Combinatorics

Llull, in keeping with medieval logic, conceived of his Art as a tool for forming judgements and syllogisms. With this end in mind, he began by assigning a letters to various concepts of the Art. Then, by means of binary and ternary combinations of letters, he established the necessary relationship between the terms of a judgement or of a number of judgements. Llull called this operation ‘fer cambres’ [‘the formation of compartments’]. This entire mechanism was directed towards a specific end: to discover in any subject area the appropriate terms for forming judgements and syllogisms and thus to construct logical reasoning by a form of mathematical necessity. Here, that is to say, in this attempt, at once ingenuous and possessed of genius, to mechanise and mathematise knowledge, a distant anticipation of modern symbolic logic, certainly lay the roots of that peculiar seductive power exerted by Llull’s Art throughout history, from the time of Nicholas of Cusa to that of Leibniz.