From the Tree to the Labyrinth

10

On Llull, Pico, and Llullism

We have only to leaf through a few studies on Christian Kabbalism (for instance, Secret 1964; French 1972; Evans 1973) to meet up with the cliché of Ramon Llull the Kabbalist, served up with minimal variations. Llull as magus and alchemist appears in the context of magic in the Prague of Rudolf II, as well as in the library of John Dee, who “was deeply immersed in Llullism and apparently accepted the traditional attitude toward the Llullist-cabalist synthesis” (French 1972: 113). Llull is present in the works of professed Kabbalists (such as Burgonovus, Paulus Scalichius, and the superficial and credulous Belot)¹ as well as in those of the enemies of Kabbalism, like Martino Del Rio,² to the point that, when Gabriel Naudé came to write his Apologie pour tous les grands hommes qui ont été accusés de magie (Paris, 1625) he felt obliged to defend the poor Catalan mystic energetically against any suspicion of necromancy. To add to the confusion, “in a later Renaissance transformation, the letters B through K used in the Llullian Ars became associated with the Hebrew letters that the cabalists contemplated and that supposedly signified angel names and the attributes of God. These Hebrew letters, which were thought to have a summoning power over the angels, were the same ones used by practical cabalists like John Dee” (French 1972: 49).

Numerology, magic geometry, astrology, and Llullism are inextricably confused, in part because of the series of pseudo-Llullian alchemistic works that invaded the sixteenth-century scene. Furthermore, the names of the Kabbalah could also be carved on seals, and a whole magical and alchemical tradition made seals with a circular structure popular (Llull practiced his art on a circular wheel). And, for his part Athanasius Kircher, in his 1665 Arithmologia, also illustrated a number of magic seals in the form of numerical tables.³

However, what influence the Kabbalistic tradition had on Llull is not something we need to discuss in the present context. Llull was born in Majorca—a crossroads on the margins of Europe where encounters took place among Christian, Arabic, and Hebrew cultures, and it is certainly not impossible that someone living where three great monotheistic religions met could have been subject to the influence, visual at least, of Kabbalistic speculation. Llull’s Ars combines letters on three concentric wheels and, from the very beginnings of the Kabbalistic tradition, in the Sefer Yetzirah (“Book of Creation,” written at an uncertain date between the second and sixth centuries), the combining of the letters is associated with their inscription on a wheel. What is certain, however, is that nothing is further from Kabbalistic practices than Llull’s Ars, at least as formulated by its founder.

10.1. What Exactly is Llull’s

Ars

?

If we are to understand the internal mechanics of the Ars, we must first review a few principles of Llull’s system of mathematical combinations.

We have permutation when, given n different elements, every possible change in their order has been realized. The typical case is the anagram.⁴ We have disposition when n elements are arranged t by t, but in such a way that the order also has differential value (AB and BA, for instance, represent two different dispositions).⁵ We have combination when, if we have to arrange n elements t by t, inversions of order are not relevant (AB and BA, for instance, represent the same combination).⁶

The calculus of the permutations, dispositions, and combinations may be used to solve a number of technical problems, but it could also be used for the purposes of discovery—to delineate, in other words, possible future “scenarios.” In semiotic terms, what we have is a system of expression (made up of symbols and syntactic rules) such that, by associating the symbols with a content, various “states of things” (or of ideas) can be imagined. In order for the combinatory system to be most effective, however, it must be assumed that there are no restrictions on thinking all possible universes. Once we begin to designate certain universes as not possible, either because they are improbable in the light of the evidence of our past experience or because they do not correspond to what we consider to be the laws of reason, then external criteria come into play that induce us, not merely to discriminate among the results of the system of combinations, but also to introduce restrictive rules into the system itself. In the case of Llull, what we have is a proposal for a universal and limitless system of combinations, which as such will fascinate later thinkers, but which at its very inception is severely limited, for reasons both theological and logical.

Llull’s Ars involves an alphabet of nine letters, from B to K (no distinction is made between I and J), and four combinatory figures. In a Tabula Generalis, Llull establishes a list of six sets of nine entities each (the six are: Absolute Principles or Divine Dignities, Relative Principles, Questions, Subjects, Virtues, Vices). Each entity may be assigned to one of the nine letters (our Figure 10.1).

Taking Aristotle’s list of categories as a model, the nine Divine Dignities or attributes of God’s being (Bonitas, Magnitudo, Aeternitas or Duratio, Potestas, Sapientia, Voluntas, Virtus, Veritas, and Gloria) are subjects of predication while the other five columns contain predicates.

Figure 10.1

The Ars includes four figures or illustrations, which in the various manuscripts are highlighted in different colors.⁷

PRIMA FIGURA. Llull’s first figure represents a case of disposition. The nine Absolute Principles are assigned to the letters. Llull explores all the possible combinations among these principles so as to produce propositions such as Bonitas est magna (“Goodness is great”), Duratio est gloriosa (“Duration is glorious”), and so on. The principles appear in nominal form when they are the subject and in adjectival form when they are the predicate, so that the sides of the polygon inscribed in the circle are to be read in two directions (we may read Bonitas est magna, as well as Magnitudo est bona). The possible dispositions of nine elements two by two, when inversions of order are also allowed, permit Llull to formulate seventy-two propositions (see Figure 10.2).

Figure 10.2

The figure permits regular syllogisms “ut ad faciendam conclusionem possit medium invenire” (“if the middle term be suitable for reaching a conclusion”) (Ars brevis II).⁸ To demonstrate that Goodness can be great, it is argued that “omne id quod magnificetur a magnitudine est magnum—sed Bonitas est id quod magnificetur a magnitudine—ergo Bonitas est Magna” (“everything made great by greatness is great—but Goodness is what is made great by greatness—therefore Goodness is great”).

SECUNDA FIGURA. Llull’s circle (unlike the one in his first figure) does not involve any system of combinations. It is simply a visual-mnemonic device that allows us to remember the connections (already foreordained) among various types of relationships and various types of entities (see Figure 10.3).

Figure 10.3

For example, both difference and concordance, as well as contrariety, can be considered with reference to (i) two sensitive entities, such as stone and plant; (ii) one sensitive and one intellectual, such as body and soul; and (iii) two intellectual entities, such as soul and angel.

TERTIA FIGURA. This figure evidently represents a case of combination, considering that in it all possible pairings of the letters are considered, excluding inversions of order (the table includes BC, for example, but not CB), and the doublets generated are thirty-six, inserted into what Llull dubs thirty-six chambers. But the chambers are virtually seventy-two, because each letter may indifferently become subject or predicate, that is, a BC can also be read as a CB (Bonitas est magna also gives Magnitudo est bona, see Ars magna VI, 2, and Figure 10.4).⁹

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).

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.”

10.3. Llull’s Trees and the Great Chain of Being

If Llull’s ideas did not come from the Hebrew Kabbalah, where did he get them from?

