnaeus isolated whales in a separate order of mammals, the Mutica and the birds into Aves.

    A preference for dyadic relations led naturalists to classify humans as more perfect than chimpanzees or gorillas. Indeed, the whole of creation was arranged in a scalae naturae, from the lowliest amoebae to the most elevated humans – indeed white, European males (Wood, 2007). This language of higher and lower still persists, for example, in the distinction between lower vertebrates (fish, reptiles and amphibians) and higher vertebrates (birds and mammals). If we look at Ernst Haeckel’s famous evolutionary tree (1866; see figure 3 below), we see the European oak. The tree defines the evolutionary progression from Monera and Amoebae to humans. The labels at the side of the tree show the grades of perfection, through which animals have passed. But the relations are not simply those of perfection; they are ancestor/descendant relations: ‘A is the ancestor of B.’ Monadic relations were broken down and replaced by dyadic relations of ancestry to provide evidence for evolution. Darwin (1859: 184) suggested that whales might be descended from a group of bears, after increasingly adventurous forays for food at the water’s edge. (Today, a group of hoofed mammals, the mesonychids, are the favoured candidate.) The discovery of Archaeopteryx showed the affinity of birds with dinosaurs. One thing you will notice about Haeckel’s tree is that it has side branches. There is no straight chain of descent from amoebae to humans. Lying hidden here in Haeckel’s diagram are triadic relations.

    It fell to German entomologist Willi Hennig to clarify them. He proposed classification through sister group relationships: ‘B is more closely related to C than either is to A.’ B and C are said in this case to be sister groups (Hennig, 1966: 139). So, crocodiles are more closely related to birds than they are to other reptiles. A dyadic relation – reptiles are ancestral to birds – is replaced by a triadic relation. As I noted earlier the statement that ‘Hoofed animals are ancestral to whales’ is transformed into ‘Mesonychids are more closely related to whales than they are to other hoofed animals. And similarly, the statement that ‘Great apes are ancestral to humans’ is transformed into one which states that ‘Chimpanzees are more closely related to humans than to other great apes.’ This is the substance of the revolution in thought that Hennig brought about. Hennig himself still used evolutionary parlance to justify the triadic relation. An ancestral species was thought to split into daughter species, each the ancestor of a particular sister group. ‘Evolution in this sense (transformation) is also connected with speciation: if a species (reproductive community) is split into two mutually isolated communities of reproduction. For Hennig, there is always a change (transformation) of at least one character of the ancestral species in at least one of the daughter species’ (Hennig, 1966: 88). If B and C are sisters, with respect to A, then B and C share a common ancestor that is more recent than either shares with A.

    So the conclusion is that monadic and dyadic relations hardly qualify as the basis of classification. Any two organisms can be related in some way. Only when we introduce a third do we have a definitive classification. Classifications of more than three organisms are to be composed by the number of triadic relations (or three-taxon statements). Nelson and Platnick’s cladogram isolates this triadic aspect of a classification: for an example, see Figure 4, the cladogram of birds, in relation to their (so-called reptilian) sister groups. The cladogram summarises the distribution of feathers in different dinosaur groups (Padian, 2000). Sinosauropteryx has fibrous feathers, which form a thick, relatively short and dense covering of the entire body. True feathers, which have a central shaft, two vanes, and barbs, attach only to the forelimbs and tail. They are found in the oviraptor Caudipteryx, the coelurosaur Protarcheopteryx as well as Archaeopteryx and living birds. Feathers that confer the power of flight are restricted to Archaeopteryx and living birds, where they occur in the same pattern. In each, slightly different feathers (the primaries) attach to the hand from those (the secondaries) that attach to the forelimb (Perrins in Burn, 1980: 169).

