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Philosophy is a game with objectives and no rules.
Mathematics is a game with rules and no objectives.
Theology is a game whose object is to bring rules into the subjective.

Tuesday, December 9, 2008

Antecedents of Mathematical Logic

A striking aspect of Leibniz's thought was the recurring notion of a universal symbolic language. In 1666 he published an article entitled Dissertatio de arte combinatoria, with subtitle "General Method in Which All Truths of the Reason Are Reduced to a Kind of Calculation." This early work establishes the theme of the gigantic project which was Leibniz's lifelong goal. The project involved bringing together all knowledge in a single compendium, with each division of the arts and sciences reduced to its primary propositions and related to other subjects in such a way that any portion or desired fact could be extracted at will, and from which the whole body of human knowledge could be reconstructed. It would provide a tool for learning without a teacher and would point up areas in which further investigation was needed.

The most remarkable feature of the plan was the lingua characteristica, a system of symbols representing logical ideas which would constitute a universal language of reasoning and would facilitate thought in the same way that mathematical symbols facilitate calculation. In the Chinese ideogram, which represents a concept rather than a sound, Leibniz saw a possible model for his "alphabet of thoughts."

Although he was unable to bring to fruition either his grand design for an encyclopedia of knowledge or the symbolic language into which it was to be translated, Leibniz's ideas were embodied in the mathematical logic developed by George Boole and Giuseppe Peano in the 19th century and by Alfred North Whitehead and Bertrand Russell in the 20th, and these ideas foreshadowed modern cybernetics and computer theory.

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