by Umberto Eco
Figure 10.4
Once the combinatory system has been set in motion, we proceed to what Llull calls the “evacuation of the chambers.” For example, taking the BC chamber, and referring to the Tabula Generalis, we first read chamber BC according to the Absolute Principles and we obtain Bonitas est magna, then we read it according to the Relative Principles and we obtain Differentia est concordans (Ars magna II, 3). In this way we obtain twelve propositions: Bonitas est magna, Diffferentia est magna, Bonitas est differens, Differentia est bona, Bonitas est concordans, Differentia est concordans, Magnitudo est bona, Concordantia est bona, Magnitudo est differens, Concordantia est differens, Magnitudo est concordans, Concordantia est magna. Returning to the Tabula Generalis and assigning to B and C the corresponding questions (utrum or “whether” and quid or “what”) with their respective answers, we can derive, from the twelve propositions, twenty-four questions (of the type Utrum Bonitas sit magna? [Whether Goodness is great?] and Quid est Bonitas magna? [What is great Goodness?]) (see Ars magna VI, 1).
QUARTA FIGURA. In this case the mechanism is mobile, in the sense that we have three concentric circles decreasing in circumference, placed one on top of the other, and usually held together at the center with a knotted string. Revolving the smaller inner circles, we obtain triplets (see Figure 10.5).
These are produced from the combination of nine elements into groups of three, without the same element being repeated twice in the same triplet or chamber. Llull, however, adds to each triplet the letter t—an operator by which it is established that the letters that precede are to be read with reference to the first column of the Tabula Generalis, as Principles or Dignities, whereas those that follow are to be read as Relative Principles. Since the t changes the meaning of the letters, as Platzeck (1954: 140–143) explains, it is as if Llull were composing his triplets by combining, not three, but six elements (not merely BCD, for instance, but BCDbcd). The combinations of six elements into groups of three give (according to the rules of the combinatory system) twenty chambers.
Figure 10.5
Consider now the reproduction in Figure 10.6 of the first of the tables elaborated by Llull to exploit to the full the possibilities of his fourth figure (each table being composed of columns of twenty chambers each). In the first column we have BCDbcd, in the second BCEbce, in the third BCFbcf, and so on and so forth, until we have obtained eighty-four columns and hence 1,680 chambers.
If we take, for instance, the first column of the Tabula Generalis, the chamber bctc (or BCc) is to be read as b = bonitas, c = magnitudo, c = concordantia. Referring to the Tabula Generalis, the chambers that begin with b correspond to the first question (utrum), those that begin with c to the second question (quid), and so on. As a result, the same chamber bctc (or BCc) is to be read as Utrum bonitas in tantum sit magna quod contineat in se res concordantes et sibi coessentiales (“Whether goodness is great insofar as it contains within it things in accord with it and coessential to it”).
Figure 10.6
Quite apart from a certain arbitrariness in “evacuating the chambers,” in other words, in articulating the reading of the letters of the various chambers into a discourse, not all the possible combinations (and this observation is valid for all the figures) are admissible. After describing his four figures in fact, Llull prescribes a series of Definitions of the various terms in play (of the type Bonitas est ens, ratione cujus bonum agit bonum [“Goodness is something as a result of which a being that is good does what is good”]) and Necessary Rules (which consist of ten questions to which, it should be borne in mind, the answers are provided), so that such chambers generated by the combinatory system as contradict these rules must not be taken into consideration.
This is where the first limitation of the Ars surfaces: it is capable of generating combinations that right reason must reject. In his Ars magna sciendi, Athanasius Kircher will say that one proceeds with the Ars as one does when working out combinations that are anagrams of a word: once one has obtained the list, one excludes all those permutations that do not make up an existing word (in other words, twenty-four permutations can be made of the letters of the Italian word ROMA, but, while AMOR, MORA, ARMO, and RAMO make sense in Italian and can be retained, meaningless permutations like AROM, AOMR, OAMR, or MRAO can, so to speak, be cast aside). In fact Kircher, working with the fourth figure, produces nine syllogisms for each letter, even though the combinatory system would allow him more, because he excludes all the combinations with an undistributed middle, which precludes the formation of a correct syllogism.10
This is the same criterion followed by Llull, when he points out, for example, in Ars magna, Secunda pars principalis, apropos of the various ways in which the first figure can be used, that the subject can certainly be changed into the predicate and vice versa (for instance, Bonitas est magna and Magnitudo est bona), but it is not permitted to interchange Goodness and Angel. We interpret this to mean that all angels are good, but that an argument that asserts the “since all angels are good and Socrates is good, then Socrates is an angel” is unacceptable. In fact we would have a syllogism with an unquantified middle.
But the combinatory system is not only limited by the laws of the syllogism. The fact is that even formally correct conversions are only acceptable if they predicate according to the truth criteria established by the rules—which rules, it will be recalled, are not logical in nature but philosophical and theological (cf. Johnston 1987: 229). Bäumker (1923: 417–418) realized that the aim of the ars inveniendi (or art of invention) was to set up the greatest possible number of combinations among concepts already provided, and to draw from them as a consequence all possible questions, but only if the resulting questions could stand up to “an ontological and logical examination,” permitting us to discriminate between correct combinations and false propositions. The artist, says Llull, must know what is convertible and what is not.
