1512 | Samizdat

July 4, 2016

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.

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.

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.

May 25, 2016

Eco: Horapollo’s Hieroglyphica

Albrecht Dürer (1471-1528), The Sun, the Moon and a Basilisk, circa 1512. The Sun, the Moon and the Basilisk (half eagle, half serpent, hatched from a cock’s egg by a serpent), represent Eternity. This drawing from a fragment is on the back of a manuscript translation of the Hieroglyphica by Horapollo translated by Willibald Pirkheimer, an associate of Dürer. Alexander Cory’s 1840 edition is posted on the Sacred Texts site, and the 1595 Mercier and Hoeschel edition in Latin and Greek is hosted on Archive.org due to the kind courtesy of the Getty Research Institute and the Sloan Foundation. 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 1419 Cristoforo de’ Buondelmonti acquired from the island of Andros a mysterious manuscript that was soon to excite the curiosity of philosophers such as Ficino: the manuscript was the Greek translation (by a certain Philippos) of the Horapòllonos Neiloùs ieroglyphikà.

The original author, Horapollo–or Horus Apollos, or Horapollus–was thus qualified as “Nilotic.” Although it was taken as genuinely archaic throughout the Renaissance, scholars now believe this text to be a late Hellenistic compilation, dating from as late as the fifth century AD.

As we shall see, although certain passages indicate that the author did possess exact information about Egyptian hieroglyphs, the text was written at a time when hieroglyphic writing had certainly fallen out of use. At best, the Hieroglyphica seems to be based on some texts written a few centuries before.

The original manuscript contained no images. Illustrations appeared only in later editions: for instance, though the first translation into Italian in 1547 is still without illustrations, the 1514 translation into Latin was illustrated by Dürer.

The text is divided into short chapters in which it is explained, for example, that the Egyptians represented age by depicting the sun and the moon, or the month by a palm branch.

There follows in each case a brief description of the symbolic meaning of each figure, and in many cases its polysemic value: for example, the vulture is said to signify mother, sight, the end of a thing, knowledge of the future, year, sky, mercy, Minerva, Juno, or two drachmas.

Sometimes the hieroglyphic sign is a number: pleasure, for example, is denoted by the number 16, because sexual activity begins at the age of sixteen. Since it takes two to have intercourse, however, this is denoted by two 16’s.

Humanist philosophical culture was immediately fascinated by this text: hieroglyphs were regarded as the work of the great Hermes Trismegistus himself, and therefore as a source of inexhaustible wisdom.

To understand the impact of Horopollo’s text on Europe, it is first necessary to understand what, in reality, these mysterious symbols were. Horopollo was describing a writing system, whose last example (as far as Egyptologists can trace) is on the Theodosius temple (AD 394).

Even if these inscriptions were still similar to those elaborated three thousand years before, the Egyptian language of the fifth century had changed radically. Thus, when Horopollo wrote his text, the key to understanding hieroglyphs had long been lost.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 145-6.

May 2, 2016

Eco: The Arbor Scientarium

Ramon Llull, Liber de ascensu et decensu intellectus, 1304, first published 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.

“The Lullian art was destined to seduce later generations who imagined that they had found in it a mechanism to explore the numberless possible connections between dignities and principles, principles and questions, questions and virtues or vices.

Why not even construct a blasphemous combination stating that goodness implies an evil God, or eternity a different envy? Such a free and uncontrolled working of combinations and permutations would be able to produce any theology whatsoever.

Yet the principles of faith, and the belief in a well-ordered cosmos, demanded that such forms of combinatorial incontinence be kept repressed.

Lull’s logic is a logic of first, rather than second, intentions; that is, it is a logic of our immediate apprehension of things rather than of our conceptions of them. Lull repeats in various places that if metaphysics considers things as they exist outside our minds, and if logic treats them in their mental being, the art can treat them from both points of view.

Consequently, the art could lead to more secure conclusions than logic alone, “and for this reason the artist of this art can learn more in a month than a logician can in a year.” (Ars magna, X, 101).

What this audacious claim reveals, however, is that, contrary to what some later supposed, Lull’s art is not really a formal method.

The art must reflect the natural movement of reality; it is therefore based on a notion of truth that is neither defined in the terms of the art itself, nor derived from it logically. It must be a conception that simply reflects things as they actually are.

Lull was a realist, believing in the existence of universals outside the mind. Not only did he accept the real existence of genera and species, he believed in the objective existence of accidental forms as well.

Thus Lull could manipulate not only genera and species, but also virtues, vices and every other sort of differentia as well; at the same time, however, all those substances and accidents could not be freely combined because their connections were determined by a rigid hierarchy of beings (cf. Rossi 1960: 68).

In his Dissertatio de arte combinatoria of 1666, Leibniz wondered why Lull had limited himself to a restricted number of elements. In many of his works, Lull had, in truth, also proposed systems based on 10, 16, 12 or 20 elements, finally settling on 9. But the real question ought to be not why Lull fixed upon this or that number, but why the number of elements should be fixed at all.

In respect of Lull’s own intentions, however, the question is beside the point; Lull never considered his to be an art where the combination of the elements of expression was free rather than precisely bound in content.

Had it not been so, the art would not have appeared to Lull as a perfect language, capable of illustrating a divine reality which he assumed from the outset as self-evident and revealed.

The art was the instrument to convert the infidels, and Lull had devoted years to the study of the doctrines of the Jews and Arabs. In his Compendium artis demonstrativa (“De fine hujus libri“) Lull was quite explicit: he had borrowed his terms from the Arabs.

Lull was searching for a set of elementary and primary notions that Christians held in common with the infidels. This explains, incidentally, why the number of absolute principles is reduced to nine (the tenth principle, the missing letter A, being excluded from the system, as it represented perfection or divine unity).

One is tempted to see in Lull’s series the ten Sefirot of the kabbala, but Plazteck observes (1953-4: 583) that a similar list of dignities is to be found in the Koran. Yates (1960) identified the thought of John Scot Erigene as a direct source, but Lull might have discovered analogous lists in various other medieval Neo-Platonic texts–the commentaries of pseudo-Dionysius, the Augustinian tradition, or the medieval doctrine of the transcendental properties of being (cf. Eco 1956).

The elements of the art are nine (plus one) because Lull thought that the transcendental entities recognized by every monotheistic theology were ten.

Lull took these elementary principles and inserted them into a system which was already closed and defined, a system, in fact, which was rigidly hierarchical–the system of the Tree of Science.

To put this in other terms, according to the rules of Aristotelian logic, the syllogism “all flowers are vegetables, X is a flower, therefore X is a vegetable” is valid as a piece of formal reasoning independent of the actual nature of X.

For Lull, it mattered very much whether X was a rose or a horse. If X were a horse, the argument must be rejected, since it is not true that a horse is a vegetable. The example is perhaps a bit crude; nevertheless, it captures very well the idea of the great chain of being (cf. Lovejoy 1936) upon which Lull based his Arbor scientiae (1296).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 64-7.

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Tag: 1512

July 4, 2016

Eco: Primitives and Organization of Content, 2

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May 25, 2016

Eco: Horapollo’s Hieroglyphica

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May 2, 2016

Eco: The Arbor Scientarium

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