Still life with Leibniz
Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, Ch. 5 §26
Connected with the Identity of Indiscernibles is the assertion that every substance has an infinite number of predicates. That this must be the case, is evident from the mere fact that every substance must have a predicate corresponding to every moment of time. But Leibniz goes further than this. The state of a substance at each moment is analyzable into an infinite number of predicates. This might itself be deduced from the fact that the present state has relations to all past and future states, which relations, according to Leibniz, must affect the present state—indeed it is in this that their truth consists. But another factor is the representation of the whole universe, which necessarily involves infinite complexity in each state of each substance. This infinite complexity is a mark of the contingent. There is a difference, Leibniz says, between the analysis of the necessary and that of the contingent. The analysis from the subsequent by nature to the prior by nature comes to an end in necessary matter with the primitive notions, as the analysis of numbers ends with unity. But in contingents or existents, this analysis goes to infinity, without ever reaching primitive elements.∗ Again he points out that it is impossible for us to have knowledge of individuals, and to determine exactly the individuality of anything.
∗ Russell here cites (G. III. 582), and this passage is a convenient elaboration of a portion of Leibniz’s letter to Bourguet found there: “Il y a de la difference en cela entre l'analyse des necessaires, et l'analyse des contingens: l'analyse des necessaires, qui est celle des essences, allant a natura posterioribus ad natura priora, se termine dans les notions primitives, et c'est ainsi que les nombres se re solvent en unités. Mais dans les contingens ou existences cette analyse a natura posterioribus ad natura priora va à l'infini, sans qu'on puisse jamais la reduire à des elemens primitifs.”