Russell's book on Leibniz appeared in 1900. That it is important, because of its subject and because of its author, hardly needs to be argued. An examination of it, or of parts of it, after more than half a century is therefore in order. Yet the title I chose indicates only part of my intent. The other part is to examine certain ideas, irrespective of what either Leibniz or Russell thought and of what the latter thought about the thoughts of the former. The title best suited to this part is Individuals, Natures, Relations, and Change. The mixed form of presentation, analytic and quasihistorical, has very great advantages. For the nature of the philosophical enterprise is such that an analyst is lost without some grasp or, at least, some image of “structural history.” The danger is that only very few, if any, are masters of two trades; in this case, logical analysis and historical scholarship. I, for one, make no pretense whatsoever of being a scholar. Naturally, I have read in Leibniz; and I did not skip or take lightly anything in the letters to Arnauld and Clarke; but I have by far not read everything that is available. Reading about Leibniz, aside from Russell, of which I did but little, I found Latta and, particularly, Joseph sometimes helpful. More often, though, I felt that the former's Hegelianism and the latter's Aristotelianism had got between them and their subject.

We have undertaken to discuss the nature of mathematical systems, the way in which they are discovered, and the uses to which they are put in the empirical sciences. The empirical sciences employ mathematical systems in framing final formulations, but adopt mathematical techniques long before reaching that stage. It is a prerequisite that the mathematics they employ has been developed separately and within its own domain. We shall return to the relation between mathematics and the empirical sciences before we are done, but in the meanwhile we shall be constrained to begin by discussing the situation in mathematics in isolation from any empirical considerations.

The concept of simultaneity, and the associated problems of synchronization of moving clocks and establishment of a universal time scale, were given little or no attention prior to the twentieth century. In 1905, however, Einstein analyzed the concept of simultaneity on the basis of two principal postulates:

1. (1) Absolute velocity is meaningless (relativity postulate),

2. (2) The velocity of light in a vacuum is the same for all unaccelerated observers.

I wish to take issue with a statement in the report by Dr. Max Rieser on the International Congress for the Philosophy of Science, which appeared in the October 1955 issue of your journal. It reads: “As for an explanation of the unexpected absence of the scholars of the satellite countries, it should be borne in mind that they were all educated and grown up before the communist revolutionary upheaval and therefore naturally more susceptible of defection from the Marxist orthodoxy than the Russians. …”