It is well known that in the seventeenth century, in the wake of the Galilean revolution, the question of the ontological foundations of physics was posed in a particularly acute manner. And when they tried to address it, the majority of Spinoza's contemporaries found themselves confronted with a problematic that in the end came down to the following alternative: either the new physics was ontologically true, but then it would have to be possible to deduce it, at least in its most general statements, from principles drawn from a metaphysics; or else it could not be so deduced, but then the question of its ontological validity would remain suspended, or would have to be resolved negatively. For Spinoza, to be sure, the second solution was out of the question. But it does seem that he was initially tempted to opt for the first. In a note to the Preface to the second part of the Short Treatise, just after having said, in Paragraph 7, that bodies are modes of the attribute of extension, he deduces immediately, in Paragraph 8, that the individual essence of each body is characterised by a certain ‘[proportion] of motion and rest’; and he specifies in Paragraph 12: ‘say of 1 to 3’. It is thus indeed a matter of a relation, in the strict mathematical sense, between a quantity of motion and a quantity of rest – whatever ‘quantity of rest’ might mean. And since the whole universe must be considered as a single individual, Spinoza will quite naturally come to say, in Letter XXXII, that the fundamental law of the physical world must be that of the conservation of the same relation between motion and rest at the level of nature as a whole (servata semper … eadem ratione motus ad quietem). From which, one might expect, all physics would have had to follow.

But it is notable that, in the Ethics itself, Spinoza abandons this formulation. In the definition of the physical individual that he gives us after Proposition 13 of Part II, he simply tells us that an individual consists in a set of bodies that mutually communicate their motions ‘in a certain fixed manner’ or ‘according to a certain law’ (certa quaddam ratione); but he does not tell us what this law is, nor even what type of law it is.