I think there is a moral to this story, namely that it is more important to have beauty in one’s equations, than to have them fit experiment…. It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory. (Wechsler 1978, p.5)
How does the scientist use the scientific aesthetizing to appraisal theory? Aesthetic standards of above-mentioned are all tools that scientists appraised the theory. Here, we only enumerate two representative scientists' works. H. Hertz forms the rule of choosing the theory picture through three standards. Except logical consistency and empirical adequacy or corresponding with the phenomenon, there are simplicity and distinctness. He says: “Two permissible and correct images of the same external objects may yet differ in respect of appropriateness. Of two images of the same object that is the more appropriate which pictures more of the essential relations of the object -- the one which we may call the more distinct. Of two images of equal distinctness the more appropriate is the one which contains, in addition to the essential characteristics, the smaller number of superfluous or empty relations -- the simpler of the two.[And Hertz adds the remark that] empty relations cannot be altogether avoided.” In this case, the intelligible variety regarding the simplicity and distinctness is causing under-determination in choosing theories which are different ones, but equivalent in experiences, and having same appropriateness. This has introduced the need of scientific anesthetizing judgment conversely. The third standard of Hertz is aesthetic standards of choosing theory picture. (Majer 1990, pp.61-63) Einstein uses one pair of scales to appraise the scientific theory, that is, external confirmation and inner perfection. The latter standard is an esthetic one that means premise (basic conception and basic relation) of theory “naturalness” and “logical simplicity”. (Li 1985) Jardine introduces aesthetic qualities to say aesthetic virtues, who spread out three aesthetic types of scientists who appraise to scientific theory. This is: Owe aesthetic virtues to the theory or hypothesis directly, because the theory or hypothesis has some aesthetic virtues; Owe aesthetic virtues to the phenomenon which was observed by theory or hypothesis, because theory or hypothesis can prove demonstrating some aesthetic virtues in their explaining phenomenon. Owe aesthetic virtues to the description (imitating, expounding, diagram, drawing, etc.) of the phenomenon, because the theory or hypothesis demonstrates aesthetic virtues in the description of phenomenon that they explain. (Jardine 1991, pp.208-209)
Even if experience standard could have a final and ultimate standard about if scientific theory is foothold, why we appraise it with the esthetic standard? Once I analyzed it in two papers (Li 1985, 1992) about value evaluation to scientific theory, aesthetic evaluation occupies into it naturally, and it can't be absent. Here the reason is only slightly say just a few to aesthetic evaluation.
Why we use the esthetic evaluation is obviously scientist must to make the choice in many theories that satisfy equally the experience standard, in order to choose the beautiful theory among them. Moreover, as logical empiricists state correctly that there are many difference between the theories of the same equivalence class which are completely trivial and irrelevant with respect to the empirical content of these theories: difference of notation, of languages, of formulation, of representation, and so forth. But their view that all the non-empirical difference are irrelevant with respect to the choice among different theories can’t be accepted. Some are not! If we call the former differences “differences of style”, then it does not exhaust the difference among empirically equivalent theory; besides difference of “style”, there are other differences too, like one Hertz of so-called simplicity and uniqueness, which are relevant for the choice among different (yet empirically equivalent) theory. Let us call these non-stylistic but somehow relevant differences “aesthetic” differences. (Majer 1990, pp.62-63) In fact, people can always produce a kind of theory and even a lot of theories to explain the known fact, or even prophesy some new fact. In this case, the close examination standard to the theory can only be aesthetic.