An admiring reader of the Catalan mystic, Leibniz (in his 1666 Dissertatio de arte combinatoria) asked himself why Llull had stopped at such a limited number of elements. Given that the virtues are traditionally seven (four cardinal virtues and three theological), why did Llull, who increases them to nine, not go further? If, among the Absolute Principles, Truth and Wisdom are included, why not Beauty and Number?

In point of fact, in various of his works, Llull had proposed at one time ten, at another twelve, and at yet another twenty principles, finally settling on nine. Scholars have inferred—given that his Absolute Principles are nine, plus a tenth (labeled with an A) that is left out of the combinatory pool, because it represents divine Unity and Perfection—that he was influenced by the ten Sephirot of the Kabbalah (cf. Millás Vallicrosa 1958). But we have already seen that this analogy will not get us far. Platzeck (1953: 583) observes that a comparable list of Dignities could be found in the Koran, while, in his Compendium artis demonstrativae (“De fine hujus libri”), Llull claims to have borrowed the terms of the Ars from the Arabs.

Still, we are not obliged to recognize at all costs extra-Christian influences, because the list of divine Dignities could have been handed down to him from a long and venerable Classical, Patristic, and Scholastic tradition. From the Divine Names of Pseudo-Dionysius the Areopagite to the thought of mature Scholasticism, we find an idea, Aristotelian in origin, which runs through the entire reflective tradition of the Christian world, the idea of the transcendental properties of being: there are certain characteristics common to all being and found supereminently in the divine being, such as the One, the Good, the True (some include the Beautiful), and all of these properties are mutually converted into one another, in the sense that everything that is true is good and vice versa, and so on and so forth.

Furthermore, all the experts concur in identifying in Llull two basic sources of inspiration.

(i). One has its origin in Augustine Platonism, for which there exists a world of divine ideas which we know by internal enlightenment and innate disposition. In chapter 7 of his De Trinitate, Augustine affirms that God is called great, good, wise, blessed, and true, and His very greatness is His wisdom, while His goodness, which is greatness and wisdom, is truth, and to be blessed and wise means nothing more than to be true and good, and so on. These are pretty much Llull’s Dignities, which, as was the case in Augustine, cannot but be known a priori, since they are imprinted by God himself on our souls. If Llull had not been convinced of this innatism he would not have thought it possible to dialogue with the infidels on the basis of the fundamental notions common to all mankind.

Platzeck (1953, 1954) has reconstructed a series of sources that Llull could have drawn upon in formulating his own list of divine Dignities, from Boethius to Richard of Saint Victor, from John of Salisbury to Arabic logicians like Algazel (on whom Llull wrote a commentary), not to mention Euclid, filtered through Boethius, who speaks of a number of principles that ought to be well known in and of themselves (dignitas would in that case be a translation of axioma): “The fact that the three religious communities present in the Mediterranean basin—Christian, Arab, and Hebrew—averred that these dignities or perfections were absolute in God authorized Llull to posit them, in imitation of Euclid’s, as prior axioms or dignitates or conceptiones animi communes” (Platzeck 1953: 609).

(ii). The other source is the idea, Neo-Platonic in origin, of the Great Chain of Being (cf. Lovejoy 1936). Primitive Neo-Platonism, taken up in the Middle Ages in more or less tempered form, taught that the universe, entirely divine in nature, is the emanation of an unknowable and ineffable One, through a series of degrees of being, or hypostases, produced by necessity down to the lowest matter. Beings are thus arranged at progressively increasing distances from the divine One, and participate to an ever-decreasing extent in a divine nature that becomes degraded little by little to the point of disappearing altogether on the lower rungs of the ladder (or chain) of beings. From this state of affairs two principles follow, one cosmological, the other ethical-mystical. In the first place, if every step on the ladder of being is a phase of the same divine emanation, there exist relations of similarity, kinship, analogy between a lower state and the higher states—and from this root are derived all the theories of cosmic similarity and sympathy. In the second place, if the emanational ladder, on the one hand, represents a descent from the inconceivable perfection of the One to the lower degrees of matter, on the other, knowledge, salvation, and mystic union (strongly identified with each other in the Neo-Platonist view) imply an ascent, a return to the higher planes of the Great Chain of Being.

This tempered medieval Neo-Platonism will endeavor to reduce as much as possible the identity between the divine nature and the various states of creation, and, with Thomas Aquinas, will finally see the chain in terms of participation (which implies, not a necessary emanation of the divinity, but a free act by which God confers existence on his own creatures; and the stages of the chain are related to each other, not by an inevitable inner likeness, but by analogy. Nevertheless, this image of the Great Chain of Being is always in some way present in medieval thought, even when we cannot trace a direct relationship to Neo-Platonism. We have only to recall that every medieval thinker had meditated upon a text of the third or fourth century, the commentary to the Ciceronian Somnium Scipionis by Macrobius, whose Platonic and Neo-Platonic inspiration is obvious. Macrobius places at the top of the ladder of being the Good, the first cause of all things, then the Nous or Intelligence, born of God himself, which contains the Ideas as archetypes of all things. The Nous, contemplating itself and knowing itself, produces a World-Soul, which is diffused—preserving its unity—throughout the multiplicity of the created universe. Not a number, but the origin and matrix of all numbers, the Soul generates the numbered plurality of beings, from the celestial spheres down to the sublunar bodies: “Mind emanates from the Supreme God and Soul from Mind, and Mind, indeed, forms and suffuses all below with life, and since this is the one splendor lighting up everything and visible in all, like a countenance reflected in many mirrors arranged in a row, and since all follow on in continuous succession, degenerating step by step in their downward course, the close observer will find that it creates all the following things and fills them with life, and since this unique light illuminates everything and is reflected in everything, and just as a single countenance may be reflected in various consecutive mirrors, all things follow each other in a continuous succession, degenerating bit by bit down to the end of the series—so that the attentive observer may seize an interconnection of the parts, from God on High down to the last dregs of things, bound to each other without any interruption” (Macrobius 1952).

There is a passage in Llull’s Rhetorica (ed. 1598: 199) that is practically a literal echo of Macrobius and confirms this basic principle of likeness among the various levels of being, as a result of which what was predicated in the definition of the original Dignities is realized in each being: “things receive from their likeness with the Divine Principle their conceptually defined places that at the same time correspond to their level of being” (Platzeck 1953: 601).

