The Metaphysics of Impenetrability: Euler's Conception of Force

IN this paper I want to examine in some detail one eighteenth-century attempt to restructure the foundations of mechanics, that of Leonhard Euler. It is now generally recognized that the idea, due to Mach, that all that happened in the eighteenth century was the elaboration of a deductive and mathematical mechanics on the basis of Newton's laws is misleading at best. Newton's Principia needed much more than a reformulation in analytic terms if it was to provide the basis for the comprehensive mechanics that was developed in the eighteenth century. Book II of the Principia, in particular, where the problem of the resistance offered to the motion of a finite body by a fluid medium was raised, was generally (and rightly) thought to be in large part mistaken and confused. There were also a number of areas crucial to the unification of mechanics which Newton did not deal with at all in the Principia: particularly the dynamics of rigid, flexible and elastic bodies, and the dynamics of several bodies with mutual interactions. Although a start had been made on some of these topics in the seventeenth century (notably by Galileo, Beeckman, Mersenne, Huygens, Pardies, Hooke, and Leibniz), it was only in the eighteenth century that they were subjected to detailed examination, and Euler's contribution to the development of these topics, and hence to the unification of mechanics, was immense.' Running parallel with this extension and unification of mechanics, there was also a growing concern with foundational questions. These centred upon Newton's conception of force. The general attitude to this conception was one of ambivalence, but many in the eighteenth century thought it to be at best seriously incomplete and at worst an 'obscure and metaphysical being capable of nothing but spreading darkness over a * Department of General Philosophy, University of Sydney, N.S.W. 2006 Australia. This paper arose out of a much shorter version presented at a seminar in the Department of History and Philosophy of Science, University of Melbourne, during my time spent there as a Visiting Research Fellow. I am grateful to the participants in the seminar for their comments and particularly to Rod Home for his comments on a draft of the paper. The final version of the paper has benefited from the comments of two anonymous referees.