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Tag: Leibniz

Eco: Some Ghosts of the Perfect Language

Gregor Reisch, Margarita philosophica, Pearl of Wisdom, 1503

Gregor Reisch (1467-1525), title page of Margarita philosophica, or the Pearl of Wisdom, Freiburg, 1503. Multiple copies of this work are preserved. 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. 

“We have often paused to draw attention to side-effects. Without forced comparisons and without exaggerated claims, it seems permissible at this point to ask informed readers to reconsider various chapters of the history of philosophy, especially those concerning the advent of contemporary logic and linguistic analysis.

Would these developments have been possible without the secular debate on the nature of the perfect language, and, in particular, the various projects for philosophical a priori languages?

In 1854, George Boole published his Investigations of the Laws of Thought. He announced his intention to discover the fundamental laws governing the mental operations of the process of reasoning. He observed that without presupposing these laws, we could not explain why the innumerable languages spread around the globe have maintained over the course of centuries so many characteristics in common (II, 1).

Frege began his Begriffsschrift (on ideography, 1879) with a reference to Leibniz’s characteristica. In The Philosophy of Logical Atomism (1918-9), Russell noted that in a perfectly logical language, the relation of a word to its meaning would always be one to one (excepting words used as connectives).

When he later wrote Principia mathematica with Whitehead, he noted that, although their language possessed a syntax, it could, with the addition of a vocabulary, become a perfect language (even though he also admitted that is such a language were to be constructed it would be intolerably prolix).

For his part, Wittgenstein, renewing Bacon’s complaint concerning the ambiguity of natural languages, aspired to create a language whose signs were univocal (Tractatus logico-philosophicus, 1921-2, 3.325ff) and whose propositions mirrored the logical structure of reality itself (4.121).

Carnap proposed constructing a logical system of objects and concepts such that all concepts might be derived from a single nucleus of prime ideas (Der logische Aufbau der Welt, 1922-5). In fact, the entire logical positivist movement was heir to the Baconian polemic against the vagaries of natural languages productive of nothing but metaphysical illusions and false problems (cf. Recanati 1979).

These philosophers all hoped to construct a scientific language, perfect within its chosen range of competence, a language that would be universal as well; none, however, claimed that such a language would ever replace natural language.

The dream had changed, or, perhaps, its limitations had finally, reluctantly been accepted. From its search for the lost language of Adam, philosophy had by now learned to take only what it could get.

In the course of centuries through which our particular story has run, another story began to disentangle itself as well–the search for a general or universal grammar. I said in the introduction that this was not a story that I intended to tell here.

I shall not tell it because the search for a single corpus of rules underneath and common to all natural languages entailed neither the invention of a new language nor a return to a lost mother tongue. None the less, the search for what is constant in all languages can be undertaken in two ways.

The first way is to follow empirical and comparative methods; this requires compiling information on every language that exists–or existed (cf. Greenberg 1963).

The second way can be traced back to the time in which Dante (influenced or not by the doctrines of the Modists) attributed the gift of a forma locutionis to Adam. On this line of thought, scholars have more often tried to deduce the universal laws of all languages, and of human thought, from the model of the only language they knew–scholastic Latin–and in 1587 Francisco Sanchez Brocense was still doing so with his Minerva, seu causis linguae latinae.

The novelty of the Grammaire générale et raisonnée of Port Royal (1660) was simply the decision of taking as a model a modern language–French.

Choosing this way requires never being brushed by the scruple that a given language represents only a given way of thinking and of viewing the world, not universal thought itself.

It requires regarding what is called the “genius” of a language as affecting only the surface structures rather than the deep structure, allegedly the same for all languages.

Only in this way will be be possible to regard as universal, because corresponding to the only logic possible, the structures discovered in the language in which one is used to think.

Nor does it necessarily alter the problem to concede that–certainly–the various languages do exhibit differences at their surface level, are often corrupted through usage or agitated by their own genius, but still, if universal laws exist, the light of natural reason will uncover them because, as Beauzée wrote in his article on grammar in the Encyclopédie, “la parole est une sorte de tableau dont la pensée est l’original.”

Such an argument would be acceptable, but in order to uncover these laws one needs to represent them through a metalanguage applicable to every other language in the world. Now, if one chooses as metalanguage one’s own object language, the argument becomes circular.

In fact, as Simone has put it (1969: XXXIII), the aim of the Port Royal grammarians…

“…is therefore, in spite of the appearances of methodological rigor, prescriptive and evaluative, in so far as it is rationalist. Their scope was not to interpret, in the most adequate and coherent way possible, the usages permitted by the various languages.

If it were so, a linguistic theory should coincide with whole of the possible usages of a given tongue, and should take into account even those that native speakers consider as “wrong.”

Instead, their aim was to emend this variety of uses in order to make them all conform to the dictates of Reason.”

What makes the search for a universal grammar of interest in our story is, as Canto has noted (1979), that in order to be caught within the vicious circle, it is only necessary to make one simple assumption: the perfect language exists, and it is identical to one’s own tongue.

Once this assumption is made, the choice of the metalanguage follows: Port Royal anticipates de Rivarol.

This is a problem that remains for all attempts–contemporary ones included–to demonstrate that syntactic or semantic universals exist by deducing them from a given natural language, used simultaneously both as a metalanguage and as object language.

It is not my argument here that such a project is desperate: I merely suggest that it represents but another example of the quest for a philosophical a priori language in which, once again, a philosophical ideal of grammar presides over the study of a natural language.

Thus (as Cosenza has shown, 1993) those modern day branches of philosophy and psychology which deliberately appeal to a language of thought are also descendants of those older projects.

Such a “mentalese” would supposedly reflect the structure of mind, would be purely formal and syntactical calculus (not unlike Leibniz’s blind thought), would use non-ambiguous symbols and would be based upon innate primitives, common to all species.

As happened with Wilkins, it would be deduced according to a “folk psychology,” naturally within the framework of a given historical culture.

There are perhaps more remote descendants of the a priori projects, which have sought to found a language of mind not upon Platonic abstractions but upon the neuro-physiological structures of the brain.

Here the language of mind is the language of the brain; the software is founded upon the hardware. This is a new departure; since the “ancestors” of our story never dreamed of venturing this far, and many of them were not even certain that the res cogitans was located in the brain rather than the heart or the liver (even though an attractive wood cut showing the localization of the faculty of language in the brain–as well as those for imagination, estimation and memory–already appears in the fifteenth century in Gregor Reysch’s Margarita philosophica.

Differences are sometimes more important than identities or analogies; still, it would hardly be a waste of time if sometimes even the most advanced students in the cognitive sciences were to pay a visit to their ancestors.

It is frequently claimed in American philosophy departments that, in order to be a philosopher, it is not necessary to revisit the history of philosophy. It is like the claim that one can become a painter without having seen a single work of Raphael, or a writer without having ever read the classics.

Such things are theoretically possible; but the “primitive” artist, condemned to an ignorance of the past, is always recognizable as such and rightly labelled as a naïf. It is only when we reconsider past projects revealed as utopian or as failures that we are apprised of the dangers and possibilities for failure for our allegedly new projects.

The study of the deeds of our ancestors is thus more than an antiquarian pastime, it is an immunological precaution.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 312-6.

Eco: The Last Flowering of Philosophic Languages

Anne-Pierre-Jacques De Vismes, Pasilogie, ou de la musique, consideree comme langue universelle, 1806

Anne-Pierre-Jacques De Vismes (1745-1819), Pasilogie, ou de la musique, considérée comme langue universelle, Paris, 1806. 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. 

“Nor was even this the end of attempts at creating a philosophic language. In 1772 there appeared the project of Georg Kalmar, Praecepta grammatica atque specimina linguae philosophicae sive universalis, ad omne vitae genus adcomodatae, which occasioned the most significant discussion on our topic written in Italian.

In 1774, the Italian-Swiss Father Francesco Soave published his Riflessioni intorno alla costituzione di una lingua universaleSoave, who had done much to spread the sensationalist doctrine to Italy, advanced a criticism of the a priori languages that anticipated those made by the Idéologues (on Soave see Gensini 1984; Nicoletti 1989; Pellerey 1992a).

Displaying a solid understanding of the projects from Descartes to Wilkins and from Kircher to Leibniz, on the one hand Soave advanced the traditional reservation that it was impossible to elaborate a set of characters sufficient to represent all fundamental concepts; on the other hand, he remarked that Kalmar, having reduced these concepts to 400, was obliged to give different meanings to the same character, according to the context.

Either one follows the Chinese model, without succeeding in limiting the characters, or one is unable to avoid equivocations.

Unfortunately, Soave did not resist the temptation of designing a project of his own, though outlining only its basic principles. His system of classification seems to have been based on Wilkins; as usual he sought to rationalize and simplify his grammar; at the same time, he sought to augment its expressive potential by adding marks for new  morphological categories such as dual and the neuter.

Soave took more care over his grammar than over his lexicon, but was mainly interested in the literary use of language: from this derives his radical skepticism about any universal language; what form of literary commerce, he wondered, could we possibly have with the Tartars, the Abyssinians or the Hurons?

In the early years of the next century, Soave’s discussion influenced the thinking of Giacomo Leopardi, who had become an exceptionally astute student of the Idéologues.

In his Zibaldone, Leopardi treated the question of universal languages at some length, as well as discussing the debate between rationalists and sensationalists in recent French philosophy (see Gensini 1984; Pellerey 1992a).

Leopardi was clearly irritated by the algebraic signs that abounded in the a priori languages, all of which he considered as incapable of expressing the subtle connotations of natural languages:

“A strictly universal language, whatever it may be, will certainly, by necessity and by its natural bent, be both the most enslaved, impoverished, timid, monotonous, uniform, arid, and ugly language ever.

It will be incapable of beauty of any type, totally uncongenial to imagination [ . . . ] the most inanimate, bloodless, and dead whatsoever, a mere skeleton, a ghost of a language [ . . . ] it would lack life even if it were written by all and universally understood; indeed it will be deader than the deadest languages which are no longer either spoken or written.” (23 August 1823, in G. Leopardi, Tutte le opere, Sansoni: Florence 1969: II, 814).

Despite these and similar strictures, the ardor of the apostles of philosophic a priori languages was still far from quenched.

At the beginning of the nineteenth century, Anne-Pierre-Jacques de Vismes (Pasilogie, ou de la musique considérée come langue universelle, 1806) presented a language that was supposed to be a copy of the language of the angels, whose sounds derived from the affections of the soul.

Vismes argued that when the Latin translation of Genesis 11:1-2 states that “erat terra labii unius” (a passage to which we usually give the sense that “all the world was of one language”), it used the word labium (lip) rather than lingua (tongue) because people first communicated with each other by emitting sounds through their lips without articulating them with their tongue.

