Saturday, April 17, 2021

Footnote LN31

LN31. Two useful accounts of Leibniz's philosophy are found in Bertrand Russell's A Critical Exposition of the Philosophy of Leibniz (Cambridge 1900) and H. Wildon Carr's Liebniz (Little, Brown 1929). In his inimitable style, Russell throws a spotlight on many issues typically glossed over in standard texts. Carr's account of Leibniz's Monadology is succinct and perceptive.

I don't think Carr would agree with Russell that Leibniz was a closet atheist, though I can see why Russell thought so. Once the universe is off and running, in Leibnizian thinking, it appears that there is very little for God to do.

Though I am no Leibniz enthusiast, I draw attention to the brilliance of Leibniz's philosophical thinking, as understood by these two 20th Century British philosophers.

But, as Carr observes, Monadology is more a work of art than an instrument of truth.

Leibnez's monads were inspired by the new discoveries of the microscope: microbiotic life forms, or animalcules. He decided that it was "animalcules all the way down" in an infinite series, requiring the existence of infinitesimal monads, analogous to the infinitesimal quantities of calculus, which he helped to develop. Each monad is some sort of primeval soul.

As for evolutionary development of life forms, that could not be, according to Liebniz. The hierarchy of animalcules meant to him that all things were preformed, that each form of life tracked to a monad that was built in to it.

Yet one can pick up a whiff of the theory of evolution with his thought that life forms don't really die, but change form. The monadic souls march on. That notion certainly is evocative of the modern idea that DNA constitutes a "monad" of sorts, as we have from the book The Selfish Gene by Richard Dawkins (Oxford 1976).

A short proof of the Jordan curve theorem

The following is a proposed proof. Topology's Jordan curve theorem, first proposed in 1887 by Camille Jordan, asserts that an...