Essai de représentation par des nombres réels d'une analyse infinite des notions individuelles dans une infinité de mondes possibles

Abstract

The aim of this study is to try to make use of real numbers for representing an infinite analysis of individual notions in an infinity of possible worlds.

As an introduction to the subject, the author shows, firstly, the possibility of representing Boole's lattice of universal notions by an associate Boole's lattice of rational numbers.

But, in opposition to the universal notions, definable by a finite number of predicates, an individual notion, cannot (as Leibniz pointed out) admits this sort of definition, because each state of an individual subject is characterized by the values (present or absent, applicable or inapplicable) taken by an infinite number of predicates, each of whom may appear or disappear in the next state.

The notion of “degree of identification of an individual notion” is then introduced and arithmetized by a rational number.

As an individual notion can be defined by a convergent succession of degrees of identification, the real characteristic number of such an individual notion can be defined by the corresponding convergent succession of rational numbers, satisfying Cauchy's conditions for the convergence of successions.