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Tag: Lull

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: 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: John Wilkins

Wilkins_An_Essay_towards_a_real

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

“Already in Mercury, a book principally devoted to secret writing, published in 1641, Wilkins had begun to design a project for universal language. It was not until 1668, however, that he was ready to unveil his Essay towards a Real Character, and a Philosophical Language–the most complete project for a universal and artificial philosophical language that the seventeenth century was ever to produce.

Since “the variety of Letters is an appendix to the Curse of Babel” (p. 13), after a dutiful bow in the direction of the Hebrew language and a sketch of the evolution of languages from Babel onwards (including an examination of the Celto-Scythian hypothesis that we considered in ch. 5), and after an acknowledgment of his precursors and his collaborators in the compilation of classifications and of the final dictionary, Wilkins turned to his major task–the construction of a language founded on real characters “legible by any Nation in their own Tongue” (p. 13).

Wilkins observed that most earlier projects derived their list of characters from the dictionary of one particular language rather than drawing directly on the nature of things, and from that stock of notions held in common by all humanity.

Wilkins‘ approach required, as a preliminary step, a vast review of all knowledge to establish what these notions held in common by all rational beings really were.

Wilkins never considered that these fundamental notions might be Platonic ideas like Lull’s dignities. His list was rather based upon empirical criteria and he sought those notions to which all rational beings might either attest or, reasonably, be expected to attest: thus, if everybody agrees on the idea of a God, everybody would likewise agree on the botanical classification supplied to him by his colleague John Ray.

In reality, the image of the universe that Wilkins proposed was the one designed by the Oxonian culture of his time. Wilkins never seriously wondered whether other cultures might have organized the world after a different fashion, even though his universal language was designed for the whole of humanity.

The Tables and the Grammar

In appearance the classification procedure chosen by Wilkins was akin to the method of the Porphyrian Tree of Aristotelian tradition. Wilkins constructed a table of 40 major genera (see figure 12.1) subdivided into 251 characteristic differences.

Umberto Eco, The Search for the Perfect Language, Figure 12.1, p. 240

Umberto Eco, The Search for the Perfect Language, Figure 12.1, p. 240. 

Umberto Eco, The Search for the Perfect Language, Figure 12.1-2, p. 241

Umberto Eco, The Search for the Perfect Language, Figure 12.1-2, p. 241.

From these he derived 2,030 species, which appear in pairs. Figure 12.2 provides a simplified example of the procedure: starting from the major genus of Beasts, after having divided them into viviparous and oviparous, and after having subdivided the viviparous ones into whole footed, cloven footed and clawed, Wilkins arrives at the species Dog / Wolf.

Umberto Eco, The Search for the Perfect Language, Figure 12.2, p. 242

Umberto Eco, The Search for the Perfect Language, Figure 12.2, p. 242.

I might add parenthetically that Wilkins‘ tables occupy a full 270 pages of his ponderous folio, and hope that the reader will excuse the summary nature of the examples which follow.

After presenting the tables, which supposedly design the whole knowable universe, Wilkins turned his attention to his natural (or philosophical) grammar in order to establish morphemes and the markers for derived terms, which can permit the generation, from the primitives, of declensions, conjugations, suffixes and so on.

Such a simplified grammatical machinery should thus allow the speaker to articulate discourses, as well as to produce the periphrases through which terms from a natural language might be defined entirely through the primitives of the artificial one.

Having reached this stage, Wilkins was able to present his language of real characters. In fact, it splits into two different languages: (1) the first is an ideogrammatic form of writing, vaguely Chinese in aspect, destined to appear in print but never to be pronounced; (2) the second is expressed by alphabetic characters and is intended to be pronounced.

It is possible to speak properly of two separate languages because, even though the pronounceable characters were constructed according to the same compositional principle as the ideograms, and obey the same syntax, they are so different that they need to be learned apart.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 238-42.

Eco: The English Debate on Character and Traits

Gerardus_Johannes_Vossius_(1577-1649),_by_Anonymous

Anonymous, Gerardus Johannes Vossius (1577-1649), 1636, inscribed (verso): GERH.JOH. VOSSIUS CANONICUS CANTUARIENSIS PROFESSOR HISTORIARII AMSTELO…AET LX Ao 1636. Held at the Universiteitsmuseum Amsterdam. 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 1654 John Webster wrote his Academiarum examen, an attack on the academic world, which had allegedly given an insufficient amount of attention to the problem of universal language.

Like many of this English contemporaries, Webster was influenced by Comenius‘ propaganda for a universal language. He foresaw the birth of a “Hieroglyphical, Emblematical, Symbolical, and Cryptographical learning.”

Describing the general utility of algebraic and mathematical signs, he went on to note that “the numerical notes, which we call figures and ciphers, the Planetary Characters, the marks for minerals, and many other things in Chymistry, though they be alwaies the same and vary not, yet are understood by all nations in Europe, and when they are read, every one pronounces them in their own Countrey’s language and dialect.” (pp. 24-5).

Webster was not alone; other authors were taking up and elaborating ideas which had first originated with Bacon. Another writer championing universal characters was Gerhard Vossius in De arte grammatica, 1635 (1.41).

Nevertheless, for the men from whose ranks the Royal Society would later be formed, Webster’s demand for research in hieroglyphic and emblematic characters sounded too much like Father Kircher’s Egyptian linguistics.

In effect, Webster was indeed thinking of a language of nature in opposition to the institutionalized language of men (see Formigari 1970: 37).

Responding to Webster, in another pamphlet, also published in 1654 (Vindiciae academiarum, to which Wilkins himself added an introduction), Seth Ward denounced the mystic propensities of his opponent (see Slaughter 1982: 138ff).

Ward made no objection to the idea of the real character as such, provided that it was constructed upon the algebraic model invented by Viète in the sixteenth century and elaborated by Descartes, where letters of the alphabet stand for mathematical quantities.

It is, however, evident that what Ward thought of was not what Webster had in mind.

Ward argued that only the real character of which he spoke could be termed as “a naturall Language and would afford that which the Cabalists and Rosycrucians have vainely sought for in the Hebrew” (p. 22).

In his introduction Wilkins went even further: Webster, he wrote, was nothing but a credulous fanatic. Even in his Essay, which we will soon discuss, Wilkins could not resist shooting, in his introduction, indignant darts in Webster’s direction without naming him directly.

In spite of all this, however, the projects of the religious mystics did have something in common with those of the “scientists.” In that century the play of reciprocal influence was very complex and many have detected relationships between Lullists or Rosicrucians and the inventors of philosophical languages (see Ormsby-Lennon 1988; Knowlson 1975; and, of course, Yates and Rossi).

Nevertheless, in contrast to the long tradition of the search for the lost language of Adam, the position of Ward, with the aid of Wilkins, was entirely secular.

This is worth emphasizing: there was no longer any question of discovering the lost language of humanity; the new language was to be a new and totally artificial language, founded upon philosophic principles, and capable of realizing, by rational means, that which the various purported holy languages (always dreamt of, never really rediscovered) had sought but failed to find.

In every one of the holy and primordial languages we have so far considered, at least in the way they were presented, there was an excess of content, never completely circumscribable, in respect of expression.

By contrast, the search was now for a scientific or philosophical language, in which, by an unprecedented act of impositio nominum, expression and content would be locked in permanent accord.

Men such as Ward and Wilkins thus aimed at being the new Adam; it was this that turned their projects into a direct challenge to the older tradition of mystic speculation. In the letter to the reader that introduced the Essay, Wilkins writes:

“This design would likewise contribute much to the clearing of some of our modern differences in Religion, by unmasking many wild errors, that shelter themselves under the disguise of affected phrases; which being Philosophically unfolded, and rendered according to the genuine and natural importance of Words, will appear to be inconsistencies and contradictions. (B1r).”

This was nothing less than a declaration of war on tradition, a promise of a different species of therapy that would finally massage out the cramps in language; it is the first manifestation of that skeptical-analytic current of thought, exquisitely British, that, in the twentieth century, would use linguistic analysis as an instrument for the confutation of metaphysics.

Despite the persistence of the Lullian influences, there can be no doubt that, in order to realize their project, British philosophers paid close attention to Aristotle’s system of classification.

The project of Ward is an example. It was not enough simply to invent real characters for the new language; it was necessary also to develop a criterion that would govern the primitive features that would compose these characters:

“All Discourses being resolved in sentences, these into words, words signifying either simple notions or being resolvable into simple notions, it is manifest, that if all the sorts of simple notions be found out, and have Symboles assigned to them, those will be extremely few in respect of the other [ . . . ] the reason of their composition easily known, and the most compounded ones at once will be comprehended [ . . . ] so to deliver the nature of things. (Vindiciae, 21).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 218-21.

Eco: Kircher’s Polygraphy

Kircher, the Steganographic Ark, from Polygraphia Nova, p. 130

Athanasius Kircher (1602-80), the steganographic ark, Polygraphia nova et universalis ex combinatoria arte detecta, 1663. 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. 

Kircher wrote his Polygraphia nova et universalis ex combinatoria arte detecta in 1663, several years after his early works on Egypt and hieroglyphics, but he was concerned with the problem of universal writing from the beginning of the decade, and it seems evident that he was at the same time fascinated by the hieroglyphic mysteries and the polygraphic publicity.

It is also significant that in this same volume Kircher designed not only a polygraphy, or international language open to all, but also, in the wake of Trithemius, a steganography, or secret language in which to cipher messages.

What (at the end of the previous chapter) seemed to us a contradiction appeared to Kircher rather as a natural connection. He cited, at the outset, an Arab proverb: if you have a secret, hide it or reveal it (“si secretum tibi sit, tege illud, vel revela“).

Such a decision was not so obvious, after all, since in his works on Egyptology Kircher had chosen a “fifty-fifty solution,” saying something by concealing it, alluding without revealing.