Through a thorough comparison not only of their texts but also of the illustrations that appear in various manuscripts of the two authors, Yates (1960) believed she could identify an unmediated source in the thought of John Scotus Eriugena. It is significant that for Eriugena the Divine Names or attributes are seen as primordial causes, eternal forms on the basis of which the world is configured, and from them there proceeds a primary matter, hyle or chaos, which we reencounter in the thought of Llull, author of a Liber Chaos or Book of Chaos). Along these lines, Yates (1960: 104 et seq.) identifies the first idea of the Ars in a passage from Eriugena’s De divisione naturae, in which fifteen primordial causes are mentioned (Goodness, Essence, Life, Reason, Intelligence, Wisdom, Virtue, Beatitude, Truth, Eternity, Greatness, Love, Peace, Unity, Perfection), but Eriugena adds that the number of causes is infinite and that they can therefore be arranged, for purposes of contemplation, in a series of arbitrary successions (the term Eriugena uses is convolvere, to cause them to rotate, so to speak, and Yates moreover reminds us that Eriugena, like other authors of his time, used the method of concentric circles to define the divine attributes and their combinations—though for contemplative and not inventive purposes). Obviously, the analogy with Kabbalistic procedures does not escape Yates, though she does not attempt to explain it in terms of direct dependence: “We should ask, not so much whether Llull was influenced by the Kabbalah, but whether Kabbalism and Llullism, with its Scotist basis, are not phenomena of a similar type, the one arising in the Jewish, and the other in the Christian tradition, which both appear in Spain at about the same time, and which might, so to speak, have encouraged one another by engendering similar atmospheres, or perhaps by actively permeating one another” (1960: 112; Llull and Bruno. Collected Essays 1982, p. 112).

Maybe Yates allowed herself to be bedazzled by similarities that seem less surprising when we recall that many analogous themes are to be found in other medieval Neo-Platonic texts (of the School of Chartres, for example). But precisely because of this it is undeniable that there are present in Llull’s texts ideas that Eriugena bequeathed to subsequent thinkers. Moreover, in the ninth century, Eriugena had contributed to the diffusion of the treatise by Pseudo-Dionysius On the Divine Names, one of the most important sources of medieval Neo-Platonic thought, at least in its tempered medieval form.

From the point of view of our investigation, ascertaining exactly where Llull got the idea of the Dignities is less relevant than recognizing that “Llull is a Platonist or a Neo-Platonist from top to bottom” (Platzeck 1953: 595). It is important to stress that the Dignities are not produced by the Ars, but constitute its premises, and they are the premises of the Ars because they are the roots of a chain of being.

To understand the metaphysical roots of the Ars we must turn to Llull’s theory of the Arbor scientiae (1296). Between the first versions of the Ars and that of 1303, Llull has come a long way (his journey is described by Carreras y Artau and Carreras y Artau 1939: 1:394), making his device capable of resolving, not only theological and metaphysical problems, but also problems of cosmology, law, medicine, astronomy, geometry, and psychology. The Ars becomes more and more a tool to take on the entire encyclopedia of learning, picking up the suggestions found in the countless medieval encyclopedias and looking forward to the encyclopedic utopia of Renaissance and Baroque culture.

The Ars may appear at first sight to be free from hierarchical structures, because, for example, the divine Dignities are defined in a circular fashion one being used to define the other. The relationships are not arranged in a hierarchical system (though they in fact refer to an implicit hierarchy between things sensitive and things intellectual, or between substances and accidents). But a hierarchical principle insinuates itself into the list of questions (whether something exists, what it is, in what way does it exist, etc.) and the list of Subjects is certainly hierarchical (God, Angel, Heaven, Man, down to the elements and tools). The Dignities are defined in a circular fashion because they are determined by the First Cause: but, it is on the basis of the Dignities that the ladder of being begins. And the Ars is supposed to make it possible to argue about every element in this ladder, or about every element in the furniture of the universe, about every accident and every possible question.

The image of this ladder of being is the Tree of Science, which has as its roots the nine Dignities and the nine Relations, and is then subdivided into sixteen branches, to each of which corresponds a separate tree. Each of these sixteen trees, to which an individual representation is dedicated, is divided into seven parts (roots, trunk, limbs, branches, leaves, flowers and fruit). Eight trees clearly correspond to eight subjects in the Tabula Generalis, and constitute the Arbor Elementalis (which represents the elementata, that is, the objects of the sublunar world made up of the four elements, stones, trees, animals), the Arbor Vegetalis, the Arbor Sensualis, the Arbor Imaginalis (the mental images that are the likenesses of the things represented in the other trees), the Arbor Humanalis (which concerns memory, understanding, and will and includes the various sciences and arts invented by man), the Arbor Coelestialis (astronomy and astrology), the Arbor Angelicalis and the Arbor Divinalis (the divine Dignities). To this list should be added the Arbor Moralis (virtues and vices), the Arbor Eviternalis (the realms of the afterworld), the Arbor Maternalis (Mariology), the Arbor Christianalis (Christology), the Arbor Imperialis (government), the Arbor Apostolicalis (the Church), the Arbor Exemplificalis (the contents of knowledge), and the Arbor Quaestionalis (which includes 4,000 questions on the various arts). But it can be definitively said that this forest of trees corresponds to the columns of the Tabula Generalis, even if we cannot always identify what term corresponds to what other.

As Llinares writes (1963: 211–212):

the various trees are hierarchically arranged, the higher trees participate of the lower. The “vegetable” tree, for instance, participates of the tree of the elements, the “sensual” tree of both, while the tree “of imagination” is constructed on the preceding three, at the same time as it makes comprehensible the tree that follows, in other words, the “human” tree. In this way, in an ascending movement, Ramon Llull constructs a system of the universe and of human knowledge grouped around three central themes: the world, man, and God.… Logic has given way to metaphysics, which is concerned first of all to explain and interpret, since the philosopher considers the primitive and real elements, and through them descends to particular objects, which he studies thanks to them.¹²

Carreras y Artau and Carreras y Artau (1939: 1:400), followed by Llinares (1963: 208 et seq.), note that an almost biological dynamism is evident in the trees, in contrast with the logical-mathematical staticity of Llull’s Ars in the preceding period. But we have already observed that the mastery of the Ars presupposes a preliminary knowledge that is precisely that conveyed by the trees. At least this is fully the case with the Ars generalis ultima and the Ars brevis, both subsequent in date to the formulation of the Arbor scientiae.

As we saw in Chapter 1, medieval thought has recourse to the figure of the tree (the Porphyrian tree) to represent the way in which genera formally include species and species are included in genera. If we observe just one of the illustrations in the Logica nova of 1303, we see a Porphyrian tree to which Llull affixes both the letters from B to K and the list of Questions. We might be tempted to conclude that the Dignities, and all the other entities of the Ars, are themselves the genera and species of the Porphyrian tree. But it is no accident that the illustration should be entitled Arbor naturalis et logicalis. Llull’s tree is not only logical, but natural too.

A Porphyrian tree is a formal structure. It defines formally the relationship between genera and species. (It is only a didactic convention that in its canonical form it always represents substances like Body or Animal.) The Porphyrian tree is initially an empty tree that anyone and everyone can fill out according to the classification they wish to produce. The trees that Llull presents in his Arbor scientiae on the other hand are “full” trees, or, if you will, representations of the Great Chain of Being as it metaphysically is—and must be. Platzeck (1954: 145 et seq.) is right therefore when he affirms that the analogy between Llull’s trees and the Porphyrian tree is only apparent: “its gradation is not the fruit of a logical framework but of the fact that the dignities manifest themselves, in created things, in different degrees.”

