The notions or categories of causality and determinism have accompanied the formation of modern sciences, and primarily those of physics. The current nowaday use tends often, but wrongly, to get them identifed in the reevaluations to which they are submitted in physics itself. In this work we intend to clarify the first of these notions, more precisely physical causality, by following its elaboration with the beginnings of dynamics, through its first utilizations and conceptualizations in the making of the mathematization of mechanics, before being extended to physics in a general way. We will see how, while having been supported by one of the traditional philosophical aspects of the idea of causality (that one of "efficient cause"), physical causality breaks with the metaphysical meaning that was previously attached to it. Rather more than in the Newton's Principia, it is in the re-elaboration made by d'Alembert, in his Treatise of dynamics, of the laws of motion considered as principles, and expressed by differential calculus, that the idea of physical causality is explicitly considered indissociably of its effect, that is the change of motion. The respective thoughts of Newton and d'Alembert on the notions of cause and force are, in this respect, in opposition with regard to the properly physical nature of this change. The change of motion was viewed by d'Alembert as immanent to motion, for its cause could be circumscribed by its effect, whereas it remained mathematical and metaphysical in the newtonian conception of the external force taken as a mathematical substitute of the cause, which was the common way to consider forces before Lagrange's analytical mechanics. It was the physical conception inherited from d'Alembert that should then prevail through lagrangean analytical mechanics that permitted to re-integrate physically and rationally the concept of force in its eulerian differential transcription.
Causality; Physical causality; Efficient cause; Time; Legality; Galileo; Descartes; Newton; Kant; d'Alembert; Lagrange; Differential and integral calculus; History of dynamics; History of mechanics