Music was not a human invention (pp. 1-20), and this is demonstrated by the fact that animals can understand music more easily than verbal speech: horses are naturally roused by the sound of trumpets as dogs are by whistles. What is more, when presented with a musical score, people of different nations all play it the same way.

Vismes presents enharmonic scales of 21 notes, one for each letter of the alphabet. He did this by ignoring the modern convention of equal temperament, and treating the sharp of one note as distinct from the flat of the note above.

Since Vismes was designing a polygraphy rather than a spoken language, it was enough that the distinctions might be exactly represented on a musical stave.

Inspired, perhaps, indirectly by Mersenne, Vismes went on to demonstrate that if one were to combine his 21 sounds into doublets, triplets, quadruplets, etc., one would quickly arrive at more syntagms than are contained in any natural language, and that “if it were necessary to write down all the combinations that can be generated by the seven enharmonic scales, combined with each other, it would take almost all of eternity before one could hope to come to an end.” (p. 78).

As for the concrete possibility of replacing verbal sounds by musical notes, Vismes devotes only the last six pages of his book to such a topic–not a great deal.

It never seems to have crossed Visme’s mind that, in taking a French text and substituting tones for its letters, all he was doing was transcribing a French text, without making it comprehensible to speakers of other languages.

Vismes seems to conceive of a universe that speaks exclusively in French, so much so that he even notes that he will exclude letters like K, Z and X because “they are hardly ever used in languages” (p. 106).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 302-4.

Eco:Eighteenth Century Projects

Telemaque_1st_page

François Fénelon (1651-1715), Telemachus, or the first page of the first book of Les Aventures de Télémaque, first published anonymously in 1699, and translated into English in London in 1715. 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.  

“Even under the weight of the Enlightenment critique, the dream of the perfect language refused to die. In 1720 there appeared a “Dialogue sur la facilité qu’il y auroit d’établir un Caractère Universel qui seroit commun à toutes les Langues de l’Europe, et intelligible à différens Peuples, qui le liroient chacun dans la propre Langue” (in the Journal littéraire de l’anné 1720).

As the title itself suggests, the project was for a polygraphy, in the sense we saw in Kircher, and, at most, it is worthy of note in that its attempt to include a contracted grammar points the way to future developments.

In any case, the proposal is distinguished by including an appeal, by the anonymous author, for a commission which would develop the project and for a prince who would impose its adoption.

Such an appeal “cannot help but remind us of a possibility, which must have seemed evident in the year 1720, that a phase of stability for Europe was about to open, and that, consequently, sovereigns might be expected to be more willing to patronize linguistic and intellectual experiments” (cf. Pellerey 1992a: 11).

In his article on “Langue” in the Encyclopédie, even a rationalist like Beauzée had to concede that, since it would be difficult to come to an agreement over a new language, and an international language still seemed to him to be necessary, Latin had to remain the most reasonable candidate.

For their part, the empiricists among the encyclopedists felt duty-bound to consider the idea of a universal language, too. As a sort of coda to the article on “Langue,” Joachim Faiguet wrote four pages on a project for a langue nouvelle. Couturat and Leau (1903: 237) consider this as representing a first attempt at overcoming the problems inherent in the a priori languages and at sketching out an example of the a posteriori languages we will be discussing in the next chapter.

As his model, Faiguet took a natural language–French. He formed his lexicon on French roots, and concentrated on the delineation of a simplified and regularized grammar, or a “laconic” grammar.

Following the authors in the previous century, Faiguet eliminated those grammatical categories that seemed to him redundant: he suppressed the articles, substituted flexions with prepositions (bi for the genitive, bu for the dative, and de and po for the ablative), transformed adjectives (indeclinable) into adverbial forms, standardized all plurals (always expressed by an s); he simplified verb conjugations, making them invariable in number and person, adding endings that designated tenses and modes (I give, you give, he gives became Jo dona, To dona, Lo dona); the subjunctive was formed by adding an r to the stem, the passive by the indicative plus sas (meaning to be: thus to be given became sas dona).

Faiguet’s language appears as wholly regular and without exceptions; every letter or syllable used as endings had a precise and unique grammatical significance. Still, it is parasitic on French in a double sense: not only is it a “laconicized” French at the expression-level; it is French that supplies the content-level as well. Thus Faiguet’s was little less than a sort of easy-to-manage Morse code (Bernadelli 1992).

The most important projects for a priori languages in the eighteenth century were those of Jean Delormel (Projet d’une langue universelle, 1795), of Zalkind Hourwitz (Polygraphie, ou l’art de correspondre à l’aide d’un dictionaire dans toutes les langues, même celles dont on ne possède pas seulement les lettres alphabétiques, 1800), and of Joseph de Maimieux (Pasigraphie, 1797).

As can be seen, De Maimieux’s project was a pasigraphy–that is, a universal written language. Since, however, in 1799 this same author had also formulated a pasilalie–adding rules for pronouncing his language–his project can be considered as an a priori language.

For its part, Hourwitz’s project was for a polygraphy, too–even though he seemed unaware that his was by no means the first project of this type. Still, in its structure, Hourwitz’s polygraphy was an a priori language.

Although all three projects still followed the principles laid down in the seventeenth century tradition, they were different in three fundamental ways: their purposes, the identification of their primitives, and their grammars.

Delormel presented his scheme to the Convention; De Maimieux published his Pasigraphie under the Directory; Hourwitz wrote under the Consulate: every religious motivation had disappeared.

De Maimieux spoke of communication between European nations, between Europeans and Africans, of providing a means of checking the accuracy of translations, of speeding up diplomacy and civil and military undertakings, of a new source of income for teachers, writers and publishers who should “pasigraphize” books written in other languages.

Hourwitz added to this list other purely practical considerations, such as the advantages in the relations between doctors and patients or in courtroom procedures. As one symptom of a new political and cultural atmosphere, instead of using the Lord’s Prayer as a sample translation, Hourwitz chose the opening of Fénelon’s Aventures de Télemaque–a work which, despite its moralizing bent, was still a piece of secular literature portraying pagan gods and heroes.

The revolutionary atmosphere imposed, or at least encouraged, considerations of fraternité. Thus Delormel could claim that:

“in this revolutionary moment, when the human spirit, regenerating itself among the French people, leaps forward with renewed energy, is it too much to hope that perhaps [ . . . ] we might offer to the public a new language as well, a language that facilitates new discoveries by bringing students of various nations together, a language that serves as a common term for all languages, a language easy to grasp even for men with but a slight aptitude for instruction, a language, in short, which will soon make out of all the people of mankind a single, grand family? [ . . . ] The Light of Reason brings men together and thus reconciles them; this language, by facilitating its communication, will help to propagate that Light.” (pp. 48-50).

Each of the authors was aware of the objections made by the authors of the Encyclopédie; thus the a priori languages which they proposed were all ordered according to an encyclopedia-like structure, easy to understand and designed upon the model of the eighteenth century system of knowledge.

Gone was the grandiose pansophist afflatus that animated baroque encyclopedias; the criterion of selection was rather that of Leibniz: the inventors of the languages behaved as if they were conscientious librarians hoping to make consultation as easy as possible, without worrying whether or not their ordering corresponded to the theater of the world.

Absent as well was the search for “absolute” primitives; the fundamental categories were the large-scale divisions of knowledge; under these were listed dependent notions attached as sub-headings.

Delormel, for example, assigned different letters of the alphabet to several encyclopedic classes in a way reminiscent not so much of Wilkins as of the anonymous Spaniard–grammar, art of speech, states of things, correlatives, useful, pleasurable, moral, sensations, perception and judgement, passions, mathematics, geography, chronology, physics, astronomy, minerals, etc.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 293-6.

Eco: The “Library” of Leibniz and the Encyclopédie

ENC_SYSTEME_FIGURE

Jean le Rond d’Alembert and Denis Diderot, Figurative System of Human Knowledge, or the Tree of Diderot and d’Alembert, from the Encyclopédie, circa 1752. 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. 

“During the Enlightenment there began to develop a critical attitude towards any attempt to construct a system of a priori ideas. It was a critique founded, in large part, upon the considerations advanced by Leibniz.

Thus it was in terms that closely recalled Leibniz’s own description of an ideal library that, in his introduction to the Encyclopédie, d’Alembert was to sound the death knell for projects for philosophical a priori languages.

Presented with the practical problem of organizing an encyclopedia and justifying the way that it divided its material, the system of scientific knowledge began to take on the appearance of a labyrinth, a network of forking and twisting paths that put paid to any notion that knowledge might be represented in a tree diagram of any sort.

Knowledge might still be divided into branches, “some of which converge at a common center; and, since, starting from the center, it is impossible to follow all the branches at once, the choice [of pathway] is determined by the nature of the different intellects.”

The philosopher was whoever discovered the hidden passageways within that labyrinth, the provisional interconnections, the web of mutually dependent associations which constituted such a network as a geographical representation.

For this reason the authors of the Encyclopédie decided that each single article would appear as only one particular map, which, in its small way, might reflect the entire global map:

“objects approach each other more or less closely, presenting different aspects according to the perspective chosen by the particular geographer [ . . . ].

Thus it is possible to imagine that there are as many systems of human knowledge as there are representations of the world constructed according to differing projections [ . . . ].

Often, an object placed in one particular class on account of one or another of its properties may reappear in another class because of other properties.”

Following the suggestion of Locke, the Enlightenment was less concerned with the search for perfect languages than with the provision of therapies for already existing ones.

After denouncing the limits of natural languages, Locke (Essay, III, X) had passed to an analysis of the abuse which must occur whenever words are used that do not correspond to clear and distinct ideas, whenever they are used inconsistently, whenever they are employed with the affectation of obscurity, whenever words are taken for things, whenever they are used for things which possess no meaning, and whenever we imagine that others must necessarily associate with the words we use the same ideas as we do.

Locke fixed a set of norms to combat these abuses, and, since Locke was not concerned with lexical or syntactical reform, but simply with subjecting usage to a measure of vigilance and philosophical common sense, these norms had no bearing on the theme of philosophical languages.

Instead of a systematic reform of language, Locke modestly suggested that we be more conscientious in the way we use words to communicate with one another.

This was to be the line adopted by the encyclopedists of the Enlightenment and those whom they inspired.

The encyclopedists launched their attack on philosophical a priori languages principally in their entry under the heading “Caractère,” which was the result of the collaboration of several authors.

Du Marsais made an initial distinction between numerical characters, characters representing abbreviations, and literal characters; these last were further subdivided into emblematic characters (still the accepted interpretation of hieroglyphics) and nominal characters, primarily the characters of the alphabet.