Llull too (Platzeck reminds us) needs a differentia specifica, but it is not an accident (however essential) that can be abstracted from the species under consideration: instead, it represents the degree of its ontological participation. This is why Llull’s criticism (see De venatione medii inter subjectum et praedicatum in Opera parva [Palma, 1744], I: 4) of the syllogism Every animal is a substance, Every man is an animal, Therefore every man is a substance is so interesting. The syllogism seems to be formally valid, but for Llull it is not “necessary” because the way in which man is a substance is marked by the distance between man and the first causes in the descent of the Great Chain of Being (therefore, man is indeed a substance, but only to a certain degree). Llull needs to come up with a “natural medium” that is nonlogical, a sort of immediate kinship. He therefore reformulates the syllogism (and accepts it) as follows: Every rational animal is a rational substance, Every man is a rational animal, Therefore every man is a rational substance. This looks like mere terminological wordplay, but for Llull it is a question of finding a kind of soft affinity among things, with neither leap nor interruption. And here we recognize that rationality is a difference that already divides the substance, that reappears at each step of the ladder, and that is conferred upon man alone through a chain of descending steps.

“The Scholastic logician uses only definitions adapted to the logic of the classes; the Raimondist admits every kind of distinction, as long as they are based on a real relationship between things” (Platzeck 1954: 155).

Llull’s presumed logic is not formal, it is a rhetoric that serves to express an ontology.¹³

In the light of these remarks it is understandable why on the one hand Llull organizes his Ars so as to find, in every possible argument, a middle term that allows him to form a demonstrative syllogism, but excludes some syllogisms, however correct, even if formally there is a middle term. His middle term is not that of formal scholastic logic. It is a middle that binds by likeness the elements of the Great Chain of Being, it is a substantial middle, not a formal one. This is why Llull is able to reject certain premises as unacceptable, even though the combinatory system makes them imaginable. The middle does not unite things formally, it is in things. Llull’s middle is not the middle term of an Aristotelian syllogism, it does not establish the cause identified by the definition, or the genus under which a species is to be subsumed: it is a “general label” that characterizes every form of participation, connection, kinship between two things, to such an extent that, in the elementary predications of his first and third figures, Llull does not even need to insert a copula. The greatness of goodness is not predicated, their consubstantial, incontrovertible, self-evident identity is simply recognized.¹⁴

Furthermore, in the rhymed Catalan version of his Logica Algazelis, Llull declares: “De la logica parlam tot breu—car a parlar avem de deu” (“Of logic we will speak briefly—because we have to speak of God”). The Ars is not a revelatory mechanism capable of designing cosmological structures as yet unknown: it discovers nothing; it supports probable arguments on the basis of ideas already known (or assumed to be known).

10.4. Pico’s

Revolutio Alphabetaria

We have one more knot to untie, a knot that lies at the junction between medieval Llullism and Renaissance and Baroque Llullism (and beyond)—it regards the supposed Llullism of Pico della Mirandola. Whether or not Pico was influenced by Kabbalistic texts is no longer an issue. At most, the discussion is still moot as to exactly what texts friends like Flavius Mithridates and others introduced him to. Idel (1988a: 205) reminds us that, for Yohanan Alemanno, friend and inspirer of Pico, “the symbolic cargo of language was becoming transformed into almost mathematical type of command. Thus, Kabbalistic symbolism was transformed (or retransformed) into a magical incantatory language.” Hence, Pico could affirm that no word can have any virtue in magical operations if it is not Hebrew or coming from Hebrew: “nulla nomina ut significativa, et in quantum nomina sunt, singula et per se sumpta, in Magico opere virtutem habere possunt, nisi sint Hebraica, vel inde proxima derivata” (“No name, insofar as it is endowed with meaning and insofar as it is a name, taken singly in and of itself, can produce a magical effect, unless it is Hebrew or closely derived from Hebrew”) (Conclusiones cabalisticae 22).¹⁵

What is the source, however, of the conviction, which we find in a number of authors, that Pico’s Kabbalism owed a debt to Llull (whose Ars brevis and Ars generalis ultima Pico was certainly familiar with; see Garin 1937: 110)? To give but one example, the most curious document regarding this association is probably the book by Jean-Marie de Vernon (Histoire véritable du bienheureux Raymond Lulle, Paris, 1668: 347–348), which, attributing to Llull no fewer than 4,000 works declares that 2,225 of them were in the library of Pico!

The answer is simple, at least in the first instance. The responsibility must be ascribed to a few lines—anything but perspicuous—in Pico’s Apologia, where, speaking of the Kabbalistic tradition, Pico draws a parallel that, to quote Wirszubski (1989: 259), is “the first of its kind in modern letters”:

Duas scientias hoc etiam nomine honorificarunt. Unam quae dicitur חכמת הצרדך [hokmat haseruf], id est ars combinandi, et est modus quidam procedendi in scientijs et est simile quid sicut apud nostros dicitur ars Raymundi, licet forte diverso modo procedant. Aliam quae est de virtutibus rerum superiorum que sunt supra lunam et est pars magiae naturalis supremae. Utraque istarum apud Hebraeos etiam dicitur Cabalam propter rationem iam dictam, et de utraque istarum etiam aliquando fecimus mentionem in conclusionibus nostris. Illa enim est ars combinandi quam ego in conclusionibus meis voco alphabetariam revolutionem. Et ista quae est de virtutibus rerum superiorum quae uno modo potest capi ut pars magiae naturalis. (They also honored two sciences with this name. One is called חכמת הצרדך [hokmat haseruf], that is the combinatory art, and it is a certain way of proceeding in the sciences, similar to what we call the ars Raymundi, even though on occasion they may proceed in a different manner. The other which has to do with the powers of the higher things that are above the moon is part of the supreme natural magic. Both these two sciences are called Kabbalah among the Hebrews for the reason previously mentioned. And we have spoken of both some time ago in our Conclusiones. The first in fact is the combinatory art that I refer to in my Conclusiones as the revolutio alphabetaria. And the second is the one that has to do with the powers of higher things, which can be thought of as a part of natural magic) (Apologia, 5, 28, my emphasis).

Let us consider this fundamental moment in the Apologia. The trouble is that, in drawing this parallel between the ars combinandi and the ars Raymundi, Pico is more interested in the differences than in the similarities. In the passage cited, Pico makes a distinction between a Kabbalah of names and a theosophical Kabbalah. Now the first part of the Kabbalah, or the first way of understanding the Kabbalah, is the ars combinandi, which Pico has already (in the Conclusiones cabalisticae) dubbed the revolutio alphabetaria. Observe that, in the Abulafian tradition, the word revolutio stands for combination in general (Wirszubski 1989: 137), but the term certainly implies a rotatory connotation, which calls to mind the Kabbalistic or Llullian wheels (or, as we will see, steganographic wheels, à la Johannes Trithemius). In any case, the term could be also used metaphorically, as a more or less visual image of the combinatory swirling typical of the Kabbalistic technique of the anagram or Temurah. Frances Yates, while recognizing that Pico’s ars combinandi is derived from the combinatory practices of Abulafia, decides to deal only with the second type of Kabbalah—something she has of course every right to do—dismissing the first by saying that Pico considers it to be somehow similar to the art of Raimon Llull (Yates 1964: 113).

