Here is a passage from Leibniz where he half decrypts half encrypts the big idea sparking his discovery of the differential calculus.
It is true that God sees all at once the whole sequence of this universe, when he chooses it, and that thus he has no need of the connexion of effects and causes in order to foresee these effects. But since his wisdom causes him to choose a sequence in perfect connexion, he cannot but see one part of the sequence in the other.
It is one of the rules of my system of general harmony, that the present is big with the future, and that he who sees all sees in that which is that which shall be.
What is more, I have proved conclusively that God sees in each portion of the universe the whole universe, owing to the perfect connexion of things. He is infinitely more discerning than Pythagoras, who judged the height of Hercules by the size of his footprint. There must therefore be no doubt that effects follow their causes determinately, in spite of contingency and even of freedom, which nevertheless exist together with certainty or determination.
I have a vague memory of having once looked on the Latin text, where the word big was gravis, meaning pregnant, in the original. But it was a long time ago, and I’ll need to check that out again sometime.
Incidentally, working out the logical analogue of differential calculus is the object of my efforts on differential logic. This work led me to develop an extension of Peirce’s alpha graphs that is efficient enough in both conceptual and computational terms to carry the load. For an introduction, see the following articles.
- Differential Logic • Introduction
- Differential Logic • Part 1 • Part 2 • Part 3
- Differential Propositional Calculus • Part 1 • Part 2
- Gottfried Wilhelm (Freiherr von) Leibniz, Theodicy : Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil, edited with an introduction by Austin Farrer, translated by E.M. Huggard from C.J. Gerhardt’s edition of the Collected Philosophical Works, 1875–1890. Routledge 1951. Open Court 1985. Paragraph 360, page 341.
cc: Peirce List