1. See RuPL, Louis Couturat’s La logique de Leibniz, Paris: Alcan, 1901, RePL and Ish.
2. Thus in the Monadology Leibniz writes: “The passing state ticwhich enfolds and represents a multitude in unity or in the simple substance is merely what is called perception” (Monadology, #14, [1714]: G. VI. 608) Elsewhere, however, he implies that the state of a monad contains a multitude of minute perceptions at any time, as in his reply of July 1698 to Pierre Bayle’s criticisms (G.IV. 517–524) and his letter to Jean Bernoulli (21/2/1699: GM. III. 574–575). For further discussion of Leibniz’s theory of perception, see Mark Kulstad, “Some difficulties in Leibniz’s Definition of Perception”, pp 65–78 in LCIE.
3. See Russell’s Our Knowledge of the External World, London: Allen & Unwin, 1914, 1952, and his “On the Experience of Time”, The Monist, 25, 1915, pp 212–233, and “On Order in Time”, Proceedings of the Cambridge Philosophical Society 32, May 1936, pp 216–228. It is interesting to note that Russell retracts none of his criticisms of Leibniz’s relationalism in the preface to the second edition of RuPL in 1937, and never acknowledges indebtedness to him on this score in his papers on temporal order. Russell’s criticisms of Leibniz on dynamical grounds, on the other hand, contain the same confusion that exists in Leibniz’s writings, namely that between the relational nature of space and time and the relativity of motion to a particular frame of reference. It has been one of the great achievements of 20th century philosophy of science to demonstrate the independence of these two issues. But although Russell, Hike Leibniz, conflated ‘relational’ with ‘relative’ he almost put his finger on a fatal flaw of Leibniz’s theory: its inability to sustain a definition of sameness of place through time, or affine connection. For details of these points, see Howard Stein’s “Newtonian Space-Time”, The Texas Quarterly, Autumn 1967, pp 174–200.
4. Russell argues: “The definition of one state of a substance seems impossible without time. A state is not simple, on the contrary it is infinitely complex. It contains traces of all past states, and is big with all future states. It is further a reflection of all simultaneous states of other substances. Thus no way remains of defining one state, except as the state at one time.” (RuPL, p 52). Russell assumes here what he is supposed to be proving: that simultaneity cannot be defined except by presupposing an absolute time. Leibniz, on the contrary, is guilty of no such circular reasoning, since he defines simultaneity in terms of compatibility of states.
5. Although it is clear that Leibniz always regards the relation G as asymmetric, it is hard to see how this is justified by the appeal to the law of the series: for this law would determine not only all the states which come after any given state in the series, but equally all those which precede it too. The lack of explanation why G should be regarded as asymmetric must therefore be considered as a serious deficiency in Leibniz’s rationalistic foundation for time.