“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).
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.