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Tag: Ramon Lull

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: Dee’s Magic Language

true-faithful-relation

Florence Estienne Méric Casaubon (1599-1671), A True and Faithful Relation of what Passed for Many Yeers between Dr. John Dee [ . . . ] and Some Spirits, London, 1659. This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author’s life plus 100 years or less. 

“In his Apologia compendiaria (1615) Fludd noted that the Rosicrucian brothers practiced that type of kabbalistic magic that enabled them to summon angels. This is reminiscent of the steganography of Trithemius. Yet it is no less reminiscent of the necromancy of John Dee, a man whom many authors considered the true inspirer of Rosicrucian spirituality.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Eco: 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.

The Mystery of ben Belimah

“In the history of Jewish literature, Nahmanides is often considered to exemplify the “most Jewish” spirit; he was the one among Spanish Jews who expressed the deepest convictions regarding the Judaism of his time and embodied what was best and highest in it. From the point of view of a “refined” Judaism or the pure halakhah, it must indeed appear as an aberration that so clear a mind, one that easily penetrated the most complicated halakhic problems, should have become involved with the Kabbalah.

But it is precisely this dimension of his personality that must be grasped if we wish to understand the phenomenon. Without the Kabbalah and its contemplative mysticism Nahmanides, would be as little understood in his Jewish context as would, in the Christian context, a man like Ramón Lull (who was active in Catalonia a generation later and whose teaching exhibited structurally many analogies with the doctrine of the sefiroth) if one ignored his Ars contemplativa, in which his Christianity reached its culmination, and judged him solely on the basis of his wide-ranging activities in all other possible domains.

From this point of view, Nahmanides’ commentary on Yesirah, which develops his conception of God, is of particular importance. The gnostic doctrine of the aeons and the Neoplatonic doctrine of the emanation are combined, and we see how well they harmonize with a Jewish consciousness.

The monotheism of Nahmanides, the Jewish coloration of which is certainly beyond question, is unaware of any contradiction between the unity of God and its manifestation in the different sefiroth, each of which represents one of the aspects by which the kabhod of God reveals itself to the Shekhinah.

In his commentary on the Torah, in which he had to deal only with God’s activity in His creation, making use of the symbols of theosophy, Nahmanides could avoid touching upon this crucial point; he only discussed it in this document intended for kabbalists.

From whom Nahmanides actually received the esoteric tradition is an open question. He does mention, in his commentary on Yesirah, the Hasid Isaac the Blind, but not as his master. Nor does the letter that Isaac sent to him and to his cousin Jonah Gerondi, of whom we shall have occasion to speak later, indicate any direct discipleship.

Nahmanides refers to Yehudah ben Yaqar as his master, especially in the halakhic writings. Contrariwise, in a series of undoubtedly genuine traditions going back to Nahmanides’ most important disciple, Solomon ibn Adreth, there emerges the thoroughly enigmatic figure of a kabbalist by the name of ben Belimah—the personal first name is never mentioned—who is said to have been the connecting link between him and Isaac the Blind.

Meir ibn Sahula, in his commentaries on the traditions of Nahmanides (fol. 29a), contrasts those he had received from ben Belimah with those deriving from Isaac. In very old marginal notes emanating from the circle of Gerona and preserved in Ms. Parma, de Rossi 68, mention is made of a debate between Nahmanides and ben Belimah over the fate of Naboth’s spirit (1 Kings 22); the debate suggests that ben Belimah posited some kind of transmigration of souls or metamorphosis also for the higher spirits, even within the world of the sefiroth up to binah.

The existence of such a kabbalist therefore seems established beyond doubt, no matter how enigmatic his name. It is neither a family name nor a patronymic. Belimah is not known to me as a woman’s name, and it is extremely unlikely that Solomon ibn Adreth would have transmitted the name in a corrupted form to his disciples.

There remains the hypothesis of a pseudonym deliberately substituted for another name that was kept secret for reasons unknown to us and in a manner completely contrary to the habit of this circle. The pseudonym seems to be derived from B. Hullin 89a, where Job 26:7 is applied to Moses and Aaron who, when assailed by the Israelites, changed themselves into nothing!

The kabbalist in question thus may possibly have been a [ . . . ] ben Moses (rather than [ . . . ] ben Aaron). B. Dinur’s suggestion that the pseudonym refers to R. Jonah ben Abraham Gerondi (because of his attitude in the Maimonidean controversy) seems improbable. Perhaps new manuscript discoveries will one day clarify matters.

In any case, this name, whose literal translation would be “son of the Nought” or “son of seclusion,” provokes the historian’s curiosity. It remains uncertain whether ben Belimah should be located in Gerona, which is quite possible, or in Provence, where Nahmanides could have met with him during his youth.”

Gershom Scholem, Origins of the Kabbalah, pp. 389-91.

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