Finally, the second part of the title of Kircher’s work reveals that, in designing his polygraphy, Kircher was also using Lull’s art of combination (contrary to the opinion of Knowlson 1975: 107-8).

In the enthusiastic preface that the author addressed to the emperor Ferdinand III, he celebrated polygraphy as “all languages reduced to one” (“linguarum omnium ad nam reductio“).

Using polygraphy, “anyone, even someone who knows nothing other than his own vernacular, will be able to correspond and exchange letters with anybody else, of whatever their nationality.”

Thus Kircher’s polygraphy was in reality a pasigraphy, that is, a project for a written language, or international alphabet, which was not required to be spoken.

It is easy to confuse Kircher’s project with a double pentaglottic dictionary, in A and B versions (both in Latin, Italian, Spanish, French and German). In Kircher’s time, English was not considered an important international language, and, in his Character, Becher had assumed that French was sufficient, as a vehicular language, for English, Italian, Spanish and Portuguese native speakers.

Ideally, Kircher thought (p. 7) that his dictionary should also include Hebrew, Greek, Bohemian, Polish, Lithuanian, Hungarian, Dutch, English and Irish (“linguae doctrinales omnibus communes“)–as well as Nubian, Ethiopic, Egyptian, Congolese, Angolan, Chaldean, Arabic, Armenian, Persian, Turkish, Tartar, Chinese, Mexican, Peruvian, Brazilian and Canadian.

Kircher did not, it seems, feel himself ready to confront such a gigantic task; perhaps he intuited that the missionary activity, followed eventually by colonialism, would drastically simplify the problem (transforming many exotic languages into mere ethnological remnants): Spanish would substitute for Mexican, French for Canadian, Portuguese for Brazilian, and various pidgins would substitute for all the rest.

Kircher’s A and B dictionaries each contain 1,228 items. The grounds for selection were purely empirical: Kircher chose the words that seemed to him most commonly used.

Dictionary A served to encode messages. It started with a list of common nouns and verbs, in alphabetical order. There followed alphabetic lists of proper nouns (regions, cities, persons), and of adverbs and prepositions.

Added to this there was also a list of the conjugations of both the verbs to be and to have. The whole material was subdivided into 32 tables, marked by Roman numerals, while every item of each table was marked by an Arabic numeral.

The dictionary was set out in five columns, one for each of the five languages, and the words in each language were listed in their proper alphabetical order. Consequently, there is no necessary semantic correspondence between the terms recorded on the same line, and only the terms scored with the same Roman and Arabic numbers were to be considered synonymous.

We can see this best by giving the first two lines of the dicti0nary:

Umberto Eco, The Search for the Perfect Language, p. 198

Umberto Eco, The Search for the Perfect Language, p. 198. 

The Roman numerals refer to tables found in dictionary B; the Arabic numerals refer to the items themselves. Latin acts as the parameter language: for each specific term, the numbers refer to the Latin alphabetic ordering.

For example, the code for the French word abstenir is I.4, which indicates that the position of its Latin synonym, abstinere, is fourth in the Latin column I (obviously, to encode the Latin word abstinere, one also writes I.4).

To decode the message, it was necessary to use dictionary B. This too was arranged in 32 tables, each assigned a Roman numeral. But for each column (or language) the words did not follow their alphabetic order (except the Latin one), while the Arabic numbers marking each term were in an increasing arithmetical order.

Thus all the terms on the same line were synonymous and each synonym was marked by the same Arabic number.

Again, it is easiest to see how this worked by citing the first two lines of the first table:

Umberto Eco, The Search for the Perfect Language, p. 199

Umberto Eco, The Search for the Perfect Language, p. 199. 

Thus, if one wants to send the Latin word abdere (to hide), according to the dictionary A one encodes it as I.2. A German addressee, receiving the message I.2, goes to dictionary B, first table, German column, and looks for the second word, which is exactly verbergen (to hide).

If the same addressee wants to know how to translate this term in Spanish, one finds in the same line that the synonymous term is esconder.

However, Kircher found that a simple lexicon did not suffice; he was forced to invent 44 supplementary signs (notae) which indicated the tense, mood and number of verbs, plus 12 more signs which indicated declensions (nominative, genitive, dative, etc., both singular and plural).

Thus, to understand the following example, the sign N meant nominative, while a sign like a D indicated the third person singular of the past tense. In this way, the ciphered expression “XXVII.36N, XXX.21N, II.5N, XXIII.8D, XXVIII.10, XXX.20” can be decoded as “Petrus noster amicus, venit ad nos” (literally, “Peter our friend came to us”), and on the basis of Latin, can be transformed into an equivalent sentence in any of the other four languages.

Kircher proudly claims that, by dictionary A, we can write in any language even though though we know only our own, as well as that, with dictionary B, we can understand a text written in an unknown language.

The system also works when we receive a non-ciphered text written in a natural foreign language. All we have to do is to look up the reference numbers for each foreign word in dictionary A (where they are listed in alphabetical order), then, with the reference numbers, find the corresponding words in dictionary B, in the column for our own language.

Not only was this process laborious, but the entire project was based on the assumption that all other languages could be directly reduced to the Latin grammar. One can imagine the results of such a method if one thinks of translating literally, word by word, a German sentence into an English one.

Kircher never confronted the problem of why an item-by-item translation should be syntactically correct, or even comprehensible, in the new language. He seemed to rely on the good will and good sense of whoever used his system.

Yet even the most willing users might slip up. In August 1663, after reading the Polygraphia, Juan Caramuel y Lobkowitz wrote to Kircher to congratulate him on his wonderful invention (Mss Chigiani f. 59 v., Biblioteca Apostolica Vaticana; cf. Casciato et al. 1986: table 5).

Appropriately, Caramuel chose to congratulate Kircher in his own polygraphy. Yet his first problem was that Kircher’s own first name, Athanasius, did not appear in the list of proper names. Adopting the principle that where a term is missing, an analogous one must be sought, Caramuel addressed his letter to “Anastasia.”

Moreover, there are passages that can be decoded fairly easily, while for others one suspects that the labor of consulting the dictionary to obtain reference numbers for every word proved so tedious that even Caramuel began to nod.

Thus we find ourselves in front of a passage which, in Latin, would need to be translated as follows: “Dominus + sign of vocative, Amicus + sign of vocative, multum sal + sign of vocative, Anastasia, a me + sign of accusative, ars + sign of accusative, ex illius + sign of ablative, discere posse + sign of second person plural, future active, non est loqui vel scribere sub lingua + ablative, communis + ablative.”

After many heroic efforts, one can try to render it (in a sort of “Me Tarzan-You Jane” language) as “O Lord and Friend, O witty Athanasius, to me (?) you could learn from him an art (which) is not speaking and writing under a common language.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 196-200.

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.

bpt6k5401042m

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: The Kircherian Ideology

original

Athanasius Kircher (1602-80), Egyptian pyramids by Gioseffo Petrucci, Prodromo apologetico alli studi chiercheriani, Amsterdam, 1677, reprinted from Sphinx Mystagoga, a selection of images related to Athanasius Kircher in the Stanford University Archives, curated by Michael John Gorman, 2001. 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 would be idle to hold Kircher responsible for his inability to understand the nature of hieroglyphic writing, for which in his time nobody had the key. Yet his ideology magnified his errors.

“Nothing can explain the duplicity of the research of Kircher better than the engraving which opens the Obeliscus Pamphilius: in this cohabit both the illuminated image of Philomatià to whom Hermes explains every mystery and the disquieting gesture of Harpocrates who turns away the profane, hidden by the shadow of the cartouche.” (Rivosecchi 1982: 57).

The hieroglyphic configurations had become a sort of machine for the inducing of hallucinations which then could be interpreted in any possible way.

Rivosecchi (1982: 52) suggests that Kircher exploited this very possibility in order to discuss freely a large number of potentially dangerous themes–from astrology to alchemy and magic–disguising his own opinions as those of an immemorial tradition, one in which, moreover, Kircher treated prefigurations of Christianity.

In the midst of this hermeneutic bulimia, however, there glimmers the exquisitely baroque temperament of Kircher at play, delighting in his taste for the great theater of mirrors and lights, for the surprising museographic collection (and one has only to think of that extraordinary Wunderkammer which was the museum of the Jesuit Collegio Romano).

Only his sensitivity to the incredible and the monstrous can explain the dedication to the Emperor Ferdinand III that opens the third volume of Oedipus:

“I unfold before your eyes, O Most Sacred Caesar, the polymorphous reign of Morpheus Hieroglyphicus. I tell of a theater in which an immense variety of monsters are disposed, and not the nude monsters of nature, but adorned by the enigmatic Chimeras of the most ancient of wisdoms so that here I trust sagacious wits will draw out immeasurable treasures for the sciences as well as no small advantage for letters.

Here there is the Dog of Bubasti, the Lion Saiticus, the Goat Mendesius, here there is the Crocodile, horrible in the yawning of its jaws, yet from whose uncovered gullet there emerges the occult meanings of divinity, of nature, and of the spirit of Ancient Wisdom espied through the vaporous play of images.

Here there are the Dipsodes thirsting for blood, the virulent Asp, the astute Icneumon, the cruel Hippopotami, the monstrous Dragons, the toad of swollen belly, the snail of twisted shell, the hairy caterpillar and the innumerable other specters which all show the admirably ordered chain which extends itself into the depths of nature’s sanctuaries.

Here is presented a thousand species of exotic things in many and varied images, transformed by metamorphosis, converted into human figures, and restored once more to themselves again in a dance of the human and the savage intertwined, and all in accordance with the artifices of the divine; and finally, there appears the divinity itself which, to say with Porphyry, scours the entire universe, ordering it with all things in a monstrous connubium; where now, sublime in its variegated face, it raises its canine cervix to reveal itself as Cenocephalus, now as the wicked Ibis, now as the Sparrow-hawk wrapped in a beaky mask.

