From the Tree to the Labyrinth (71 page)

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).

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.