appendix: what is a natural law?

Let me first elucidate the central issues concerning natural laws, and if what I am going to say is going to sound trivial, it is because I intend, I do not know with degree of success, to sound as trivial as I can - since I fear I may lose sight of the wood for the tress.

When Aristotle presented the two definitions of man, one as a rational animal and one as a featherless biped, he was hoping that everyone would find the one definition congenial, and the other problematic - chiefly be­cause both are true. The uncongenial definition would not be uncongenial were it false, he felt. This is why Antisthenes, who opposed Aristotle’s theory of definitions and who considered Aristotle a pompous professor anyway, threw in his face a plucked chicken, which is a featherless biped, to illustrate the falsity of the definition of man as a featherless biped and thus to dispel the uncongenial air about it. (Notice that the plucked chicken refutes ‘man is a featherless biped’ if and only if the word ‘is’ in it is symmetrical as in a definition.)

A few centuries later Sir Karl Popper, who has been called Antisthenes Redivivus, by the way, wrote a paper on the same topic, proposing the metaphysical hypothesis that for every universal statement which is not a law of nature there exists somewhere in the universe an instance contrary to it. Popper himself withdrew this hypothesis as implausible - let us take note of this fact - and thence came to accept the contradictory hypothesis that there exists some true universal statement which is not a law of nature. (See his Logic of Scientific Discovery, Appendix *x.) Let me state at once that I share the feeling of quite a few who find this hypothesis very problematic as well; and at the very least it certainly is also a meta­physical hypothesis. I wish to stress, first and foremost, that we have here two contradictory hypotheses, formed in a language which is of necessity acceptable and comprehensible to all with the exception of the word ‘natural law’ or its equivalent, and that both hypotheses are meta­physical.

The two contradictory hypotheses, let me reformulate, are ‘all true universal statements are natural laws’, and ‘some true universal state­ments are not natural laws’. A logical positivist, such as David Hume, may be interpreted to have said, a natural law is any true universal statement, thus rendering our two hypotheses a tautology and a contradiction re­spectively. Also, Hume may be interpreted as having said, a natural law is any statement about causes, we never observe causes but only constant conjunctions, and therefore causation is a meaningless concept. Conse­quent on this reading, both of our metaphysical hypotheses become meaningless. I wish to stress that there are here two readings of Hume, identical in content, and different in wording. The one says, we have no concept of causations; we have a concept of constant conjunction which is confused with that of causation. The other reading of the same texts is, we have no concept of causation except that of constant conjunction.

The literature on natural laws may be presented, at the first approxim­ation (to exclude statistics and such), as the question, is there a deeper connection between one couple of events constantly in conjunction then between any other couple of events constantly in conjunction? We do have an ordinary concept of deeper connexion: we all feel that a couple of businessmen are seen often together either because they are similar - say they have similar interests - and so frequent the same establishments, or because they cooperate and collude. We will all consider their being to­gether accidental in the first case and due to some (efficient) cause in the second. Similarly, we all agree that many phenomena looked very natural to non-scientists and to scientists of the past, yet are mere accidents.

But this argument carries little force: these intuitive cases do not take us very far. There are many universal statements concerning the prop­erties of matter which were alleged to be true but which experiments in high or low temperatures have refuted empirically and thus we know to be false, or to be true only after they are properly qualified, perhaps, to ordinary temperatures. There is little trouble here as yet. But consider a universal statement which remains unrefuted even on the present widened domain of experienced temperatures. Suppose we were not able to refute it ever; will it thereby qualify as a law of nature? This question is the watershed of philosophy, dividing positivism from all else.

The idea of essential definition, like that of man as a rational animal, is that the universe is law-abiding, like a righteous person; that in the fibre of the universe there are certain constraints which prevent the universe from entering certain states. Of course we would like the constraints to exclude some logically possible states, and so the theory of essential definitions cannot be accepted in its Aristotelian form. We want essential definitions, however, not as tautologies yet not as any old true universal statement (such as man is a featherless biped).

