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Eco: The Limits of Classification

John Wilkins, An Essay, the Lords Prayer, Ch.II, p. 7

John Wilkins (1614-1672), An Essay Towards a Real Character and a Philosophical Language, London, John Martin, 1668. Chapter II, p. 7, a discussion of the changes in the Lord’s Prayer. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“Using 40 genera and 251 differences, Wilkins‘ tables manage to define 2,030 species. If, however, the division were dichotomic, as happens with the Aristotelian system of classification, in which each genus was assigned two decisive differences which constituted to new species below, and in which each of these new species then played the role of genera at the lower level in the process of dichotomization, there should have been at least 2,048 species (as well as 1,025 intermediary genera plus the category at the apex) and an equal number of differences.

If the figures do not add up in the way that they should, it is clear that, in reconstructing a single general tree from the 41 particular trees represented in the tables, one would not find a constant dichotomic structure.

The structure is not dichotomic because Wilkins mixes substances and accidents together; but since, as Dalgarno had recognized, the number of accidents is infinite, there is no way that they can be hierarchically ordered.

In fact, Wilkins must classify fundamental and Platonic conceptions, like God, world or tree, together with drinks, like beer, political offices, military and ecclesiastical ranks–in short, the whole notional world of a seventeenth century Englishman.

It suffices to look at figure 12.1 to see that the accidents are subdivided into five categories each yielding from three to five genera. There are three subdivisions of the genus Herb as well as of the genus Transcendental things.

With a dichotomic structure it would be easy, once having established the number of embedded levels, to control the total number of entities in the system; once the pattern has been broken, however, and more than two subdivisions allowed to appear at each nodal point, the whole system begins to spin out of control.

The system is open to new discoveries, but, at the same time, surrenders its control over the number of primitives.

When he reaches the last differences, Wilkins arranges them in pairs. Yet, as he is the first to recognize, he has made his arrangement “for the better helming of the memory” (p. 22), not according to a rigorous criterion of opposition.

He informs us that pairs are based sometimes on opposition and sometimes on affinity. He admits to having coupled his differences in an arguable way, but says that he did so “because I knew not to provide for them better” (p. 22).

For instance, in the first genus, General Transcendental, the third difference, Diversity, generates as the second of its species Goodness and its opposite, Evil; but the second difference, Cause, generates as its third species Example and Type.

These two categories are not opposed; in fact it is not clear what their relation to each other is. We can imagine some sort of relation of affinity or similarity; yet, in whatever case, the criterion seems weak and ad hoc.

Among the accidents of Private Relations, under the species Economical Relations, we find both Relations of Consanguinity (like Progenitor / Descendant, Brother / Half-Brother, Coelebs / Virgin–but Coelebs has among its synonyms both Bachelour and Damosel, while Virgin only Maid) and Relations of Superiority (Direct / Seduce, Defending / Deserting).

It is clear that all of these oppositions lack a constant criterion. Among the same Private Relations there are also the Provisions, which includes pairs such as Butter / Cheese, but also actions such as Butchering / Cooking and Box / Basket.

Frank has observed that Wilkins considered as semantically equivalent different kinds of pseudo-opposition as they appear in natural languages, which can work by antonymy (good / evil), by complementarity (husband / wife), by conversely (buy / sell), by relativity (over / under, bigger / smaller), by temporal gradation (Monday / Tuesday / Wednesday), by quantitative gradation (centimeter / meter / kilometer), by antipodality (north / south), by orthogonality (north-east / south-east), or by vectorial conversely (depart / arrive).

It is hardly by chance that Wilkins is repeatedly forced to justify his language on mnemonic grounds. In fact, Wilkins takes some of his procedures from the traditional arts of memory.

His criterion for establishing pairs is based on the most common mnemonic habits. Rossi (1960: 252) notes that Wilkins‘ botanist, John Ray, complained that he was not permitted to follow the commandments of nature, but rather the exigencies of regularity, almost as if he were forced to adapt his classification more to requirements of the traditional theaters of memory than to the canons of modern taxonomies.

Nor is it even clear what, in the tree of genera (figure 12.1), the subdivisions in lower case actually mean. They cannot be differences, because the differences appear later, in successive tables, and determine how, in each of the 40 major genera, the dependent species are to be generated.

Some of these lower-case entities seem to serve as super-genera; yet others appear in an adjectival form. Certain of these latter look like differences in the Aristotelian tradition–like animate / inanimate, for example. We might regard them as pseudo-differences.

However, if the generative path “substances + inanimate = ELEMENTS” seems to follow an Aristotelian criterion, the disjunctions after animate are established in a quite different fashion.

Animate substances are divided into parts and species, the species are divided into vegetative and sensitive, the vegetative species into imperfect and perfect, and it is only at the end of these disjunctions that it is possible to isolate genera like Stone or Metal.

This is not the only instance of this sort of confusion. Moreover, given a pair of opposed categories, such as Creator / creature, the first term of the division is a genus, but the second appears as a pseudo-difference through which, after other disjunctions, it is possible to isolate other genera.

Likewise, in the group Herb, Shrub and Tree, the last two are genera; the first is a sort of super-genus (or pseudo-difference) subdivided into three further genera.

