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).