Suppose this is so; suppose God has forbidden the universe from under­taking or exhibiting some logically possible events. Now the universe does not undertake or exhibit all possible events - this is a corollary of the trite claim that some events are exclusive of each other for one given space-time region. The question is, then, the following. Consider any universal statement which is not a statement of a constraint; the universe is permitted but not forced to exhibit at least once in its four dimensional menifold an instance contrary to it.

I have used the word ‘constraint’ now, rather than ‘cause’ or ‘law of nature’, because this word cannot be rejected by positivists without their getting into some difficulty in economics, for example, or even in math­ematics. Now, in these fields constraints are represented by certain uni­versal statements taken to be true. But in these fields not all universal statements taken to be true are regarded as constraints. Hence, we may now contemplate the nature of constraints and see, after offering some criteria of constraints, whether all true universal statements are state­ments of constraint.

Here we can easily consider the form of the subjunctive conditional as peculiarly agreeable to the formulation of constraint-like statements; similarly, we can consider those conditionals which are clearly contrary- to-fact as obviously non-constraint-like statements. (See C. I. Lewis, An Analysis of Knowledge and Valuation, VII, 6.) Suppose a statement (X)[P (X)^Q(X)] is true by accident, then we could imagine that if I somehow succeeded to be a P without being a Q, then the statement would thereby become false. If, on the contrary, it is not an accident but a constraint on all Jf’s which are P’s that they cannot be non-(2’s, then I would not manage to be a non-0 P: if I were a P I would also thereby be a Q willy nilly. And so, the subjunctive conditional naturally seems to serve as the form of natural constraint. The contrary-to-fact conditional is one which may easily be designed to be true by accident. Take any description of an accident A₉ say ‘today is Tuesday’; the universal state­ment (X) \~A^P(X)\ is true by the mere virtue of the accident that A is true.

Of course, many contrary-to-fact conditionals are erroneously viewed as false, many are considered to be true not as accidents but as constraints. The same may be said about subjunctive conditionals and more. Thus, though if I were to jump from my roof, etc. I would fall, etc., the law of gravity expressed thus may be an old and refuted version, such as Galileo’s. Yet there was the feeling, particularly strongly expressed by Nelson Goodman, that if we could offer a criterion to distinguish these, from others which may be restated as subjunctive, then we would come closer to finding which universal statements are true laws of nature and hence true, and which are not. Here we come (again?) to the historical fact that natural necessity, which relates to the fibre of the universe and thus to metaphysics, concerns philosophers interested not so much in the universe as in the validation of science - perhaps as knowledge and thus as the truth; perhaps as merely probable.

Popper’s experiment in offering criteria for natural necessity is regrett­able not so much on account of its repeated failure. After all, experiments like that sometimes succeed only after a few minor amendations, and though W. A. Suchting’s strictures are eminently valid they may call for only minor amendation. And so Popper conceeded (addendum to the 1968 edition of his work) that Suchting’s strictures were correct, made small amendments, and declared he lost interest. Meanwhile Suchting has refuted the latest amendment as well. In any case, we may note, Popper’s experiment in offering criteria for natural necessity is regrettable because it is performed (as he tells us in his Addendum) in order to prove the obvious to the heathens - an aim I consider unworthy of a scholar of his stature - namely, that we may know what is natural necessity in the abstract without thereby knowing whether a given true universal state­ment is accidental or not. I think it is obvious that this is so; we know what is a tautology or a logical necessity, yet we have no decision procedure for it; why should we be in possession of stronger tools regarding the decidability of natural necessity then regarding logical necessity?

I think Popper is in error in ascribing to Goodman the hope of finding such a decision procedure.