D’Alembert accepted the criticisms that had traditionally been made of the characters used in natural languages, and then discussed the various projects for the construction of real characters, showing an extensive knowledge of the projects in the previous century.

It was a discussion which often confused characters that were ontologically real, that directly expressed, that is, the essence of the things they represented, with characters that were only logically real, capable, that is, of expressing by convention a single idea unequivocally. Still, d’Alembert advanced a number of criticisms that applied equally to both types.

In contrast to those of the seventeenth century, philosophers in the Enlightenment had radically changed the focus of their reflection on language. It now seemed clear that thought and language influenced each other, each proceeding with the other step by step, and that, consequently, language, as it evolved, would constantly modify thought.

Thus it no longer made sense to accept the rationalist hypothesis of a single grammar of thought, universal and stable, which all languages in one way or another reflected. No system of ideas postulated on the basis of abstract reasoning could thus ever form an adequate parameter of and criterion for the formation of a perfect language.

Language did not reflect a preconstituted mental universe, but collaborated in its growth.

The Idéologues demonstrated the impossibility of postulating a universal way of thinking, independent of the human semiotic apparatus. Destutt de Tracy (Eléments d’idéologie, I, 546, n.) argued that it was not possible to confer on all languages the attributes of algebra. In the case of natural languages:

“we are often reduced to conjectures, inductions, and approximations [ . . . ]. Almost never can we have a perfect certainty that an idea which we have constructed for ourselves under a certain sign and by various means is really utterly and entirely the same as the idea that those who taught us the sign as well as anyone else who might subsequently use the sign might attribute to it.

Hence words may often, insensibly, take on differences in meaning without anyone noting these changes; for this reason we might say that while every sign is perfectly transparent for whomever invents it, it is somewhat vague and uncertain for those who receive it [ . . . ].

I might even carry this further: I said that every sign is perfect for whomever invents it, but this is only really true at the precise instant when he invents the sign, for when he uses this same sign in another moment in his life, or when his mind is in another disposition, he can no longer be entirely sure that he has gathered up under this sign the same collection of ideas as he had the first time he used it.” (pp. 583-5).

Tracy understood that the prerequisite of all philosophical languages was the absolute and univocal correspondence between signs and the ideas they represented. An examination, however, of the seventeenth century English systems led him to the conclusion that “it is impossible that the same sign possess the same meaning for all who use it [ . . . ]. We thus must give up the idea of perfection.” (Eléments d’idéologie, II, 578-9).

This was a theme that was common to empiricist philosophy, to which all the Idéologues referred. Locke had already noted that although the names glory and gratitude were

“the same in every Man’s mouth, through a whole country, yet the complex, collective Idea, which everyone thinks on, or intends by that name, is apparently very different in Men using the same language. [ . . . ]

For though in the Substance Gold, one satisfies himself with Color and Weight, yet another thinks solubility in Aqua Regia, as necessary to be join’d with that Color in his Idea of Gold, as any one does its Fusibility; Solubility in Aqua Regia, being a Quality as constantly join’d with its Color and and Weight, as Fusibility, or any other; others put its Ductility or Fixedness, etc. as they had been taught by Tradition and Experience.

Who, of all these, has establish’d the right termination of the word Gold?” (Essay, III, IX, 8, 13).

Returning to the Idéologues, Joseph-Marie Degérando, whose criticisms of Wilkins we have already encountered, observed (Des signes et l’art de penser considérés dans leur rapports mutuels, 1800) that the ensemble of associated ideas represented by the word man would be more extensive in the mind of a philosopher than in that of a common laborer, and that the word liberty could not have meant in Sparta what it did in Athens (I, 222-3).

The impossibility of elaborating a philosophic language is finally due to the fact that since languages develop through a set of stages, a development that the Idéologues delineated with great precision, there was no way of deciding the linguistic stage of development that a perfect language should represent.

Choosing to reflect one stage rather than another, a philosophical language will then continue to reflect all the limitations of that linguistic stage, while just to overcome these limitations humanity had passed to further and more articulate stages.

Once it had been perceived that the process of linguistic change is continuous, that language is subject to change not only at its prehistoric point of origin, but also in the present day, it became obvious that any thought of reviving the idea of a philosophic language was destined to fail.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 288-92.

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: Blind Thought, 2

Wittgenstein, Ludwig

Ludwig Wittgenstein (1899-1951), portrait by Moritz Nähr (1859-1945), 1930, held by the Austrian National Library under Accession Number Pf 42.805: C (1). 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 70 years or less. 

“As Leibniz observed in the Accessio ad arithmeticum infinitorum of 1672 (Sämtliche Schriften und Briefen, iii/1, 17), when a person says a million, he does not represent mentally to himself all the units in that number. Nevertheless, calculations performed on the basis of this figure can and must be exact.

Blind thought manipulates signs without being obliged to recognize the corresponding ideas. For this reason, increasing the power of our minds in the manner that the telescope increases the power of our eyes, it does not entail an excessive effort.

“Once this has been done, if ever further controversies should arise, there should be no more reason for disputes between two philosophers than between two calculators. All that will be necessary is that, pen in hand, they sit down together at a table and say to each other (having called, if they so please, a friend) “let us calculate.” (In Gerhardt 1875: VII, 198ff).

Leibniz’s intention was thus to create a logical language, like algebra, which might lead to the discovery of unknown truths simply by applying syntactical rules to symbols. When using this language, it would no more be necessary, moreover, to know at every step what the symbols were referring to than it was necessary to know the quantity represented by algebraic symbols to solve an equation.

Thus for Leibniz, the symbols in the language of logic no longer stood for concrete ideas; instead, they stood in place of them. The characters “not only assist reasoning, they substitute for it.” (Couturat 1901: 101).

Dascal has objected (1978: 213) that Leibniz did not really conceive of his characteristica as a purely formal instrument apparatus, because symbols in his calculus are always assigned an interpretation. In an algebraic calculation, he notes, the letters of the alphabet are used freely; they are not bound to particular arithmetical values.

For Leibniz, however, we have seen that the numerical values of the characteristic numbers were, so to speak, “tailored” to concepts that were already filled with a content–“man,” “animal,” etc.

It is evident that, in order to demonstrate that “man” does not contain “monkey,” the numerical values must be chosen according to a previous semantic decision. It would follow that what Leibniz proposed was really a system both formalized and interpreted.

Now it is true that Leibniz’s posterity elaborated such systems. For instance, Luigi Richer (Algebrae philosophicae in usum artis inveniendi specimen primum, “Melanges de philosophie et de mathématique de la Societé Royale de Turin,” 1761: II/3), in fifteen short and extremely dry pages, outlined a project for the application of algebraic method to philosophy, by drawing up a tabula characteristica containing a series of general concepts (such as aliquid, nihil, contingens, mutabile) and assigning to each a conventional sign.

The system of notation, semicircles orientated in various ways, makes the characters hard to distinguish from one another; still, it was a system of notation that allowed for the representation of philosophical combinations such as “This Possible cannot be Contradictory.”

This language is, however, limited to abstract reasoning, and, like Lull, Richer did not make full use of the possibilities of combination in his system as he wished to reject all combinations lacking scientific utility (p. 55).

Towards the end of the eighteenth century, in a manuscript dating 1793-4, we also find Condorcet toying with the idea of a universal language. His text is an outline of mathematical logic, a langue des calculs, which identifies and distinguishes intellectual processes, expresses real objects, and enunciates the relations between the expressed objects and the intellectual operations which discover the enunciated relations.

The manuscript, moreover, breaks off at precisely the point where it had become necessary to proceed to the identification of the primitive ideas; this testifies that, by now, the search for perfect languages was definitively turning in the direction of a logico-mathematical calculus, in which no one would bother to draw up a list of ideal contents but only to prescribe syntactic rules (Pellerey 1992a: 193ff).

We could say that Leibniz’s characteristica, from which Leibniz had also hoped to derive metaphysical truths, is oscillating between a metaphysical and ontological point of view, and the idea of designing a simple instrument for the construction of deductive systems (cf. Barone 1964: 24).

Moreover, his attempts oscillate between a formal logic (operating upon unbound variables) and what will later be the project of many contemporary semantic theories (and of artificial intelligence as well), where syntactic rules of a mathematical kind are applied to semantic (and therefore interpreted) entities.

But Leibniz ought to be considered the forerunner of the first, rather than of the second, line of thought.

The fundamental intuition that lies behind Leibniz’s proposal was that, even if the numbers were chose arbitrarily, even if it could not be guaranteed that the primitives posited for the same of argument were really primitive at all, what still guaranteed the truth of the calculus was the fact that the form of the proposition mirrored an objective truth.

Leibniz saw an analogy between the order of the world, that is, of truth, and the grammatical order of the symbols in language. Many have seen in this a version of the picture theory of language expounded by Wittgenstein in the Tractatus, according to which “a picture has logico-pictorial form in common with what it depicts” (2.2).

Leibniz was thus the first to recognize that the value of his philosophical language was a function of its formal structure rather than of its terms; syntax, which he called habitudo or propositional structure, was more important than semantics (Land 1974: 139).

“It is thus to be observed that, although the characters are assumed arbitrarily, as long as we observe a certain order and certain rule in their use, they give us results which always agree with each other. (Dialogus in Gerhardt 1875: VII, 190-3).

Something can be called an “expression” of something else whenever the structure [habitudines] subsisting in the expression corresponds to the structure of that which it wishes to express [ . . . ].

From the sole structure of the expression, we can reach the knowledge of the properties of the thing expressed [ . . . ] as long as there is maintained a certain analogy between the two respective structures.” (Quid sit idea in Gerhardt 1875: VII, 263-4).

What other conclusion could the philosopher of preestablished harmony finally have reached?”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 281-4.

Eco: Blind Thought

lambert_organon01_1764_0005_800px

Johann Heinrich Lambert (1728-1777), Neues Organon, Leipzig, Johann Wendler, 1764. 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. 

“We have seen that Leibniz came to doubt the possibility of constructing an alphabet that was both exact and definitive, holding that the true force of the calculus of characteristic numbers lay instead in its rules of combination.

Leibniz became more interested in the form of the propositions generated by his calculus than in the meaning of the characters. On various occasions he compared his calculus with algebra, even considering algebra as merely one of the possible forms that calculus might take, and thought more and more of a rigorously quantitative calculus able to deal with qualitative problems.

One of the ideas that circulated in his thought was that, like algebra, the characteristic numbers represented a form of blind thought, or cogitatio caeca (cf. for example, De cognitione, veritate et idea in Gerhardt 1875: IV, 422-6). By blind thought Leibniz meant that exact results might be achieved by calculations carried out upon symbols whose meanings remained unknown, or of which it was at least impossible to form clear and distinct notions.

