Sonntag, 26. Juni 2011

Leibniz' Dream

The Edge of Chaos
Gottfried Wilhelm Leibniz, who holds the distinction of being the only philosopher
a biscuit was named after, once expressed the hope that every philosophical dispute may be settled by calculation:
"The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [calculemus], without further ado, to see who is right." [1]
To this end, he proposed two concepts, which were to be employed in this calculation: the characteristica universalis, which was to be a kind of conceptual language, able to symbolically represent concepts of mathematics, science, and metaphysics alike, consisting of what he called real characters, capable of directly corresponding to an idea, embodying it in the way a number embodies the idea of quantity, as opposed to merely referring to it, as words do; and the calculus ratiocinator, a system or device used to perform logical deductions within the framework set by the characteristica.
It is not precisely clear whether Leibniz intended for the ratiocinator to be an actual machine -- after all, Leibniz was one of the pioneers of mechanical calculation machines with the construction of the Stepped Reckoner --, or merely an abstract calculus, a forerunner to modern symbolic logic -- whether it was software or hardware, so to speak.