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Eco: Primitives and Organization of Content, 2

Ramon Llull, Arbor naturalis et logicalis, Liber de logica nova, Valencia, Alonso de Proaza, 1512

Ramon Llull (1232-1315), Arbor naturalis et logicalis, Liber de logica nova, Valencia, 1512. A Porphyrian Tree of logical relations, original c. 1305, logica nova edition 1512. 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. 

“Nevertheless, such a dictionary-like structure would not allow us to define the difference between a cat and a tiger, or even between a canine and a feline animal. To do this, it is necessary to insert differences into the classification.

Aristotle, in his studies of definition, said that, in order to define the essence of a thing, we should select such attributes which “although each of them has a wider extension than the subject, all together they have not” (Posterior Analytics II, 96a, 35).

Such a structured representation was known in the Middle Ages as Porphyry’s Tree (because it was derived from the Isagoge of the Neo-Platonic philosopher Porphyry, living in the second-third century AD), and was still taken as a definitional model by the English searchers for a real character.

In a Porphyrian Tree each genus is divided by two differences which constitute a pair of opposites. Each genus, with the addition of one of its divisive differences, produces an underlying species, which is so defined by its genus and its constitutive difference.

Umberto Eco, The Search for the Perfect Language, Figure 10.2, p. 225

Umberto Eco, The Search for the Perfect Language, Figure 10.2, p. 225. 

In figure 10.2, there is an example of how a Porphyrian Tree establishes the difference between human beings and gods (understood as natural forces) and between human beings and beasts.

The terms in upper-case refer to genera and species while those in lower-case refer to differences, that is, to particular accidents which occur only in a given species. We see that the diagram defines a human being as a “rational and mortal animal,” which, in classical terms, is considered a satisfactory definition because there cannot be a rational and mortal animal which is not a human being, and only human beings are so.

Unfortunately this diagram does not tell us anything about the differences between dogs and cats, or horses and wolves, or cats and tigers. In order to obtain new definitions, new differences need to be inserted into the diagram.

Besides this, we can see that, although differences occur in one species, in this tree there are differences, such as “mortal/immortal,” which occur in two different species.

This makes it difficult to know whether or not the same differences will be reproduced at some further point in the tree when it becomes necessary to specify the difference not just between dogs and cats, but also between violets and roses, diamonds and sapphires, and angels and demons.

Even taxonomy as practiced by modern zoology defines through dichotomies. Dogs are distinguished from wolves, and cats from tigers, on the basis of a dichotomy by taxonomic entities known as taxa (figure 10.3).

Umberto Eco, The Search for the Perfect Language, Figure 10.3, p. 226

Umberto Eco, The Search for the Perfect Language, Figure 10.3, p. 226. 

Yet modern zoologists are well aware that a system of classification is not the same as a system of definitions.

Classification does not capture the essence of the thing itself; it simply embeds things in a system of increasingly inclusive classes, where the lower nodes are linked by entailment to the upper ones: if something is a Canis familiaris, it cannot but be, by entailment, a Canis, a canid and a fissiped.

But Canidae and Fissipeda are taken as primitives only in the framework of the classification and are not considered as semantic primitives.

Zoologists know that, within their classification, at the node Canidae they must presuppose a set of properties common to the whole family, and that at the node Carnivora there is a set of properties common to the whole order: in the same vein, “mammal” is not a semantic primitive but a technical name which stands for (more or less) “viviparous animal which nourishes its young by the secretion of milk through its mammary glands.”

The name of a substance can be either designative (thus indicating the genus to which that substance belongs) or diagnostic, that is, transparent and self-definatory.

In Species plantarum by Linnaeus (1753), given the two species, Arundo calamogrostis and Arundo arenaria, their designative names show that they belong to the same genus and establish their difference; however, their properties are then made clearer by a diagnostic description which specifies that the Arundo calamogrostis is “calycibus unifloris, cumulo ramoso,” while the Arundo arenaria is “calycibus unifloris, foliis involutiis, mucronato pungentibus” (see Slaughter 1982: 80).

However, the terms used for this description are no longer pseudo-primitives–like those of the metalanguage of taxas; they are terms of the common natural language used for diagnostic purposes.

By contrast, for the authors of a priori languages, each expression had to express all the properties of the designated thing. We shall see how such a difficulty will affect all the projects discussed in the following chapters.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 225-7.

Eco: The Ars Magna of Raymond Lull

Raymond Lull, Tabula Generalis, pg. 57, Eco, Search for a Perfect Language, 1995

Raymond Lull (1232-1316), Tabula Generalis, figure 4.1, Lull’s Alphabet, from Umberto Eco, The Search for a Perfect Language, Blackwell, Oxford, 1995, pg. 57. 

“A near contemporary of Dante, Ramòn Llull (Latinized as Lullus and Anglicized as Lull–and sometimes as Lully) was a Catalan, born in Majorca, who lived probably between 1232 (or 1235) and 1316.

Majorca during this period was a crossroads, an island where Christian, Jewish and Arab cultures all met; each was to play a role in Lull’s development. Most of his 280 known works were written initially in Arabic or Catalan (cf. Ottaviano 1930).

Lull led a carefree early life which ended when he suffered a mystic crisis. As a result, he entered the order of Tertian friars.

It was among the Franciscans that all of the earlier strands converged in his Ars magna, which Lull conceived as a system for a perfect language with which to convert the infidels. The language was to be a universal; it was to be articulated at the level of expression in a universal mathematics of combination; its level of content was to consist of a network of universal ideas, held by all peoples, which Lull himself would devise.

St. Francis had already sought to convert the sultan of Babylonia, and the dream of establishing universal concordance between differing races was becoming a recurrent theme in Franciscan thought. Another of Lull’s contemporaries, the Franciscan Roger Bacon, foresaw that contact with the infidels (not merely Arabs, but also Tartars) would require study of foreign languages.

The problem for him, however, was not that of inventing a new, perfect language, but of learning the languages that the infidels already spoke in order to convert them, or, failing that, at least to enrich Christian culture with a wisdom that the infidels had wrongfully appropriated (“tamquam ab iniustis possessoribus“).

The aims and methods of Lull and Bacon were different; yet both were inspired by ideals of universality and of a new universal crusade based on peaceful dialogue rather than on arms.

In this utopia the question of language played a crucial role (cf. Alessio 1957). According to legend, Lull was to die martyred at the hands of the Saracens, to whom he had appeared, armed with his art, believing it to be an infallible means of persuasion.

Lull was the first European philosopher to write doctrinal works in the vulgar tongue. Some are even in popular verses, so as to reach readers who knew neither Latin nor Arabic: “per tal che hom puscha mostrar / logicar e philosophar / a cels que win saben lati / ni arabichi” (Compendium, 6-9).

His art was universal not merely in that it was designed to serve all peoples, but also in that it used letters and figures in a way (allegedly) comprehensible even to illiterates of any language.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 53-4.

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