[ . . . ] now, delighting in its virgin aspect, under the shell of the Scarab it lies concealed as the sting of the Scorpion [these descriptions carry on for four more pages] in this pantomorphic theater of nature  unfolded before our gaze, under the allegorical veil of occult meanings.”

This is the same spirit which informed the medieval taste for encyclopedias and for libri monstruorum, a genre which reappears from the Renaissance onwards under the “scientific” guise of the medical studies of Ambroise Paré, the naturalist works of Ulisse Aldrovandi, the collection of monsters of Fortunio Liceti, the Physica curiosa of Gaspar Schott.

Here it is combined, with a quality of frenzied dissymmetry that is almost Borrominian, recalling the aesthetic ideals presiding over the construction of the hydraulic grottos and mythological rocailles in the gardens of the period.

Beyond this, however, Rivosecchi has put his finger on another facet of the Kircherian ideology. In a universe placed under the sign of an ancient and powerful solar deity, the myth of Osiris had become an allegory of the troubled search for stability in the world still emerging from the aftermath of the Thirty Years War, in which Kircher was directly involved.

In this sense, we might read the dedications to Ferdinand III, which stand out at the beginning of each volume of the Oedipus, in the same light as the appeals of Postel to the French monarchy to restore harmony a century before, or as the analogous appeals of Bruno, or as Campanella’s celebration of a solar monarchy, prelude to the reign of Louis XIV, or as the calls for a golden century which we will discuss in the chapter on the Rosicrucians.

Like all the utopian visionaries of his age, the Jesuit Kircher dreamed of the recomposition of a lacerated Europe under a stable monarchy. As a good German, moreover, he repeated the gesture of Dante and turned to the Germanic, Holy Roman emperor.

Once again, as in the case of Lull, though in ways so different as to void the analogy, it was the search for a perfect language that became the instrument whereby a new harmony, not only in Europe, but across the entire planet, was to be established.

The knowledge of exotic languages, aimed not so much at recovering their original perfection, but rather at showing to the Jesuit missionaries “the method of bearing the doctrine of Christ to those cut off from it by diabolic malice” (preface to China, but also Oedipus, I, I, 396-8).

In the last of Kircher’s works, the Turris Babel, the story of the confusion of tongues is once again evoked, this time in an attempt to compose “a grandiose universal history, embracing all diversities, in a unified project of assimilation to Christian doctrine. [ . . . ]

The peoples of all the world, dispersed after the confusion, are to be called back together from the Tower of the Jesuits for a new linguistic and ideological reunification.” (Scolari 1983: 6).

In fact, hungry for mystery and fascinated by exotic languages though he was, Kircher felt no real need to discover a perfect language to reunite the world in harmony; his own Latin, spoken with the clear accents of the Counter-Reformation, seemed a vehicle perfectly adequate to transport as much gospel truth as was required in order to bring the various peoples together.

Kircher never entertained the thought that any of the languages he considered, not even the sacred languages of hieroglyphics and kabbalistic permutations, should ever again be spoken. He found in the ruins of these antique and venerated languages a garden of private delight; but he never conceived of them as living anew.

At most he toyed with the idea of preserving these languages as sacred emblems, accessible only to the elect, and in order to show their fecund impenetrability he needed elephantine commentaries.

In every one of his books, he showed himself as a baroque scholar in a baroque world; he troubled more over the execution of his tables of illustrations than over the writing (which is often wooden and repetitive).

Kircher was, in fact, incapable of thinking other than in images (cf. Rivosecchi 1982: 114). Perhaps his most lasting achievement, and certainly his most popular book, was the Ars magna lucis et umbrae of 1646.

Here he explored the visible in all its nooks and crannies, drawing from his exploration a series of scientifically valid intuitions which even faintly anticipate the invention of the techniques of photography and the cinema.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 162-5.

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: Infinite Songs & Locutions

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Giordano Bruno (1548-1600), memory wheel, De Umbris Idearum, 1582, reconstructed by Dame Frances Yates, Warburg Institute. Frances Yates wrote Giordano Bruno and the Hermetic Tradition, Chicago, 1964. 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.  

 “Between Lull and Bruno might be placed the game invented by H.P. Harsdörffer in his Matematische und philosophische Erquickstunden (1651: 516-9). He devises 5 wheels containing 264 units (prefixes, suffixes, letters and syllables).

This apparatus can generate 97,209,600 German words, including many that were still non-existent but available for creative and poetic use (cf. Faust 1981: 367). If this can be done for German, why not invent a device capable of generating all possible languages?

The problem of the art of combination was reconsidered in the commentary In spheram Ioannis de sacro bosco by Clavius in 1607. In his discussion of the four primary qualities (hot, cold, dry and wet), Clavius asked how many pairs they might form.

Mathematically, we know, the answer is six. But some combinations (like “hot and cold,” “dry and wet”) are impossible, and must be discarded, leaving only the four acceptable combinations: “Cold and dry” (earth), “hot and dry” (fire), “hot and wet” (air), “cold and wet” (water).

We seem to be back with the problem of Lull: a conventional cosmology limits the combinations.

Clavius, however, seemed to wish to go beyond these limits. He asked how many dictiones, or terms, might be produced using the 23 letters of the Latin alphabet (u being the same as v), combining them 2, 3, 4 at a time, and so on until 23.

He supplied a number of mathematical formulae for the calculations, yet he soon stopped as he began to see the immensity of the number of possible results–especially as repetitions were permissible.

In 1622, Paul Guldin wrote a Problema arithmeticum de rerum combinationibus (cf. Fichant 1991: 136-8) in which he calculated the number of possible locutions generated by 23 letters. He took into account neither the question of whether the resulting sequences had a sense, nor even that of whether they were capable of being pronounced at all.

The locutions could consist of anything from 2 to 23 letters; he did not allow repetitions. He arrived at a result of more than 70,000 billion billion. To write out all these locutions would require more than a million billion billion letters.

To conceive of the enormity of this figure, he asked the reader to imagine writing all these words in huge notebooks: each of these notebooks had 1,000 pages; each of these pages had 100 lines; each of these lines could accommodate 60 characters.

One would need 257 million billion of these notebooks. Where would you put them all? Guldin then made a careful volumetric study, imagining shelf space and room for circulation in the libraries that might store a consignment of these dimensions.

If you housed the notebooks in large libraries formed by cubes whose sides measured 432 feet, the number of such cubic buildings (hosting 32 million volumes each) would be 8,050,122,350. And where would you put them all? Even exhausting the total available surface space on planet earth, one would still find room for only 7,575,213,799!

In 1636 Father Marin Mersenne, in his Harmonie universelle, asked the same question once again. This time, however, to the dictiones he added “songs,” that is, musical sequences.

With this, the conception of universal language has begun to appear, for Mersenne realizes that the answer would necessarily have to include all the locutions in all possible languages. He marveled that our alphabet was capable of supplying “millions more terms than the earth has grains of sand, yet it is so easy to learn that one hardly needs memory, only a touch of discernment” (letter to Peiresc, c. April 1635; cf. Coumet 1975; Marconi 1992).

In the Harmonie, Mersenne proposed to generate only pronounceable words in French, Greek, Arabic, Chinese and every other language. Even with this limitation one feels the shudder provoked by a sort of Brunian infinity of possible worlds.

The same can be said of the musical sequences that can be generated upon an extension of 3 octaves, comprising 22 notes, without repetitions (shades of future 12-tone compositions!).

Mersenne observed that to write down all these songs would require enough reams of paper to fill in the distance between heaven and earth, even if every sheet contained 720 of these 22-note songs and every ream was so compressed as to be less than an inch thick.

In fact the number of possible songs amounted to 1,124,000,727,777,607,680,000 (Harmonie, 108). By dividing this figure by the 362,880 songs contained in each ream, one would still obtain a 16-digit figure, whilst the number of inches between the center of the earth and the stars is only 28,826,640,000,000 (a 14-digit figure).

Anyone who wished to copy out all these songs, a thousand per day, would have to write for 22,608,896,103 years and 12 days.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 139-41.

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: Bruno: Ars Combinatoria & Infinite Worlds, 2

1280px-6665_-_Roma_-_Ettore_Ferrari,_Monumento_a_Giordano_Bruno_(1889)_-_Foto_Giovanni_Dall'Orto,_6-Apr-2008

Ettore Ferrari (1845-1929), Giordano Bruno Burned at the Stake, a bas relief on the plinth of the monument to Bruno in Campo de’Fiori square in Rome. This photo by Giovanni Dall’Orto © 2008. The copyright holder of this photo allows anyone to use for any purpose, provided that the copyright holder is properly attributed. Redistribution, derivative work, commercial use, and all other use is permitted.  

 

“Thus this language claimed to be so perfect as to furnish the keys to express relations between things, not only of this world, but of any of the other infinite worlds in their mutual concordance and opposition.

Nevertheless, in its semiotic structure, it was little more than an immense lexicon, conveying vague meanings, with a very simplified syntax. It was a language that could be deciphered only by short-circuiting it, and whose decipherment was the privilege only of the exegete able to dominate all its connections, thanks to the furor of Bruno’s truly heroic style.

In any case, even if his techniques were not so different from those of other authors of arts of memory, Bruno (like Lull, Nicholas of Cusa and Postel, and like the reformist mystics of the seventeenth century–at whose dawn he was to be burnt at the stake) was inspired by a grand utopian vision.

His flaming hieroglyphical rhetoric aimed at producing, through an enlargement of human knowledge, a reform, a renovation, maybe a revolution in the consciousness, customs, and even the political order of Europe. Of this ideal, Bruno was the agent and propagandist, in his wandering from court to European court.

Here, however, our interest in Bruno is limited to seeing how he developed Lullian techniques. Certainly, his own metaphysics of infinite worlds pushed him to emphasize the formal and architectonic aspects of Lull’s endeavor.

