4. THE CONSEQUENCES

Llull is not a forgotten anticipator, nor a mere precursor. Llull's work, which had to pay the unexpected toll of being augmented with all kinds of apocrypha that were falsely attributed to him, was well known and appreciated by many influential thinkers of the Renaissance and after. He had a strong influence on -but no explicit recognition by- such people as Montaigne, Pascal, Descartes or Newton (who had Llull in his library, a fact that put him on a par with his arch-enemy Leibniz). Giordano Bruno and Leibniz not only got the influence but were not afraid to acknowledge it. Leibniz is our most direct connection with Llull. By looking for a universal notation and a universal way of acquiring and developing knowledge more or less inspired by the methods of Mathematics (his mathesis universalis), he avidly absorbed Llull, critically adapted him and proposed an objective and mechanical way of founding Logic and rational inquiry. In this he failed, after leaving a string of unpublished notes (which included an algebra of thought and a graph formalism), and only some 150 years later could his blocked program be unleashed by Boole's insights. But other Leibniz ideas went ahead, notably his push for concept decomposition and analysis which had two unexpected derivations: (1) the analysis of minute quantities (the "infinitesimals", on whose development and rights his discussion with Newton turned dismally bitter) and (2) the actual construction in the 1670's of a calculating machine (the first practical multiplier, which prompted an unanticipated reflection by Leibniz on the idoneity of the binary system for calculating). Leibniz's thoughtful 1666 'Dissertatio de arte combinatoria' is not only good and interesting reading for today's logicians and mathematicians It is the best criticism and homage that Llull has ever received: by recognizing his merits and adapting his ideas to the modern needs of Science, Leibniz did all to include Llull in our scientific heritage, and did us a favor in the process.