    Nelson and Platnick’s conclusions would come as no surprise to Peirce. In A Guess at the Riddle, (c. 1890) Peirce adopts the branching metaphor of a network of roads to explain how all multiple facts may be reduced to triplet facts. Any number of termini may be connected by roads with a fork – triadic relations – but only two termini may be connected by roads without a fork – dyadic relations ( Figure 5. Peirce’s diagram of roads (Figure 4), is redrawn where the termini appear as self returning roads; Wood, 2007), in order to introduce nothing beyond the road itself. Thus, the three essential elements for a network of roads are about the termini, roadway-connections and branching patterns; and in like manner, the three fundamental categories in systematics are facts about an object, facts about two objects (relation), and facts about several objects (synthetic facts)’ (Peirce in Hoopes, 1991: 182-3). Peirce’s fundamental categories are equivalent to the three founding relations of classification (Wood, 1996, 2002), namely features, similarities and homologies. Features are first; they exist in one species considered alone. Similarities are second; they relate one species to another in time and space. Homologies are third; they show that two species are more closely related to one another than they are to the third. The third species reveals the thirdness of the sister species; it provides the context within which the other two find their relationship (see table 1). If we look deeper into Peirce’s work it is obvious that his semiotics dates back to earlier general science. Triadic relations are obvious descendants of the medieval notions of triangular logic and parsimony.

    Three stages of classification
    Wood (1996), describes three stages of classification: fundamental, derivative and general. The fundamental stage of classification involves the collection of representative specimens of the species to be studied. In the derivative stage, characters are conceptualised and the character states for particular species recorded. The general stage is the generation of a classification as the most economical summary of the data (parsimony) and the discovery of the defining characters of taxa. Each stage of classification involves a different kind of pattern. A fundamental pattern consists of the observed features of all morphological variants of a given species, which are, at this stage, not yet conceptualised. A derivative pattern is a pattern of similarity shared by a number of species. A general pattern describes the pattern of homologies inherited by organisms through common descent. Sharing is meaning in the derivative context, and congruence, the nested hierarchical relationship between patterns of similarity, is meaning in the general context.

    Character concepts begin life in the fundamental stage as features identified in single species. The derivative stage of character conceptualisation is the clash between firsts. Character concepts are tested against out-group specimens of different species, and if found not to be applicable are modified or abandoned. The general stage is the clash between seconds. Similarities that are incongruent with the most parsimonious pattern are meaningless. They are homoplasies rather than homologies, confusing rather than revealing thirdness in the study group. Each stage of classification involves the discovery of a particular kind of sign. In the context of a given stage, features, similarities and homologies are signs, (sensu Peirce; see Figure 4), with particular objects and interpretants.

    In the fundamental stage, the sign is that a particular object specimen has a distinctive feature, for example ‘Sinosauropteryx has fibrous feathers.’ The interpretant is ‘… as opposed to true feathers’, which brings in the whole web of anatomical comparisons that embeds the study. The interpretant creates a character, a relation of exclusion: ‘feathers fibrous or true’, the fundamental stage of classification. In the derivative stage (Figure 7), different specimens are brought into relation. Hence the features of the oviraptor Caudipteryx and living birds signify that the two are similar in an object ‘having true feathers’. The interpretant here is the whole data matrix, which described the distribution of similarities across the whole study group. This character matrix forms the basis of the cladistic analysis of relationships, these days often performed with the aid of computerised algorithms, such as PAUP* (Swofford, 2007) or Hennig86 (Farris 1986) for the derivative stage of classification. In the general stage the analysis of the data matrix reveals that certain similarities function as homologies at some level of generality. In other words, these similarities identify sister group relationships and define taxa within the classification.

    Developments in systematics
    One of the saddest things for me since Hennig’s brilliant work has been the subsequent developments in systematics. The basic concepts in cladistics revolve around hypotheses of homology, synapomorphy, and groups, cladograms (phylogenetic trees, sensu Hennig, 1965, 1966). However, in addition to Hennig’s contributions have been various other methods proposed which purport to be cladistics, but involve basic premises other than parsimony, synapomorphy and monophyletic groups (cladograms). With the increasing importance of computers various different phylogenetic inference methods methods have considered to be improvements over cladistic methods. In addition to maximum parsimony, and Least Squares Maximum Parsimony which are based on the hennigian approach, there have been developments in phenetics (e.g. UPGMA and many various clustering algorithms), and so-called statistical approaches such as maximum likelihood, neighbor joining, and Bayesian Inference (Glenner et al., 2004, Huelsebeck, 2008, Huelsenbeck et al. 2007), which to my mind are departures from cladistics rather than developments of it.