In a page in which he defined his calculus as the only true example of the Adamic language, Leibniz provides an illuminating set of examples:

“All human argument is carried out by means of certain signs or characters. Not only things themselves but also the ideas which those things produce neither can nor should always be amenable to distinct observation: therefore, in place of them, for reasons of economy we use signs.

If, for example, every time that a geometer wished to name a hyperbole or a spiral or a quadratrix in the course of a proof, he needed to hold present in his mind their exact definitions or manner in which they were generated, and then, once again, the exact definitions of each of the terms used in his proof, he would be likely to be very tardy in arriving at his conclusions. [ . . . ]

For this reason, it is evident that names are assigned to the contracts, to the figures and to various other types of things, and signs to the numbers in arithmetic and to magnitudes in algebra [ . . . ]

In the list of signs, therefore, I include words, letters, the figures in chemistry and astronomy, Chinese characters, hieroglyphics, musical notes, steganographic signs, and the signs in arithmetic, algebra, and in every other place where they serve us in place of things in our arguments.

Where they are written, designed, out sculpted, signs are called characters [ . . . ]. Natural languages are useful to reason, but are subject to innumerable equivocations, nor can be used for calculus, since they cannot be used in a manner which allows us to discover the errors in an argument by retracing our steps to the beginning and to the construction of our words–as if errors were simply due to solecisms or barbarisms.

The admirable advantages [of the calculus] are only possible when we use arithmetical or algebraic signs and arguments are entirely set out in characters: for here every mental error is exactly equivalent to a mistake in calculation.

Profoundly meditating on this state of affairs, it immediately appeared as clear to me that all human thoughts might be entirely resolvable into a small number of thoughts considered as primitive.

If then we assign to each primitive a character, it is possible to form other characters for the deriving notions, and we would be able to extract infallibly from them their prerequisites and the primitive notions composing them; to put it in a word, we could always infer their definitions and their values, and thereby the modifications to be derived from their definitions.

Once this had been done, whoever uses such characters in their reasoning and in their writing, would either never make an error, or, at least, would have the possibility of immediately recognizing his own (or other people’s) mistakes, by using the simplest of tests.” (De scientia universalis seu calculo philosophico in Gerhardt 1875: VII, 198-203).

This vision of blind thought was later transformed into the fundamental principle of the general semiotics of Johann Heinrich Lambert in his Neues Organon (1762) in the section entitled Semiotica (cf. Tagliagambe 1980).

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 279-81.

Eco: The Encyclopedia and the Alphabet of Thought

Encyclopedie_frontispice_section_256px

Charles-Nicolas Cochin (1715-1790), Frontispiece of L’Encyclopédie ou Dictionnaire raisonné des sciences, des artes, et des métiers, abbreviated as L’Encyclopédie, or Encyclopedia. One source claims that this illustration was entitled Lycurgus blessé dans une sédition, while another states that it depicts la Raison et la Philosophie arrachant son voile à la Vérité rayonnante de lumière. Drawn by Cochin in 1764, it was engraved by Benoît-Louis Prévost (1735-1804) in 1765. 

“The idea of a universal encyclopedia was something that Leibniz was never to give up. Leibniz was, for a long period, a librarian; as such, and as a historian and érudit, he could not have failed to follow the pansophic aspirations and encyclopedic ferment that filled the closing years of the seventeenth century–tremors that would yield their fruits in the century to come.

For Leibniz, the interest in the idea of a universal encyclopedia grew less and less as the basis of an alphabet of primitive terms, and more and more as a practical and flexible instrument which might provide for everyone an access to and control over the immense edifice of human learning.

In 1703, he wrote the Nouveaux essais sur l’entendement humain (which did not appear until 1765, after Leibniz’s death). This book was a confutation of the doctrines of Locke, and ends with a monumental fresco of the encyclopedia of the future.

The point of departure was a rejection of Locke’s tripartite division of knowledge into physical, ethical and logical (or semiotic). Even such a simple classification was untenable, Leibniz argued, because every item of knowledge might reasonably be considered from more than one of the three divisions.

We might treat the doctrine of spirits either as a philosophical or as a moral problem, placing it in the province either of logic or of ethics. We might even consider that a knowledge of the spirit world might prove efficacious for certain practical ends; in which case we might want to place it in the physical province.

A truly memorable story might deserve a place in the annals of universal history; yet it might equally well deserve a place in the history of a particular country, or even of a particular individual. A librarian is often undecided over the section in which a particular book needs to be catalogued (cf. Serres 1968: 22-3).

Leibniz saw in an encyclopedia the solution to these problems. An encyclopedia would be a work that was, as we might now say, polydimensional and mixed, organized–as Gensini observes (Gensini 1990: 19)–more according to “pathways” than by a classification by subject matters; it would be a model of a practico-theoretical knowledge that invited the user to move transversally, sometimes following deductive lines, as mathematicians do, and sometimes moving according to the practical purposes of the human users.

It would be necessary also to include a final index that would allow the user to find different subjects or the same subject treated in different places from different points of view (IV, 21, De la division des sciences).

It is almost as if Leibniz intended here to celebrate as a felix culpa that monument of non-dichotomical incongruity that was the encyclopedia of Wilkins; as if he were writing a rough draft for the very project that d’Alembert was to set forth at the beginning of the Encyclopédie. Dimly shining from beneath the project of Wilkins, Leibniz has recognized the first idea of a hypertext.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 278-9.

Eco: The Problem of the Primitives

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria, frontispiece

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, frontispiece, Dissertation on the Art of Combinations or On the Combinatorial Art, Leipzig, 1666. 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.

“What did Leibniz’s ars combinatoria have in common with the projects for universal languages? The answer is that Leibniz had long wondered what would be the best way of providing a list of primitives and, consequently, of an alphabet of thoughts or of an encyclopedia.

In his Initia et specimina scientiae generalis (Gerhardt 1875: VII, 57-60) Leibniz described an encyclopedia as an inventory of human knowledge which might provide the material for the art of combination.

In the De organo sive arte magna cogitandi (Couturat 1903: 429-31) he even argued that “the greatest remedy for the mind consists in the possibility of discovering a small set of thoughts from which an infinity of other thoughts might issue in order, in the same way as from a small set of numbers [the integers from 1 to 10] all the other numbers may be derived.”

It was in this same work that Leibniz first made hints about the combinational possibilities of a binary calculus.

In the Consilium de Encyclopedia nova conscribenda methodo inventoria (Gensini 1990: 110-20) he outlined a system of knowledge to be subjected to a mathematical treatment through rigorously conceived propositions. He proceeded to draw up a plan of how the sciences and other bodies of knowledge would then be ordered: from grammar, logic, mnemonics topics (sic) and so on to morals and to the science of incorporeal things.

In a later text on the Termini simpliciores from 1680-4 (Grua 1948: 2, 542), however, we find him falling back to a list of elementary terms, such as “entity,” “substance” and “attribute,” reminiscent of Aristotle’s categories, plus relations such as “anterior” and “posterior.”

In the Historia et commendatio linguae characteristicae we find Leibniz recalling a time when he had aspired after “an alphabet of human thoughts” such that “from the combination of the letters of this alphabet, and from the analysis of the vocables formed by these letters, things might be discovered and judged.”

It had been his hope, he added, that in this way humanity might acquire a tool which would augment the power of the mind more than telescopes and microscopes had enlarged the power of sight.

Waxing lyrical over the possibilities of such a tool, he ended with an invocation for the conversion of the entire human race, convinced, as Lull had been, that if missionaries were able to induce the idolators to reason on the basis of the calculus they would soon see that the truths of our faith concord with the truths of reason.

Immediately after this almost mystical dream, however, Leibniz acknowledged that such an alphabet had yet to be formulated. Yet he also alluded to an “elegant artifice:”

“I pretend that these marvelous characteristic numbers are already given, and, having observed certain of their general properties, I imagine any other set of numbers having similar properties, and, by using these numbers, I am able to prove all the rules of logic with an admirable order, and to show in what way certain arguments can be recognized as valid by regarding their form alone.” (Historia et commendatio, Gerhardt 1875: VII, 184ff).

In other words, Leibniz is arguing that the primitives need only be postulated as such for ease of calculation; it was not necessary that they truly be final, atomic and unanalyzable.

In fact, Leibniz was to advance a number of important philosophical considerations that led him to conclude that an alphabet of primitive thought could never be formulated. It seemed self-evident that there could be no way to guarantee that a putatively primitive term, obtained through the process of decomposition, could not be subjected to further decomposition.

This was a thought that could hardly have seemed strange to the inventor of the infinitesimal calculus:

There is not an atom, indeed there is no such thing as a body so small that it cannot be subdivided [ . . . ] It follows that there is contained in every particle of the universe a world of infinite creatures [ . . . ] There can be no determined number of things, because no such number could satisfy the need for an infinity of impressions.” (Verità prime, untitled essay in Couturat 1903: 518-23).

If no one conception of things could ever count as final, Leibniz concluded that we must use the conceptions which are most general for us, and which we can consider as prime terms only within the framework of a specific calculus.

With this, Leibniz’s characteristica breaks its link with the research into a definitive alphabet of thought. Commenting on the letter to Mersenne in which Descartes described the alphabet of thoughts as a utopia, Leibniz noted:

“Even though such a language depends upon a true philosophy, it does not depend upon its perfection. This is to say: the language can still be constructed despite the fact that the philosophy itself is still imperfect.

As the science of mankind will improve, so its language will improve as well. In the meantime, it will continue to perform an admirable service by helping us retain what we know, showing what we lack, and inventing means to fill that lack.

Most of all, it will serve to avoid those disputes in the sciences that are based on argumentation. For the language will make argument and calculation the same thing.” (Couturat 1903: 27-8).

This was not only a matter of convention. The identification of primitives cannot precede the formulation of the lingua characteristica because such a language would not be a docile instrument for the expression of thought; it is rather the calculating apparatus through which those thoughts must be found.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 275-7.

Eco: Characteristica and Calculus

Gottfried Wilhelm von Leibniz, Dissertatio de Arte Combinatoria

Gottfried Wilhelm von Leibniz (1646-1716), Dissertatio de Arte Combinatoria, an excerpt from his first doctoral dissertation, Dissertation on the Art of Combinations, Leipzig, 1666. 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 theme of invention and discovery should remind us of Lull; and, in fact, Lull’s ars combinatoria was one of Leibniz’s first sources. In 1666, at the age of twenty, Leibniz composed his own Dissertatio de arte combinatoria (Gerhardt 1875: IV, 27-102). But the dream of the combinatoria was to obsess him for the rest of his life.

In his short Horizon de la doctrine humaine (in Fichant 1991), Leibniz dealt with a problem that had already troubled Father Mersenne: how many utterances, true, false or even nonsensical, was it possible to formulate using an alphabet of 24 letters?

