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