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.

Universal characteristic and calculus ratiocinator

What is usually understood by the name "symbolic logic", is what Leibniz called a calculus ratiocinator and is only a part of the Universal Characteristic. In symbolic logic Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set-inclusion, and the empty set; but the aim of Leibniz's researches was, as he said, to create "a kind of general system of notation in which all the truths of reason should be reduced to a calculus. This could be, at the same time, a kind of universal written language, very different from all those which have been projected hitherto; for the characters and even the words would direct the reason, and the errors -- excepting those of fact -- would only be errors of calculation. It would be very difficult to invent this language or characteristic, but very easy to learn it without any dictionaries". He fixed the time necessary to form it: "I think that some chosen men could finish the matter within five years"; and finally remarked: "And so I repeat, what I have often said, that a man who is neither a prophet nor a prince can never undertake any thing more conducive to the good of the human race and the glory of God".

Related Topics:
Symbolic logic - Calculus ratiocinator - Conjunction - Disjunction - Negation - Identity - Inclusion - Empty set

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In his last letters he remarked: "If I had been less busy, or if I were younger or helped by well-intentioned young people, I would have hoped to have evolved a characteristic of this kind"; and: "I have spoken of my general characteristic to the Marquis de l'Hôpital and others; but they paid no more attention than if I had been telling them a dream. It would be necessary to support it by some obvious use; but, for this purpose, it would be necessary to construct a part at least of my characteristic; -- and this is not easy, above all to one situated as I am".

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Leibniz thus formed projects of both what he called a characteristica universalis, and a calculus ratiocinator. It is not hard to see that these projects are interconnected, since a perfect universal characteristic would comprise a logical calculus. Leibniz did not publish the incomplete results which he had obtained, and consequently his ideas had no continuators, with the exception of Lambert and some others, up to the time when Boole, De Morgan, Schröder, MacColl, and others rediscovered his theorems. Frege remarked that his own symbolism is meant to be a calculus ratiocinator as well as a lingua characteristica.

Related Topics:
Calculus ratiocinator - Lambert - Boole - De Morgan - Schröder - MacColl - Frege

~ ~ ~ ~ ~ ~ ~ ~ ~ ~