One of his mnemonic treatises, De lampade combinatoria lulliana ad infinita propositiones et media inveniendi (1586), opens by mentioning the limitless number of propositions that the Ars is capable of generating, and then says: “The properties of the terms themselves are of scant importance; it is only important that they show an order, a texture, an architecture.” (I, ix).

In the De umbris idearum (1582) Bruno described a set of movable, concentric wheels subdivided into 150 sectors. Each wheel contained 30 letters, made up of the 23 letters of the Latin alphabet, plus 7 letters from the Greek and Hebrew alphabets to which no letter corresponded in Latin (while, for instance, A could also stand for Alpha and Alef).

To each of the single letters there corresponded a specific image, representing for each respective wheel a different series of figures, activities, situations, etc. When the wheels were rotated against each other in the manner of a combination lock, sequences of letters were produced which served to generate complex images. We can see this in Bruno’s own example (De umbris, 163):

Giordano Bruno, De umbris, 163

Reproduced from Umberto Eco, The Search for the Perfect Language, James Fentress, trans., Blackwell: Oxford, 1995, p. 136, from Giordano Bruno, De umbris idearum, 1582, p. 163. 

In what Bruno called the “Prima Praxis,” the second wheel was rotated so as to obtain a combination such as CA (“Apollo in a banquet”). Turning the third wheel, he might obtain CAA (“Apollo enchained in a banquet”). We shall see in a moment why Bruno did not think it necessary to add fourth and fifth wheels as he would do for the “Secunda Praxis,” where they would represent, respectively, adstantia and circumstantias.

In his “Secunda Praxis,” by adding the five vowels to each of the 30 letters of his alphabet, Bruno describes 5 concentric wheels, each having 150 alphabetical pairs, like AA, AE, AI, AO, AU, BA, BE, BO, and so on through the entire alphabet.

These 150 pairs are repeated on each of the 5 wheels. As in the “Prima Praxis,” the significance changes with every wheel. On the first wheel, the initial letter signifies a human agent, on the second, an action, on the third, an insignia, on the fourth, a bystander, on the fifth, a set of circumstances.

By moving the wheels it is possible to obtain images such as “a woman riding on a bull, combing her hair while holding a mirror in her left hand, accompanied by an adolescent carrying a green bird in his hand” (De umbris, 212, 10).

Bruno speaks of images “ad omnes formationes possible, adaptabiles” (De umbris, 80), that is, susceptible of every possible permutation. In truth, it is almost impossible to write the number of sequences that can be generated by permutating 150 elements 5 at a time, especially as inversions are allowed (De umbris, 223).

This distinguishes the art of Bruno, which positively thirsts after infinity, from the art of Lull.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 135-7.

Eco: Bruno: Ars Combinatoria and Infinite Worlds

1280px-Relief_Bruno_Campo_dei_Fiori_n1

Ettore Ferrari (1845-1929), The Trial of Giordano Bruno by the Roman Inquisition, bronze relief, Campo de’Fiori, Rome. This bas relief graces the pedestal of the statue of Bruno at Campo de’Fiori in Rome. The collected works of Giordano Bruno (1548-1600) are in the Bibliotheca Bruniana Electronica at the Warburg Institute, with others at the Esoteric Archives. This photo dated 2006 by Jastrow is in the public domain. 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.    

Giordano Bruno’s cosmological vision presented a world without ends, whose circumference, as Nicholas of Cusa had already argued, was nowhere to be found, and whose center was everywhere, at whatever point the observer chose to contemplate the universe in its infinity and substantial unity.

The panpsychism of Bruno had a Neoplatonic foundation: there was but a single divine breath, one principle of motion pervading the whole of the infinite universe, determining it in its infinite variety of forms.

The master idea of an infinite number of worlds was compounded with the notion that every earthly object can also serve as the Platonic shade of other ideal aspects of the universe. Thus every object exists not only in itself, but as a possible sign, deferral, image, emblem, hieroglyph of something else.

This worked also by contrast: an image can lead us back to the unity of the infinite even through its opposite. As Bruno wrote in his Eroici furori, “To contemplate divine things we need to open our eyes by using figures, similitudes, or any of the other images that the Peripatetics knew under the name of phantasms” (Dialoghi italiani, Florence: Sansei, 1958: 1158).

Where they did not emerge directly from his own inflamed imagination, Bruno chose images found in the Hermetic repertoire. These served as storehouses of revelations because of a naturally symbolic relationship that held between them and reality.

Their function was no longer, as in previous arts of memory, that of merely helping to order information for ease of recall, or this was, at least, by now a minor aspect: their function was rather that of helping to understand. Bruno’s images permitted the mind to discover the essence of things and their relations to each other.

The power of revelation stored inside these images was founded on their origin in far-off Egypt. Our distant progenitors worshipped cats and crocodiles because “a simple divinity found in all things, a fecund nature, a mother watching over the universe, expressed in many different ways and forms, shines through different subjects and takes different names” (Lo spaccio della bestia trionfante, Dialoghi italiani, 780-2).

But these images possess more than the simple capacity to reawaken our dormant imagination: they possess an authentic power to effect magical operations on their own, and functioned, in other words, in exactly the same way as the talismans of Ficino.

It is possible, of course, to take many of Bruno’s magical claims in a metaphorical sense, as if he was merely describing, according to the sensibility of his age, intellectual operations. It is also possible to infer that these images had the power to pull Bruno, after prolonged concentration, into a state of mystic ecstasy (cf. Yates 1964: 296).

Still, it is difficult to ignore the fact that some of Bruno’s strongest claims about the theurgic potential of seals appeared in a text that bore the significant title of De Magia:

“nor even are all writings of the same utility as these characters which, by their very configuration, seem to indicated things themselves. For example, there are signs that are mutually inclined to one another, that regard each other and embrace one another; these constrain us to love.

Then there are the opposite signs, signs which repel each other so violently that we are induced to hatred and to separation, becoming so hardened, incomplete, and broken as to produce in us ruin. There are knots which bind, and there are separated characters which release. [ . . . ]

These signs do not have a fixed and determined form. Anyone who, obeying his own furor, or the dictates of his soul, naturally creates his own images, be these of things desired or things to hold in contempt, cannot help but represent these images to himself and to his spirit as if the imagined things were really present.

Thus he experiences his own images with a power that he would not feel were he to represent these things to himself in the form of words, either in elegant oration, or in writing.

Such were the well-defined letters of the ancient Egyptians, which they called hieroglyphs or sacred characters. [ . . . ] by which they were able to enter into colloquies with the gods and to accomplish remarkable feats with them. [ . . . ]

And so, just as, where there lacks a common tongue, men of one race are unable to have colloquies with those of another, but must resort instead to gestures, so relations of any sort between ourselves and certain powers would be impossible were we to lack the medium of definite signs, seals, figures, characters, gestures, and other ceremonies.”

(Opera latine conscripta, Naples-Florence, 1879-1891, vol. III: 39-45).

Concerning the specific iconological material that Bruno employs, we find figures deriving directly from the Hermetic tradition, such as the Thirty-six Decans of the Zodiac, others drawn from mythology, necromantic diagrams that recall Agrippa or John Dee, Lullian suggestions, animals, plants and allegorical figures deriving from the repertoire of emblems and devices.

This is a repertoire with an extraordinary importance in the history of iconology, where the ways in which a certain seal, for example, refers back to a specific idea are largely governed by rhetorical criteria: phonetic similarities (a horse, equus, can correspond to an honest, aequus, man); the concrete for the abstract (a Roman soldier for Rome); antecedent for the consequent; accident for subject (or vice versa); and so on.

Sometimes the analogy  is based upon the similarity of the initial syllable (asinus for asyllum); and certainly Bruno did not know that this procedure, as we shall see in chapter 7, was followed by the Egyptians themselves when using their hieroglyphs.

At other times the relations might be based on kabbalistic techniques such as anagrams or paronomasias (like palatio standing for Latio: cf. Vasoli 1958: 285-6).”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 132-5.

Eco: Lullian Kabbalism, 2

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Jan Amos Komensky, or Johann (John) Amos Comenius (1592-1670), from Opera didactica omnia, Amsterdam, 1657. 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.  

“Numerology, magic geometry, music, astrology and Lullism were all thrown together in a series of pseudo-Lullian alchemistic works that now began to intrude onto the scene. Besides, it was a simple matter to inscribe kabbalistic terms onto circular seals, which the magical and alchemical tradition had made popular.

It was Agrippa who first envisioned the possibility of taking from the kabbala and from Lull the technique of combination in order to go beyond the medieval image of a finite cosmos and construct the image of an open expanding cosmos, or of different possible worlds.

In his In artem brevis R. Lulli (appearing in the editio princeps of the writings of Lull published in Strasbourg in 1598), Agrippa assembled what seems, at first sight, a reasonably faithful and representative anthology from the Ars magna.

On closer inspection, however, one sees that the number of combinations deriving from Lull’s fourth figure has increased enormously because Agrippa has allowed repetitions.

Agrippa was more interested in the ability of the art to supply him with a large number of combinations than in its dialectic and demonstrative properties. Consequently, he proposed to allow the sequences permitted by his art to proliferate indiscriminately to include subjects, predicates, rules and relations.

Subjects were multiplied by distributing them, each according to its own species, properties and accidents, by allowing them free play with terms that are similar or opposite, and by referring each to its respective causes, actions, passions and relations.

All that is necessary is to place whatever idea one intends to consider in the center of the circle, as Lull did with the letter A, and calculate its possible concatenations with all other ideas.

Add to this that, for Agrippa, it was permissible to add many other figures containing terms extraneous to Lull’s original scheme, mixing them up with Lull’s original terms: the possibilities for combination become almost limitless (Carreras y Artau 1939: 220-1).