The point was to determine the number of truths capable of expression and the number of expressions capable of being put into writing. Given that Leibniz had found words of 31 letters in Latin and Greek, an alphabet of 24 letters would produce 2432 words of 31 letters.

But what is the maximum length of an expression? Why should an expression not be as long as an entire book? Thus the sum of the expressions, true or false, that a man might read in the course of his life, imagining that he reads 100 pages a day and that each page contains 1,000 letters, is 3,650,000,000.

Even imagining that this man can live one thousand years, like the legendary alchemist Artephius, it would still be the case that “the greatest expressible period, or the largest possible book that a man can read, would have 3,650,000,000,000 [letters], and the number of truths, falsehoods, or sentences expressible–that is, readable, regardless of pronounceability or meaningfulness–will be 24365,000,000,001 – 24/23 [letters].”

We can imagine even larger numbers. Imagine our alphabet contained 100 letters; to write the number of letters expressible in this alphabet we would need to write a 1 followed by 7,300,0000,000,000 (sic) zeros. Even to write such a number it would take 1,000 scribes working for approximately 37 years.

Leibniz’s argument at this point is that whatever we take the number of propositions theoretically capable of expression to be–and we can plausibly stipulate more astronomical sums than these–it will be a number that vastly outstrips the number of true or false expressions that humanity is capable of producing or understanding.

From such a consideration Leibniz concluded paradoxically that the number of expressions capable of formulation must always be finite, and, what is more, that there must come a moment at which humanity would start to enunciate them anew.

With this thought, Leibniz approaches the theme of the apochatastasis or of universal reintegration–what we might call the theme of the eternal return.

This was a line of speculation more mystical than logical, and we cannot stop to trace the influences that led Leibniz to such fantastic conclusions.

It is plain, however, that Leibniz has been inspired by Lull and the kabbala, even if Lull’s own interest was limited to the generation of just those propositions that expressed true and certain knowledge and he thus would never have dared to enlarge his ars combinatoria to include so large a number of propositions.

For Leibniz, on the contrary, it was a fascination with the vertiginous possibilities of discovery, that is of the infinite number of expressions of which a simple mathematical calculation permitted him to conceive, that served as inspiration.

At the time he was writing his Dissertatio, Leibniz was acquainted with Kircher’s Polygraphia, as well as with the work of the anonymous Spaniard, of Becher, and of Schott (while saying that he was waiting for the long-promised Ars magna sciendi of the “immortal Kircher“).

He had yet to read Dalgarno, and Wilkins had still not published his Essay. Besides, there exists a letter from Kircher to Leibniz, written in 1670, in which the Jesuit confessed that he had not yet read Leibniz’s Dissertatio.

Leibniz also elaborated in the Dissertatio his so-called method of “complexions,” through which he might calculate, given n elements, how many groups of them, taken t at a time, irrespective of their ordering, can be ordered.

He applied this method to syllogisms before he passed to his discussion of Lull (para. 56). Before criticizing Lull for limiting the number of his elements, Leibniz made the obvious observation that Lull failed to exploit all the possibilities inherent in his combinatorial art, and wondered what could happen with variations of order, which could produce a greater number.

We already know the answer: Lull not only limited the number of elements, but he rejected those combinations that might produce propositions which, for theological and rhetorical reasons, he considered false.

Leibniz, however, was interested in a logica inventiva (para. 62) in which the play of combinations was free to produce expressions that were heretofore unknown.

In paragraph 64 Leibniz began to outline the theoretical core of his characteristica universalis. Above all, any given term needed to be resolved into its formal parts, the parts, that is, that were explicitly entailed by its definition.

These parts then had to be resolved into their own components, and so on until the process reached terms which could not, themselves, be defined–that is, the primitives. Leibniz included among them not only things, but also modes and relations.

Other terms were to be classified according to the number of prime terms they contained: if they were composed from 2 prime terms, they were to be called com2nations; if from 3 prime terms, com3nations, and so forth. Thereby a hierarchy of classes of increasing complexity could be created.

Leibniz returned to this argument a dozen years later, in the Elementa characteristicae universalis. Here he was more generous with his examples. If we accept the traditional definition of man as “rational animal,” we might consider man as a concept composed of “rational” and “animal.”

We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate.

Given the preposition “all men are animals,” the number for the subject (men), is 6; the number for animals is 2; the resulting fraction is 6/2 = 3. Three being an integer, consequently, the preposition is true.

If the number for monkey were 10, we could demonstrate the falsity of either the proposition “all men are monkeys” or “all monkeys are men:” “the idea of monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6” (Elementa, in Couturat 1903: 42-92). These were principles that had all been prefigured in the Dissertatio.

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 271-5.

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, 2

John Wilkins, An Essay, the Lords Prayer, Ch.II, p. 8

John Wilkins (1614-1672), An Essay Towards a Real Character and a Philosophical Language, London, John Martin, 1668. Chapter II, p. 8, 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. 

“Let us try to understand a little better what is happening here. Suppose we wanted to use the real character to understand the difference between a dog and a wolf. We discover only that the dog, Zitα, is the first member of the first specific pair of the fifth difference of the genus Beasts, and that the wolf Zitαs, is the opposing member of this pair (s being the character for specific opposition).

But in this way the character says what is the position of a dog in a universal classification of beasts (which, like Fish and Bird are animate sensitive sanguineous substances), without providing information either on the physical characteristics of dogs or on the difference between a dog and a wolf.

To learn more about dogs and wolves we must read further in the tables. Here we can learn (1) that clawed viviparous animals have toes at the end of their feet; (2) that rapacious viviparous animals have generally “six short pointed incisors, or cutting teeth, and two long fangs to hold their prey;” (3) that the head of dog-kind beasts is oblong, while the head of cat-kind animals is roundish; (4) that the larger of the dog-kind fall into two further groups–“either that which is noted for tameness and docility; or for wildness and enmity to sheep.”

With this, we finally know the difference between a dog and a wolf.

Thus genera, differences and species only serve to “taxonomize” entities rather than to define the properties by which we recognize them. To make these properties evident it is necessary to attach a running commentary to the classification.

Within Aristotelian classification, defining man as a rational animal was perfectly adequate. But this is not adequate for Wilkins, for he lived in an age that wished to discover the physical and biological nature of things.

He thus needed to know what were the morphological and behavioral characteristics of dogs as well. Yet his tables only allowed him to express this information in the form of additional properties and circumstances, and this additional information had to be expressed in natural language because the characteristic language lacked the formulae to render it evident.

This consecrates the failure of Wilkins‘ project, considering that, according to his project, “we should, by learning the Character and the Names of things, be instructed likewise in their Natures” (p. 21).

One might wish at least to call Wilkins a pioneer of modern, scientific taxonomy (like the taxonomy shown in figure 10.3). Yet, as Slaughter has noted, he has lumped together the pre-scientific taxonomies and folk taxonomy.

To classify, as we usually do, onions and garlic as foodstuffs and lilies as flowers is an instance of folk taxonomy: from a botanical point of view, onions, garlic and lilies are all members of the Liliaceae family.

See how Wilkins, when he classifies dogs, starts out using morphological criteria, then goes on mixing functional and even geographical criteria.

What, then, is that character Zitα that tells us so little about dogs, forcing us to learn more by inspecting the tables? One might compare it with a pointer which permits access to information stored in the computer’s memory–and which is not provided by the form of the character itself.

The speakers who wished to use the characteristic language as their natural idiom should have already memorized all that information in order to understand the character. But that is exactly the same type of competence requested of speakers who, instead of Zitα, say cane, dog, per or Hund.

For this reason, the encyclopedic information that underlies the list of primitives negates the compositional principle of Wilkins‘ language. Wilkins‘ primitives are not primitives at all. His species do not emerge from the composition of genera and differences alone; they are also names used as pegs to hang up encyclopedic descriptions.

Moreover, not even genera and differences are primitive, since they can be defined only through encyclopedic definitions. They neither are innate notions, nor can be immediately grasped by intuition: if one could still say so of the ideas of “God” or “world,” one would hardly do so for, let us say, “naval and ecclesiastical relations.”

Genera and differences are not primitive notions because–if they were–they should be definable by nature, while the tables are conceived just in order to define them by means of a natural language, Wilkins‘ English.

If Wilkins‘ classification were logical consistent, it should be possible to assume that it is analytically true that the genus of Beasts entails Animate Substance, which in its turn entails Creatures Considered Distributively.

Even this, in fact, is not always the case. The opposition vegetative / sensitive, for example, in the table of genera serves to distinguish Stone and Tree (and has an uncertain status); but the same opposition reappears (not once but twice) in the table of the World (see figure 12.6, where repeated terms are in bold).

Thus, on the basis of figure 12.1, one should admit that everything vegetative is necessarily an animate creature, while according to figure 12.6, one should (rather contradictorily) admit that everything vegetative is necessarily an element of both the spiritual and the corporeal world.

It is obvious that these various entities (be they genera, species or whatever) are considered under a different point of view every time they appear in the tables. Yet, in this case, we are no longer confronting a classification whose purpose is to construct a tree of organized terms in which every entity is unequivocally defined by the place it holds within the classification; we are, instead, confronting a great encyclopedia in which it is only expected that the same topics will be treated from more than one point of view in different articles.

Umberto Eco, The Search for the Perfect Language, Figure 12.6, p. 257

Umberto Eco, The Search for the Perfect Language, Figure 12.6, p. 257.

Consulting the table for Economic Relations, we find, among its species, the pair Defending versus Deserting. If we turn to the table for Military Relations we still find Defense; though this time it is opposed to Offense.

It is true that when defense is considered as an economic relation and the opposite of desertion, it is written Coco, while considered as a type of military action, the opposite of offense, it is written Sibα.

Thus two different characters denote two different notions. Yet are they really different notions rather than one notion considered from two viewpoints? As a matter of fact, the ideas of economic defence and military defence seem to have something in common.

In both cases we are facing an act of war, which is seen the first time as a patriotic duty and the second time as a response to the enemy. The fact that the two notions are conceptually related, however, implies that within the structure of pseudo-dichotomies there also exist transversal connections, linking the nodal points in different sections of the tree.

Yet is such connections exist, then the tree is no more a hierarchical tree; it is rather a network of interrelated ideas.

In his work De signes, written in 1800, Joseph-Marie Degérando accused Wilkins of continually confusing classification with division:

“Division differs from classification in that the latter bases itself upon the intimate properties of the objects it wishes to distribute, while the former follows a rule to a certain end to which these objects are destined.

Classification apportions ideas into genera, species, and families; division allocates them into regions of greater or lesser extent. Classification is the method of botanists; division is the method by which geography is taught.

