Friday, March 26, 2021

Footnote Vhu53

Vhu53. In a jibe at empiricists, Leibniz compared them to unreasoning animals.
Common souls are ruled like empirics, purely by sense examples; but rational souls examine by reason (wherever possible) how far past examples are applicable to their present case. The brute souls, therefore, cannot apprehend necessary and general truths, just as an empiric can never be sure that what has often succeeded with him, without his knowing why, will again succeed with him in the future.
Further, said Leibniz,
It is probable there are rational souls more perfect than we are, we think of them as Genii and hope to be one day of their number. The order of the universe seems to require it.
As quoted in Leibniz by H. Wildon Carr (Little Brown 1929).

Footnote wyz23

wyz23. In Leibniz (Little Brown 1929), H. Wildon Carr writes:
The word monad originally was used to denote the unit of arithmetic, the monad, the dyad, the triad, etc. Yet even in ancient philosophy it was sometimes used to mean simply the individual, something which like the atom of Democritus was by definition indivisible. Leibniz meant by it a living being, using it to denote the individual which is really indivisible, as distinguished from a mathematical unit or atom, which is only indivisible by definition and cannot be indicated in any real existent. In modern philosophy the word had been used by Giordano Bruno in the identical meaning which Leibniz afterwards gave it, and Bruno had developed from it a doctrine in all essentials resembling Leibniz's conception. So striking is the resemblance that it seems as though Leibniz must have derived his doctrine from him. This cannot be the case, however, for Leibniz had worked out his system long before he adopted the name, and he had thought it out independently of any previously existing doctrine and of the name he afterwards gave it. The name monad is, in fact, employed for a new definition of substance, a definition intended to express the distinctive meaning of a new concept.

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...