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Yet this confusion, obvious as it is, has played no small part in the notion that descriptive analysis is artificial and unreal.
If it be admitted that the formulas of scientific description express definite logical and mathematical relationships, whose meaning and truth is independent of the exigencies of discourse, it may yet be contended that the application of these relationships to nature is arbitrary. I can only reply that just these relations are found to subsist in nature; if they were not, the scientist would not account them verified. If it be objected that nature never exactly corresponds to such formula, I may then ask for specific cases. And when the disparity between the case and the formula is pointed out, some new and similar formula will be at the same time exhibited.?
But, it may be asked, does not the formula always leave something out; does it not, for the sake of practical convenience, always over-simplify nature? Of course it leaves something out. In empirical procedure, it is as important to omit the irrelevant as to include that which is germane. And it is further true, as has been stated above, that science is peculiarly, if not exclusively, interested in discovering identities and constants. And these find expression in the formulas of science to the exclusion of individual differences. But it does not follow that this procedure involves over-simplification. For that would mean either that the formulas omit something which they intend to cover; or that the identities and constants they do cover are not actually present in nature. But neither of the charges can be substantiated. Science abstracts, but does so deliberately. And to abstract is not to inventor falsify — but only to discriminate and select.
See below, pp. 232–234. ? See below, pp. 236-237. See pp. 54-55.
• Were science to assert that nature is only what is expressed in the formula, it would be guilty of what James calls “vicious intellectualism.” As a matter of fact science makes no such assertion. On the contrary it specifically provides for individual differences by its use of 'variables.' See below, pp. 234-235.
It will appear, in short, that the ideal of 'descriptive economy' is not a fantastic hobby, but a canon of knowledge. The discovery of this ideal has not debased science, but has enriched logic and methodology. Through adopting it, science has not departed from reality, but has acquired a closer and more sure grasp of reality.
$ 7. There is one further charge against the descriptive method, that is held to involve not only physical science, The Option of but logic and mathematics as well. It is said Hypotheses that the choice of hypotheses is optional. Now as respects physical science, it is clear that this option has to do with the preliminary stages of investigation, and not with the conclusion finally adopted. The trial of a hypothesis is optional; but its success, or verification, is determined. Furthermore, the internal relations of the hypothesis itself are determined. The hypothesis selected for trial must be logically and mathematically correct.
But it may now be urged that logical and mathematical correctness is optional. And this consideration assumes a growing importance in the light of recent developments in the philosophy of mathematics. It is often said that logical and mathematical truths depend on the arbitrary selection of postulates.? Time will show, I believe, that such expressions are one-sided, and, when taken unqualifiedly, misleading. There are evidently compensating considerations. In the first place, no logician and mathematician, however modern he may be, invents postulates in order to build systems on them; like the physical scientist, he searches for the postulates that will determine certain facts. As a recent writer expresses it, while postulates are not necessary from,” they are necessary for; namely, for
1 Cf. e.g. F. C. S. Schiller: “Axioms as Postulates,” in Personal Idealism. Cf. on the other hand, T. P. Nunn: The Aims of Scientific Method, Ch. V.
2 Cf. e.g. E. V. Huntington: "Sets of Independent Postulates for the Algebra of Logic,” Transactions of the Amer. Math. Soc., Vol. V, 1904. “These postulates are simply conditions arbitrarily imposed on the fundamental concepts,” etc. (p. 290). Cf. also Poincaré: Science and Hypothesis, pp. 37-39.
the solution of the problem.”ı So postulates are in the
1 end verified, and not merely chosen. In the second place, there are well recognized canons or criteria, by which postulates may be judged, such as 'purity,' 'consistency, 'independence, etc. And finally, all systems, whether the postulates be chosen or not, are made up of terms, relations, propositions and implications, which, whatever is done with them, are certainly not chosen to be what they are. In short, here, as elsewhere, thought accommodates itself to things, and its option is confined to selection from among them.
$ 8. In the background of every mind that hesitates to accept the descriptive method as valid and adequate,
will be found one or both of the notions of The 'Real' Cause, and explanation which science has gradually aban'Mere' De
doned, the notion of - 'power' or the notion scription
of 'good.'3 More commonly the two will be fused in the notion of 'activity.' This is regarded as the real cause, by which ‘mere' description is judged and found wanting. It becomes a question as to whether the development of scientific method has thrown light on the meaning of 'cause'; or has simply abandoned it. The answer depends, evidently, on the validity of this extrascientific notion of cause, which science once employed, and which is now defended by the critics of science.
