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[1] Read before the Kosmos Club, at the University of California, May 4, 1908. Reprinted by permission from the University of California Chronicle, Vol. X, No. 4.

[2] It is by no means unusual for modern scientists to deny the truth of this characterization, so far as regards this alleged recourse to the concept of causation. They deny that such a concept—of efficiency, activity, and the like—enters, or can legitimately enter, into their work, whether as an instrument of research or as a means or guide to theoretical formulation. They even deny the substantial continuity of the sequence of changes that excite their scientific attention. This attitude seems particularly to commend itself to those who by preference attend to the mathematical formulations of theory and who are chiefly occupied with proving up and working out details of the system of theory which have previously been left unsettled or uncovered. The concept of causation is recognized to be a metaphysical postulate, a matter of imputation, not of observation; whereas it is claimed that scientific inquiry neither does nor can legitimately, nor, indeed, currently, make use of a postulate more metaphysical than the concept of an idle concomitance of variation, such as is adequately expressed in terms of mathematical function.

The contention seems sound, to the extent that the materials—essentially statistical materials—with which scientific inquiry is occupied are of this non-committal character, and that the mathematical formulations of theory include no further element than that of idle variation. Such is necessarily the case because causation is a fact of imputation, not of observation, and so cannot be included among the data; and because nothing further than non-committal variation can be expressed in mathematical terms. A bare notation of quantity can convey nothing further.

If it were the intention to claim only that the conclusions of the scientists are, or should be, as a matter of conservative caution, overtly stated in terms of function alone, then the contention might well be allowed. Causal sequence, efficiency or continuity is, of course, a matter of metaphysical imputation. It is not a fact of observation, and cannot be asserted of the facts of observation except as a trait imputed to them. It is so imputed, by scientists and others, as a matter of logical necessity, as a basis of a systematic knowledge of the facts of observation.

Beyond this, in their exercise of scientific initiative, as well as in the norms which guide the systematisation of scientific results, the contention will not be made good—at least not for the current phase of scientific knowledge. The claim, indeed, carries its own refutation. In making such a claim, both in rejecting the imputation of metaphysical postulates and in defending their position against their critics, the arguments put forward by the scientists run in causal terms. For the polemical purposes, where their antagonists are to be scientifically confuted, the defenders of the non-committal postulate of concomitance find that postulate inadequate. They are not content, in this precarious conjuncture, simply to attest a relation of idle quantitative concomitance (mathematical function) between the allegations of their critics, on the one hand, and their own controversial exposition of these matters on the other hand. They argue that they do not "make use of" such a postulate as "efficiency," whereas they claim to "make use of" the concept of function. But "make use of" is not a notion of functional variation but of causal efficiency in a somewhat gross and highly anthropomorphic form. The relation between their own thinking and the "principles" which they "apply" or the experiments and calculations which they "institute" in their "search" for facts, is not held to be of this non-committal kind. It will not be claimed that the shrewd insight and the bold initiative of a man eminent in the empirical sciences bear no more efficient or consequential a relation than that of mathematical function to the ingenious experiments by which he tests his hypotheses and extends the secure bounds of human knowledge. Least of all is the masterly experimentalist himself in a position to deny that his intelligence counts for something more efficient than idle concomitance in such a case. The connection between his premises, hypotheses, and experiments, on the one hand, and his theoretical results, on the other hand, is not felt to be of the nature of mathematical function. Consistently adhered to, the principle of "function" or concomitant variation precludes recourse to experiment, hypotheses or inquiry—indeed, it precludes "recourse" to anything whatever. Its notation does not comprise anything so anthropomorphic.

The case is illustrated by the latter-day history of theoretical physics. Of the sciences which affect a non-committal attitude in respect of the concept of efficiency and which claim to get along with the notion of mathematical function alone, physics is the most outspoken and the one in which the claim has the best prima facie validity. At the same time, latter-day physicists, for a hundred years or more, have been much occupied with explaining how phenomena which to all appearance involve action at a distance do not involve action at a distance at all. The greater theoretical achievements of physics during the past century lie within the sweep of this (metaphysical) principle that action at a distance does not take place, that apparent action at a distance must be explained by effective contact, through a continuum, or by a material transference. But this principle is nothing better than an unreasoning repugnance on the part of the physicists to admitting action at a distance. The requirement of a continuum involves a gross form of the concept of efficient causation. The "functional" concept, concomitant variation, requires no contact and no continuum. Concomitance at a distance is quite as simple and convincing a notion as concomitance within contact or by the intervention of a continuum, if not more so. What stands in the way of its acceptance is the irrepressible anthropomorphism of the physicists. And yet the great achievements of physics are due to the initiative of men animated with this anthropomorphic repugnance to the notion of concomitant variation at a distance. All the generalisations on undulatory motion and translation belong here. The latter-day researches in light, electrical transmission, the theory of ions, together with what is known of the obscure and late-found radiations and emanations, are to be credited to the same metaphysical preconception, which is never absent in any "scientific" inquiry in the field of physical science. It is only the "occult" and "Christian" "Sciences" that can dispense with this metaphysical postulate and take recourse to "absent treatment."

[3] A broad exception may perhaps be taken at this point, to the effect that this sketch of the growth of the scientific animus overlooks the science of the Ancients. The scientific achievements of classical antiquity are a less obscure topic to-day than ever before during modern times, and the more there is known of them the larger is the credit given them. But it is to be noted that, (a) the relatively large and free growth of scientific inquiry in classical antiquity is to be found in the relatively peaceable and industrial Greek communities (with an industrial culture of unknown pre-Hellenic antiquity), and (b) that the sciences best and chiefly cultivated were those which rest on a mathematical basis, if not mathematical sciences in the simpler sense of the term. Now, mathematics occupies a singular place among the sciences, in that it is, in its pure form, a logical discipline simply; its subject matter being the logic of quantity, and its researches being of the nature of an analysis of the intellect's modes of dealing with matters of quantity. Its generalisations are generalisations of logical procedure, which are tested and verified by immediate self-observation. Such a science is in a peculiar degree, but only in a peculiar degree, independent of the detail-discipline of daily life, whether technological or institutional; and, given the propensity—the intellectual enterprise, or "idle curiosity"—to go into speculation in such a field, the results can scarcely vary in a manner to make the variants inconsistent among themselves; nor need the state of institutions or the state of the industrial arts seriously color or distort such analytical work in such a field. Mathematics is peculiarly independent of cultural circumstances, since it deals analytically with mankind's native gifts of logic, not with the ephemeral traits acquired by habituation.

[4] "Natural laws," which are held to be not only correct formulations of the sequence of cause and effect in a given situation but also meritoriously right and equitable rules governing the run of events, necessarily impute to the facts and events in question a tendency to a good and equitable, if not beneficent, consummation; since it is necessarily the consummation, the effect considered as an accomplished outcome, that is to be adjudged good and equitable, if anything. Hence these "natural laws," as traditionally conceived, are laws governing the accomplishment of an end—that is to say, laws as to how a sequence of cause and effect comes to rest in a final term.