Gottfried Leibniz

Gottfried Wilhelm von Leibniz (also Leibnitz) (Leipzig July 1 (June 21 O.S.), 1646 – November 14, 1716 in Hannover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer.

Leibniz's work on formal logic

The principles of the logic of Leibniz, and consequently of his whole philosophy, reduce to two:

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• All our ideas are compounded of a very small number of simple ideas which form the alphabet of human thought.
• Complex ideas proceed from these simple ideas by a uniform and symmetrical combination which is analogous to arithmetical multiplication.

With regard to the first principle, the number of simple ideas is much greater than Leibniz thought; and, with regard to the second principle, logic considers three operations -- which are now known as logical multiplication, logical addition, and negation -- instead of only one.

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Characters were, with Leibniz any written signs, and "real" characters were those which represent ideas directly—as the Chinese ideography was thought to—and not the words for them. Among real characters, some simply serve to represent ideas, and some serve for reasoning. Egyptian and Chinese hieroglyphics and the symbols of astronomers and chemists belong to the first category, but Leibniz declared them to be imperfect, and desired the second category of characters for what he called his universal characteristic. It was not in the form of an algebra that Leibniz first conceived his characteristic, probably because he was then a novice in mathematics, but in the form of a universal language or script. It was in 1676 that he first dreamed of a kind of algebra of thought, and it was the algebraic notation which then served as model for the characteristic.

Related Topics:
Characters - Chinese ideography - Hieroglyphic - Universal characteristic - Algebra of thought

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Leibniz attached so much importance to the invention of proper symbols that he attributed to this alone the whole of his discoveries in mathematics. And, in fact, his infinitesimal calculus affords a most brilliant example of the importance of, and Leibniz's skill in devising, a suitable notation.

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