On the origins and foundations of Laplacian determinism
Abstract
In this paper I examine the foundations of Laplace's famous statement of determinism in 1814, and argue that rather than derived from his mechanics, this statement is based on general philosophical principles, namely the principle of sufficient reason and the law of continuity. It is usually supposed that Laplace's statement is based on the fact that each system in classical mechanics has an equation of motion which has a unique solution. But Laplace never proved this result, and in fact he could not have proven it, since it depends on a theorem about uniqueness of solutions to differential equations that was only developed later on. I show that the idea that is at the basis of Laplace's determinism was in fact widespread in enlightenment France, and is ultimately based on a reinterpretation of Leibnizian metaphysics, specifically the principle of sufficient reason and the law of continuity. Since the law of continuity also lies at the basis of the application of differential calculus in physics, one can say that Laplace's determinism and the idea that systems in physics can be described by differential equations with unique solutions have a common foundation.
We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. An intelligence which … (Laplace, 1814, p. 3).
 Publication:

Studies in History and Philosophy of Science
 Pub Date:
 March 2014
 DOI:
 10.1016/j.shpsa.2013.12.003
 Bibcode:
 2014SHPSA..45...24V
 Keywords:

 Determinism;
 Laplace;
 Leibniz;
 Principle of sufficient reason;
 Continuity