From Preface to the General Science, 1677:
Whence it is manifest that if we could find characters or signs appropriate for expressing all our thoughts as definitely and as exactly as arithmetic expresses number or geometric analysis between lines, we could in all subjects in so far as they are amenable to reasoning accomplish what is done in Arithmetic and Geometry.
For all inquiries which depend on reasoning would be performed by the transpositions of characters and by a kind of calculus, which would immediately facilitate the discovery of beautiful results. For we should not have to break our heads as much as is necessary today, and yet we should be sure of accomplishing everything the given facts allow.
Moreover, we should be able to convince the world what we should have found or concluded, since it would be easy to verify the calculation either by doing it over or by trying out tests similar to that of casting out nines in arithmetic. And if someone would doubt my results, I should say to him: “Let us calculate, Sir,” and thus by taking to pen and ink, we should soon settle the question.
(It is painfully clear to me that Leibniz never met a Liberal Arts major. We would be absolutely horrified of each other.)
One more line, and I promise I will stop:
This language will be the greatest instrument of human reason.
I daresay that this is the highest effort of the human mind, and when the project will be accomplished it will simply be up to men to be happy since they will have an instrument which will exalt reason no less than what the Telescope does to perfect our vision.
I’ll be happy when I don’t have to calculate anything, Gottfried…