We find things causally connected together in our experience, but in order to talk about causation we have to recognize these connections as causal, which means we have to supply the Idea of Cause and actively apply it to what we experience. As usual, Whewell insists that the Idea is actively drawn from our own minds, not passively received from outside our minds; and we can tell because, unlike our experiences of causal situations, which are particular, contingent, etc., we can, and do, and sometimes must, make rigorously universal and necessary claims about causes, claims which will go well beyond anything we actually have experienced. "Every effect has a cause" is necessarily, universally, rigorously true; not merely probably, usually, and as far as we can tell. The modal disparity between our experiences and our claims means that our mind is actively performing an induction, taking an Idea or Conception and organizing experience with it. The arguments of people like Hume do have some force: when we see one billiard ball striking another, we just see one thing happen and then another thing happen. Our understanding of causes, however, does not see them solely in this light; we do not merely passively observe billiard balls doing this then that -- we recognize the one ball as striking the other and making it move. Because of this, Whewell agrees with the response of Scottish metaphysicians to Hume -- an adequate account of causation must account for the universality of our Idea of Cause in a way that Hume's doesn't. And likewise he agrees with Kant's response to Hume -- an adequate account of causation must account not just for the universality but also for the necessity involved in our Idea of Cause. And Whewell thinks that something like this is necessary to account for serious physics at all, which can be seriously called knowledge because it applies necessary truths about causes to causes in the world (p. 176):
Axioms concerning Cause, or concerning Force, which as we shall see, is a modification of Cause, will flow from an Idea of Cause, just as axioms concerning space and number flow from the ideas of space and number or time. And thus the propositions which constitute the science of Mechanics prove that we possess an idea of cause, in the same sense in which the propositions of geometry and arithmetic prove our possession of the ideas of space and of time or number.
When we consider the Idea of Cause, then, we can formulate Axioms expressing the necessity and universality of the Idea. For our purposes, there are three Axioms in particular that are important, which might be colloquially formulated in the following way.
I. Nothing can take place without a cause.
II. Effects are proportional to their causes, and causes are measured by their effects.
III. Reaction is equal and opposite to action.
The first of these is in some sense the most general Axiom possible for the Idea of Cause; if you are talking about Causes in a sense where the first axiom is false, you are not actually talking about the Idea of Cause itself, but about something else that you are associating with the Idea. It is for practical purposes self-evident; even if we attempt to deny it, we will find our reasoning continually slipping back into a format that presupposes that it is true. What is more, since science studies causes, the first Axiom is absolutely essential to scientific inquiry; it is virtually its constitutive principle.
With the second Axiom we consider not merely Cause as such, but causes insofar as they can be compared with other causes. When we talk of force, for instance, we talk of one force as being greater than another; we also talk of some causes as having greater scope or power. So how do we generally identify this greater-than relation among causes? We look at the effects, and compare causes in terms of their effects (p. 179): "Hence the effect is an unfailing index of the amount of the cause; and if it be a measurable effect, it gives a measure of the cause." It is true that this can sometimes be more complicated than it sounds -- causes can sometimes be added together, for instance -- but the complications can themselves be seen as merely more complicated applications of the one Axiom, sometimes with the addition of other assumptions for the particular kind of cause we are considering.
Whewell is always somewhat more obscure when talking about the third Axiom, but it seems from a number of things he says that he takes the Axiom to apply whenever we have a Cause effecting motion -- or building a tendency to motion -- in something capable of resisting in some way. The most obvious example of this is the movement of bodies, and these are the examples Whewell most often uses. We recognized that bodies exist because they resist us. When we press on a body, we can make it move, but the body presses on us as we are pressing on it. At least in these resisting cases, then, causation is naturally understood to be mutual: I press the wall, the wall presses me, these are equal and opposite, so that I am the cause of some kind of tendency to motion in the wall and the wall is the cause of some kind of tendency to motion in me, according to a common rule. Each can be regarded as cause, each can be regarded as effect, and they mutually depend on each other. Thus, just as the second Axiom considers Cause under the condition of measurement, so the third Axiom considers it under the condition of mutuality in a common rule of measurement. One way of understanding this, which allows us to recognize why Whewell considers this Axiom to be very important, is that when we are talking about causes in real life we are usually talking about changes in causal terms. We experience a change, and then we use the Idea of Cause to clarify what the causal action is. And if we are simply interested in describing the cause-effect link, we are simply trying to give a rule for their going together; and therefore we will have a causal action insofar as it is exerted by the cause and the same causal action insofar as it is received in the effect, and it won't generally matter which way we're looking at it. In causal matters, action always has something that can be identified as a reaction. Thus the necessary connection of action and reaction seems to be taken by Whewell to be perfectly general. The equality is not always going to be possible to assume, because we can't rule out the possibility that action and reaction, while related, may not be commensurable in a way that allows us to talk about equality (we may not be able to establish a common rule). But in physical causes of physical changes, the action and reaction both admit (at least in principle) of being measured in physical terms and therefore being linked with each other according to a common rule of measurement. If a hot body and cool body come into contact, the hot body warms the cool body, the cool body cools the hot body; these can be measured and placed under a common rule, as we do in thermodynamics. And this just is to apply the third Axiom to such a particular case.
