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Tag: George Dalgarno

Eco: Side-effects

Leipzig_Leibniz_Denkmal_02

Ernst Hähnel, statue of Leibniz, 1883, Leipzig, Germany. Photo © Ad Melkens / Wikimedia Commons.  

“Thus all of the ingenuity expended upon the invention of philosophic a priori languages allowed Leibniz to invent a language of a radically different type, which–though remaining a priori–was no longer a practical, social instrument but rather a tool for logical calculation.

In this sense, Leibniz’s language, and the contemporary language of symbolic logic that descended from it, are scientific languages; yet, like all scientific languages, they are incapable of expressing the entire universe, expressing rather a set of truths of reason.

Such languages do not qualify as a universal language because they fail to express those truths that all natural languages express–truths of fact. Scientific languages do not express empirical events.

In order to express these we would need “to construct a concept which possesses an incalculable number of determinations,” while the completely determined concept of any individual thing or person implies “spatial-temporal determinations which, in their turn, imply other spatial-temporal successions and historical events whose mastery is beyond the human eye, and whose control is beyond the capacity of any man.” (Mugnai 1976: 91).

None the less, by anticipating what was to become the language of computers, Leibniz’s project also contributed to the development of programs well adapted for the cataloguing of the determinations of individual entities, which can tell us that there exists an entity called Mr. X such that this entity has booked a flight from A to B.

We may well fear that by controlling our determinations so well the computer eye has begun to infringe on our privacy, checking on the hour in which we reserved a room in a certain hotel in a certain city. This, then, is one of the side-effects of a project that commenced with the idea of expressing a merely theoretical universe populated with universal ideas such as goodness, angels, entity, substance, accidents, and “all the elephants.”

Dalgarno could never have imagined it. Passing through the mathematical filter of Leibniz, renouncing all semantics, reducing itself to pure syntax, his philosophical a priori language has finally managed to designate even an individual elephant.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 287-8.

Eco: From Leibniz to the Encyclopédie

Gottfried_Wilhelm_Leibniz_c1700

Johann Friedrich Wentzel (1670-1729), Gottfried Wilhelm Leibniz (1646-1716), circa 1700. 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 1678 Leibniz composed a lingua generalis (in Couturat 1903). After decomposing all of human knowledge into simple ideas, and assigning a number to each, Leibniz proposed a system of transcription for these numbers in which consonants stood for integers and vowels for units, tens and powers of ten:

Umberto Eco, The Search for the Perfect Language, p. 270

Umberto Eco, The Search for the Perfect Language, p. 270. 

In this system, the figure 81,374, for example, would be transcribed as mubodilefa. In fact, since the relevant power of ten is shown by the following vowel rather than by the decimal place, the order of the letters in the name is irrelevant: 81,374 might just as easily be transcribed as bodifalemu.

This system might lead us to suspect that Leibniz too was thinking of a language in which the users might one day discourse on bodifalemu or gifeha (= 546) just as Dalgarno or Wilkins proposed to speak in terms of nekpot or deta.

Against this supposition, however, lies the fact that Leibniz applied himself to another, particular form of language, destined to be spoken–a language that resembled the latino sine flexione invented at the dawn of our own century by Peano.

This was a language whose grammar was drastically simplified and regularized: one declension for nouns, one conjunction for verbs, no genders, no plurals, adjectives and adverbs made identical, verbs reduced to the formula of copula + adjective.

Certainly, if my purpose were to try to delineate the entire extent of the linguistic projects undertaken by Leibniz throughout the course of his life, I would have to describe an immense philosophical and linguistically monument displaying four major aspects:

(1) the identification of a system of primitives, organized in an alphabet of thought or in a general encyclopedia;

(2) the elaboration of an ideal grammar, inspired probably by the simplifications proposed by Dalgarno, of which the simplified Latin is one example;

(3) the formulation of a series of rules governing the possible pronunciation of the characters;

(4) the elaboration of a lexicon of real characters upon which the speaker might perform calculations that would automatically lead to the formulation of true propositions.

The truth is, however, that by the end of his career, Leibniz had abandoned all research in the initial three parts of the project. His real contribution to linguistics lies in his attempts at realizing the fourth aspect.

Leibniz had little interest in the kinds of universal language proposed by Dalgarno and Wilkins, though he was certainly impressed by their efforts. In a letter to Oldenburg (Gerhardt 1875: VII, 11-5), he insisted that his notion of a real character was profoundly different from that of those who aspired to a universal writing modeled on Chinese, or tried to construct a philosophic language free from all ambiguity.

Leibniz had always been fascinated by the richness and plurality of natural languages, devoting his time to the study of their lineages and the connections between them. He had concluded that it was not possible to identify (much less to revive) an alleged Adamic language, and came to celebrate the very confusio linguarum that others were striving to eliminate (see Gensini 1990, 1991).