    It terms of cladistic development since 1981, Siebert and Williams (1998) noted that was a problem of maximum parsimony methods and the problem of homology. To make the point that the Hennigian approach and subsequent similar computerised methods were based on evolutionary models they advocated the new method originally developed by Nelson and Platnick (1991) as one step in furthering the cause of diminishing dependency. In citing Nelson:

    “Conventional parsimony analysis also interprets information derived from observations as relative relationship, but through the lens of a particular model of character evolution, operating on a binary representation of those observations. Nelson (1992: 360) succinctly described this lens as a: “Model of character evolution that requires synapomorphy to have unique origin (optimised as 1 at a node with distal 0s as reversal or vice versa)””,

    they suggested that concentrating on the relationship part of Hennig’s three-taxon requirement, they recoded characters into three-item statements to obtain the optimal cladograms. This was effectively a development on “transformed cladistics” (Platnick, 1979) which removed the dependency of hypotheses about characters and hypotheses of groups relying on ancestors, to the idea that hypotheses about characters give us hypotheses about groups which could be interpreted as hierarchy. This supports the idea that the systematics (cladistics) of organisms are studied prior to evolutionary interpretation.

    Summary and conclusions.

    “entia non sunt multiplicanda praeter necessitatem“ (William of Ockham, 14° century).

    In summary, I would note that we have come as far as we can in systematics for the present time. This has tremendous impact on what I think might be the future of systematics. It is clear to me that the general principles of systematics and classification including the basic principles of parsimony and relationship have been discovered and shown to be deeply entrenched in medieval ideas of science. Significant re-interpretation in the light of 18 and 19th century logic has come about with even more information emerging in the 19th and 20th centuries, to show that systematics is fundamental to understand evolution and nothing can be interpreted prior to systematic study. I think the future problems of homology and relationships will be solved by the techniques of systematics familiar to those in the late 19th and early 21st centuries. I think the basis of cladistics uses the philosophy of Saussure and Pierce and hence can be retraced back to medieval philosophy and it will be hard to improve on three-item statements (triadic relations), parsimony, and tree-like hierarchies to express information about the diversity of Life on Earth.

    Literature cited
    Blumenbach, 1779. Handbuch der Naturgeschichte. Manual of Natural History. Göttingen, J. C. Dieterich.
    Burn, D. M. (1980, ed.) The Colour Encyclopaedia of the Animal Kingdom. Peerage, London.
    Darwin, C. 1851. A monograph on the fossil Lepadidae, or, pedunculated cirripedes of Great Britain.[Vol. 1]
    Darwin, C. 1854 [=1855]. A monograph on the fossil Balanidae and Verrucidae of Great Britain. [Vol. 2]
    Darwin, C. 1859. The Origin of Species. James Murray, London.
    Farris, J. S. 1986. Hennig86; A cladistics package. Distributed by the author.
    Glenner H, Hansen AJ, Sørensen MV, Ronquist F, Huelsenbeck JP, Willerslev E. 2004 Bayesian inference of the metazoan phylogeny; a combined molecular and morphological approach. Curr. Biol. 21; 1 4(18): 1644-9.
    Haeckel, E. 1866. Generelle Morphologie der Organismen. Berlin: Georg Reimer. 462 pp.
    Hennig, W. 1950. Grundzüge einer Theorie der Phylogenetische Systematik . Deutscher Zentralverlag, Berlin.
    Hennig, W. 1965. Phylogenetic Systematics, Ann.Rev.Entomol., 10; 97-116.
    Hennig, W. 1966. Phylogenetic Systematics. University of Illinois Press, Urbana.
    Hoopes, J. 1991. Peirce on signs: writings on semiotic. University of North Carolina Press.
    Huelsenbeck 2008 Jun. A Bayesian perspective on a non-parsimonious parsimony model. Syst Biol. ;57(3):406-19.
    Huelsenbeck, J.P. Ronquist, F. and Hall, B. 2007. MrBayes: A program for the Bayesian inference of phylogeny Manual.
    Huxley,T. H. (1858-62). On Species and Races, and Their Origin. Proceedings of the Royal Institution of Great Britain (1860) Scientific Memoirs II. PRI 3: 195-200; AnMNH 5 (1860): 344-46; SM 2: 388-94.
    Liszka, J. J. 1996. A General Introduction to the semiotic of Charles Sanders Peirce. Indiana University Press.
    Maddison, D. R., K.-S. Schulz, and W. P. Maddison. 2007. The Tree of Life Web Project. Pages 19-40 in: Zhang, Z.-Q. & Shear, W.A., eds. Linnaeus Tercentenary: Progress in Invertebrate Taxonomy. Zootaxa 1668:1-766.
    Nelson, G. J. and Platnick, N. I. 1981. Systematics and Biogoegraphy; Cladistics and vicariance. New York, Columbia University Press
    Owen, R. 1858. Address of the president. Report of the 28th meeting of the British Association for the Advancement of Science, held at Leeds, pp. xlix–cx.
    Padian, K. 1999. Charles Darwin’s views of classification in theory and in practice. Systematic Biology 48:352-364.
    Peirce, Charles Sanders. Collected Papers of Charles Sanders Peirce. Volumes I and II. Cambridge: Harvard University Press, 1960.
    Peirce, Charles Sanders. Collected Papers of Charles Sanders Peirce. Volumes V and VI. Cambridge: Harvard University Press, 1960.
    Peirce, Charles Sanders. Collected Papers of Charles Sanders Peirce. Volume VIII. Cambridge: Harvard University, Press, 1958.
    Siebert, D. J. & Williams, D. M. – 1998. Recycled. Cladistics 14(4): 143-49.
    Swofford, D. Latest Update 2007. PAUP* V.IV. Sinauer Associates, Sunderland Massachusetts.
    Wood, S. (1966) Systematics of the Macrourid Fishes. University of Cambridge, doctoral dissertation. iii+155 pp., 4 tables, 57 figures.
    Wood, S.W. (2002) The holographic principle in biological development
    and quantum physics. In Bowden, K. G. (ed.), pp. 199-245, Correlations: Proceedings of ANPA 23. Alternative Natural. Philosophy Association.
    Wood, S. 2007. Comprehensive Categories of Life.