Valerio de Valeriis seems to want the same in his Aureum opus (1589), when he says that the Ars “teaches further and further how to multiply concepts, arguments, or any other complex unto infinity, tam pro parte vera quam falsa, mixing up roots with roots, roots with forms, trees with trees, the rules with all these other things, and very many other things as well” (“De totius operis divisione“).

Authors such as these still seem to oscillate, unable to decide whether the Ars constitutes a logic of discovery or a rhetoric which, albeit of ample range, still serves merely to organize a knowledge that it has not itself generated.

This is evident in the Clavis universalis artis lullianae by Alsted (1609). Alsted is an author, important in the story of the dream of a universal encyclopedia, who even inspired the work of Comenius, but who still–though he lingered to point out the kabbalist elements in Lull’s work–wished to bend the art of combination into a tightly articulated system of knowledge, a tangle of suggestions that are, at once, Aristotelian, Ramist and Lullian (cf. Carreras y Artau 1939: II, 239-49; Tega 1984: I, 1).

Before the wheels of Lull could begin to turn and grind out perfect languages, it was first necessary to feel the thrill of an infinity of worlds, and (as we shall see) of all of the languages, even those that had yet to be invented.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 130-2.

Eco: Lullian Kabbalism

Roma1493

Unknown artist, Roma 1493, depicting the city of Rome as it appeared in that year. This woodcut was published in Hartmann Schedel (1440-1514), Schedelsche Weltchronik, Nürnberg, 1493, on folio lvii verso and lviii recto. Known in English as the Nuremberg Chronicle, or Schedel’s World Chronicle, the work commissioned by Sebald Schreyer (1446-1520) and Sebastian Kammermeister (1446-1503) was lushly illustrated with the first depictions of many cities. 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 now reached a point where we must collect what seem the various membra disiecta of the traditions we have been examining and see how they combined to produce a Lullian revival.

We can begin with Pico della Mirandola: he cited Lull in his Apologia of 1487. Pico, of course, would have been aware that there existed analogies between the permutational techniques of Lull and the temurah (which he called “revolutio alphabetaria“).

He was acute enough, however, to realize that they were two different things. In the Quaestio Sexta of the Apologia, where Pico proved that no science demonstrates the divinity of Christ better than magic and the kabbala, he distinguished two doctrines which might be termed kabbalist only in a figurative (transumptive) sense: one was the supreme natural magic; the other was the hokmat ha-zeruf of Abulafia that Pico termed an “ars combinandi,” adding that “apud nostros dicitur ars Raymundi licet forte diverso modo procedat” (“it is commonly designated as the art of Raymond, although it proceeds by a different method”).

Despite Pico’s scruples, a confusion between Lull and the kabbala was, by now, inevitable. It is from this time that the pathetic attempts of the Christian kabbalists to give Lull a kabbalistic reading begin.

In the 1598 edition of Lull’s works there appeared, under Lull’s name, a short text entitled De auditu kabbalistico: this was nothing other than Lull’s Ars brevis into which had been inserted a number of kabbalistic references.

It was supposedly first published in Venice in 1518 as an opusculum Raimundicum. Thorndike (1923-58: v, 325) has discovered the text, however, in manuscript form, in the Vatican Library, with a different title and with an attribution to Petrus de Maynardis.

The manuscript is undated, but, according to Thorndike, its calligraphy dates it to the fifteenth century. The most likely supposition is that it is a composition from the end of that century in which the suggestions first made by Pico were taken up and mechanically applied (Scholem et al. 1979: 40-1).

In the following century, the eccentric though sharp-witted Tommaso Garzoni di Bagnacavallo saw through the imposture. In his Piazza universale du tutte le arti (1589: 253), he wrote:

“The science of Raymond, known to very few, might be described with the term, very improper in itself, of Cabbala. About this, there is a notion common to all scholars, indeed, to the whole world, that in the Cabbala can be found teachings concerning everything [ . . . ] and for this reason one finds in print a little booklet ascribed to him [Lull] (though on this matter people beyond the Alps write many lies) bearing the title De Auditu Cabalistico. This is nothing but a brief summary of the Arte Magna as abbreviated, doubtlessly by Lull himself, into the Arte Breve.”

Still, the association persisted. Among various examples, we might cite Pierre Morestel, who published an Artis kabbalisticae, sive sapientiae diviniae academia in 1621, no more than a modest compilation from the De auditu.

Except for the title, and the initial identification of the Ars of Lull with the kabbala, there was nothing kabbalistic in it. Yet Morestel still thought it appropriate to include the preposterous etymology for the word kabbala taken from De auditu: “cum sit nomen compositum ex duabus dictionibus, videlicet abba et ala. Abba enim arabice idem quod pater latine, et ala arabice idem est quod Deus meus” (“as this name is composed of two terms, that is abba and ala. Abba is an Arabic word meaning Latin pater; ala is also Arabic, and means Deus meus“).

For this reason, kabbala means “Jesus Christ.”

The cliché of Lull the kabbalist reappears with only minimum variation throughout the writings of the Christian kabbalists. Gabriel Naudé, in his Apologie pour tous les grands hommes qui ont esté accuséz de magie (1625), energetically rebutted the charge that the poor Catalan mystic engaged in the black arts.

None the less, French (1972: 49) has observed that by the late Renaissance, the letters from B to K, used by Lull, had become associated with Hebrew letters, which for the kabbalists were names of angels or of divine attributes.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 128-30.

(Editorial Note: wallowing in the bibliography of Raimon Llull is not for the meek. I encountered many culs-de-sac and could not find digital versions of many of the works mentioned by Eco in this segment. If you have URLs to works which are not linked in this excerpt from Eco, please share them using the comment feature. Thank you.)

Eco: Kabbalism & Lullism in the Steganographies

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Johannes Trithemius (1462-1516), Polygraphiae libri sex, Basel, 1518. Courtesy of the Shakespeare Folger Library as file number 060224. Joseph H. Peterson at the Esoteric Archives digitized a copy of the complimentary work on steganography held by the British Library in 1997. That work is listed as Trithemius, Steganographic: Ars per occultam Scripturam animi sui voluntatem absentibus aperiendi certu, 4to, Darmst. 1621. London, British Library. 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.   

“A peculiar mixture of kabbalism and neo-Lullism arose in the search for secret writings–steganographies. The progenitor of this search, which was to engender innumerable contributions between humanism and the baroque, was the prolific Abbot Johannes Trithemius (1462-1516).

Trithemius made no references to Lull in his works, relying instead on kabbalistic tradition, advising his followers, for instance, that before attempting to decipher a passage in secret writing they should invoke the names of angels such as Pamersiel, Padiel, Camuel and Aseltel.

On a first reading, these seem no more than mnemonic aids that can help either in deciphering or in ciphering messages in which, for example, only the initial letters of words, or only the initial letters of even-numbered words (and so on according to different sets of rules), are to be considered.

Thus Trithemius elaborated texts such as “Camuel Busarchia, menaton enatiel, meran sayr abasremon.” Trithemius, however, played his game of kabbala and steganography with a great deal of ambiguity. His Poligraphia seems simply a manual for encipherment, but with his posthumous Steganographia (1606 edition) the matter had become more complex.

Many have observed (cf. Walker 1958: 86-90, or Clulee 1988: 137) that if, in the first two books of this last work, we can interpret Trithemius‘ kabbalist references in purely metaphorical terms, in the third book there are clear descriptions of magic rituals.

Angels, evoked through images modeled in wax, are subjected to requests and invocations, or the adept must write his own name on his forehead with ink mixed with the juice of a rose, etc.

In reality, true steganography would develop as a technique of composing messages in cipher for political or military ends. It is hardly by chance that this was a technique that emerged during the period of conflict between emerging national states and flourished under the absolutist monarchies.

Still, even in this period, a dash of kabbalism gave the technique an increased spice.

It is possible that Trithemius‘ use of concentric circles rotating freely within each other owed nothing to Lull: Trithemius employed this device not, as in Lull, to make discoveries, but simply to generate or (decipher) cryptograms.

Every circle contains the letters of the alphabet; if one rotates the inner wheel so as to make the inner A correspond, let us say, to the outer C, the inner B will be enciphered as D, the inner C as E and so on (see also our ch. 9).

It seems probable that Trithemius was conversant enough with the kabbala to know certain techniques of temurah, by which words or phrases might be rewritten, substituting for the original letters the letters of the alphabet in reverse (Z for A, Y for B, X for C, etc.).

This technique was called the “atbash sequence;” it permitted, for example, the tetragrammaton YHWH to be rewritten as MSPS. Pico cited this example in one of his Conclusiones (cf. Wirzubski 1989: 43).

But although Trithemius did not cite him, Lull was cited by successive steganographers. The Traité des chiffres by Vigenère (1587) not only made specific references to Lullian themes, but also connected them as well to the factorial calculations first mentioned in the Sefer Yezirah.

However, Vigenère simply follows in the footsteps of Trithemius, and, afterwards, of Giambattista Della Porta (with his 1563 edition of De furtivis literarum notis, amplified in subsequent editions): he constructed tables containing 400 pairs generated by 20 letters; these he combined in triples to produce what he was pleased to call a “mer d’infini chiffrements à guise d’un autre Archipel tout parsemé d’isles . . . un embrouillement plus malaisé à s’en depestrer de tous les labrinthes de Crete ou d’Egypte” (pp. 193-4), a sea of infinite cryptograms like a new Archipelago all scattered with isles, an imbroglio harder to escape from than all the labyrinths of Crete and Egypt.

The fact that these tables were accompanied by lists of mysterious alphabets, some invented, some drawn from Middle Eastern scripts, and all presented with an air of secrecy, helped keep alive the occult legend of Lull the kabbalist.

There is another reason why steganography was propelling a Lullism that went far beyond Lull himself. The steganographers had little interest in the content (or the truths) expressed by their combinations.

Steganography was not a technique designed to discover truth: it was a device by which elements of a given expression-substance (letters, numbers or symbols of any type) might be correlated randomly (in increasingly differing ways so as to render their decipherment more arduous) with the elements of another expression-substance.

