A PRAGMATIC INTERPRETATION OF NEWTON’S RULES

saying how the rules are pragmatic, here is how I suggest interpreting (or re-interpreting) them.

1. Given that your aim is to establish a general causal law on the basis of observed phenomena, you will need to intro­duce a cause or causes of those phenomena.

2. When you introduce a cause or causes for a given phenomenon, try (“so far as possible”) to assign those causes to other phenomena of the same kind. This means trying to determine empirically whether such an assignment is warranted by those phenomena. For example, if it has been empirically established that the fact that the acceleration of unsupported bodies toward the earth is caused by an inverse­square force of attraction exerted by the earth, try to deter­mine empirically how our moon orbiting the earth would accelerate toward the earth if it suddenly lost its inertial motion—in order to see whether the same cause could be assigned to both motions. To do this, we do not assume that nature is simple, or that simplicity is a sign of truth, even if we agree that the hypothesis that one force is acting here is simpler than the hypothesis that the forces acting here are not the same.

3. Given that you are trying to establish a law governing the cause(s) introduced, you will need to generalize. If you have empirically established that some causal property holds for all the bodies you have observed, then try to generalize this to all bodies, or if exceptions are discovered, try to gen­eralize to some restricted class of bodies. The generalization you make is to be justified empirically by reference to what sort of bodies, and how many, were selected for observation, what else is known about such bodies, how the observations were made, and so forth. It is not to be justified by assuming that “nature is always simple and ever consonant with itself.”

4. If you have followed rules 1 to 3 in an empirically de­fensible way, and have arrived at a causal law, then you may infer that the law is true or approximately true. You are jus­tified in doing so until phenomena are discovered that cast doubt on the law as it stands.

Rules 1 to 3 tell you what you should try to do if you want to establish a causal law. Rule 4 tells you that if you have followed rules 1 to 3, and have done so (and not merely tried to do so) in an empirically defensible way, then you are justified in inferring the truth or approximate truth of any law you have arrived at. If you infer a cause of certain phenomena without sufficient empirical argument that the cause exists and does in fact produce the phenomena, or if you have generalized the cause you have inferred to other cases without having observed sufficiently many and varied instances, then you are not justified in inferring the law. 'lhe fact that you have made a causal inference or an inductive one does not count at all in favor of the truth or probability of your conclusion. Nor does it count that you have tried to make an inference that is empirically warranted. It depends entirely on whether the causal or inductive inference is empirically warranted.

'lhe causal-inductive rules 1 to 3 themselves do not provide an epistemic justification for believing the con­clusion.

I have spoken of an inference as being “empirically warranted” or “empirically defensible.” How is that to be determined, except by appeal to rules? And if the latter are Newton's rules, either in my formulation or his, all of this becomes circular. My response is that determining whether inferences are empirically warranted or defensible is an em­pirical and a local matter, not subject to general a priori causal or inductive rules that tell you what you can or should reasonably infer from what. As John Stuart Mill—a cham­pion of induction—noted, whether an inductive inference from “all observed As are Bs” to “all As are Bs” is empiri­cally warranted depends on, and varies with, the nature of the As and Bs in question, the size and variety of the sample of observed As, how the sample was selected for observation, and so forth—all empirical matters. Saying simply that the nature of the As and Bs, and the size, variety, and the method of selection of the sample should be “appropriate” to make the inference is both vague and circular. When we assess Newton's inference to the claim that the force causing bodies to fall toward the earth is the same force as that which causes the moon to fall toward the earth, we do so by examining the calculations and empirical laws he is using in proposition 4 (the moon argument).

Newton's rules, in my formulation, might be criticized as being rather trivial. 'lhey say, in effect: make causal and inductive inferences from observed phenomena, so long as you are empirically justified in doing so. It is a bit like giving the following rule of strategy to a chess player: checkmate your opponent's king when you can—without telling the chess player how to do so. (Indeed, William Whewell, a se­vere critic of Newton's rules, but not his physics, invoked this sort of criticism.)

I believe Newton would reply, and rightly so, that the rules, even in my formulation, are not so trivial. Newton was concerned to distinguish his methodology from two others of which he was very critical. One was Descartes' ra­tionalist methodology (as expressed, e.g., in his “Rules for the Direction of the Mind”). The other was hypothetico- deductivism of a sort practiced by Christiaan Huygens. In response to Descartes' idea that you defend a law of nature by showing how it follows deductively from a priori intuitions— basic self-evident propositions (such as “all bodies are ex­tended in space”) that cannot be doubted—Newton replied that it cannot be done: “The extension of bodies is known to us only through our senses,” not by some a priori “intui­tion.” In response to the hypothetico-deductivist idea that it suffices to defend a law, such as the law of gravity, by showing that it explains and predicts observed phenomena (which Newton called “synthesis”), Newton replies that you need to show more. You need to argue empirically from the phe­nomena that the cause of those phenomena is gravity, and not something else, and that this cause can be generalized to all bodies.

In what way are these rules pragmatic? They are so in the sense that they tell you what you should try to do if you have a certain end in mind: if you want to defend a causal law, at least one that is not derivable from other established causal laws, then you should try to make a causal infer­ence to the existence of the cause from the observed phe­nomena, and you should try to generalize this by appealing to a range of other observed cases. Other methods, such as Cartesian rationalism and hypothetico-deductivism, will not suffice to defend the law in a way that provides a jus­tification for believing it. But in this sense, aren't Newton's rules, as he formulated them, pragmatic as well? Don't they also tell you how to try to defend a causal law? If so what's the difference?

'lhe answer is that, in my formulation, the rules are merely pragmatic, while in Newton's formulation, they are supposed to be epistemic as well. Because Newton believes that nature is simple, and because he bases his Rules 1-3 on that assumption, he can appeal to the rules themselves as providing a crucial part of the justification for believing the inferred causal law: it is because “nature is simple and does not indulge in the luxury of superfluous causes” that, from the facts about the moon introduced in the “moon ar­gument,” and from facts about how bodies fall to the earth, Newton can invoke his Rule 2 to infer that the force keeping the moon in its orbit is the same force as that producing falling bodies on the earth. On my interpretation, if you follow the rules above, you are not justified in believing the conclusion you reach—unless you have followed the rules in an empirically justified way, which the rules themselves don't tell you how to do. If you follow Newton's original rules, then, he claims, you are justified in believing the conclusion.

In the present formulation of Newton's rules, simplicity plays no ontological or epistemic role. In using these rules, you do not have to assume that nature is simple or that simpler theories are more likely to be true than complex theories.

Finally, as noted earlier, you may have followed rules 1 to 3 as I have formulated them, and reached a causal-inductive conclusion without being epistemically justified in believing the conclusion, despite your best efforts. If so, and if you have no other arguments for the conclusion that provide a suffi­cient epistemic basis either, then that conclusion is a specu­lation for you (in a sense of speculation understood in terms of ES-evidence). I suggest that Newton's argument can be understood as one that follows the pragmatically formulated rules I propose, even though his argument does not provide a sufficient empirical basis for someone in his epistemic sit­uation to believe the law of gravity in its most general form. What it does do is provide reasons for someone in that epi- stemic situation to pursue the law, take it seriously, and try to find additional evidence for it—in short, reasons to try to turn a speculation into an empirically established proposi­tion—one that is “deduced from phenomena.”