However that may be, a combination of letters cannot help recalling the techniques of Llull, and this is why Pico says that the two practices are similar. Whereupon, however, he points out that the similarity is only apparent: “licet forte diverso modo procedant” (“even though by chance/perhaps they may proceed in a different manner”). The ambiguous adverbial expression forte (“perhaps” or “by chance”) is a teaser. If Pico had wished to allude to a substantial difference, he would have had his good reasons: as we have seen, the letters in Llull’s combinatory system refer to theological entities, to divine Dignities, and they therefore refer to a system of combinations which, though it appears to occur at the alphabetical level, in fact subsists in the realm of contents. The Abulafian Kabbalistic system, on the other hand, is exercised on the substance of the expression, on letters of the Torah, or on those elements of the form of the expression that are the letters of the alphabet.

Still, this explanation could easily be confuted on the basis of the Kabbalistic belief that every letter of the Hebrew alphabet has a meaning, at least a numerological meaning. So the Kabbalah too, though it may seem to be combining and permutating alphabetical elements, is really permutating and combining concepts. Apart, then, from their different theological backgrounds, ars Raymundi and ars combinandi are not substantialiter different from each other. They are so forte, “by chance,” or with regard to their outcomes, or the way they are used.

It is our conviction that Pico had understood that what distinguished Kabbalistic thought from that of Llull was that the reality that the Kabbalistic mystic must discover is not yet known and can reveal itself only through the spelling out of the letters in their whirlwind permutations. Consequently, though it may be only in a mystical sense (in which the combinations serve only as a motor of the imagination), the Kabbalah pretends to be a true ars inveniendi, in which what is to be found is a truth as yet unknown. The combinatory system of Llull, on the other hand, is (as we saw) a rhetorical tool, through which the already known may be demonstrated—what the ironclad system of the forest of the various trees has already fixed once and for all, and that no combination can ever subvert.¹⁶

That Pico had understood perfectly, with his aside, this point, is also confirmed by his Conclusiones cabalisticae:

Nullae sunt litterae in tota lege, quae in formis, coniunctionibus, separationibus, tortuositate, directione, defectu, superabundantia, minoritate, maioritate, coronatione, clausura, apertura, & ordine, decem numerationum secreta non manifestent. (There are no letters in the whole Law which in their forms, conjunctions, separations, crookedness, straightness, defect, excess, smallness, largeness, crowning, closure, openness and order, do not reveal the secrets of the ten numerations.) (Farmer 1998: 359)

Furthermore, if we bear in mind that these numerationes are the Sephirot, we can appreciate the revelatory power with which he endows his ars combinandi. What results this whirling dervish of an art leads him to, well beyond all philological common sense, but evincing without question a combinatorial energy that knows no limits, we may gather from the famous passage in the Heptaplus dedicated to the Bereishit.

Here for the first time we encounter what will turn out to be a distinguishing feature not only of Kabbalism but of the whole later hermetic tradition: given a discourse that already in and of itself dares to enunciate unfathomable mysteries, it is assumed to allude even further, to mysteries still higher and more occult. For Pico, in the Second Proem, the Mosaic account of the creation of the world alludes, in every one of its parts, and according to seven different levels of reading, to the creation of the world of the angels, of the celestial world and the sublunar world, as well as to man as microcosm: “Thus indeed this book of Moses, if any such, is a book marked with seven seals and full of all wisdom and all mysteries” (Pico della Mirandola 1965: 81). In the sixth chapter of the Third Exposition (“On the Angelic and Invisible World”), for instance, the creation of the fish, birds, and earthbound animals is seen as a revelation of the creation of the angelic cohorts. If there are unfathomable and unfathomed mysteries to discover, nothing must be taken as known. The combinations must be venturesome and, at least as far as intentions go, innocent and open-minded. Here is the famous passage, typically Kabbalistic in tone, in which Pico launches into the most uninhibited permutational and anagrammatical operations:

Applying the rules of the ancients to the first phrase of the work, which is read Beresit by the Hebrews and “In the beginning” by us, I wanted to see whether I too could bring to light something worth knowing. Beyond my hope and expectation I found what I myself did not believe as I found it, and what others will not believe easily: the whole plan of the creation of the world and of all things in it disclosed and explained in that one phrase.… Among the Hebrews, this phrase is written thus: בראשיח, berescith. From this, if we join the third letter to the first, comes the word אב, ab. If we add the second to the doubled first, we get בבד, bebar. If we read all except the first, we get ראשית, resith. If we connect the fourth to the first and last, we get שבת, sciabat. If we take the first three in the order in which they come, we get כרא, bara. If, leaving out the first, we take the next three, we get ראש, rosc. If, leaving out the first and second, we take the two following, we get אש, es. If, leaving out the first three, we join the fourth to the last, we get שת, seth. Again, if we join the second to the first, we get רב, rab. If after the third we set the fifth and fourth, we get איש, hisc. If we join the first two to the last two, we get ברית, berith. If we add the last to the first, we get the twelfth and last word, which is תב, thob, the thau being changed into the letter thet, which is very common in Hebrew.

Let us see first what these words mean in Latin, then what mysteries of all nature they reveal to those not ignorant of philosophy. Ab means “the father”; bebar “in the son” and “through the son” (for the prefix beth means both); resit, “the beginning”; sabath, “the rest and end”; bara, “created”; rosc, “head”; es, “fire”; seth, “foundation”; rab, “of the great”; hisc, “of the man”; berit, “with a pact”; thob, “with good.” If we fit the whole passage together following this order, it will read like this: “The father, in the Son and through the Son, the beginning and end or rest, created the head, the fire, and the foundation of the great man with a good pact.” This whole passage results from taking apart and putting together that first word. (Pico della Mirandola 1965: 171–172)

Pico’s ars combinandi has nothing in common with the ars Raymundi. Ramon Llull used his art to demonstrate credible things; Pico uses his to discover things incredible and unheard-of. Nevertheless, the various misapprehensions that will later arise probably derive from the fact that it is precisely Pico’s example that will free Llullism from its original fetters.

It is certainly not a question of seeing in Pico’s uncoupling of the Kabbalistic Ars combinandi from the Ars Raymundi, and in the dizzying permutational exercises that Pico encourages, the detonator that liberated in the coming centuries Llull’s Ars from its early limitations, taking it (as we will see), beyond theology and beyond rhetoric, to nourish the formal speculations of modern logic and the random brainstorming that characterizes so much of contemporary heuristics.

