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Eco: George Dalgarno

Dalgarno_Ars_Signorum

George Dalgarno (1626-1687), title page of Ars Signorum, printed by J. Hayes, London, 1661. Published 20 years before Didascalocophus, Ars signorum preceded Bishop Wilkin‘s speculations on a “real character and a philosophical language.” 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.

“It is difficult to make a precise evaluation of George Dalgarno’s Ars signorum, published in 1661. In contrast to Wilkin’s Essay, Dalgarno’s tables are summary and the text, in its expository sections, is written in a language that is extremely cryptic, sometimes contradictory, and almost always strikingly allusive.

The book is filled with printer’s errors, especially where Dalgarno provides examples of real characters–not an inconsiderable problem in reading a language where the misprint of one letter changes the whole sense of the character.

We might note that the difficulty in printing a text free of errors shows how cumbersome the philosophic languages were, even for their own creators.

Dalgarno was a Scottish schoolmaster who passed most of his life at Oxford, where he taught grammar at a private school. He was in touch with all the contemporary scholars at the university, and in the list of acknowledgements at the beginning of his book he mentions men such as Ward, Lodwick, Boyle and even Wilkins.

It is certain that, as he was preparing his Essay (published seven years later), Wilkins contacted Dalgarno and showed him his own tables. Dalgarno regarded them as too detailed, and chose to follow what seemed to him an easier path.

When Wilkins finally made his project public, however, Dalgarno felt himself to be the victim of plagiarism. The suspicion was unjust: Wilkins had accomplished what Dalgarno had only promised to do.

Besides, various other authors had already anticipated many of the elements appearing in the project of Dalgarno. Still, Wilkins resented the insinuation of wrong-doing. In the acknowledgements that prefaced his Essay, Wilkins was prodigal with his thanks to inspirers and collaborators alike, but the name of Dalgarno does not appear–except in an oblique reference to “another person.” (b2r).

In any case, it was the project of Wilkins that Oxford took seriously. In 1668 the Royal Society instituted a commission to study the possible applications of the project; its members included Robert Hook, Robert Boyle, Christopher Wren and John Wallis.

Although we are not informed of the conclusions that they finally reached, subsequent tradition, from Locke to the Encyclopédie, invariably treated Wilkins as the author of the most important project.

Perhaps the only scholar who considered Dalgarno respectfully was Leibniz, who, in a rough draft for his own encyclopedia, reproduced Dalgarno’s list of entities almost literally (see Rossi 1960: 272).

Wilkins, of course, was perfectly at home at the Royal Society. He served as its secretary, and could freely avail himself of the help, advice, patronage and attention of his fellow members. Dalgarno, by contrast, was not even a member of the university.

Dalgarno saw that a universal language needed to comprehend two distinct aspects: first, a content-plane, that is, a classification of all knowledge, and that was a task for a philosopher; second, an expression-level, that is, a grammar that organized the characters so that they can properly denote the content elements–and this was a task for a grammarian.

Dalgarno regarded himself as a grammarian rather than a philosopher; hence he merely outlined the principles of classification upon which his language would be based, hoping that others might carry this task to fruition.

As a grammarian, Dalgarno was sensitive to the problem that his language would need to be spoken and not just written. He was aware of the reserves Descartes had expressed about the difficulty of devising a philosophic language that might be pronounced by speakers of differing tongues; thus he introduced his project with a phonetic analysis which sought to identify those sounds which were most easily compatible with the human organs of speech.

The letters from which he later composed his character were not, as they might seem, chosen arbitrarily; he chose instead those which he considered most easy to utter. Even when he came to elaborate the syntagmatic order of his character, he remained concerned with ease of pronunciation.

To this end, he made sure that consonants were always followed by vowels, inserting in his character a number of diphthongs whose function is purely euphonious. This concern certainly ensured ease of pronunciation; unfortunately, it also rendered his character increasingly difficult to identify.

After phonetics, Dalgarno passed to the problem, of the semantic primitives. He believed that these could all be derived solely in terms of genus, species and difference, arguing that such a system of embedded dichotomies was the easiest to remember (p. 29).

For a series of logico-philosophical reasons (explained pp. 30ff), he excluded negative differences from his system, retaining only those which were positive.

The most ambitious feature of Dalgarno’s project (and Wilkin’s as well) was that his classification was to include not only natural genera and species (comprehending the most precise variations in animals and plants) but also artifacts and accidents–a task never attempted by the Aristotelian tradition (see Shumaker 1982: 149).

In fact, Dalgarno based his system of classification on the rather bold assumption that all individual substances could be reduced to an aggregate of accidents (p. 44). This is an assumption which, as I have tried to show elsewhere (Eco 1984: 2.4.3), arises as an almost mechanical consequence of using Porphyry’s Tree as a basis for classification; it is a consequence, moreover, that the entire Aristotelian tradition has desperately tried to ignore.

Dalgarno confronted the problem, even though recognizing that the number of accidents was probably infinite. He was also aware that the number of species at the lowest order was unmanageably large–he calculated that they would number between 4,000 and 10,000.

This is probably one of the reasons why he rejected the help of Wilkins, who was to persevere until he had classified 2,030 species. Dalgarno feared that such a detailed classification ran the risk of a surgeon who, having dissected his cadavers into minute pieces, could no longer tell which piece belonged to Peter and which to John (p. 33).

In his endeavor to contain the number of primitives, Dalgarno decided to introduce tables in which he took into consideration only fundamental genera (which he numbered at 17), together with the intermediary genera and the species.

Yet, in order to gather up all the species in this tripartite division, Dalgarno was forced to introduce into his tables a number of intermediate disjunctions. These even received names in the language: warm-blooded animals, for example, are called NeiPTeik; quadrupeds are named Neik.

