Equilibrium and Explanation in 18th Century Mechanics

The received view of the Scientific Revolution is that it was completed withthe publication of Isaac Newton's (1642-1727) {em Philosophiae NaturalisPrincipia Mathematica} in 1687. Work on mechanics in the century or more following was thought to be merely a working out the mathematical details ofNewton's program, in particular oftranslating his mechanics from its synthetic expression into analytic form. Ishow that the mechanics of Leonhard Euler (1707--1782) and Joseph-LouisLagrange (1736--1813) did not begin with Newton's Three Laws. They providedtheir own beginning principles and interpretations of the relation betweenmathematical description and nature. Functional relations among the quantifiedproperties of bodies were interpreted as basic mechanical connections betweenthose bodies. Equilibrium played an important role in explaining the behaviorof physical systems understood mechanically. Some behavior was revealed to bean equilibrium condition; other behavior was understood as a variation fromequilibrium. Implications for scientific explanation are then drawn fromthese historical considerations, specifically an alternative account ofmechanical explanation and unification. Trying to cast mechanicalexplanations (of the kind considered here) as Kitcher-style argument schemafails to distinguish legitimate from spurious explanations. Consideration ofthe mechanical analogies lying behind the schema are required