It was, in short, merely a technique in which one symbol replaced another. This encouraged formalism: steganographers sought ever more complex combinatory stratagems, but all that mattered was engendering new expressions through an increasingly mind-boggling number of purely syntactic operations. The letters were dealt with as unbound variables.

By 1624, in his Cryptometrices et cryptographie libri IX, Gustavus Selenus was designing a wheel of 25 concentric volvelles, each of them presenting 24 pairs of letters. After this, he displays a series of tables that record around 30,000 triples. From here, the combinatory possibilities become astronomical.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 126-8.

Eco: Postel’s Universalistic Utopia

Guillaume Postel, The Great Key, Eliphas Levi, The Key of the Great Mysteries, 1861

Guillaume Postel (1510-81), The Great Key, in Eliphas Levi (1810-75), La Clef des Grands MystèresThe Key of the Great Mysteries, 1861.

“A special place in the story of the renewal of Hebrew studies belongs to the French utopian thinker and érudit, Guillaume Postel (1510-81). Councillor to the kings of France, close to the major religious, political and scientific personalities of his epoch, Postel returned from a series of diplomatic missions to the Orient, voyages which enabled him to study Arabic and Hebrew as well as to learn of the wisdom of the kabbala, a changed and marked man.

Already renowned as a Greek philologist, around 1539, Postel was appointed to the post of “mathematicorum et peregrinarum linguarum regius interpretes” in that Collège des Trois Langues which eventually became the Collège de France.

In his De originibus seu de Hebraicae linguae et gentis antiquitate (1538), Postel argued that Hebrew came directly from the sons of Noah, and that, from it, Arabic, Chaldean, Hindi and, indirectly, Greek had all descended as well.

In Linguarum duodecem characteribus differentium alphabetum, introductio (1538), by studying twelve different alphabets he proved the common derivation of every language. From here, he went on to advance the project of a return to Hebrew as the instrument for the peaceable fusion of the peoples of differing races.

To support his argument that Hebrew was the proto-language, Postel developed the criterion of divine economy. As there was but one human race, one world and one God, there could be but one language; this was a “sacred language, divinely inspired into the first man” (De Foenicum litteris, 1550).

God had educated Adam by breathing into him the capacity to call things by their appropriate names (De originibus, seu, de varia et potissimum orbit Latino ad hanc diem incognita aut inconsyderata historia, 1553).

Although Postel does not seem to have thought either of an innate faculty for languages or of a universal grammar, as Dante had done, there still appears in many of his writings the notion of an Averroist active intellect as the repository of the forms common to all humanity, in which the roots of our linguistic faculty must be sought (Les très merveilleuses victoires des femmes du nouveau monde together with La doctrine du siècle doré, both from 1553).

Postel’s linguistic studies were connected to his particular vision of a religious utopia: he foresaw the reign of universal peace.

In his De orbis terrae concordia (1544:I) he clearly states that his studies in language would help to lay the foundations upon which a universal concord could be created. He envisioned the creation of a linguistic commonwealth that would serve as living proof to those of other faiths that not only was the message of Christianity true, but equally it verified their own religious beliefs: there are some principles of a natural religion, or sets of innate ideas held by all peoples (De orbis, III).

Here was the spirit that had inspired Lull and Nicholas of Cusa. Yet Postel was convinced that universal peace could only be realized under the protection of the king of France: among the world’s rulers the king of France alone held a legitimate claim to the title of king of the world.

He was the direct descendent of Noah, through Gomer, son of Japheth, founder of the Gallic and Celtic races (cf. particularly Les raisons de la monarchie, c. 1551). Postel (Trésor des propheties de l’univers, 1556) supported this contention with a traditional etymology (see, for example, Jean Lemaire de Belges, Illustration de Gaule et singularitez de Troye, 1512-3, fol. 64r): in Hebrew, the term gallus meant “he who overcame the waves;” thus the Gauls were the people who had survived the waters of the Flood (cf. Stephens 1989:4).

Postel first attempted to convert Francis I to his cause. The king, however, judged him a fanatic, and he lost favor at court. He went to Rome, hoping to win over to his utopian schemes Ignatius of Loyola, whose reformist ideals seemed kindred to his own.

It did not take Ignatius long, however, to realize that Postel’s ambitions were not identical to those of the Jesuits. Accepting Postel’s project might have placed their vow of obedience to the pope at risk.

Besides, Ignatius was a Spaniard, and the idea of turning the king of France into the king of the world would hardly have appealed to him. Although Postel continued long afterwards to look upon the Jesuits as the divine instrument for the creation of universal peace, he himself was forced to leave the company after a mere year and a half.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 75-7.

Eco: The Concordia Universalis of Nicholas of Cusa

Tafel18

Meister des Marienlebens, Kreuzigung, Passionsalter aus Bernkastel-Kues, 1460. 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 seductive potentiality of Lull’s appeal to the principle of universal concord is revealed by the resumption of his project, two centuries later, by Nicholas of Cusa. Nicholas is famous as the figure who revived Plato during the years between the crisis of scholasticism and the beginning of the Renaissance.

Nicholas also propounded the idea of an infinitely open universe, whose centre was everywhere and whose circumference nowhere. As an infinite being, God transcended all limits and overcame every opposition.

As the diameter of a circle increased, its curvature diminished; so at its limit its circumference became a straight line of infinite length.

Likewise, in God all opposites coincide. If the universe had a centre, it would be limited by another universe. But in the universe, God is both centre and circumference. Thus the earth could not be the centre of the universe.

This was the starting point for a vision of the plurality of worlds, of a reality founded on mathematical principles, which can be submitted to continuous investigation, where the world, if not infinite in a strict sense, was at least capable of assuming an infinite number of guises.

The thought of Nicholas is rich in cosmological metaphors (or models) founded upon the image of the circle and the wheel (De docta ignorantia, II, 11), in which the names of the divine attributes (explicitly borrowed from Lull) form a circle where each supports and confirms the others (I, 21).

The influence of Lull is even more explicitly revealed when Nicholas notes that the names by which the Greeks, Latins, Germans, Turks and Saracens designate the divinity are either all in fundamental accord, or derive from the Hebrew tetragrammaton (see the sermon Dies sanctificatus).

The ideas of Lull had spread to the Veneto towards the close of the fourteenth century. Nicholas probably came into contact with them in Padua. Their diffusion was, in part, a reaction against a scholastic Aristotelianism now in crisis; yet the diffusion also reflected the feverish cultural atmosphere generated by close contacts with the East.

Just as Catalonia and Majorca had been frontier territories in contact with the Muslim and Jewish worlds at the time of Lull, so the Venetian Republic had opened itself to the world of Byzantium and of the Arab countries two centuries later. The emerging currents of Venetian humanism were inspired by a new curiosity and respect for other cultures (cf. Lohr 1988).

It was thus appropriate that in this atmosphere there should have reemerged the thought of a figure whose preaching, whose theological speculations, and whose research on universal language were all conceived with the aim of building an intellectual and religious bridge between the European West and the East.

Lull believed that true authority could not be based on a rigid unity, but rather on the tension between various centers. It was the laws of Moses, the revelations of Christ and the preaching of Mohammed that, taken together, might produce a unified result.

Lull’s doctrine acted as a mystical and philosophical stimulus and seemed an imaginative and poetic alternative to the encyclopedia of Aristotelian scholasticism, but it provided a political inspiration as well.

The works of a writer who had dared to put his doctrine into the vernacular proved congenial to humanists who, on the one hand, had begun to celebrate the dignity of their own native tongues, but, on the other hand, wondered how it was possible to establish a rational discussion which broke the boundaries of national traditions, a philosophy which could reanimate the body of encyclopedic scholasticism by injecting the leaven of exotic new doctrines, expressed in languages still entirely unknown.

In his De pace fidei, Nicholas opened a polemical dialogue with the Muslims. He asked himself Lull’s question: how might the truth of Christian revelation be demonstrated to followers of the two other monotheistic religions?

Perhaps, Nicholas mused, it was a mistake to translate the persons of the Trinity as “Father,” “Son” and “Holy Ghost.” Perhaps they should have been given more philosophical names (better understandable by other cultures).

In his ecumenical fervor, Nicholas even went so far as to propose to the Jews and the Muslims that, if they would accept the Gospels, he would see that all Christians received circumcision. It was a proposal, as he confessed at the end, whose practical realization might present certain difficulties. (De pace fidei, XVI, 60).

Nicholas retained from Lull the spirit of universal peace as well as his metaphysical vision. Yet before the thrilling potential of Nicholas’s own vision of an infinity of worlds could be translated into a new and different version of the art of combination, new ideas would have to fertilize the humanist and Renaissance world.

The rediscovery of the art of combination would have to wait for the rediscovery of Hebrew, for Christian kabbalism, for the spread of Hermeticism, and for a new and positive reassessment of magic.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 69-72.

 

Eco: The Arbor Scientarium, 2

Ramon Llull, Arbor Scientiae, Rome, 1295

Ramon Llull, Arbor Scientiae, Rome, 1295. 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.  

“Between the first and last versions of his art, Lull’s thought underwent a long process of evolution (described by Carreras y Artau 1939: I, 394), in order to render his art able to deal not only with theology and metaphysics, but also with cosmology, law, medicine, astronomy, geometry and psychology.

Increasingly, the art became a means of treating the entire range of knowledge, drawing suggestions from the numerous medieval encyclopedias, and anticipating the encyclopedic dreams of the Renaissance and the baroque.

All this knowledge, however, needed to be ordered hierarchically. Because they were determinations of the first cause, the dignities could be defined circularly, in reference to themselves; beyond the dignities, however, began the ladder of being. The art was designed to permit a process of reasoning at every step.