If one wishes for an even clearer example, when an Army is drawn up in battle formation, each brigade under its general, each battalion under its commander, each company under its captain, this is an image of division; when, however, the state of this army is presented on a role, which principally consists of en enumeration of the officers of each rank, then of the subalterns, and finally of the soldiers, this is an image of classification (IV, 399-400).”

Degérando is doubtlessly thinking here of Leibniz’s notion of the ideal library and of the structure of the Encyclopédie of which we will later speak), that is, of a criterion for subdividing matter according to the importance that it has for us.

Yet a practical classification follows criteria different from those which should rule a system of primitives based on metaphysical assumptions.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 254-8.

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.

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: First Attempts at a Content Organization

kircher_108

Athanasius Kircher (1602-80), Frontispiece of Obeliscus Pamphilius, Obeliscus Pamphilius: Hoc est Interpretatio nova & hucusque intenta obelisci Hieroglyphici, eBook courtesy of GoogleBooks, published by Lud. Grignani 1650, held by Ghent University. 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. 

“Probably in 1660, three years before the publication of the Polygraphia, Kircher wrote a manuscript bearing the title Novum hoc inventum quo omnia mundi idiomata ad unum reducuntur (Mss. Chigiani I, vi, 225, Biblioteca Apostolica Vaticana; cf. Marrone 1986).

Schott says that Kircher kept his system a secret at the express wish of the emperor, who had requested that his polygraphy be reserved for his exclusive use alone.

The Novum inventum was still tentative and incomplete; it contained an extremely elementary grammar plus a lexicon of 1,620 words. However, the project looks more interesting that the later one because it provides a list of 54 fundamental categories, each represented by an icon.

These icons are reminiscent of those that one might find today in airports and railway stations: some were schematically representative (like a small chalice for drinking); others were strictly geometrical (rectangles, triangles, circles).

Some were furthermore superficially derived from Egyptian hieroglyphics. They were functionally equivalent to the Roman numbers in the Polygraphia (in both texts, Arabic numbers referred to particular items).

Thus, for example, the square representing the four elements plus the numeral 4 meant water as an element; water as something to drink was instead expressed by a chalice (meaning the class of drinkable things) followed by the numeral 3.

There are two interesting features in this project. The first is that Kircher tried to merge a polygraphy with a sort of hieroglyphical lexicon, so that his language could be used (at least in the author’s intention) without translating it into a natural language.

Seeing a “square + 4,” the readers should immediately understand that the named thing is an element, and seeing “chalice + 3” they should understand that one is referring to something to drink.

The difficulty was due to the fact that, while both Kircher’s Polygraphia and Becher’s Character allow a translating operator (be it a human being or a machine) to work independently of any knowledge of the meaning of the linguistic items, the Novum inventum requires a non-mechanical and quasi-philosophical knowledge: in order to encode the word aqua as “square + 4,” one should previously know that it is the name of an element–information that the term of a natural language does not provide.

Sir Thomas Urquhart, who published two volumes describing a sort of polygraphy (Ekskubalauron, 1652, and Logopandecteision, 1653), noted that, arbitrary as the order of the alphabet might be, it was still easier to look things up in alphabetical order than in a categorical order.

The second interesting feature of Kircher’s initial project is certainly given by the effort to make the fundamental concepts independent of any existing natural language.

Its weakness is due to the fact that the list of the 54 categories was notably incongruous: it included divine entities, angelic and heavenly, elements, human beings, animals, vegetables, minerals, the dignities and other abstract concepts deriving from the Lullian Ars, things to drink, clothes, weights, numbers, hours, cities, food, family, actions such as seeing or giving, adjectives, adverbs, months of the year.

It was perhaps the lack of internal coherency in this system of concepts that induced Kircher to abandon this line of research, and devote himself to the more modest and mechanical method used in the Polygraphia.

Kircher’s incongruous classification had a precedent. Although he regarded Kircher as the pioneer in the art of polygraphy, in his Technica curiosa (as well as in his Jocoseriorum naturae et artiis sive magiae naturalis centuriae tres) Gaspar Schott gave an extended description of a 1653 project that was certainly earlier than Kircher’s (the Novum inventum is dedicated to Pope Alexander VII, who ascended the pontifical throne only in 1655).

The project was due to another Jesuit, a Spaniard (“whose name I have forgotten,” as Schott says on p. 483), who had presented in Rome (on a single folio) an Artificium, or an Arithmeticus nomenclator, mundi omnes nationes ad linguarum et sermonis unitatem invitans (“Artificial Glossary, inviting all the nations of the world to unity of languages and speech”).

Schott says that the anonymous author wrote a pasigraphy because he was a mute. As a matter of fact the subtitle of the Artificium also reads Authore linguae (quod mirere) Hispano quodam, vere, ut dicitur, muto (“The author of this language–a marvelous thing–being a Spaniard, truly, it is said, dumb”).

According to Ceñal (1946) the author was a certain Pedro Bermudo, and the subtitle of the manuscript would represent a word play since, in Castilian, “Bermudo” must be pronounced almost as Ver-mudo.

It is difficult to judge how reliable the accounts of Schott are; when he described Becher’s system, he improved it, adding details that he derived from the works of Kircher. Be that as it may, Schott described the Artificium as having divided the lexicon of the various languages into 44 fundamental classes, each of which contained between 20 and 30 numbered items.

Here too a Roman number referred to the class and an Arabic number referred to the item itself. Schott noted that the system provided for the use of signs other than numbers, but gave his opinion that numbers comprised the most convenient method of reference since anyone from any nation could easily learn their use.

The Artificium envisioned a system of designating endings, (marking number, tense or case) as complex as that of Becher. An Arabic number followed by an acute accent was the sign of the plural; followed by a grave accent, it became the nota possessionis.

Numbers with a dot above signified verbs in the present; numbers followed by a dot signified the genitive. In order to distinguish between vocative and dative, it was necessary to count, in one case, five, and, in the other, six, dots trailing after the number.

Crocodile was written “XVI.2” (class of animals + crocodile), but should one have occasion to address an assembly of crocodiles (“O Crocodiles!”), it would be necessary to write (and then read) “XVI.2′ . . . . . ‘.

It was almost impossible not to muddle the points behind one word with the points in front of another, or with full stops, or with the various other orthographic conventions that the system established.

In short, it was just as impracticable as all of the others. Still, what is interesting about it is the list of 44 classes. It is worth listing them all, giving, in parenthesis, only some examples of the elements each contained.

  1. Elements (fire, wind, smoke, ashes, Hell, Purgatory, centre of the earth).
  2. Celestial entities (stars, lightning, bolts, rainbows . . .).
  3. Intellectual entities (God, jesus, discourse, opinion, suspicion, soul, stratagems, or ghosts).
  4. Secular statuses (emperor, barons, plebs).
  5. Ecclesiastical states.
  6. Artificers (painters, sailors).
  7. Instruments.
  8. Affections (love, justice, lechery).
  9. Religion.
  10. Sacramental confession.
  11. Tribunal.
  12. Army.
  13. Medicine (doctor, hunger, enema).
  14. Brute animals.
  15. Birds.
  16. Fish and reptiles.
  17. Parts of animals.
  18. Furnishings.
  19. Foodstuffs.
  20. Beverages and liquids (wine, beer, water, butter, wax, and resin).
  21. Clothes.
  22. Silken fabrics.
  23. Wool.
  24. Homespun and other spun goods.
  25. Nautical and aromas (ship, cinnamon, anchor, chocolate).
  26. Metal and coin.
  27. Various artifacts.
  28. Stone.
  29. Jewels.
  30. Trees and fruits.
  31. Public places.
  32. Weights and measures.
  33. Numerals.
  34. Time.
  35. Nouns.
  36. Adjectives.
  37. Verbs.
  38. Undesignated grammatical category.
  39. Undesignated grammatical category.
  40. Undesignated grammatical category.
  41. Undesignated grammatical category.
  42. Undesignated grammatical category.
  43. Persons (pronouns and appellations such as Most Eminent Cardinal).
  44. Vehicular (hay, road, footpad).

The young Leibniz would criticize the absurdity of arrangements such as this in his Dissertatio de arte combinatoria, 1666.

This sort of incongruity will affect as a secret flaw even the projects of a philosophically more sophisticated nature–such as the a priori philosophic languages we will look at in the next chapter.

This did not escape Jorge Luis Borges. Reading Wilkins, at second hand as he admits (in Other Inquisitions, “The analytical idiom of John Wilkins“), he was instantly struck by the lack of a logical order in the categorical divisions (he discusses explicitly the subdivisions of stones), and this inspired his invention of the Chinese classification which Foucault posed at the head of his The Order of Things.

In this imaginary Chinese encyclopedia bearing the title Celestial Emporium of Benevolent  Recognition, “animals are divided into: (a) belonging to the emperor, (b) embalmed, (c) tame, (d) sucking pigs, (e) sirens (f) fabulous, (g) stray dogs. (h) included in the present classification, (i) frenzied, (j) innumerable, (k) drawn with a very fine camelhair brush, (l) et cetera, (m) having just broken the water pitcher, (n) that from a long way off look like flies.”).

Borge’s conclusion was that there is no classification of the universe that is not arbitrary and conjectural. At the end of our panorama of philosophical languages, we shall see that, in the end, even Leibniz was forced to acknowledge this bitter conclusion.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 203-8.

Eco: Dee’s Magic Language

true-faithful-relation

Florence Estienne Méric Casaubon (1599-1671), A True and Faithful Relation of what Passed for Many Yeers between Dr. John Dee [ . . . ] and Some Spirits, London, 1659. 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 his Apologia compendiaria (1615) Fludd noted that the Rosicrucian brothers practiced that type of kabbalistic magic that enabled them to summon angels. This is reminiscent of the steganography of Trithemius. Yet it is no less reminiscent of the necromancy of John Dee, a man whom many authors considered the true inspirer of Rosicrucian spirituality.

In the course of one of the angelic colloquies recorded in A True and Faithful Relation of what Passed for Many Yeers between Dr. John Dee [ . . . ] and Some Spirits (1659: 92), Dee found himself in the presence of the Archangel Gabriel, who wished to reveal to him something about the nature of holy language.

When questioned, however, Gabriel simply repeated the information that the Hebrew of Adam, the language in which “every word signifieth the quiddity of the substance,” was also the primal language–a notion which, in the Renaissance, was hardly a revelation.

After this, in fact, the text continues, for page after page, to expatiate on the relations between the names of angels, numbers and secrets of the universe–to provide, in short, another example of the pseudo-Hebraic formulae which were the stock in trade of the Renaissance magus.

Yet it is perhaps significant that the 1659 Relation was published by Meric Casaubon, who was later accused of partially retrieving and editing Dee’s documents with the intention of discrediting him.

