Gottfried Wilhelm Leibniz was the last schoolman and the first modern logician. He invented different types of formalization of Aristotelian logic which in parts anticipated George Boole's calculus. Most of Leibniz' papers had not been published until about 1900, thus he has exerted only little influence on the development of modern logic. The papers in this section deal with his calculus of characteristic numbers which he invented in April 1679. It is a complete arithmetization of Aristotelian logic in its intensional interpretation. The characteristic numbers have been used by Lukasiewicz in his formalisation of Aristotelian logic and may have been a source of inspiration for Gödel in his famous arithmization of predicate logic.

• On Leibniz' characteristic numbers
  Studia Leibnitiana Band 43/2002, Seite 161
  147 k [PDF] Opens new window


• G. W. Leibniz - die Utopie der Denkmaschine
  228 k [PDF](in German) Opens new window


• On Negation in Leibniz' System of Charachteristic numbers
  221 k [PDF]. Opens new window
In the spring of 1679, Leibniz invented a famous interpretation of Aristotelian logic by means of his characteristic numbers. Leibniz was able to show that, within his model, all classical laws of "positive" Aristotelian logic (a term logic without negation) hold, if one uses a certain proper arithmetical interpretation of the Aristotelian quantors A, E, I, and O. While this construction of characteristic numbers is a highly esteemed result today, Leibniz himself was apparently not content with his achievement. His last notes on this subject show how hard he struggled with different unsuccessful attempts of allowing also for term negation within his formalism. Later on he never resumed his work on characteristic numbers.
By proving a negative result on characteristic numbers we show in this paper why Leibniz was bound to fail, and we also demonstrate how to enlarge his system in order to include term negation in a formal correct way.