It was also a fundamental tenet of his monadology that each individual had a unique perspective on the world, as if a city would be represented from as many different viewpoints as the different positions of its inhabitants.

It would have been incongruous for the philosopher who held this doctrine to oblige everyone to share the same immutable grillwork of genera and species, without taking into account particularities, diversities and the particular “genius” of each natural language.

There was but one facet of Leibniz’s personality that might have induced him to seek after a universal form of communication; that was his passion for universal peace, which he shared with Lull, Cusanus and Postel.

In an epoch in which his english predecessors and correspondents were waxing enthusiastic over the prospect of universal languages destined to ease the way for future travel and trade, beyond an interest in the exchange of scientific information, Leibniz displayed a sensitivity towards religious issues totally absent even in high churchmen like Wilkins.

By profession a diplomat and court councillor, Leibniz was a political, rather than an academic, figure, who worked for the reunification of the church. This was an ecumenicism that reflected his political preoccupations; he envisioned an anti-French bloc of Spain, the papacy, the Holy Roman Emperor and the German princes.

Still, his desire for unity sprang from purely religious motives as well; church unity was the necessary foundation upon which a peaceful Europe could be built.

Leibniz, however, never thought that the main prerequisite for unity and peace was a universal tongue. Instead, he thought that the cause of peace might be better served by science, and by the creation of a scientific language which might serve as a common instrument in the discovery of truth.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 269-1.

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: George Delgarno, 2

George Delgarno, Didascalocophus, Theater in Oxford, 1680

George Dalgarno (1626-1687), Didascalocophus, or the Deaf and Dumb mans Tutor, Theater in Oxford, 1680. 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. 

“Figure 11.1 presents an extremely simplified, partial reconstruction of the tables, which limits itself to following only two of the subdivisions–animals with uncleft hooves and the principle passions.

The 17 fundamental genera are printed in bold capitals, and are marked with 17 capital letters. Intermediate genera and species are represented in lower case. Dalgarno also employs three “servile” letters: R signifies a reversal in meaning (if pon means love, pron means hate); V indicates that the letters that precede it are to be read as numbers; L signifies a medium between two extremes.

Umberto Eco, The Search for the Perfect Language, Figure 11.1, p. 231

Umberto Eco, The Search for the Perfect Language, figure 11.1, p. 232.

See for instance how from concrete, corporeal, physical entities, signified by an N, animals are deduced. See also how, in order to reach the subdivision animal, Dalgarno introduces an intermediate division (animal/inanimate) which is neither a genus nor a species, and is not marked by any letter.

The animals are subdivided into three classes–aquatic, aerial and terrestrial. Among the terrestrial animals (k) appear those with uncleft hooves [η], or perissodactyls. Thus the character Nηk stands for the class of perissodactyls. At this point, however, Dalgarno adds several sub-species–viz. the horse, elephant, mule and donkey.

As far as the accidents (E) are concerned, see for instance how the principal passions (o) are classified as species of the sensitive (P). After this, we are presented with a list that is not dichotomized: admiration takes pom as its character, because P is the fundamental genus and o is the intermediate genus.  The m, however, is just the “number” that the species admiration is assigned in the list’s order.

It is curious that, for animals, the intermediate genus is given by the third letter in the character and the species by the second vowel, while for the accidents the opposite happens.

Dalgarno acknowledges the existence of such an irregularity, without offering any explanation (p. 52). The motive is doubtless euphony; still, there seems to have been nothing to prevent Dalgarno from assigning to the intermediate genera of concrete beings vowels instead of consonants and to the species consonants instead of vowels. In this way, he could have used the same criterion throughout the table.

The problem, however, is more complex than it seems. The expression Nηk applied to the perissodactyls is motived by the divisions; only an arbitrary decision, on the contrary, motivates the decision to specify elephant with the addition of an a.

But it is not the arbitrariness of the choice itself which creates problems; it is rather that while k means “those terrestrials which are animal because they are animated and therefore physically concrete” (so that the division explains or reflects in some way the nature of the thing itself), the a at the end of Nηka (sic) only means “that thing which is numbered a on the list of perissodactyls and is called elephant.”

The same observation applies to the m in pom. All it really signifies is “position number m on the list of those sensitive accidents which are principal passions, i.e. admiration.” Since the dichotomic division does not reach the lower species, Dalgarno is forced to tack on lists in an alphabetical or almost alphabetical order.

Dalgarno (p. 42) noted, however, that this procedure was simply a mnemonic artifice for those who did not wish to learn the defining name. At the end of the book there is indeed a philosophical lexicon giving the characters for many terms in Latin.

In particular, there exists at the end of this list a special section devoted to concrete physical objects. Thus is seems that a philosophical definition of final species is possible; the only difficulty is that, given the purely exemplary nature of the lexicon, Dalgarno has left the naming of a large number of species up to the speaker, who can infer it from the tables.

