This isn't Whewell's most complete discussion, but it's the one I happen to have on hand:
If we call to mind the axioms which we formerly stated, as containing the most important conditions involved in the idea of Cause, it will be seen that our conviction in this case depends upon the first axiom of Causation, that nothing can happen without a cause. Every change in the velocity of the moving body must have a cause; and if the change can, in any manner, be referred to the presence of other bodies, these are said to exert force upon the moving body: and the conception of force is thus evolved from the general idea of cause. Force is any cause which has motion, or change of motion, for its effect; and thus, all the change of velocity of a bodywhich can be referred to extraneous bodies,--as the air which surrounds it, or the support on which it rests,--is considered as the effect of forces; and this consideration is looked upon as explaining the difference between the motion which really takes place in the experiment, and that motion which, as the law asserts, would take place if the body were not acted on by any forces.
Thus the truth of the first law of motion depends upon the axiom that no change can take place without a cause; and follows from the definition of force, if we suppose that there can be none but an external cause of change. But in order to establish the law, it was necessary further to be assured that there is no internal cause of change of velocity belonging to all matter whatever, and operating in such a manner that the mere progress of time is sufficient to produce a diminution of velocity in all moving bodies. It appears from the history of mechanical science, that this latter step required a reference to observation and experiment; and that the first law of motion is so far, historically at least, dependent upon our experience.
William Whewell, Philosophy of the Inductive Sciences, vol. 1 (London: John W. Parker, 1847) pp. 217-218.
He also considers the other laws of motion in the same way, connecting them to basic causal principles.