2.8 THE IDEA OF TABLEAUX

The truth-deriving procedures Llull suggested were mainly two. One proceeded in the positive sense: concepts were combined (following the directing graphs) and, if mutually reinforcing, they proved the conclusion "by analogy". The negative dual was that at some point the concepts that were being currently manipulated turned out to be mutually inconsistent (contradictory); that meant that the initial postulated truth was automatically disproved, thereby proving the contrary. This is the first appearance in the literature of something not unlike Beth's 1955 semantic tableaux (or Popper's 1959 refutational ideas in Science). It is, however, a mere l3th-century anticipation of present-day developments, which -unlike all the other insights mentioned- have not been directly influenced by Llull's ideas or by Leibniz's rendition of them.