Sometimes, however, Dalgarno gives taxonomically accurate examples: for instance the name for garlic, nebghn agbana (but for Dalgarno it is nebgηn agbana) is decoded by Slaughter (1982: 152) as follows: n=concretum physicum, ein radice, b vesca, g = qualitas sensibilis, h = sabor, n = pingue, a = partes annuae, gfoliumbaccidens mathematicuma = affectprimalongum. 

But even in this instance, “the tables only classify and name up to a point; the lexicon provides the rest of the definition but not the classification” (Slaughter 1982: 152).

Dalgarno may not have considered it indispensable to arrive at a classification of complex entities in all their particularities, yet making definitions requires classification. As a result the decision on how to classify complex entities, and, consequently, what name to give them, seems left as it were to the discretion of the user of the language.

Thus, ironically, a system that was intended to provide a single set of objective and univocal definitions ends up by lending itself to the creative fancies of its users. Here are some of Dalgarno’s own suggestions (I have separated the radicals with a slash to make them more decipherable):

horse = Nηk/pot = animal with uncleft hoof/courageous [why could we not say the same of the elephant?]

mule = Nηk/sof/pad = animal with uncleft hoof / deprived / sex

camel = nek/braf/pfar = quadruped with cloven hoof/humped/back

palace = fan/kan = house / king

abstemious = sof / praf / emp = deprived / drink / adjectival

stammering = grug / shaf / tin = illness [the opposite of gug, health] / impediment / speaking

gospel = tib / sηb = teach / way of being

Dalgarno also admitted that the same object regarded from a different perspective might take different names. The elephant can be called Nηksyf (uncleft hoof / superlative) or Nηkbeisap (uncleft hoof / mathematical accident / architectural metaphor for the proboscis).

It is not a system that is at all easy to memorize. The difference between Nηke, donkey, and Nηko, mule, is minimal and easy to muddle. Dalgarno advised the reader to use old mnemonic tricks.

The name for table was fran; the name for plough was flan; Dalgarno suggested associating the first with FRANce and the second with FLANders. In this way the speaker needed to learn both a philosophical language and a mnemonic code.

Dalgarno somewhat compensates the reader for the transcendental difficulties in the lexicon and the rules of composition by providing a grammar and syntax of great simplicity.

All that remains of the categories of classical grammar is the noun along with several pronouns (I = lal, you = lêl, he = lel . . . ). Adverbs, adjectives, comparatives and even verbal forms are derived by adding suffixes to nouns.

Thus from sim (good) one can generate simam (very good) and sinab (better). From pon (love) we can get pone (lover), pono (loved) and ponomp (lovable). To translate verbs, Dalgarno thought all that was necessary was the copula: “we love” becomes “we” + present tense + copula + “lovers” (that is, “we are lovers;” see p. 65).

The notion that verbs could all be reduced to the copula plus an adjective already circulated among the Modists in the thirteenth century; it was taken up by Campanella in the Philosophia rationalis (1638) and accepted by both Wilkins and Leibniz.

Dalgarno’s treatment of syntax was no less radical (see Pellerey 1992c). Although other projects for philosophic languages preserved the Latin model, Dalgarno eliminated the declensions for nouns.

All that counted was word order: the subject preceded the verb and the verb preceded the object. The ablative absolute was rendered by temporal particles which stood for terms like cum, post or dum.

The genitive was rendered either by an adjectival suffix or by a formula of possession (shf = to belong). Shumaker has commented (1982: 155) that forms of the latter type are adopted by pidgin English, in which the phrase “master’s hand” is rendered “hand-belong-master.”

Simplified to this degree, the language seems syntactically crude. Yet Dalgarno, deeply suspicious of rhetorical embellishments, was convinced that only an essential logical structure gave a language an austere elegance.

Besides, grace, elegance and transparent clarity were given full play in the composition of the names, and for this reason, Dalgarno compared his language to the philosophical language par excellence, ancient Greek.

One final aspect of Dalgarno’s system that he shared with both Wilkins and Lodwick has been underlined by Frank (1979: 65ff). By using particles, prefixed and suffixed to names, to transform nouns into other grammatical categories, changing their meanings thereby, and inserting prepositions, such as per, trans, praeter, supra, in and a, among the mathematical accidents–and thus as equivalent to nouns–Dalgarno tended “to postulate an all-comprehending semantics which took over all, or almost all of the functions traditionally assigned to grammar.”

Dalgarno, in other words, abolished the classical distinction between categorematic terms, or terms that have independent meanings, and syncategorematic terms, or terms which acquire a meaning only within a context.

This, in logic, is equivalent to the distinction between logical variables that can be bound to specific meanings and logical connectives. This is a tendency that is contrary to the tenets of modern logic; yet it is consistent with some trends in contemporary semantics.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 231-7.

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