What is certain is that with Pico is affirmed, in harmony with his defense of the dignity and rights of man, the invitation to dare, to invenire or discover, even if it was more in keeping with the tendentious suggestions of Flavius Mithridates than with those of factorial calculus. What was needed at this point was for someone to suggest that, if we are going to continue to talk about being, the being chosen must be a being as yet unmade, rather than a being that already exists. And it was Pico who (perhaps without intending to) steered modern thought in this direction. Which is, when you get down to it, another way of saying that “man, for Pico, is divine insofar as he creates; because he creates himself and his world; not because he is born God, but because he makes himself God. Throughout the entire universe, operatio sequitur esse. … For Pico, in man, and in man alone, esse sequitur operari” (Garin 1937: 95).

This is the sense in which, to use Pico’s own words, the ars combinandi and the ars Raymundi “diverso modo procedunt.” In this sense we may cancel the ambiguous expression forte (“by chance, perhaps, accidentally”), possibly inserted out of prudence, possibly because Pico’s intuition was still in its first vague glimmerings. Once the adverb has been eliminated, in that brief aside, we pass from the idea of man as subject to the laws of the cosmos to that of a man who constructs and reconstructs without fear of the vertigo of the possible, fully accepting its risk.

10.5. Llullism after Pico

With the advent of the Renaissance the unlimited combinatory system will tend to express a content that is equally unlimited, and hence ungraspable and inexpressible.

In the 1598 edition of Llull’s combinatorial writings, a work entitled De auditu kabbalistico appears under his name. Thorndike (1929, V: 325) already pointed out that the De auditu first appeared in Venice in 1518 as a little work by Ramon Llull, “opusculum Raimundicum,” and that it was consequently a work composed in the late fifteenth century. He hypothesized that the work might be attributed to Pietro Mainardi, an attribution later confirmed by Zambelli (1965). It is remarkable, however, that this opuscule of Mainardi’s should be dated “in the last years of the fifteenth century, in other words, immediately following the drafting of Pico’s theses and his Apologia” (Zambelli 1995[1965]: 62–63), and that this minor forgery was produced under his influence, however indirect (see Scholem 1979: 40–41). The brief treatise gives two etymological Arabic roots for the word “Kabbalah”: Abba stands for father while ala means God. It is difficult not to be reminded of similar exercises on Pico’s part.

This confirms that by this time Llull had been officially enrolled among the Kabbalists, as Tommaso Garzoni di Bagnacavallo will confirm in his Piazza universale di tutte le professioni (Venice, Somasco, 1585):

The science of Ramon, known to very few, could also be called, though with an inappropriate word, Kabbala. And from it is derived that common rumor among all the scholars, indeed among all persons, that the Kabbala teaches everything … and to this effect there is in print a little book attributed to him (although this is the way that lies are composed beyond the Alps) entitled De Auditu Cabalistico, which is nothing more when you get down to it than a very brief summary of the Arte magna, which was definitely abbreviated by him in that other work, which he calls Arte breve.¹⁷

Among the later examples from “beyond the Alps,” we may cite Pierre Morestel, who published in France in 1621, with the title Artis kabbalisticae, sive sapientiae divinae academia, a modest anthology of the De auditu¹⁸ (with an official imprimatur no less, since the author proposed to demonstrate exclusively, as Llull himself did, Christian truths), with nothing Kabbalistic about it, apart from the title, the initial identification of Ars and Kabbalah, and the repetition of the etymology found in the De auditu.

Figure 10.7

An additional stimulus to Neo-Llullism came from ongoing research into coded writings or steganographies. Steganography developed as a ciphering device for political and military purposes, and the greatest steganographer of modern times, Trithemius (1462–1516) uses ciphering wheels that work in a similar way to Llull’s moving concentric circles. To what extent Trithemius was influenced by Llull is unimportant for our purposes, because the influence would in any case have been purely graphic. The wheels are not used by Trithemius to produce arguments, simply to encode and decode. The letters of the alphabet are inscribed on the circles and the rotation of the inner circles decided whether the A of the outer circle was to be encoded as B, C, or Z (the opposite was true for decoding; see Figure 10.7).

But, although Trithemius does not mention Llull, he is mentioned by later steganographers. Vigenère’s Traité des chiffres¹⁹ explicitly takes up Llullian ideas at various points and relates them to the factorial calculus of the Sefer Yetzirah.

There is a reason why steganographies act as propagators of a Llullism that goes beyond Llull. The steganographer is not interested in the content (and therefore in the truth) of the combinations he produces. The elementary system requires only that elements of the steganographic expression (combinations of letters or other symbols) may be freely correlated (in ever different ways, so that their encoding is unpredictable) to elements of the expression to be encoded. They are merely symbols that take the place of other symbols. The steganographer, then, is encouraged to attempt more complex combinations, of a purely formal nature, in which all that matters is a syntax of the expression that is ever more vertiginous, and every combination is an unconstrained variable.

Thus, we have Gustavus Selenus,²⁰ in his 1624 Cryptometrices et Cryptographiae, going so far as to construct a wheel of twenty-five concentric circles combining twenty-five series of twenty-four doublets each. And, before you know it, he presents us with a series of tables that record circa 30,000 doublets. The possible combinations become astronomical (see Figure 10.8).

If we are going to have combinations, why stop at 1,680 propositions, as Llull did? Formally, we can say everything.

It is with Agrippa that the possibility is first glimpsed of borrowing from both the Kabbalah and from Llullism the simple technique of combining the letters, and of using that technique to construct an encyclopedia that was not an image of the finite medieval cosmos but of a cosmos that was open and expanding, or of different possible worlds.

His In artem brevis R. Llulli (which appears along with the other works of Llull in the Strasburg edition of 1598) appears at first sight to be a fairly faithful summary of the principles of the Ars, but we are immediately struck by the fact that, in the tables that are supposed to illustrate Llull’s fourth figure, the number of combinations becomes far greater, since repetitions are not avoided.

As Vasoli (1958: 161) remarks,

Agrippa uses this alphabet and these illustrations only as the basis for a series of far more complex operations obtained through the systematic combination and progressive expansion of Llull’s typical figures and, above all, through the practically infinite expansion of the elementa. In this way the subjects are multiplied, defining them within their species or tracing them back to their genera, placing them in relation with terms that are similar, different, contrary, anterior or posterior, or again, referring them to their causes, effects, actions, passions, relations, etc. All of which, naturally, makes feasible a practically infinite use of the Ars.

The Carreras y Artau brothers (1939: 220–221) observe that in this way Agrippa’s art is inferior to Llull’s because it is not based on a theology. But, at least from our point of view and from that of the future development of combinatory systems, this constitutes a strong point rather than a weakness. With Agrippa, Llullism is liberated from theology.

Figure 10.8

Rather, if we must speak of a limit, it is clear that, for Agrippa too, the point is not to lay the foundations for a logic of discovery, but instead for a wide-ranging rhetoric, at most to complicate the list of disciplines configured by his encyclopedia, but always in such a way as to provide—as is the case with a mnemonic technique—notions that can be manipulated by the proficient orator.

