(2014) Perspectives on theory of controversies and the ethics of communication, Dordrecht, Springer.
On the "sum of all differences" and the origin of mathematics according to Leibniz
mathematical and philosophical aspects
The principle of identity played an important part in Leibniz's system of the world. He situated it at the very foundation of mathematics (cf. letter to Clarke). Such a principle, however, now seems to be so general and abstract that one can hardly believe that we are able to derive all the mathematics from it. However, we have to trust on Leibniz and his systematic mind to have written in his letters to Clarke only what he truly felt and had felt for a long time. The purpose of the present study is to establish the truth of his statements by explaining how Leibniz perceived and used this principle in the effective creation of both the calculations and the concepts of his mathematics.For Leibniz, the actual mathematical embodiment of the principle undoubtedly was (as he called it) the "sum of all differences," an important mathematical procedure, which was only invented by Leibniz, and is still in use today. In this perspective, I successively examine in this paper the Arithmetical triangle in De Arte Combinatoria, then in the Differential Calculus, and finally the Harmonic triangle.
Serfati, M. (2014)., On the "sum of all differences" and the origin of mathematics according to Leibniz: mathematical and philosophical aspects, in D. Riesenfeld & G. Scarafile (eds.), Perspectives on theory of controversies and the ethics of communication, Dordrecht, Springer, pp. 69-80.
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