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Published online by Cambridge University Press: 05 May 2010
Leibniz said that space and time are well-founded phenomena. Few readers can make much literal sense out of this idea, so I shall describe a small possible world in which it is true. I do not contend that Leibniz had my construction in mind, but I do follow Leibnizian guidelines. The first trick is to reverse the maxim that every monad mirrors the world from its own point of view. Points of view, and hence a space of points, can be constructed from a non-relational account of the perceptions of each monad. But we cannot fabricate space alone. We must build up laws of nature simultaneously. We must also employ a measure of the simplicity of the laws of nature. Moreover we require that, in a literal sense, the perception of each monad is a sum of its Petits perceptions. The identity of indiscernibles, in its application to space, is an automatic consequence of this construction. Although I shall examine only one possible world, there is a general recipe for such constructions, in which none of the above elements can be omitted. This is a striking illustration of the way in which the many different facets of Leibniz's metaphysics are necessarily inter-connected.
1 Ishiguro, Hidé, Leibniz's Philosophy of Logic and Language, London: Duckworth, 1972. p. 104Google Scholar. She made this point originally in “Leibniz's denial of the reality of space and time,” Annals of the Japan Association for Philosophy of Science, III (March, 1967).
2 Russell, Bertrand, The Principles of Mathematics, London: Allen and Unwin, 1903; 2nd edition 1937, pp. 219–221Google Scholar. In The Philosophy of Leibniz, Cambridge University Press, 1900Google Scholar, Russell attributes to Leibniz the view that all relational statements must be analysed into statements that involve a mind, and are thus subjective. See also his paper “The relations of number and quantity,” Mind, N.S.6.
3 Rescher, Nicholas, The Philosophy of Leibniz, Englewood Cliffs: Prentice-Hall, 1967.Google Scholar
4 Jeffreys, Harold, The Theory of Probability, Oxford: Clarendon, 1939; Third edition 1961, p. 47Google Scholar. There is a more general discussion of the simplicity postulate in his Scientific Inference, Cambridge: University Press, 3rd edition 1973.Google Scholar
5 Hacking, Ian. “Infinite analysis,” Stitdia Leibnitiana, 1974.
6 Sartre, Jean-Paul, Being and Nothingness, trans. Barnes, H.E., London: Methuen, 1957, p. 468.Google Scholar