Llull was timid with respect to the form of the content. Agrippa broadens the possibilities of the form of the expression in an attempt to articulate vaster structures of content, but he does not go all the way. If he had applied the combinatory system to the description of the inexhaustible network of cosmic relations outlined in the De occulta philosophia he would have taken a decisive step forward. He did not.

Bruno, on the other hand, will try to make his version of Llull’s Ars tell everything and more. Given an infinite universe whose circumference (as Nicholas of Cusa already asserted) was nowhere and its center everywhere, from whatever point the observer contemplates it in its infinity and substantial unity, the variety of forms to be discovered and spoken of is no longer limited. The ruling idea of the infinity of worlds is compounded with the idea that each entity in the world can serve at the same time as a Platonic shadow of other ideal aspects of the universe, as sign, reference, image, emblem, hieroglyphic, seal. By way of contrast too, naturally, because the image of something can also lead us back to unity through its opposite.

The images of his combinatory system, which Bruno finds in the repertory of the hermetic tradition, or even constructs for himself from his fevered phantasy, are not merely intended, as was the case with previous mnemonic techniques, for remembering, but also for envisaging and discovering the essence of things and their relationships.

They will connect with the same visionary energy with which Pico disassembled and reassembled the first word of the sacred text. A thing can represent another thing by phonetic similarity (the horse, in Latin equus, can represent the man who is aequus or just), by putting the concrete for the abstract (a Roman warrior for Rome), by the coincidence of their initial syllables (asinus for asyllum), by proceeding from the antecedent to the consequence, from the accident to the subject and vice versa, from the insignia to the one who wears it. Or, once again, by recurring to Kabbalistic techniques and using the evocative power of the anagram and of paronomasia (palatio for Latio, cf. Vasoli 1958: 285–286).

The combinatory technique becomes a language capable of expressing, not just the events and relationships of this world, but of all of the infinite worlds, in their mutual harmony with one another.

Where are the constraints imposed by a metaphysics of the Great Chain of Being now? The title of one of Bruno’s mnemotechnical treatises, De lampade combinatoria Lulliana continues ad infinitas propositiones et media invenienda.²¹ The reference to the infinity of propositions that can be generated is unequivocal.

The problem of combinatorial techniques will be taken up by other authors, though in an openly anti-Kabbalistic key, with the express purpose of displaying skepticism in the face of the proliferation of mystical tendencies, of demonstrating the weakness and the approximative nature of the Rabbinical calculus, and of bringing the technique back to a purely formal mathematical calculus (indifferent to meaning) but nevertheless capable of predicting how many new expressions and how many new languages could be produced using only the letters of the Latin alphabet.

In German Jesuit Christopher Clavius’s In Sphaerum Ioannis de Sacro Bosco,²² the author considers how many dictiones, or how many terms, could be produced with the twenty-three letters of the Latin alphabet (at the time there was no difference between u and v or i and j, and no k or y), combining them two by two, three by three, and so on, up to words made up of twenty-three letters. Clavius supplies the mathematical formulas for this calculus, but he stops short at a certain point before the immensity of the possible results, especially if repetitions were to be included.

In 1622, Pierre Guldin composed his Problema arithmeticum de rerum combinationibus (cf. Fichant 1991: 136–138), in which he calculates all the dictions that can be generated with twenty-three letters, regardless of whether they make sense or can be pronounced, but not including repetitions. He establishes that the number of words (of variable length from two to twenty-three letters) would be more than 70,000 billion billion (to write them out would require more than a million billion billion letters). To have an idea of the implications of this number, think of writing all of these words in registers of 1,000 pages, with 100 lines per page and sixty characters per line. They would fill 257 million billion such registers. And if we wished to house them in a library—Guldin studies point by point its arrangement, its extension, how one would navigate within it, if we had at our disposal cubic structures measuring 432 feet per side, each of them capable of holding 32 million volumes, 8,052,122,350 such bookcases would be required. But what realm could accommodate so many structures? Calculating the surface available throughout the entire planet, we could accommodate only 7,575,213,799 of them!

Marin Mersenne, in various of his writings (cf. Coumet 1975), wonders how many names it would take if we were to give a different name to each individual. And not only that: to every individual hair on the head of every human being. Maybe he was echoing the traditional medieval lament for the penuria nominum or penury of names, according to which there are more things in need of a name than there are names to go around. With the appropriate formula (and the calculations Mersenne engages in are dizzying), it would be possible to generate copious lexicons for all languages.

In addition to the alphabetical dictiones, Mersenne also takes into consideration the canti or musical sequences that can be produced without repetition over the space of three octaves (we may have here an initial allusion to the notion of the dodecaphonic series), and he observes that to record all these canti would require more reams of paper than, if they were piled on top of one another, would cover the distance from earth to the heavens, even if each sheet were to contain 720 canti each with 22 notes and every ream were compressed so as to measure less than an inch: because the canti that can be produced on the basis of 22 notes are 1,124,000,727,607,680,000, and dividing them by the 362,880 that will fit on a ream, the result would still be a number of 16 figures, while the distance from the center of the earth to the stars is only 28,826,640,000,000 inches (14 figures). And if we were to write down all these canti, at the rate of 1,000 a day, it would take 22,608,896,103 years and 12 days.

There is in all this giddy rapture a consciousness of the infinite perfectibility of knowledge, for which mankind, the new Adam, has the possibility in the course of the centuries to name everything that the first Adam did not find time to baptize. In this way, the combinations aspire to compete with that ability to know the individual that belongs solely to God (whose impossibility will be sanctioned by Leibniz). Mersenne had done battle against Kabbalah and occultism, but the vertiginous gyrations of the Kabbalah had evidently seduced him, and here he is spinning the Llullian wheels for all he’s worth, no longer capable of distinguishing between divine omnipotence and the possible omnipotence of a perfect combinatorial language manipulated by man, to the point that in his Quaestiones super Genesim (cols. 49 and 52) he sees in the presence in man of the infinite a manifest proof of the existence of God.

But this ability to imagine the infinite possibilities of the combinatory technique manifests itself because Mersenne, like Clavius, Guldin, and others (the theme returns, for example, in Comenius, Linguarum methodus novissima III, 19),²³ is no longer calculating with concepts (as Llull did) but with alphabetical sequences, mere elements of expression, uncontrolled by any orthodoxy that is not that of the numbers. Without realizing it, these authors are already approaching that notion of “blind thought” that will be brought to fruition, with greater critical awareness, by Leibniz, the inaugurator of modern formal logic.

In his Dissertatio de arte combinatoria, the same Leibniz, after complaining (correctly) that Llull’s whole method was concerned more with the art of improvising a discussion than with acquiring complete knowledge of a given subject, entertained himself by calculating how many possible combinations Llull’s Ars really consented, if all of the mathematical possibilities permitted by nine elements were exploited; and he came up with the number (theoretical of course) 17,804,320,388,674,561.