Furthermore, among the quadruplets tabulated by Llull there are—by virtue of the combinatory laws—a number of repetitions. See, for example, in the columns reproduced in Figure 10.6, the chamber btch, which recurs in the second place in each of the first seven columns, and which in the Ars magna (V, 1) is translated as utrum sit aliqua bonitas in tantum magna quod sit differens (“whether a certain goodness is great insofar as it is different”) and in XI, 1, by the rule of obversion, as utrum bonitas possit esse magna sine distinctione (“whether goodness can be great without being different”)—permitting a positive answer in the first case and for a negative one in the second. The fact that the same demonstrative schema should appear several times does not seem to worry Llull, and the reason is simple. He assumes that the same question can be resolved both by each of the quadruplets in the single column that generates it and by all the other columns. This characteristic, which Llull sees as one of the virtues of the Ars, signals instead its second limitation: the 1,680 quadruplets do not generate original questions and do not provide proofs that are not the reformulation of previously tried and tested arguments. Indeed, in principle the Ars allows us to answer in 1,680 different ways a question to which we already know the answer—and it is not therefore a logical tool but a dialectical tool, a way of identifying and remembering all the useful ways to argue in favor of a preestablished thesis. To such a point that there is no chamber that, duly interpreted, cannot resolve the question to which it is adapted.
All of the above-mentioned limitations become evident if we consider the dramatic question utrum mundus sit aeternus, whether the world is eternal. This is a question to which Llull already knows the answer, which is negative, otherwise we would fall into the same error as Averroes. Seeing that the term eternity is, so to speak, “explicated” in the question, this allows us to place it under the letter D in the first column of the Tabula Generalis (see Figure 10.1). However, the D, as we saw in the second figure, refers to the contrariety between sensitive and sensitive, intellectual and sensitive, and intellectual and intellectual. If we observe the
second figure, we see that the D is joined by the same triangle to B and C. Moreover, the question begins with utrum, and, on the basis of the Tabula Generalis, we know that the interrogative utrum refers to B. We have therefore found the column in which to look for the arguments: it is the one in which B, C, and D all appear.
At this point all that is needed to interpret the letters is a good rhetorical ability, and, working on the BCDT chamber, Llull draws the conclusion that, if the world were eternal, since we already know that Goodness is eternal, it should produce an Eternal Goodness, and therefore evil would not exist. But, Llull observes, “evil does exist in the world, as we know from experience. Therefore we conclude that the world is not eternal.”
Hence, after having constructed a device (quasi-electronic, we might be tempted to say) like the Ars, which is supposed to be capable of resolving any question all by itself, Llull calls into question its output on the basis of a datum of experience (external to the Ars). The Ars is designed to convert Averroistic infidels on the basis of a healthy reason, shared by every human being (of whom it is the model); but it is clear that part of this healthy reason is the conviction that if the world were eternal it could not be good.
Llull’s Ars seduced posterity who saw it as a mechanism for exploring the vast number of possible connections between one being and another, between beings and principles, beings and questions, vices and virtues. A combinatory system without controls, however, was capable of producing the principles of any theology whatsoever, whereas Llull intends the Ars to be used to convert infidels to Christianity. The principles of faith and a well-ordered cosmology (independently of the rules of the Ars) must temper the incontinence of the combinatorial system.
We must first bear in mind that Llull’s logic comes across as a logic of first, not second, intentions, that is, a logic of our immediate apprehension of things and not of our concepts of things. Llull repeats in various of his works that, if metaphysics considers things outside the mind while logic considers their mental being, the Ars considers them from both points of view. In this sense, the Ars produces surer conclusions than those of logic: “Logicus facit conclusiones cum duabus praemissis, generalis autem artista huius artis cum mixtione principiorum et regularum.… Et ideo potest addiscere artista de hac arte uno mense, quam logicus de logica un anno” (“The logician arrives at a conclusion on the basis of two premises, whereas the artist of this general art does so by combining principles and rules.… And for this reason the artist can learn as much of this art in a month as a logician can learn of logic in a year”) (Ars magna, Decima pars, ch. 101). And with this self-confident final assertion Llull reminds us that his is not the formal method that many have attributed to him. The combinatory system must reflect the very movement of reality, and works with a concept of truth that is not supplied by the Ars according to the forms of logical reasoning, but instead by the way things are in reality, both as they are attested by experience and as they are revealed by faith.
Llull believes in the extramental existence of universals, not only in the reality of genera and species, but also in the reality of accidental forms. On the one hand, this allows his combinatory system to manipulate, not only genera and species, but also virtues, vices, and all differentiae (cf. Johnston 1987: 20, 54, 59, etc.). Nevertheless, these accidents cannot rotate freely because they are determined by an ironclad hierarchy of beings: “Llull’s Ars comes across as solidly linked to the knowledge of the objects that make up the world. Unlike so-called formal logic it deals with things and not just with words, it is interested in the structure of the world and not just in the structure of discourse. An exemplaristic metaphysics and a universal symbolism are at the root of a technique that presumes to speak both of logic and of metaphysics together and at the same time, and to enunciate the rules that form the basis of discourse and the rules according to which reality itself is structured” (Rossi 1960: 68).
