STEPHEN PFEIL.
LAW, in science and in philosophy, a gen eral formula expressing either a de facto uni formity of nature as we actually find it or a necessary property of all conceivable worlds. The first type is exemplified by the law of gravi tation, which asserts that two particles attract one another with a force varying directly as the product of their masses and inversely as the square of the distance separating them. It is quite conceivable from the purely logical standpoint that there might be a world where the attractive force might vary as the sum of the masses of the particles concerned; observa-• tion, however, teaches us that our world is not of this sort. On the other hand, the law of contradiction, which says that no proposition can at once be true and false, is of necessity valid in any universe whatever. The distinc tion between the two types of laws has been minimized into one of degree by those who bold the consistency theory of truth, for these writers claim that even such laws as that of gravitation follow from the nature of any possible universe, and that their denial involves an inconsistency, or at any rate a greater degree of inconsistency than their assertion. How ever, from the standpoint of those who main tain the correspondence theory of truth believ ing that the truth of a statement depends on whether it correctly portrays a certain con tingent real state of affairs, the distinction be tween necessary and de facto or empirical laws may well be absolute, and usually is absolute. Both necessary and empirical laws differ funda mentally from laws of right and wrong or the laws established by states. Ethical and polit ical laws are either descriptions of things as they ought to be or schemes of procedure in tended to create some desired state of affairs. Ethical and political laws may be violated without falsifying them; the violation of an ethical law is a sin; of a political law, often a crime; and many political laws contain clauses contemplating their own violation. On the other hand, to precisely the extent to which a scientific law is violated, it is not a law at all. The laws of ethics speak in the imperative; those of a natural science in the indicative. Notwithstanding the fact that, strictly speaking, a law of science is rendered invalid by a single exception, all empirical laws are either marred by exceptions or by the possibility of exceptions. Owing to the general uniformity
of nature, and especially to the particular uni formities which ages of observation have dis closed to us in certain fields, when a certain conjunction of circumstances have occurred time and again, while a certain component part of that conjunction has never or but rarely been known to occur in isolation, we are able to formulate the law that the component part is an index of the presence of its associates, and to expect that whatever exceptions this law may have will be rare in proportion to the number of times it is satisfied. Further than this we can never go; the law of gravita- . tion itself, that image of all a law of nature should be, has recently been suspected of small variations from the facts. Of small variations be it noted; the fact that we can make the quantitative errors of the laws of nature re cede further and further is what renders a mathematical physics, and in general a precise science of any sort, at once pos sible and valuable. In the case of such laws as that of recapitulation in biology and of many psychological generalizations, the enormous quantitative error is concealed by a loose termi nology, which is able to assume just such slight changes as to cover the facts throughout all the changes of the observations. Laws such as these are sometimes called empirical laws or generalization in a sense narrower than that in which this term has been employed in the present discussion. The justification for the larger sense of the phrase which has been employed here is that the distinction between the rawest generalization of a new science and the law of universal gravitation is simply one of degree: of the clearness of the terms employed, the measure of interrelation of the facts em braced with the other facts of the science, the amount of observation and research that has been made, and the rarity of observations con tradicting the law. The law of gravitation is not equally fallible to the law of recapitulation in biology, but it is similarly fallible. For a discussion of the methods by which scientific laws are established (see INDUCTION) ; the dis cussion of induction under LOGIC.