Nelson Goodman and Michael Polanyi seem strange bed fellows, yet they agree on one point; certain generalizations from experience are so implausible that they are rejected as useless - not as false - without any examination of the facts, and regardless of their possible truths. Good­man’s examples are (a) allegedly contrary-to-fact conditionals, (b) gener­alizations to arbitrarily limited space-time domains, and (c) those formu­lated by the use of arbitrarily deformed concepts like ‘Grue’. Polanyi gives the example of a paper in Nature of empirical data for the hypoth­esis, all gestation periods counted in days are multiples of II, where II is the ratio between the circumference of a circle and its diameter. He offers other examples, like Velikowski’s theory, and even his own theory of adsorption of 1914, then rejected off-hand as implausible yet now accepted. Polanyi does not complain about his own ill fate, nor does he offer a criterion for plausibility: he thinks there can be none. Goodman, 1 think, looks for a criterion, though he uses the term ‘projectibility’ rather than ‘plausibility’.

I view the problem of natural necessity as metaphysical. I therefore think that any attempt to offer an explication of it, be it Popper’s or Goodman’s, must either be inadequate or amount to a metaphysics proper. Whatever our definition of natural necessity may be, say under conditions C the statement L will express a natural necessity. We may ask, is the fulfillment of C is ever necessary? Is it necessary for L to be a natural necessity that C be true? Etc. Assuming all this to be true for moment, then it seems more reasonable to relinquish the explication of the concept of natural necessity in abstracto in favour of the concept of natural necessity relative to a given metaphysics. At the very least I propose it is easier to offer a relativized concept of natural necessity - relative to a given metaphysics - than an absolute one. I have offered such a concept above: I have suggested that a universal statement is a putative law relative to a metaphysics if and only if it conforms to that metaphysics. I have offered a vague idea - not at all formal - of what conformity to a metaphysics is, and I have illustrated it with examples from the history of science, chiefly of physics. If space permits I shall briefly repeat my slender outline. Before that let me say that in my opinion a hypothesis is plausible or projectible in Polanyi’s or Goodman’s senses if and only if it conforms to the metaphysics relative to which it is judged. This leaves open the question, when is a metaphysical hypothesis plausible, and when is any other kind of hypothesis plausible. I have tried to handle some of these questions above, but not all; in any case, let me say briefly when a hypothesis conforms to a metaphysics. Though my presentation is sketchy, it seems to me very intuitive.

A metaphysical hypothesis is implausible in any case except when it belongs to a fully fledged metaphysics. (This is why both contradictory hypotheses with which we began the present discussion were unsatisfac­tory.) A fully fledged metaphysics is a theory of the world capable of be­coming physics, or scientific. Thus, for example, Democritean atomism and other doctrines of what things are made of, look as if they can become scientific (and some of them did become scientific). Atomism as a meta­physical doctrine does not follow from a given scientific atomic theory and it does not entail any. But if we have a series of scientific theories explaining every known phenomenon, a complete scientific theory, each part of which conforms to atomism, then metaphysical atomism would follow from that complete series of scientific theories. We can then say that atomism was so enriched as to become scientific. Clearly, the law of definite proportion, reciprocal proportions, and the like, are all atomic or conform to atomism, whereas the continuum hypothesis, and thus elasticity, does not. The point can more easily be illustrated with New­tonian metaphysics which views the universe as an aggregate of impene­trable atoms governed by a finite set of central forces. When a Newtonian wishes to explain a phenomenon he looks for a central force; a law which is not that of a central force may look suspect to him, for example laws of diffusion, or it may look to him like a law which will soon find its proper Newtonian expression, like laws of chemical affinity or of electromag­netics.

All this reinforces the point that we may have an intuitive idea of a natural necessity, yet without knowing what is a true instance of it. For, and this I contend is a historical fact, what looks a natural necessity one generation may look an accidental universality at the next - I explain this by reference to our changing metaphysical framework. This is par­ticularly obvious in the case of competing (metaphysical) schools. Indeed, whereas metaphysics guides us in what we may consider a priori a plau­sible putative natural law, science guides us in criticizing our metaphysics and replacing it by a better one. Science, thus, indirectly alters our idea of natural necessity. It did so in the past, and, I contend, it may do so again.