Yet in the names only the letters for genera, intermediary genera, and species are taken into account. (Mathematical entities are considered as concrete bodies on the assumption that entities like points and lines are really forms).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 228-31.

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: Primitives and Organization of Content

The_Tyger_BM_a_1794

William Blake (1757-1827), The Tyger, 1794. Scan of a plate printed by the author collected in Songs of Experience, designed after 1789 and printed in 1794. Copies A and B are both held by the British Museum. This work is in the public domain in its country or origin and other countries and areas where the copyright term is the author’s life plus 100 years or less.

“In order to design characters that directly denote notions (if not the things themselves that these notions reflect), two conditions must be fulfilled: (1) the identification of primitive notions; (2) the organization of these primitives into a system which represents the model of the organization of content.

It is for this reason that these languages qualify as philosophical and a priori. Their formulation required individuating and organizing a sort of philosophical “grammar of ideas” that was independent from any natural language, and would therefore need to be postulated a priori.

Only when the content-plane had been organized would it be possible to design the characters that would express the semantic primitives. As Dalgarno was later to put it, the work of the philosopher had to precede that of the linguist.

For the polygraphers, invention was simply the job of assigning numbers to a collection of words from a given natural language. The inventors of philosophic a priori languages needed to invent characters that referred to things or notions: this meant that their first step was to draw up a list of notions and things.

This was not an easy task. Since the lexicon of any natural language is always finite in number, while the number of things, including physically existing objects, rational entities, accidents of all types, is potentially infinite, in order to outline a list of real characters it is necessary to design an inventory which is not only universal: it must also be in some way limited.

It is mandatory to establish which notions are the most universally common, and then to go on by analyzing the derivative notions according to a principle of compositionality by primitive features.

In this way, the entire set of possible contents that the language is able to express has to be articulated as a set of “molecular aggregates” that can be reduced to atomic features.

Suppose we had three semantic atoms such as ANIMAL, CANINE and FELINE. Using them, we might analyze the following four expressions:

Umberto Eco The Search for the Perfect Language p. 222.png

Umberto Eco, The Search for the Perfect Language, p. 222. 

Yet the features that analyze the content of the above expressions ought to be entities totally extraneous to the object language.

The semantic feature CANINE, for example, must not be identifiable with the word canine. The semantic features ought to be extra-linguistic and possibly innate entities. At least they should be postulated as such, as when one provides a computer with a dictionary in which every term of a given language can be split into minor features posited by the program.

In any case, the initial problem is how to identify these primitive and atomic features and set a limit on their number.

If one means by “primitive” a simple concept, it is very difficult to decide whether and when one concept is simpler than another. For the normal speaker, the concept of “man” is simpler–that is, easier to understand–than the one of “mammal.”

By contrast, according to every sort of semantic analysis, “mammal” is a component of (therefore simpler than) “man.” It has been remarked that for a common dictionary it is easier to define terms like infarct than terms like to do (Rey-Debone 1971: 194ff).

We might decide that the primitives depend on our world experience; they would correspond to those that Russell (1940) called “object-words,” whose meanings we learn by ostension, in the same way as a child learns the meaning of the word red by finding it associated with different occurrences of the same chromatic experience.

By contrast, according to Russell, there are “dictionary-words” that can be defined through other words, such as pentagram. Yet Russell remarks, for a child who had grown up in a room decorated with motifs in the form of a pentagram, this word would be an object one.

Another alternative would be to regard primitives as innate Platonic ideas. This solution would be philosophically impeccable; yet not even Plato himself was able to establish what and how many these innate ideas were.

Either there is an idea for every natural kind (for horses, platypuses, fleas, elms and so on–which means an atomic feature for every element of the furnishing of the world), or there are a few abstract ideas (the One, the Many, the Good and mathematical concepts), but through them it would be difficult to define compositionally a horse or a platypus.

Suppose instead we decided to order the system of primitives by dichotomic disjunctions so that, by virtue of the systematic relations obtaining between the terms, they must remain finite in number.

With such a structure we would be able to define by a finite number of atomic primitives a great number of molecular entities. A good example of this alternative is the reciprocally embedded system of hyponyms and hyperonyms used by lexicographers.

It is organized hierarchically in the form of a tree of binary disjunctions: to each opposed pair of hyponyms there corresponds a single hyperonym, which, in its turn, is opposed to another hyperonym to form the next level of hyponyms, to which a further hyperonym will correspond, and so on.

In the end, regardless of how many terms are embedded in the system, the whole structure must finish at its apex in a single patriarch-hyperonym.

Thus the example of the table on p. 222 above would take the following format:

Umberto Eco, The Search for the Perfect Language, Figure 10.1, p. 224

Umberto Eco, The Search for the Perfect Language, Figure 10.1, p. 224.

According to many contemporary authors, this kind of semantic structure would analyze the content in the format of a dictionary (as opposed to an encyclopedia).

In an encyclopedia-like representation one introduces elements of world knowledge (for example that a tiger is a yellow cat with stripes on its fur), and these elements are potentially infinite in number.

In a dictionary-like representation the features are, on the contrary, analytic, in the sense that they are the only and necessary conditions for the definition of a given content: a cat is necessarily a feline and an animal and it would be contradictory to assert that a cat is not an animal, since the feature “animal” is analytically a part of the definition of cat.

In this sense it would be easy to distinguish analytical from synthetical judgments. “A tiger is a feline animal” would be analytical, so uniquely depending on our rigorously organized dictionary competence (which is exclusively linguistic), while “tigers are man-eaters” would depend on our extra-linguistical world knowledge.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 221-5.

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