The roots of the Tree of Science were the nine dignities and the nine relations. From here, the tree then spread out into sixteen branches, each of which had its own, separate tree. Each one of the sixteen trees, to which there was dedicated a particular representation, was divided into seven parts–roots, trunk, major branches, lesser branches, leaves, fruits and flowers.

Eight of the trees clearly corresponded to eight of the subjects of the tabula generalis: these are the Arbor elementalis, which represents the elementata, that is, objects of the sublunary world, stones, trees and animals composed of the four elements; the Arbor vegetalis;  the Arbor sensualis; the Arbor imaginalis, which represents images that replicate in the mind whatever is represented on the other trees; the Arbor humanalis et moralis (memory, intellect and will, but also the various sciences and arts); the Arbor coelestialis (astronomy and astrology); the Arbor angelicalis; and the Arbor divinalis, which includes the divine dignities.

To this list are added another eight: the Arbor mortalis (virtues and vices); the Arbor eviternalis (life after death); the Arbor maternalis (Mariology); the Arbor Christianalis (Christology); the Arbor imperialis (government); the Arbor apostolicalis (church); the Arbor exemplificalis (the contents of knowledge); and the Arbor quaestionalis, which contains four thousand questions on the various arts.

To understand the structure of these trees, it is enough to look at only one–the Arbor elementalis. Its roots are the nine dignities and nine relations. Its trunk represents the conjoining of these principles, out of which emerges the confused body of primordial chaos which occupies space.

In this are the species of things and their dispositions. The principle branches represent the four elements (earth, air, fire and water) which stretch out into the four masses which are made from them (the seas and the lands).

The leaves are the accidents. The flowers are the instruments, such as hands, feet and eyes. The fruits represent individual things, such as stone, gold, apple, bird.

Calling this a “forest” of trees would be an improper metaphor: the trees overlay one another to rise hierarchically like the peaked roof of a pagoda. The trees at the lower levels participate in those higher up.

The vegetable tree, for example, participates in the tree of elements; the sensual tree participates in the first two; the tree of imagination is built up out of the first three, and it forms the base from which the next tree, the human one, will arise (Llinares 1963: 211-2).

The system of trees reflects the organization of reality itself; it represents the great chain of being the way that it is, and must metaphysically be. This is why the hierarchy constitutes a system of “true” knowledge.

The priority of metaphysical truth over logical validity in Lull’s system also explains why he laid out his art the way he did: he wished his system to produce, for any possible argument, a middle term that would render that argument amenable to syllogistic treatment; having structured the system for this end, however, he proceeded to discard a number of well-formed syllogisms which, though logically valid, did not support the arguments he regarded as metaphysically true.

For Lull, the significance of the middle term of the syllogism was thus not that of scholastic logic. Its middle term served to bind the elements of the chain of being: it was a substantial, not a formal, link.

If the art is a perfect language, it is so only to the extent to which it can speak of a metaphysical reality, of a structure of being which exists independently of it. The art was not a mechanism designed to chart unknown universes.

In the Catalan version of his Logica Algazelis, Lull writes, “De la logic parlam tot breau–car a parlor avem Deu.” (“About logic we will be brief, for it is to talk about God”).

Much has been written about the analogy between Lull’s art and the kabbala. What distinguishes kabbalistic thought from Lull’s is that, in the kabbala, the combination of the letters of the Torah had created the universe rather than merely reflected it.

The reality that the kabbalistic mystic sought behind these letters had not yet been revealed; it could be discovered only through whispering the syllables as the letters whirled.

Lull’s ars combinatoria, by contrast, was a rhetorical instrument; it was designed to demonstrate what was already known, and lock it for ever in the steely cage of the system of trees.

Despite all this, the art might still qualify as a perfect language if those elementary principles, common to all humanity, that it purported to expound really were universal and common to all peoples.

As it was, despite his effort to assimilate ideas from non-Christian and non-European religions, Lull’s desperate endeavor failed through its unconscious ethnocentrism. The content plane, the universe which his art expounded, was the product of the western Christian tradition.

It could not change even though Lull translated it into Arabic or Hebrew. The legend of Lull’s own agony and death is but the emblem of that failure.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 67-9.

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.

Eco: The Alphabet and the Four Figures, 3

12544152.0001.001-00000019

Jonathan Swift, Gulliver’s Travels, 1892 George Bell and Sons edition, Project Gutenberg. Also see Jonathan Swift, Gulliver’s Travels, A.J. Rivero, ed., New York: W.W.Norton, 2001, Part III, chapter 5. Cited in Bethany Nowviskie, “Ludic Algorithms,” in Kevin Kee, ed., Pastplay: Teaching and Learning History with Technology, Ann Arbor, MI: University of Michigan Press, 2014. 

“It follows that Lull’s art is not only limited by formal requirements (since it can generate a discovery only if one finds a middle term for the syllogism); it is even more severely limited because the inferences are regulated not by formal rules but rather by the ontological possibility that something can be truly predicated of something else.

The formal rules of the syllogism would allow such arguments as “Greed is different from goodness — God is greedy — Therefore God is different from goodness.” Yet Lull would discard both the premises and the conclusion as false.

The art equally allows the formulation of the premise “Every law is enduring,” but Lull rejects this as well because “when an injury strikes a subject, justice and law are corrupted” (Ars brevis, quae est de inventione mediorum iuris, 4.3a).

Given a proposition, Lull accepts or rejects its logical conversion, without regard to its formal correctness (cf. Johnston 1987: 229).

Nor is this all. The quadruples derived from the fourth figure appear in the columns more than once. In Ars magna the quadruple BCTB, for example, figures seven times in each of the first seven columns.

In V, 1, it is interpreted as “Whether there exists some goodness so great that it is different,” while in XI, 1, applying the rule of logical obversion, it is read as “Whether goodness can be great without being different”–obviously eliciting a positive response in the first case and a negative one in the second.

Yet these reappearances of the same argumentative scheme, to be endowed with different semantic contents, do not bother Lull. On the contrary, he assumes that the same question can be solved either by any of the quadruples from a particular column that generates it, or from any of the other columns!

Such a feature, which Lull takes as one of the virtues of his art, represents in fact its second severe limitation. The 1,680 quadruples do not generate fresh questions, nor do they furnish new proofs.

They generate instead standard answers to an already established set of questions. In principle, the art only furnishes 1,680 different ways of answering a single question whose answer is already known.

It cannot, in consequence, really be considered a logical instrument at all. It is, in reality, a sort of dialectical thesaurus, a mnemonic aid for finding out an array of standard arguments able to demonstrate an already known truth.

As a consequence, any of the 1,680 quadruples, if judiciously interpreted, can yield up the correct answer to the question for which it is adapted.

See, for instance, the question “Whether the world is eternal” (“Utrum mundus sit aeternus“). Lull already knew the answer: negative, because anyone who thought the world eternal would fall into the Averroist error.

Note, however, that the question cannot be generated directly by the art itself; for there is no letter corresponding to world. The question is thus external to the art.

In the art, however, there does appear a term for eternity, that is, D; this provides a starting point.

In the second figure, D is tied to the relative principle contrarietas or opposition, as manifested in the opposition of the sensible to the sensible, of the intellectual to the sensible, and of the intellectual to the intellectual.

The same second figure also shows that D forms a triangle with B and C. The question also began with utrum, which appears at B under the heading Questiones in the tabula generalis. This constitutes a hint that the solution needs to be sought in the column in which appear B, C and D.

Lull says that “the solution to such a question must be found in the first column of the table;” however, he immediately adds that, naturally, “it could be found in other columns as well, as they are all bound to each other.”

At this point, everything depends on definitions, rules, and a certain rhetorical legerdemain in interpreting the letters. Working from the chamber BCDT (and assuming as a premise that goodness is so great as to be eternal), Lull deduces that if the world were eternal, it would also be eternally good, and, consequently, there would be no evil.

“But,” he remarks, “evil does exist in the world as we know by experience. Consequently we must conclude that the world is not eternal.” This negative conclusion, however, is not derived from the logical form of the quadruple (which has, in effect, no real logical form at all), but is merely based on an observation drawn from experience.

The art may have been conceived as the instrument to use universal reason to show the Averroist Muslims the error of their ways; but it is clear that unless they already shared with Lull the “rational” conviction that the world cannot be eternal, they are not going to be persuaded by the art.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 62-4.

Eco: The Alphabet and the Four Figures, 2

Raymond Llull, Combinations, Strasbourg ed 1598

Umberto Eco, The Search for the Perfect Language, 1995, pg. 60. Figure 4.2, a page of combinations from the Strasbourg edition of the Ars Magna of Raymond Llull, 1598. 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.  

Taken in groups of 3, 9 elements generate 84 combinations–BCD, BCE, CDE, etc. If, in his Ars breu and elsewhere, Lull sometimes speaks of 252 (84*3) combinations, it is because to each triple can be assigned three questions, one for each of the letters of the triple (see also the Jesuit Athanasius Kircher, Ars magna sciendi, p. 14.

ArsMagnaSciendi1

Athanasius Kircher, Ars Magna Sciendi, Amsterdam, 1669. 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. 

Each triple further generates a column of 20 combinations (giving a table of 20 rows by 84 columns) because Lull transforms the triples into quadruples by inserting the letter T. In this way, he obtains combinations like BCDT, BCTB, BTBC, etc. (See examples in figure 4.2, at the top of this page).

The letter T, however, plays no role in the art; it is rather a mnemonic artifice. It signifies that the letters that precede it are to be read as dignities from the first figure, while those that follow it are to be read as relative principles as defined in the second figure.

Thus, to give an example, the quadruple BCTC must be read: B (= goodness) + C (= greatness) and therefore (switching to the second figure) C (=  concordance).

Looking at the tabula generalis, we further notice that combinations with an initial B take the question utrum, those with an initial C take quid, etc. This produces from BCTC the following reading: “Whether goodness is great inasmuch as it contains in itself concordant things.”