There is nothing, of course, surprising in the notion that a Renaissance magus invoked spirits; yet, in the case of John Dee, when he gave us an instance of cipher, or mystic language, he used other means.

In 1564, John Dee wrote the work upon which his contemporary fame rested–Monas hieroglyphica, where he speaks of a geometrical alphabet with no connection to Hebrew. It should be remembered that Dee, in his extraordinary library, had many of Lull’s manuscripts, and that many of his kabbalistic experiments with Hebrew characters in fact recall Lull’s use of letters in his art of combination (French 1972: 49ff).

Dee’s Monas is commonly considered a work of alchemy. Despite this, the network of alchemical references with which the book is filled seems rather intended to fulfill a larger purpose–that of explicating the cosmic implications deriving from Dee’s fundamental symbol, the Monad, based upon circles and straight lines, all generated from a single point.

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John Dee (1527-1609), Monas hieroglyphica, 1564, held in the Bibliothèque nationale de France. The Monad is the symbol at the heart of the illustration labeled Figure 8.1 in Eco’s  The Search for the Perfect Language, Oxford, 1995, p. 186.

In this symbol (see figure 8.1), the main circle represented the sun that revolves around its central point, the earth, and in its upper part was intersected by a semi-circle representing the moon.

Both sun and moon were supported on an inverted cross which represented both the ternary principle–two straight lines which intersect plus their point of intersection–and the quaternary principle–the four right angles formed at the intersections of the two lines.

The sum of the ternary and quaternary principles constituted a further seven-fold principle, and Dee goes even on to squeeze an eight-fold principle from the diagram.

By adding the first four integers together, he also derives a ten-fold principle. By such a manipulatory vertigo Dee then derives the four composite elements (heat and cold, wet and dry) as well as other astrological revelations.

From here, through 24 theorems, Dee makes his image undergo a variety of rotations, decompositions, inversions and permutations, as if it were drawing anagrams from a series of Hebrew letters.

Sometimes he considers only the initial aspects of his figure, sometimes the final one, sometimes making numerological analyses, submitting his symbol to the kabbalistic techniques of notariqon, gematria, and temurah.

As a consequence, the Monas should permit–as happens with every numerological speculation–the revelation of the whole of the cosmic mysteries.

However, the Monad also generates alphabetic letters. Dee was emphatic about this in the letter of dedication with which he introduced his book. Here he asked all “grammarians” to recognize that his work “would explain the form of the letters, their position and place in the alphabetical order, and the relations between them, along with their numerological values, and many other things concerning the primary Alphabet of the three languages.”

This final reference to “the three languages” reminds us of Postel (whom Dee met personally) and of the Collège des Trois Langues at which Postel was professor. In fact, Postel, to prove that Hebrew was the primal language in his 1553 De originibus, had observed that every “demonstration of the world” comes from point, line and triangle, and that sounds themselves could be reduced to geometry.

In his De Foenicum literis, he further argued that the invention of the alphabet was almost contemporary with the spread of language (on this point see many later kabbalistic speculations over the origins of language, such as Thomas Bang, Caelum orientis, 1657: 10).

What Dee seems to have done is to take the geometrical argument to its logical conclusion. He announced in his dedicatory letter that “this alphabetic literature contains great mysteries,” continuing that “the first Mystic letters of Hebrews, Greeks, and Romans were formed by God and transmitted to mortals [ . . . ] so that all the signs used to represent them were produced by points, straight lines, and circumferences of circles arranged by an art most marvelous and wise.”

When he writes a eulogy of the geometrical properties of the Hebrew Yod, one is tempted to think of the Dantesque I; when he attempts to discover a generative matrix from which language could be derived, one thinks of the Lullian Ars.

Dee celebrates his procedure for generating letters as a “true Kabbalah [ . . . ] more divine than grammar itself.”

These points have been recently developed by Clulee (1988: 77-116), who argues that the Monas should be seen as presenting a system of writing, governed by strict rules, in which each character is associated with a thing.

In this sense, the language of Monas is superior to the kabbala, for the kabbala aims at the interpretation of things only as they are said (or written) in language, whereas the Monas aims directly at the interpretation of things as they are in themselves. Thanks to its universality, moreover, Dee can claim that his language invents or restores the language of Adam.

According to Clulee, Dee’s graphic analysis of the alphabet was suggested by the practice of Renaissance artists of designing alphabetical letters using the compass and set-square.

Thus Dee could have thought of a unique and simple device for generating both concepts and all the alphabets of the world.

Neither traditional grammarians nor kabbalists were able to explain the form of letters and their position within the alphabet; they were unable to discover the origins of signs and characters, and for this reason they were uncapable (sic) to retrieve that universal grammar that stood at the bases of Hebrew, Greek and Latin.

According to Clulee, what Dee seems to have discovered was an idea of language “as a vast, symbolic system through which meanings might be generated by the manipulation of symbols” (1988: 95).

Such an interpretation seems to be confirmed by an author absent from all the bibliographies (appearing, to the best of my knowledge, only in Leibniz’s Epistolica de historia etymologica dissertatio of 1717, which discusses him in some depth).

This author is Johannes Petrus Ericus, who, 1697, published his Anthropoglottogonia sive linguae humanae genesis, in which he tried to demonstrate that all languages, Hebrew included, were derived from Greek.

In 1686, however, he had also published a Principium philologicum in quo vocum, signorum et punctorum tum et literarum massime ac numerorum origo. Here he specifically cited Dee’s Monas Hieroglyphica to derive from that matrix the letters of all alphabets (still giving precedence to Greek) as well as all number systems.

Through a set of extremely complex procedures, Ericus broke down the first signs of the Zodiac to reconstruct them into Dee’s Monad; he assumed that Adam had named each animal by a name that reproduced the sounds that that each emitted; then he elaborated a rather credible phonological theory identifying classes of letters such as “per sibilatione per dentes,” “per tremulatione labrorum,” “per compressione labrorum,” “per contractione palati,” “per respiratione per nares.”

Ericus concluded that Adam used vowels for the names of the beasts of the fields, and mutes for the fish. This rather elementary phonetics also enabled Ericus to deduce the seven notes of the musical scale as well as the seven letters which designate them–these letters being the basic elements of the Monas.

Finally, he demonstrated how by rotating this figure, forming, as it were, visual anagrams, the letters of all other alphabets could be derived.

Thus the magic language of the Rosicrucians (if they existed, and if they were influenced by Dee) could have been a matrix able to generate–at least alphabetically–all languages, and, therefore, all the wisdom of the world.

Such a language would have been more than a universal grammar: it would have been a grammar without syntactic structures, or, as Demonet (1992: 404) suggests, a “grammar without words,” a silent communication, close to the language of angels, or similar to Kircher’s conception of hieroglyphs.

Thus, once again, this perfect language would be based upon a sort of communicative short-circuit, capable of revealing everything, but only if it remained initiatically secret.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 185-90.

Eco: Infinite Songs & Locutions, 2

50arbreu_fig3_escorial

Ramon Llull (1232-1315), La Tercera Figura, from Ars brevis, Pisa, 1308. This illustration is hosted on the net by the Centre de Documentacio de Ramon Llull, while the original is held in the Escorial, MS.f-IV-12, folio 6. 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.

Mersenne and Guldin were anticipating Borge’s Babel Library ad abundantiam. Not only this, Guldin observed that if the numbers are these, who can marvel at the existence of so many different natural languages?

The art was now providing an excuse for the confusio linguarum. It justifies it, however, by showing that it is impossible to limit the omnipotence of God.

Are there more names than things? How many names, asks Mersenne (Harmonie, II, 72), would we need if were to give more than one to each individual? If Adam really did give names to everything, how long would he have had to spend in Eden?

In the end, human languages limit themselves to the naming of general ideas and of species; to name an individual thing, an indication with a finger is usually sufficient (p. 74).

If this were not so, it might easily “happen that for every hair on the body of an animal and for each hair on the head of a man we might require a particular name that would distinguish it from all others. Thus a man with 100,000 hairs on his head and 100,000 more on his body would need to know 200,000 separate words to name them all” (pp. 72-3).

In order to name every individual thing in the world one should thus create an artificial language capable of generating the requisite number of locutions. If God were to augment the number of individual things unto infinity, to name them all it would be enough to devise an alphabet with a greater number of letters, and this would provide us with the means to name them all (p. 73).

From these giddy heights there dawns a consciousness of the possibility of the infinite perfectibility of knowledge. Man, the new Adam, possesses the possibility of naming all those things which his ancestor had lacked the time to baptize.

Yet such an artificial language would place human beings in competition with God, who has the privilege of knowing all things in their particularity. We shall see that Leibniz was later to sanction the impossibility of such a language.

Mersenne had led a battle against the kabbala and occultism only to be seduced in the end. Here he is cranking away at Lullian wheels, seemingly unaware of the difference between the real omnipotence of God and the potential omnipotence of a human combinatory language.

Besides, in his Quaestiones super Genesim (cols 49 and 52) he claimed that the presence of the sense of infinity in human beings was itself a proof of the existence of God.

This capacity to conceive of a quasi-infinite series of combinations depends on the fact that Mersenne, Guldin, Clavius and others (see, for example, Comenius, Linguarum methodus novissima (1648: III, 19), unlike Lull, were no longer calculating upon concepts but rather upon simple alphabetic sequences, pure elements of expression with no inherent meaning, controlled by no orthodoxy other than the limits of mathematics itself.

Without realizing it, these authors are verging towards the idea of a “blind thought,” a notion that we shall see Leibniz proposing with a greater critical awareness.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 141-3.

Eco: Bruno: Ars Combinatoria & Infinite Worlds, 3

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Giordano Bruno (1548-1600), a mnemonic diagram, which appears towards the end of Cantus circaeus (Incantation of Circe), 1582, which also appears on the cover of Opere mnemotecniche, Vol. 1: De umbris idearum, 1582, Rita Sturlese, et al, ed. 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 her critical edition of De umbris (1991), Sturlese gives an interpretation of the use of the wheels that differs sharply from the “magical” interpretation given by Yates (1972). For Yates, the wheels generated syllables by which one memorizes images to be used for magical purposes.

Sturlese inverts this: for her, it is the images that serve to recall the syllables. Thus, for Sturlese, the purpose of the entire mnemonical apparatus was the memorization of an infinite multitude of words through the use of a fixed, and relatively limited, number of images.

If this is true, then it is easy to see that Bruno’s system can no longer be treated as an art where alphabetic combinations lead to images (as if it were a scenario-generating machine); rather, it is a system that leads from combined images to syllables.