But, to exploit these possibilities, one had to do the opposite from what Llull had done and to take seriously the combinatory incontinence of people like Guldin and Mersenne. If Llull had invented an extremely flexible syntax and then handicapped it with a very rigid semantics, what was needed was a syntax that was not hampered by any semantic limitations. The combinatory process ought to generate empty symbolic forms, not yet bound to any content. The Ars thus became a calculus with meaningless symbols.

This is a state of affairs that shows how much progress Llullism has made, providing tools for our contemporary theoreticians of artificial and computerized languages, while betraying the pious intentions of Ramon Llull. And that to reread Llull today as if he had had an inkling of computer science (apart from the obvious anachronism) would be to betray his intentions.

All Llull had in mind was speaking of God and convincing the infidel to accept the principles of the Christian faith, hypnotizing them with his whirling wheels. So the legend that claims he died a martyr’s death in Muslim territory, though it may not be true, is nonetheless a good story.

A fusion of the following articles: “La lingua universale di Ramón Llull” (Eco 1991); “Pourquoi Llulle n’était pas un kabbaliste” (Eco 1992c); and “I rapporti tra Revolutio Alphabetaria e Lullismo” (Eco 1997a). These same themes are taken up in Eco (1993) [English trans. (1995)].

1. Burgonovus, Cabalisticarum selectiora, obscvrioraque dogmata (Venice: Apud Franciscum Franciscium Senensem, 1569); Paulus Scalichius, Encyclopedia seu orbis disciplinarum tam sacrarum quam prophanarum Epistemon (Basel, 1559); Jean Belot, Les Oeuvres de M. Jean Belot cure de Milmonts, professeur aux Sciences divines et célestes. Contenant la chiromence, physionomie, l’Art de Mémoire de Raymond Llulle, traité des divinations, augures et songes, les sciences stéganographiques etc. (Rouen: Jean Berthelin, 1669).

2. Disquisitionum magicarum libri sex (Mainz: König, 1593).

3. Arithmologia, Sive De abditis Numerorum Mysterijs (Rome: Ex Typographia Varesij, 1665).

4. The number of possible permutations is given by the factorial of n (n!) which is calculated: 1*2*3* … *n. For example, three elements ABC can be combined in six triplets (ABC, ACB, BAC, BCA, CAB, CBA), distinguished only by the order of their elements.

5. The formula is n! / (n - t)!. For example, given four elements ABCD, they can be arranged into twelve possible duplets.

6. The formula is n! / t! (n - t)!. Given the four elements ABCD, they can be combined into six possible duplets.

7. The woodcuts that follow are taken from Bernardus de Lavinheta, Practica compendiosa artis Raymundi Llulli (Lyon, 1523).

8. It will be seen that, by “middle term,” Llull means something different from what was understood by Scholastic syllogists. However that may be, excluded from this first table are self-predicatory combinations like BB or CC, because for Llull the premise “Goodness is good” does not permit us to come up with a middle term (cf. Johnston 1987: 234).

9. Our references to Llull’s texts are to the Zetzner edition (Strasburg, 1598), since it is on the basis of this edition that the Llullian tradition is transmitted to later centuries. Therefore, by Ars magna we mean the Ars generalis ultima, which in the 1598 edition is entitled Ars magna et ultima.

10. Athanasius Kircher, Ars magna sciendi (Amsterdam: Jannson, 1669).

11. Sefer Yetzira, University Press of America, 2010.

12. That the emanative or participative process goes from the root to the leaves is simply a question of iconographic convention. Note how Kircher, in his Ars magna sciendi, constructs his tree of the sciences, on a model related to the Porphyrian tree, with the Dignities at the top. As for Llull, in works like the Liber de ascensu et descensu intellectus (1304), the hierarchy of beings is represented as a ladder on which the artist proceeds from the effects to the causes, from the sensitive to the intellectual, and vice versa.

13. “We are … a thousand leagues away from modern formal logic. What we have here is a logic that is material in the highest degree, and therefore a kind of Topics or art of invention” (Platzeck 1953: 579). And again: “truth or logical correctness is never formally appreciated for its own sake, but always with reference to gnoseological truth” (Platzeck 1954: 151).

14. See Johnston (1987), chapter 15, entitled “Natural Middle,” in which these points are persuasively and searchingly discussed. “[The Ars] does not require systematic coherence of a deductive nature among its arguments; it is endlessly capable of offering yet another analogical explanation of the same idea or concept, or of restating the same truth in different terms. This explains both the volume and exhaustively repetitive character of nearly all of Llull’s 240 extant writings” (Johnston 1987: 7).

15. On the other hand, Agrippa’s point of departure is the principle that “although all the demons or intelligences speak the language of the nation over which they preside, they make exclusive use of Hebrew when they interact with those who understand this mother tongue.… These names … though of unknown sound and meaning, must have, in the work of magic … greater power than significant names, when the spirit, dumbfounded by their enigma … fully convinced that it is acting under some divine influence, pronounces them in a reverent manner, even though it does not understand them, to the greater glory of the divinity” (De occulta philosophia libri III [Paris: Ex Officina Jacobi Dupuys, 1567], III:23–26). John Dee evokes angels of dubious celestiality with invocations such as Zizop, Zchis, Esiasch, Od, Iaod (cf. A True and Faithful Relation (London, printed by D. Maxwell for T. Garthwait, 1659).

16. Hillgarth (1971: 283) states that Pico, more interested in Kabbalism than in the Ars of Llull, cited Llull because he was better known than the Hebrew Kabbalah. For a subtle difference of opinion on this point, see Zambelli (1995[1965]: 59, n. 14).

17. La piazza universale di tutte le professioni del mondo, Nuovamente Ristampata & posta in luce, da Thomaso Garzoni di Bagnacavallo. Aggiuntovi in questa nuova Impressione alcune bellissime Annotazioni a discorso per discorso (Venice: Appresso Roberto Maietti, 1599).

18. Artis kabbalisticae, sive sapientiae divinae academia: in novem classes amicissima cum breuitate tum claritate digesta (Paris: Apus Melchiorem Nondiere, 1621).

19. Traité des chiffres, Ou Secretes Manieres d’Escrire (Paris: Chez Abel L’Angelier, 1587).

20. Cryptomenytices et cryptographiae libri ix (Lüneburg: Excriptum typis Johannis Henrici Fratrum, 1624).

21. De lampade combinatoria Lulliana (Wittenberg: Zacarius Cratius, 1587), inserted into the 1598 edition of Llull’s works along with De Lulliano Specierum Scrutinio, De Progressu Logicae Venationis and De Lampade Venatoria Logicorum.

22. In Sphaeram Ioannis de Sacro Bosco Commentarius (Rome: Apud Victorium Helianum, 1570.

23. The dates of composition are uncertain (ca. 1644–1648); the work was probably published at Leszno in 1648.