This produces a series of quadruples which seem, at first sight, embarrassing: the series contains repetitions. Had repetitions been permissible, there would have been 729 triples instead of 84.

The best solution to the mystery of these repetitions is that of Platzek (1953-4: 141). He points out that, since, depending on whether it precedes or follows the T, a letter can signify either a dignity or a relation, each letter has, in effect, two values.

Thus–given the sequence BCTB–it should be read as BCb. The letters in upper case would be read as dignities, and the one in lower case as a relation. It follows that, in his 84 columns, Lull was not really listing the combinations for three letters but for six. Six different elements taken three at a time give 20 permutations, exactly as many appear in each column.

The 84 columns of 20 quadruples each yield 1,680 permutations. This is a figure obtained by excluding inversions of order.

At this point, however, a new question arises. Given that all these 1,680 quadruples can express a propositional content, do they all stand for 1,680 valid arguments as well?

ArsMagnaSciendi

Athanasius Kircher, Ars Magna Sciendi sive Combinatoria, Amsterdam, 1669. Frontispiece. 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.  

Not at all, for not every sequence generated by the art is syllogistically valid. Kircher, in his Ars magna sciendi, suggests that one must deal with the resulting sequences as if they were anagrams: one starts by forming a complete list of all the possible arrangements of the letters of a particular word, then discards those that do not correspond to other existing words.

The letters of the Latin word ROMA, for example, can be combined in 24 different orders: certain sequences form acceptable Latin words, such as AMOR, MORA, RAMO; others, however, such as AOMR, OAMR, MRAO, are nonsense, and are, as it were, thrown away.

Lull’s own practice seems to suppose such a criterion. He says, for example, in his Ars magna, segunda pars principalis that in employing the first figure, it is always possible to reverse subject and predicate (“Goodness is great” / “Greatness is good”).

It would not, however, be possible to reverse goodness and angel, for while angel participates in goodness, goodness does not participate in angel, since there are beings other than angels which are good.

In other words, angel entails goodness but not vice versa. Lull also adds that the combination “Greed is good” is inherently unacceptable as well. Whoever wishes to cultivate the art, Lull says, must be able to know what is convertible and what is not.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 60-2.

Eco: The Alphabet and the Four Figures

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Raymond Llull (1232-1316), Ars magna, segunda figurageneralis et ultima, 1517, held in the Getty Research Institute and digitized by that institution in collaboration with the Internet Archive, generously posted on archive.org. 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 ars combinatoria of Lull employs an alphabet of nine letters–B to K, leaving out J–and four figures (see figure 4.1). In a tabula generalis that appears in several of his works, Lull set out a table of six groups of nine entities, one for each of the nine letters.

The first group are the nine absolute principles, or divine dignities, which communicate their natures to each other and spread throughout creation.

After this, there are nine relative principles, nine types of question, nine subjects, nine virtues and nine vices.

Lull specifies (and this is an obvious reference to Aristotle’s list of categories) that the nine dignities are subjects of predication, while the other five series are predicates. We shall see that subject and predicate are sometimes allowed to exchange their roles, while in other cases variations of order are not considered as pertinent.

First figure. This traces all the possible combinations between the dignities, thus allowing predications such as “Goodness [bonitas] is great,” “Greatness [magnitudo] is glorious,” etc.

Since the dignities are treated as nouns when they appear as a predicate, the lines connecting them can be read in both directions. The line connecting magnitudo and bonitas can, for example, be read as both “Greatness is good” and “Goodness is great.” This explains why 36 lines produce 72 combinations.

The first figure is designed to allow regular syllogisms to be inferred. To demonstrate, for example, that goodness can be great, it is necessary to argue that “all that is magnified by greatness is great–but goodness is what is magnified by greatness–therefore goodness is great.”

The first table excludes self-predications, like BB or CC, because, for Lull, there is no possibility of a middle term in an expression of the type “Goodness is good” (in Aristotelian logic, “all As are B–C is an A–therefore C is a B” is a valid syllogism because, following certain rules, the middle term A is so disposed to act as the, as it were, bond between B and C).

Second figure. This serves to connect the relative principles with triples of definitions. They are the relations connecting the divine dignities with the cosmos. Since it is intended merely as a visual mnemonic that helps to fix in the mind the various relations between different types of entity, there is no method of combination associated with the second figure.

For example, difference, concordance and opposition (contrarietas) can each be considered in reference to (1) two sensible entities, such as a plant and a stone, (2) a sensible and an intellectual entity, like body and soul, and (3) two intellectual entities, like the soul and an angel.

Third figure. Here Lull displayed all possible letter pairings. The figure contains 36 pairs inserted in what Lull calls the 36 chambers. The figure makes it seem that he intended to exclude inversions.

Yet, in reality, the figure does contemplate inversions in order, and thus the number of the chambers is virtually 72 since each letter is permitted to function as either subject or predicate (“Goodness is great” also gives “Greatness is good:” Ars magna, VI, 2).

Having established the combinations, Lull proceeds to what he calls the “evacuation of the chambers.” Taking, for example, chamber BC, we read it first according to the first figure, obtaining goodness and greatness (bonitas and magnitudo); then according to the second figure, obtaining difference and concordance, (differentia and concordantia: Ars magna, II, 3).

From these two pairs we derive 12 propositions: “Goodness is great,” “Difference is great,” Goodness is different,” “Goodness is different,” “Difference is good,” “Goodness is concordant,” “Difference is concordant,” “Greatness is good,” “Concordance is good,” “Greatness is different,” “Concordance is different,” “Greatness is concordant,” and “Concordance is great.”

Going back to the tabula generalis in figure 4.1, we find that, under the next heading, Questiones, B and C  are utrum (whether) and quid (what). By combining these 2 questions with the 12 propositions we have just constructed, we obtain 24 questions, like “Whether goodness is great?,” or “What is a great goodness?” (see Ars magna, VI, 1).

In this way, the third figure generates 432 propositions and 864 questions–at least in theory. In reality, there are 10 additional rules to be considered (given in Ars magna, VI, iv).

For the chamber BC, for example, there are the rules B and C. These rules depend on the theological definition of the terms, and on certain argumentative constraints which have nothing to do with the rules of combination.

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Quarta figura, fourth figure.

Fourth figure. This is the most famous of the figures, and the one destined to have the greatest influence on subsequent tradition. In this figure, triples generated by the nine elements are considered.

In contrast to the preceding figures, which are simply static diagrams, the fourth figure is mobile. It is a mechanism formed by three concentric circles, of decreasing size, inserted into each other, and held together usually by a knotted cord.

If we recall that in the Sefer Yezirah the combination of the letters was visually represented by a wheel or a spinning disc, it seems probable that Lull, a native of Majorca, has been influenced here by the kabbalistic tradition that flourished in his time in the Iberian peninsula.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 56-60.

 

Eco: The Ars Magna of Raymond Lull

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

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

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

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

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

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

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

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

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

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

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

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

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

Eco: Cosmic Permutability and the Kabbala of Names

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Athanasius Kircher, The Ten Sefirot, from Oedipus Aegyptiacus, published in three folio tomes in Rome, 1652-54. This was considered Kircher’s masterwork on Egyptology, and it cast a long shadow for centuries until Champollion deciphered the Rosetta Stone in 1824, unlocking the secrets of the Egyptian hieroglyphs: Kircher was exposed as an erudite fraud. Kircher cited Chaldean astrology, Hebrew kabbalah, Greek myth, Pythagorean mathematics, Arabic alchemy and Latin philology as his sources.     

“The kabbalist could rely on the unlimited resources of temurah because anagrams were more than just a tool of interpretation: they were the very method whereby God created the world.

This doctrine had already been made explicit in the Sefer Yezirah, or Book of Creation, a little tract written some time between the second and the sixth centuries. According to it, the “stones” out of which God created the world were the thirty-two ways of wisdom. These were formed by the twenty-two letters of the Hebrew alphabet and the ten Sefirot.

“Twenty-two foundation letters: He ordained them, He hewed them, He combined them, He weighed them, He interchanged them. And He created with them the whole creation and everything to be created in the future.” (II, 2).

“Twenty-two foundation letters: He fixed them on a wheel like a wall with 231 gates and He turns the wheel forward and backward.” (II, 4).

“How did He combine, weigh, and interchange them? Aleph with all and all with Aleph; Beth with all and all with Beth; and so each in turn. There are 231 gates. And all creation and all language come from one name.” (II, 5).

“How did He combine them? Two stones build two houses, three stones build six houses, four stones build twenty-four houses, five stones build a hundred and twenty houses, six stones build seven hundred and twenty houses, seven stones build five thousand and forty houses. Begin from here and think of what the mouth is unable to say and the ear unable to hear.” (IV, 16).

(The Book of Creation, Irving Friedman, ed., New York: Weiser, 1977).

Indeed, not only the mouth and ear, but even a modern computer, might find it difficult to keep up with what happens as the number of stones (or letters) increases. What the Book of Creation is describing is the factorial calculus. We shall see more of this later, in the chapter on Lull’s art of permutation.

The kabbala shows how a mind-boggling number of combinations can be produced from a finite alphabet. The kabbalist who raised this art to its highest pitch was Abulafia, with his kabbala of the names (cf. Idel 1988a, 1988b, 1988c, 1989).

The kabbala of the names, or the ecstatic kabbala, was based on the practice of the recitation of the divine names hidden in the Torah, by combining the letters of the Hebrew alphabet.

The theosophical kabbala, though indulging in numerology, acrostics and anagrams, had retained a basic respect for the sacred text itself. Not so the ecstatic kabbalah: in a process of free linguistic creativity, it altered, disarticulated, decomposed and recomposed the textual surface to reach the single letters that served as its linguistic raw material.

For the theosophical kabbala, between God and the interpreter, there still remained a text; for the ecstatic kabbalist, the interpreter stood between the text and God.”

Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 28-30.