Anyone with a basic familiarity with Newton's Laws can no doubt see where Whewell is going here. It is important to reiterate, however, that these three Axioms are not the Laws of Motion. They are general causal principles; they do not assume that we are talking about changes of motion, and they do not make any assumption about whether we are dealing with some kind of force or not. There are many different kinds of things that fall under the Idea of Cause, each of which needs to be regarded on its own terms, and there is no need to conflate them. Historians have every right to talk about historical causes, for instance; they are not at all required to think of them as physical forces, or even as reducible to physical forces. Whewell is open to the idea that it might turn out that causes in two different fields turn out to be, at base the same kind of cause -- he calls the 'jumping together' of two apparently different fields under one Idea or Conception consilience, and he thinks that this is one of the more important markers of genuine scientific progress. But consilience arises from inquiry as a sort of conclusion; there is absolutely nothing about that inquiry itself that requires us to start with the assumption that the kinds of causes considered by historians will turn out to be nothing but physical forces. And, indeed, Whewell, like most British Newtonians in the nineteenth century, thinks that there are cases of causes that certainly aren't explicable in terms of physical forces, although physical forces may ultimately be explicable in terms of them -- namely, immaterial causes. However, anywhere there is any kind of cause and effect, whether or not it is physical or not, the first Axiom will hold; anywhere we can measure the effect, the second Axiom will hold; and anywhere we can measure the cause and effect according to a common rule, the third Axiom will hold. Even in the physical sciences, there is no absolute a priori reason why we should think that Forces in statics are exactly the same kinds of things as Forces in dynamics (for instance); they both qualify as Forces, but that doesn't mean there are no differences between them. This has to be clarified down the road; we cannot merely assume that all causes, or even all forces, are of exactly the same kind.
In order to get from the Idea of Cause to Newton's Laws of Motion, we have to narrow down the Idea of Cause to get the Idea or Conception of Force. (Whewell often uses the word 'Conception' to indicate that we are dealing with a Fundamental Idea that has been specified to a particular kind of situation; but he is not entirely consistent in doing this, and, indeed, argues that it's hard to draw any sharp lines.) Whewell thinks we get the Conception of Force primarily from our consciousness of our own endeavors. We feel ourselves exerting force, and our first real acquaintance with anything that can clearly be considered a cause of change of motion is our own ability to change things by muscular exertion. This kind of causation clearly has a direction, and so we recognize Force as being a directed causation producing changes in motion and rest. There are, in fact, several features of ordinary experience that guaranteed that this Conception remained rather vague and obscure for a very long time. The foundations of mechanics as a science were already implicit in the Conception of Force and the Axioms of causation as applied to this Conception; but ordinary experience has a number of ambiguities that can trip us up. These are the usual things that are mentioned in histories of physics -- friction and air resistance and the like, which complicate measurement. In order to get mechanics out of our Conception of Force, we need systematic experiment and progressively better observation in order to get measurements right, and also need to think through the implications of something's being a cause of motion in particular (and, for instance, how that might differ from being some other kind of cause).
The same consciousness that gives us the Conception of Force also gives us the Conception of Body, or as we might also call it, Matter, as something resisting, and likewise Solidity or tangibility. Given this we can start to formulate some notion of Inertia which is the inertness or tendency of a body to be stubborn and push back when pushed. Making sense of these things require all three of the Axioms, and the third in particular, and thus we have the possibility of a science of mechanics. It's worth stating again that we need not merely reasoning from Axioms but also reliable empirical measurement if we are to build the science of mechanics. Whewell does not think you can magically pull Newton's Laws out of the three causal Axioms alone; to get each Law of Motion requires applying the Axioms to a particular kind of situation (when the causes are forces) and clarifying the way in which those Axioms apply in that particular situation. This means that Newton's Laws have a necessary aspect (derived from the causal Axioms) and an empirical aspect (derived from experimental and observational measurement of forces and motions in particular), and both are absolutely essential to how they should be understood. To see how this works, we need to turn to the Laws themselves, so the next post in this series will look at how Whewell's account applies to Newton's First Law.