The notion depends entirely upon the inner experience of activity. Fortunately this issue cannot be argued at length. A man must look for himself, as Hume did, and see whether he finds in the depths of his own nature, a power to do, which is clear, simple, and self-sufficient. He who makes the experiment, and resolutely declines to accept the confusion and vagueness of familiar immediacy as profound insight, will, I believe, conclude as Hume did. He will find sensations of bodily tensions, feelings of expectancy, etc., but no 'power.'' In other words, he will find what empirical analysis finds everywhere, a manifold of terms in relation. And when one proceeds to explain such a manifold, one will be led, as science in its field has been led, to the discovery of descriptive laws.
Karl Schmidt: “Critique of Cognition and its Principles." Jour. of Phil., Psych., and Scientific Methods, Vol. VI (1909), pp. 281–282. · Cf. Schmidt, op. cit., passim.
3 See above, pp. 53-54. •Cf. e.g. James Ward: op. cit., Vol. I, p. 64; Vol. II, pp. 79, 237, 247. i See below, pp. 261–264. Cf. Hume: Enquiry Concerning the Human Understanding, Selby-Bigge's edition, pp. 60–73.
I conclude, in other words, that in adopting the descriptive method, science has exchanged a naïve and hasty notion of cause for a refined and rigorous notion. In the sense of the term that is most intelligible, the cause is the law, or its implication. Not necessarily the mechanical law; for analysis and description is, as we have seen, by no means limited to the type exhibited in physical science. But a logical cause, a mathematical cause, an ethical cause, will, I believe, turn out, in each case, to be a law or constant. And if this is so, science is to be credited with the descriptive method, and not debited.
$ 9. The critique of science which has just been examined might be termed a 'methodological' critique, as distin
guished from the 'metaphysical' critique to The Unreality
which we must now turn. According to this of Space and Time. The critique, science has to do with 'appearance' or Kantian Argu- ‘phenomenon' rather than ‘reality,' because
of the nature of its basal concepts, space and time. These concepts, it is argued, are inherently contradictory or lacking in self-sufficiency; and physical nature, as the realm of space and time, must be supposed to be in the end resolved into something else. They must be corrected, or 'overcome,' in some higher unity, as evil is held to be transmuted into good in the providence of God.
The classic prototype of this critique is to be found in Kant. According to that writer, space and time are
: For a discussion of the application to ethics see below, pp. 116-117.
• Bergson's critique of time is a blend of the methodological and metaphysical critiques; it is examined below, pp. 230, 234-235, 255-261. For Kant, cf. Critique of Pure Reason, Max Müller's translation, second edition, pp. 328 sq.
vitiated by “antinomies.” This means that on the supposition of the reality of space and time, it is possible to pröye, with equal certainty, several contradictory pairs of theses and counter-theses; such as that space has boundaries and has not, time has a beginning and has not, space and time have indivisible elements and have not, etc. The moral, according to Kant, is that we must reject the original supposition, and deny the reality of space and time. If we regard them merely as acts of synthesis, they become indeterminate; or rather they derive their determination from something else, such as the subject matter to be synthesized, or the motive actuating the operation of synthesis. It is like saying that number is not independently real, but is only the operation of counting. The question as to how many numbers there are will then have no meaning. There will be as many numbers as the material counted requires, or as any one has occasion to enumerate. Similarly, space and time are held to conform to the subject-matter to which they are applied, or to the motive governing their employment. And it is in terms of these non-spacial and non-temporal factors, in terms of something 'higher' than nature or outside of it, that the world assumes its final shape.
In more recent times the supposed paradoxes of space and time have been traced back to a more fundamental paradox involved in 'term' and 'relation. It is argued that if two terms are to be related, they must each be related to the relation, and since these interpolated relations must again be related, we are launched upon an infinite regress. Thus the English idealist, F. H. Bradley, is brought to the conclusion “that a relational way of thought — any one that moves by the machinery of terms and relations — must give appearance, and not truth.”i Or, as his disciple, A. E. Taylor, puts it, it is in some "supra-relational” mode of experience, in which even the concept of whole and part has been transcended,
Appearance and Reality, first edition, p. 33; cf. Ch. III, passim.