10.2. Differences Between Llullism and Kabbalism
We can now grasp what the substantial differences were between the Llullian combinatory system and that of the Kabbalists.
True, in the Sefer Yetzirah (The Book of Creation), the materials, the stones, and the thirty-two paths or ways of wisdom with which Yahweh created the world are the ten Sephirot and the twenty-two letters of the Hebrew alphabet.
He hath formed, weighed, transmuted, composed, and created with these twenty-two letters every living being, and every soul yet uncreated. From two letters, or forms He composed two dwellings; from three, six; from four, twenty-four; from five, one hundred and twenty; from six, seven hundred and twenty; from seven, five thousand and forty; and from thence their numbers increase in a manner beyond counting; and are incomprehensible. (I, 1)11
The Sefer Yetzirah was assuredly speaking of factorial calculus, and suggested the idea of a finite alphabet capable of producing a vertiginous number of permutations. It is difficult, when considering Llull’s fourth figure, to escape the comparison with Kabbalistic practices—at least from the visual point of view, given that the combinatory system of the Sefer Yetzirah letters was associated with their inscription on a wheel, something underscored by a number of authors who are nonetheless extremely cautious about speaking of Kabbalism in Llull’s case (see, for example, Millás Vallicrosa 1958 and Zambelli 1965, to say nothing of the works of Frances Yates). Llull’s fourth figure, however, does not generate permutations (i.e., anagrams), but combinations.
But this is not the only difference. The text of the Torah is approached by the Kabbalist as a symbolic apparatus that speaks of mystic and metaphysical realities and must therefore be read distinguishing its four senses (literal, allegorical-philosophical, hermeneutical, and mystical). This is reminiscent of the theory of the four senses of Scripture in Christian exegesis, but at this point the analogy gives way to a radical difference.
For medieval Christian exegesis the hidden meanings are to be detected through a work of interpretation (to identify a surplus of content), but without altering the expression, that is to say, the material arrangement of the text, but, on the contrary, making a supreme effort to establish the exact reading (at least according to the questionable philological principles of the day). For some Kabbalistic currents, however, reading anatomizes, so to speak, the very substance of the expression, by means of three fundamental techniques: Notarikon, Gematria, and Temurah.
Notarikon is the acrostic technique, Gematria is made possible by the fact that in Hebrew numbers are represented by letters of the alphabet, so that each word can be associated with a numerical value derived from the sum of the numbers represented by the individual letters—the idea is to find analogies among words with a different meaning that nevertheless have the same numerical value. But the possible similarities between Llull’s procedures and those of the Kabbalists concern Temurah, the art of the permutation of letters, and therefore an anagrammatical technique.
In a language in which the vowels can be interpolated, the anagram has greater permutational possibilities than in other tongues. Moses Cordovero, for instance, wonders why in Deuteronomy we find the prohibition against wearing garments woven out of a mixture of linen and wool. His conclusion is that in the original version the same letters were combined to form another expression which warned Adam not to substitute his original garment of light with a garment of snakeskin, which represents the power of the demon.
In Abulafia we encounter pages in which the Tetragrammaton YHWH, thanks to the vocalization of its four letters and their arrangement in every conceivable order, produces four tables each consisting of fifty combinations. Eleazar of Worms vocalizes every letter of the Tetragrammaton with two vowels, using six vowels, and the number of combinations increases (cf. Idel 1988b: 22–23).
The Kabbalist can take advantage of the infinite resources of the Temurah because it is not only a reading technique, but the very process by which God created the world (as was already stated in the passage from the Sefer Yetzirah quoted above).
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bsp; The Kabbalah suggests, then, that there may be a finite alphabet that produces a dizzying number of combinations, and the one who took the art of combination to its utmost limit is precisely Abulafia (thirteenth century) with his Kabbalah of names.
As we saw in Chapter 7, the Kabbalah of names, or ecstatic Kabbalah, is practiced by reciting the divine names hidden in the text of the Torah, playing upon the various combinations of the letters of the Hebrew alphabet, altering, separating, and recombining the surface of the text, down to the individual letters of the alphabet.
For the ecstatic Kabala, language is a universe unto itself, and the structure of language reflects the structure of reality. Therefore, conversely to what happens in the Western philosophical tradition and in Arab and Jewish philosophy, in the Kabbalah language does not represent the world in the sense that a significant expression represents an extralinguistic reality. If God created the world through the emission of sounds and letters of the alphabet, these semiotic elements are not representations of something preexistent, but the forms on which the elements that compose the world are modeled.
A linguistic form that produces the world, and a series of symbols that can be infinitely combined, without the interference of any limiting rule: these are the two points on which the Kabbalistic tradition substantially differs from Llull’s Ars. As Platzeck (1964: 1:328) remarks: “Llull’s combinatory system, as a pure combination of concepts, is wholly inspired by the rigid spirit of Western logic, while the kabbalistic combinatory system is a philological game.”
