What was mechanical about mechanics? : the concept of force between metaphysics and mechanics from Newton to Lagrange

The great debates of the 18th century about the true measure of living force and the principle of least action, etc., can only be understood in depth if we realize that, at that time, mechanics was more than just mechanics.

From Newton and Leibniz to Euler, Maupertuis, d'Alembert, and Lagrange, there was a metaphysical dimension to the pertinent issues, albeit partly at an implicit level.

This gave the debates their typical flavor and texture, and influenced their outcomes deeply.

On an explicit level, there was a progressive rejection of the traditional metaphysical approach to the foundations of mechanics.

This was accompanied by profound conceptual changes in mechanics, away from force conceived as a substance, like water, and toward force conceived as a relationship between the elements in a structure of space and time.

Thus these controversies helped to turn mechanics into the discipline we recognize today.