Such a system not only aids memorization but, equally, permits the generation of an almost unlimited number of words–be they long and complex like incrassatus or permagnus, or difficult like many Greek, Hebrew, Chaldean, Persian or Arabic terms (De umbris, 169), or rare like scientific names of grass, trees, minerals, seeds or animal genera (De umbris, 152). The system is thus designed to generate languages–at least at the level of nomenclature.

Which interpretation is correct? Does Bruno concatenate the sequence CROCITUS to evoke the image of Pilumnus advancing rapidly on the back of a donkey with a bandage on his arm and a parrot on his head, or has he assembled these images so as to memorize CROCITUS?

In the “Prima Praxis” (De umbris, 168-72) Bruno tells us that it is not indispensable to work with all five wheels because, in most known languages, it is rare to find words containing syllables with four or five letters.

Furthermore, where such syllables do occur (for instance, in words like trans-actum or stu-prans), it is usually eash to devise some artifice that will obviate the necessity of using the fourth and fifth wheel.

We are not interested in the specific short cuts that Bruno used except to say that they cut out several billion possibilities. It is the very existence of such short cuts that seems significant.

If the syllabic sequences were expressing complex images, there should be no limit for the length of the syllables. On the contrary, if the images were expressing syllables, there would be an interest in limiting the length of the words, following the criteria of economy already present in most natural languages (even though there is no formal limit, since Leibniz will later remark that there exists in Greek a thirty-one-letter word).

Besides, if the basic criterion of every art of memory is to recall the unfamiliar through the more familiar, it seems more reasonable that Bruno considered the “Egyptian” traditional images as more familiar than the words of exotic languages.

In this respect, there are some passages in De umbris that are revealing: “Lycas in convivium cathenatus presentabat tibi AAA. . . . Medusa, cum insigni Plutonis presentabit AMO” (“Lycaon enchained in a banquet presents to you AAA . . . Medusa with the sign of Pluto presents AMO”).

Since all these names are in the nominative case, it is evident that they present the letters to the user of the system and not the other way around. This also follows from a number of passages in the Cantus circaeus where Bruno uses perceivable images to represent mathematical or abstract concepts that might not otherwise be imaginable or memorizable (cf. Vasoli 1958: 284ff).

That Bruno bequeathed all this to the Lullian posterity can be seen from further developments of Lullism.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 137-9.

Eco: The Nationalistic Hypothesis, 3

kircher_062

Athanasius Kircher (1602-80), his interpretation of the legendary sphere of Archimedes, using magnets to simulate the rotation of the planets. From Magnes, sive de Arte Magnetica, 1643, p. 305. Courtesy of Stanford University. 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.  

 

“Ideas similar to these were expressed by Schottel (Teutsche Sprachkunst, 1641), who celebrated the German language as the one which, in its purity, remained closest to the language of Adam (adding to this the idea that language was the expression of the native genius of a people).

Others even claimed that Hebrew had derived from German. They repeated the claim that their language had descended from Japheth, who, in this rendition, had supposedly settled in Germany.

The name of the exact locality changed, of course, to fit the needs of different authors; yet Japheth’s grandson, Ascenas, was said to have lived in the principality of Anhalt even before the confusio. There he was the progenitor of Arminius and Charlemagne.

In order to understand these claims, one must take into account the fact that, during the sixteenth and seventeenth centuries, Protestant Germany rallied to the defense of the language of Luther’s Bible.

It was in this period that claims to the linguistic primacy of German arose, and many of these assumptions “should be seen within the context of Germany’s political fragmentation after the Thirty Years War. Since the German nation was one of the main forces capable of uniting the nation, its value had to be emphasized and the language itself had to be liberated from foreign influences” (Faust 1981: 366).

Leibniz ironized on these and other theories. In a letter of 7 April 1699 (cited in Gensini 1991: 113) he ridiculed those who wished to draw out everything from their own language–Becanus, Rudbeck, a certain Ostroski who considered Hungarian as the mother tongue, an abbé Francois and Pretorius, who did respectively the same for Breton and Polish.

Leibniz concluded that if one day the Turks and Tartars became as learned as the Europeans, they would have no difficulty finding ways to promote their own idioms to the rank of mother tongue for all humanity.

Despite these pleasantries, Leibniz was not entirely immune himself to nationalist temptations. In his Nouveaux essais (III, 2) he made a good-natured jibe at Goropius Becanus, coining the verb goropiser for the making of bad etymologies.

Still, he conceded, Becanus might not always have been entirely wrong, especially when he recognized in the Cimbrian, and, consequently, in Germanic, a language that was more primitive than Hebrew.

Leibniz, in fact, was a supporter of the Celto-Scythian hypothesis, first advanced in the Renaissance (cf. Borst 1957-63: III/1, iv, 2; Droixhe 1978).

In the course of over ten years collecting linguistic materials and subjecting them to minute comparisons, Leibniz had become convinced that at the root of the entire Japhetic stock there lay a Celtic language that was common to both the Gauls and the Germans, and that “we may conjecture that this [common stock] derives from the time of the common origin of all these peoples, said to be among the Scythians, who, coming from the Black Sea, crossed the Danube and the Vistula, and of whom one part may have gone to Greece, while the other filled Germany and Gaul” (Nouveaux essais, III, 2).

Not only this: Leibniz even discovered analogies between the Celto-Scythian languages and those which we would today call the Semitic languages, due, he conjectured, to successive migrations.

He held that “there was nothing that argues either against or for the idea of a single, common origin of all nations, and, in consequence, of one language that is radical and primitive.”

He admitted that Arabic and Hebrew seemed closer than others, their numerous alterations notwithstanding. He concluded, however, that “it seems that Teutonic has best preserved its natural and Adamitic aspect (to speak like Jacques Böhm [sic]).”

Having examined various types of German onomatopoeia, he finally concluded that the Germanic language seemed most primitive.

In presenting this scheme in which a Scythian language group progressively diffused throughout the Mediterranean world, and in distinguishing this group from the other group of southern or Aramaic languages, Leibniz designed a linguistic atlas.

Most of the conjectures in Leibniz’s own particular scheme were, in the end, erroneous; nevertheless, in the light of comparative linguistic work which would come afterwards, he had some brilliant intuitions (cf. Gensini 1990: 41).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 99-102.

Eco: Conventionalism, Epicureanism and Polygenesis

Joseph_Justus_Scaliger_-_Imagines_philologorum

Giuseppe Giusto Scaligero, or Joseph Justus Scaliger (1540-1609), this illustration is from the title page of Marcus Manilus, Astronomicon a Ios. Scaligero ex vetusto codice Gemblacensi infinitis mendis repurgatum. Eiusdem Iosephi Scaligeri notae etc. Leiden. Christophorus Raphelengius for Joannes Commelin, 1599-1600, with a handwritten dedication from Scaliger to the mathematician Henri de Monantheuil, courtesy of the Leiden University Library and the Scaliger Institute. This narrative courtesy of the Warburg Institute. 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.

“By now, however, time was running out for the theories of Kircher, Guichard and Duret. Already in the Renaissance, Hebrew’s status as the original and sacred language had begun to be questioned.

By the seventeenth century, a new and complex set of arguments has evolved. We might, emblematically, place these arguments under the sign of Genesis 10. In these, attention moved away from the problem of primordial language to that of matrices linguae, or mother tongues–this was an expression first coined by Giuseppe Giusto Scaligero (Diatribe de europaeorum linguis, 1599).

Scaligero individuated eleven language families, seven major and four minor. Within each family, all languages were related; between the language families, however, kinship was impossible to trace.

The Bible, it was noted, had given no explicit information about the character of the primordial language. There were many who could thus maintain that the division of tongues had originated not at the foot of the shattered tower, but well before.

The notion of confusio could be interpreted as a natural process. Scholars set about trying to understand this process by uncovering the grammatical structures common to all languages: “It was no longer a question of “reduction,” but of a classification aimed at revealing a common system latent within all languages, while still respecting their individual differences” (Demonet 1992: 341, and II, 5, passim).

In his Histoire critique du Vieux Testament (1678), Richard Simon, considered one of the founders of modern biblical criticism, discarded the hypothesis of the divine origin of Hebrew, citing the ironic remarks of Gregory of Nyssa.

Language, he wrote, was a human invention; since human reason differs in different peoples, so languages must differ as well. God willed that different peoples speak different languages in order that “each might explain themselves in their own way.”

Meric Casaubon (De quattor linguis commentatio, 1650) accepted the idea of Grotius that–in so far as it had ever existed–the primordial language had long since disappeared.

Even if the words spoken by Adam had been inspired directly by God, humanity had since developed its languages autonomously. The Hebrew of the Bible was just one of the languages that arose after the Flood.

Leibniz also insisted that the historic language of Adam was irredeemably lost, and that, despite our best efforts, “nobis ignota est.” In so far as it had ever existed, it had either totally disappeared, or else survived only as relics (undated fragment in Gensini 1990: 197).

In this climate, the myth of a language that followed the contours of the world came to be rearticulated in the light of the principle of the arbitrariness of the sign. This was a principle that, in any case, philosophical thought had never entirely abandoned, as it formed part of the Aristotelian legacy.

In precisely this period, Spinoza, from a fundamentally nominalist point of view, asked how a general term such as man could possibly express man’s true nature, when different individuals formed their ideas in different ways:

“for example, those who are accustomed to contemplate with admiration the height of men will, on hearing the name man, think of an animal with an erect posture; those, instead, who are in the habit of contemplating some other feature, will form another of the common images of man–man as a laughing animal, as a biped, as featherless, as rational. Thus every individual will form images of universals according to the dispositions of their own bodies.” (Ethica, 1677: proposition XL, scolion I).

Implicitly challenging the idea that Hebrew was the language whose words corresponded to the nature of things, Locke considered that words used by human beings were signs of their ideas, “not by any natural connexion, that there is between particular articulated Sounds and certain Ideas, for then there would be but one Language amongst all Men; but by voluntary Imposition.” (An Essay concerning Human Understanding, 1690: III, 2, 1).

As soon as ideas lost their quality as innate, Platonic entities, becoming nominal ideas instead, language itself lost its aura of sacrality, turning into a mere instrument for interaction–a human construct.

In Leviathan (1651: I, 4, “Of Speech”), Hobbes admitted that the first author of speech could only have been God himself, and that he had taught Adam what to name the animals. Yet, immediately thereafter, Hobbes abandons the scriptural account to picture Adam as striking out on his own.

Hobbes argued that Adam continued freely to add new names “as the experience and use of the creatures should give him occasion.” In other words, Hobbes left Adam to confront his own experiences and his own needs; and it was from these needs (necessity being, as we know, the mother of all invention) that the languages after Babel were born.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 85-8.

Eco: The Arbor Scientarium

Ramon Llull, Liber de ascensu et decensu intellectus, 1304, first published 1512

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.