It would be nice, Wilkins confessed (p. 289), if each of his differences had its own transcendental denomination; yet there did not seem to be sufficient terms in the language for this.

He admitted as well that while, in theory, a well-enough individuated difference would immediately reveal the form which gave the essence to each thing, these forms remained largely unknown.

So he had to content himself by defining things through properties and circumstances.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 251-4.

Eco: An Open Classification?

John Wilkins, An Essay towards a Real Character, 1668, p. a from the Epistle

John Wilkins (1614-1672), An Essay towards a Real Character and a Philosophical Language, page a from the Epistle. London, John Martin, 1668. GoogleBooks offers a digital version of the complete text. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“In reality, Wilkins’ classification ought to be regarded as an open one. Following a suggestion of Comenius‘ (in the Via lucis), Wilkins argued that the task of constructing an adequate classification could only be undertaken by a group of scientists working over a considerable period of time, and to this end he solicited the collaboration of the Royal Society.

The Essay was thus considered no more than a first draft, subject to extensive revision. Wilkins never claimed that the system, as he presented it, was finished.

Looking back at figures 12.3 and 12.4, it is evident that there are only nine signs or letters to indicate either differences or species. Does this mean that each genus may have no more than nice species? It seems that the number nine had no ontological significance for Wilkins, and that he chose it simply because he thought nine was the maximum number of entities that might easily be remembered.

He realized that the actual number of species for each genus could not be limited. In fact, certain of the genera in the tables only have six species, but there are ten species for the Umbelliferous and seventeen for the Verticillates Non Fruticose.

To accommodate genera with over nine species Wilkins invented a number of graphic artifices. For simplicity’s sake, let us say that, in the spoken language, to specify a second group of nine species an l is added after the first consonant of the name, and that to specify a third group an r is added.

Therefore if Gαpe is normally Tulip (third species of the fourth difference of the genus Herbs according to their leaves), then Glαpe will be Ramsom, because the addition of the l means that the final e no longer indicates the third species in the genus but the twelfth.

Yet is precisely at this point that we come across a curious error. In the example we just gave, we had to correct Wilkins‘ text (p. 415). The text uses the normal English terms Tulip and Ramsom, but designates them in characters by Gαde and Glαde rather than Gαpe and Glαpe (as it should be).

If one checks carefully on the tables, one discovered that Gαde denotes Barley, not Tulip. Wilkins‘ mistake can be easily explained: regardless of whatever botanical affinities the plants might possess, in common English, the words Tulip and Barley are phonetically dissimilar, and thus unlikely to ever be confused with each other.

In a philosophical language, however, members of the same species are easy to muddle either phonetically or graphically. Without constant double-checking against the tables, it is difficult to avoid misprints and misunderstandings.

The problem is that in a characteristic language, for every unit of an expression one is obliged to find a corresponding content-unit. A characteristic language is thus not founded–as happens with natural languages–on the principle of double articulation, by virtue of which meaningless sounds, or phonemes, are combined to produce meaningful syntagms.

This means that in a language of “real” characters any alteration of a character (or of the corresponding sound) entails a change of sense.

This is a disadvantage that arises from what was intended as the great strength of the system, that is, its criterion of composition by atomic features, in order to ensure a complete isomorphism between expression and content.

Flame is Debα, because here the α designates a species of the element Fire. If we replace the α  with an a we obtain a new composition, Deba, that means Comet. When designing his system, Wilkins‘ choice of α and a was arbitrary; once they are inserted into a syntagm, however, the syntagmatic composition is supposed to mirror the very composition of the denoted thing, so that “we should, by learning the Character and the Names of things, be instructed likewise in their Natures” (p. 21).

This creates the problem of how to find the name for yet unknown things. According to Frank (1979: 80), Wilkins‘ language, dominated by the notion of a definitively pre-established Great Chain of Being, cannot be creative. The language can name unknown things, but only within the framework of the system itself.

Naturally, one can modify the tables by inserting into them a new species, but this presupposes the existence of some sort of linguistic authority with the power to permit us to think of a new thing. In Wilkins’s language neologisms are not impossible, but harder to form than in natural languages (Knowlson 1975: 101).

One might defend Wilkins‘ language by arguing that it really encompasses a rational methodology of scientific research. If, for example, we were to transform the character Detα (rainbow) into Denα we would obtain a character that we could analyze as denoting the first species of the ninth difference of the genus Element.

Yet there is no such species in the tables. We cannot take the character metaphorically, because only characters followed by transcendental particles may be so interpreted. We can only conclude that the character unequivocally designates an as yet to be discovered content, and that even if the content remains undiscovered, the character has at least told us the precise point where it is to be found.

But what and where is that “point?” If the tables were analogous to the periodic table in chemistry, then we really would know what to look for. The periodic table contains boxes which, though momentarily empty, might, one day, be filled.

Yet the language of chemistry is rigorously quantitative; the table gives the atomic number and weight of each missing element. An empty space in Wilkins‘ classification, however, merely tells us that there is a hole at that point; it does not tell us what we need to fill it up, or why the hole appears in one space rather than another.

Since Wilkins‘ language is not based on a rigorous classification, it cannot be used as a procedure of scientific discovery.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 248-51.

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