The Art and Information Technology
Understanding the Art as an epistemological creation whose relational method is based upon pairs and triads, gives a suitable degree of importance to the role played therein by combinatorics as such, to which, since the time of Leibniz’s interpretation of Llull (Dissertatio de arte combinatoria, 1666), an excessive protagonism has been attributed. Llull, specifically set out, in the Arts of the second phase, a table of ternary combinations derived from the Fourth Figure, in addition to the adjacency (half-)matrix containg 36 combinations, without repetition, of nine elements considered in pairs (that is, the Third Figure). This table presented variations of three elements considered in units of three, cyclically and without repetition, resulting in 252 possible triads. The typical mistrust of thinkers such as Francis Bacon and René Descartes or of historians of logic and mathematics from the 19th and 20th century (K. Prantl, D. Michie, M. Gardner) towards Llull’s Art, towards the calculus it implied and towards the applications it generated, depends often upon a partial and vague awareness of Ramon’s specific proposals.
To say that the Art can be included within the theoretical field of information processing means that it can be translated into computational language. Bonner has indicated that the Art’s system of argumentation presents some similarity to the Tableaux Proof Method and to the logical language, Prolog, connected with it. For T. Sales there are ten components within Llull’s system which can be included in the realm of computational concepts: from the idea of ‘calculating the results’ of logical reasoning, already explored by Leibniz, to that of an ‘alphabet of thought’, interpreted mathematically by George Boole in the mid-ninetheenth century, to that of a general method which is heuristic and deductive, to logical analysis, to the notion of a generative system, to the capacity to be treated diagrammatically, or to the graph theory governing the triangular figures of the Art.
See: Werner Künzel i Heiko Cornelius, Die «Ars Generalis Ultima» des Raymundus Lullus. Studien zu einem geheimen Ursprung der Computertheorie(Berlín, 1986; 5a ed. 1991), 102 pp. Ton Sales, "La informàtica moderna, hereva intel·lectual directa del pensament de Llull", Studia Lulliana 38 (1998), pp. 51-61.
We are all aware that information processing rests upon this dual basis: the idea of logical calculus and its subsequent automation. So, both items form part, though in a slightly rudimentary manner, of the combinatorial project which formed a basic element of Llull’s Art. Llull’s attempts were followed later by those of Leibniz. His celebrated Dissertatio de arte combinatoria, rising out of the Ars magna and its principal commentators, involved a decisive change of view in terms of judgements of Llull’s thought. Leibniz was the first to realise the future possibilities residing within the Art. The German thinker appropriated Llull’s idea of an ‘alphabet of human thought’ which functioned automatically, as it were, by means of combinations of letters, and related it to his own idea of a ‘mathesis universalis’, that is to say, of a logic conceived as generalised mathematics. ‘In accordance with this,’ wrote Leibniz, ‘when a controversy arises, there will be as much need for discussion between two philosophers as there is between two calculators. It will be sufficient to seize one’s pen, sit down at a table and say to each other: Let us calculate!’. Llull’s Art, therefore, was interpreted by Leibniz as a type of automatic thought, a form of conceptual tool which, once it had been set up, would function on its own. Leibniz held this conceptual automatism close to his heart for a long time, and he was the first person, after Pascal, to plan a calculating machine which really worked.