    Figure 1

    Darwin, C. R. Notebook B: [Transmutation of species (1837-1838)]. See the fully annotated transcription of this notebook by David Kohn in Barrett, Paul H., Gautrey, Peter J., Herbert, Sandra, Kohn, David, Smith, Sydney eds. 1987. Charles Darwin’s notebooks, 1836-1844 : Geology, transmutation of species, metaphysical enquiries. British Museum (Natural History); Cambridge: Cambridge University Press.

    Figure 2. The only figure in the first and subsequent editions of the Origin of Species (Darwin, 1859). There are two evolving lines, A and I, several historical lines ending in extinction, B, C, D, E, G, H and L, one line of stasis. At each intermediary stage there are many taxa that become rapidly extinct but various lineages live through to the present day – shown as the top line. Each median horizontal bar shows successive stages of time.

    Figure 3. Haeckel’s tree of life from Monera to Man depicted as a European oak. Note the use of grades and clades in his notion of phylogeny. Haeckel, Ernst. (1866) “Generelle Morphologie der Organismen” Berlin: Georg Reimer. 462 pp.

    Figure 4. Peirce’s Road Map (drawn as an unrooted tree).

    Figure 5. Peirce’s road map redrawn as a rooted cladogram by adding a root at the point of the black circle in Figure 4. Taxon labels and transforming characters have been added to show the cladogram as a rooted biological cladogram. The presence of feathers, whether fibrous or true, defines the Coelurosauria, which includes living birds. Archaeopteryx is similar to living birds in having flying feathers, but cladistic analysis also reveals that ‘flying feathers’ is a homology, identifying Archaeopteryx as the sister group of living birds.

    Table 1. The basis of semiotics and classification
    In Peirce’s terminology these became:
    1. Monadic: ‘X exists’ (object)
    2. Dyadic: ‘X is related to Y’ (similarity)
    3. Triadic: ‘X is more closely related to Y than either is to Z’
    (homology and classification)

    So in classificatory logic these became:
    Object — Sign — Interpretent:
    Specimen — Feature — Character
    Feature — Similarity — Character Matrix
    Similarity — Homology — Classification
    [Homology — relationship — Final named Classification]

    Comment by topher21 | January 13, 2009 | Reply

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