In a later remark in the Mechanics, Kant explicitly objects that “the terminology of inertial force (vis inertiae) must be entirely banished from natural science — Wosret
This is a pretty Newtonian declaration actually, insofar as Newton himself famously refrained from 'feigning any hypothesis ('
hypothesis non fingo') regarding
what force is. It could be said that Kant was just trying to carry though this declaration to it's end.
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Otherwise, the early modern debates over causality are actually really interesting. Christian Kerslake has a great book which covers alot of these 'contextual' issues, and one of his most important points I think is that the model of causality which we reflexively think of today (efficient causality) was, as he says, the least popular of all the available models of causality. Some excerpts:
"Both Hume and Leibniz are sensitive to the problems of justifying the concept of causality. This is in part due to the conjunction of available theories of causality in the eighteenth century: the notion that now strikes us as the most sensible approach to causality, that finite substances are responsible for the changes they cause in other substances (then called the theory of physical influx), was at the time the least popular. This was because the only way available to conceive the idea that a substance with a set of properties caused a change in another substance was through the explanation that there was a
transmission of properties from the first to the second, which was held to be inconceivable. Therefore, the notions of occasionalism and pre-established harmony became popular among philosophers as elaborate avoidances of physical influx.
On Hume: "...Hume’s philosophy can also be seen to arise from the failure of the physical influx theory: he can find no evidence from the senses of any ‘transmission’ of properties, given that all the senses provide us with are distinct impressions. Given a lack of objective ground for the order found in the world, Hume turns to custom, and, ultimately ... to the notion of a pre-established harmony."
On Kant, "One of Kant’s most celebrated moves in the
Critique of Pure Reason amounts to the construction of an abstract formalisation of the problem facing notions such as causality in the eighteenth century... . The concept of a causal relation must be synthetic: Leibniz, Kant and Hume all agree on this, if not in terminology. Furthermore, they agree in principle that the problem about causality concerns connections that should be, if they are to exist at all,
a priori. Kant’s notion of the
synthetic a priori simply names a problem faced by eighteenth-century philosophy – that of how to account for any possible
nonlogical a priori connections. How is one to synthesise
a priori two or more elements, whether they be Humean sensations, or Leibnizian perceptions?
...Kant will often address the situation functionally by simply saying that synthesis requires a 'third'. As Kant says in the Critique, ‘where is the third thing that is always requisite for a synthetic proposition in order to connect with each other concepts that have no logical (analytical) affinity?’ (
CPR A259). Kant’s answer as to what this
tertium quid is will vary enormously, but the ‘triangular’ structure of
a priori cognition will remain constant. As we will see, in the early writings Kant seeks the third thing between God and world (cf. LM 15, Ak. 28:52), whereas later time (A155/B194) and experience in general (A157/B196) are said to be third things".
On Newton and Kant: "To explain the interaction of substances, Kant appeals to universal gravitation, and this will remain as the extralogical formal principle for the reciprocal action (succession and coexistence) of his system right up to the ‘Inaugural Dissertation’. Universal gravitation, as the sphere of nature, is the ‘phenomenal eternity of the general cause’ (TP 405; Ak. 2:410). Any determinate relation between substances thus depends on the status of the ‘world-whole’ ... The principle of real, as opposed to logical, determination has its final ground in the whole. ... Against Leibniz, Kant wants both to affirm physical interaction, and also, with Newton, to shift the ground for the determination of forces to the
whole field of forces. As we will see shortly, this provides the rudiments for a scientific theory that resolves the physical influx controversies".
I wish I could quote the whole chapter, but the whole history is just so long and fascinating full of twists and turns - especially because, as Kerlsake points out, Kant actually changed his mind multiple times in the lead up to the CPR regarding the status of time, causality and force - all of which complicates his relation to Newton (quotes from Kerslake's
Immanence and the Vertigo of Philosophy).