There are deeper reasons in the application of aesthetic evaluation. In reality, far from being wheeled up only when empirical criteria have shown the theories on offer to be equally worthy, aesthetic preferences often overrule the standard empirical criteria in scientists’ choices among theories. The situation is therefore not that aesthetic criteria are applied once scientists have ascertained, on empirical standards for the acceptability of theories, which theories they may accept; rather aesthetic and empirical criteria jointly determine scientists’ standards for the acceptability of theories. Historical studies confirm that aesthetic considerations play a role in these decisions. The aesthetic factor of which we shall construct a model should therefore be considered as fully distinctive of science as scientists’ logical or empirical concerns. This does not mean, of course, that no useful distinction can be drawn between scientists’ empirical and aesthetic consideration; but it does mean that the distinctions we draw between them cannot be portrayed as a demarcation between the scientific and the extrascientific.( McAllister 1996, p.17) The more important thing is that should realize that a beautiful one of the theories equally fitted to experiences is one closer to reality on ontology, and is a more basic theory too; The non-beautiful theory is not complete, provisional, transitional, and will be replaced by the beautiful theory eventually sooner or later. Just in this kind of meaning, Einstein’s legitimate intellectual objections to the ultimate acceptability of orthodox quantum theory had everything to do with the high intellectual/personal aspirations that he had for physics -- orthodox quantum theory being capable only of claiming “the interest of shopkeepers and engineers”, in that it merely correctly predicts the results of experiments and does not help reveal to us “the Old One”. In this scientific artist's eyes, orthodox quantum theory thus is intellectually “a wretched bungle”.( Maxwell 1984, pp.7-8) J. W. N. Sullivan has a comprehensive comment on this:
Since the primary object of the scientific theory is to express the harmonies, which are found to exist in nature, we see at once that these theories must have a aesthetic value. The measure of the success of a scientific theory is, in fact, a measure of its aesthetic value, since it is a measure of the content to which it has introduced harmony in what was before chaos. It is in its aesthetic value that the justification of the scientific theory is to be found, and with it the justification of the scientific method. Since facts without laws would be of no interest, and laws without theories would have , at most, only a practical utility, we see that the motives which guide the scientific man are, from the beginning, manifestations of the aesthetic impulse.……The measure in which science falls short of art is the measure in which it is incomplete as science. (Chandrasekhar 1995, p.60)
Finally, it is necessary to clarify the relation of aesthetic evaluation and empirical evaluation. According to McAllister’s classifying, there are two kinds of different views: autonomism and reductionism. Autonomism regards scientists’ aesthetic and empirical evaluations as wholly distinct from and irreducible to one another. The mode of attention that is characteristic of aesthetic perception is disinterested, “Disinterestedness” denotes an attitude of detachment or purposelessness toward an object of perception. The disinterested stance toward an object dwells not upon the object’s aptitude to further some aim but only upon its intrinsic structure and significance. Aesthetic judgment pays no regard to utilitarian concerns. Reductionism views scientists’ aesthetic and empirical evaluations as nothing but aspects of one another. These two views represent the extremes of a spectrum of possible views, each of which posits a certain degree of interreducibility between aesthetic and empirical judgments. And scientists’ aesthetic evaluation tends in the longer term to swing into line with their empirical appraisals. Then, he puts forward the concept of aesthetic conduction. Aesthetic conduction does not consist in attributing beauty to each scientific theory to the degree to which it shows fitness to its purpose. On the contrary, the aesthetic conduction will cause scientists to regard as beautiful a theory that shows little fitness to its purpose -- i.e., empirical success -- if this theory shares the aesthetic properties of theories that scored notable empirical success. On base of aesthetical conduction, he has analyzed carefully this relation:
Aesthetic canons in science pay regard to two factors: the empirical success of theories embraced by the community and their aesthetic properties. The empirical success of a theory contributes to determine the weighting of that theory’s aesthetic properties within the community’s aesthetic canon; in turn, this canon is used to evaluate subsequent theories. An entrenched aesthetic canon will cause the community to produce and esteem aesthetically orthodox theories. Sometimes a theory emerges which, perhaps in consequence of new assumptions or techniques, shows unprecedented aesthetic properties. Such a theory is likely at first to be resisted in virtue of the established aesthetic canon. Only when this theory, or others similar to it, has shown sufficient empirical success does the weighting of its aesthetic properties rise substantially. This allows the new theory to win acceptance on aesthetic as well as empirical criteria. The revision of the canon ensures that subsequent theories showing the new aesthetic properties are more likely to be accepted, enabling the community to pursue further the assumptions or techniques that constitute the new style of theorizing. (McAllister 1996, pp. 61, 62, 66, 160)
Compared with experience judgment, aesthetical judgment has sometimes the function of lagging behind on time. J. Bernstein wrote: “In science like in art, sound aesthetic judgment are usually arrived at only in retrospect. A really new art form or scientific idea is almost certain at first to appear ugly. The obviously beautiful, in both science and the arts, is more often than not an extension of the familiar. It is sometimes only with the passage of time that a really new idea begins to seem beautiful.” I think, the lagging the function of the aesthetic judgment of the scientific theory may only takes place on non-inventor himself. As to inventor, aesthetic feeling, including the appreciation of the new aesthetic factor, is often immediately. First-hand experiences of some great scientists, as Poincaré and Einstein etc, are the clear proof.
In the evaluation or justification of scientific theory, which standard is more important of empirical standard and aesthetics standard? It is a question that different people have different views. Dirac thought aesthetic standard is the most important. J. Wechsler adheres to the opposite view: In art, aesthetic is the finished painting, sonnet, or sonata which are normally the subject of our criticism or appreciation. Science doesn’t exhibit products for aesthetic criticism in this way; there is hardly any recognized vocabulary of aesthetic criticism and response for science. The usual criterion “success” of a scientific product -- an equation, a physical model, or a written paper -- is whether it works, that is, predict, explain. Aesthetical judgments operate in the cognitive processes of arriving at that product.(Wechsler 1978, p.3) Drac’s view seems extreme and some absolute, which lack the due flexibility, but Wechsler's view has obvious mistakes. First, scientific aesthetical judgments not only work in the process of scientific invention, but also work in the evaluation and justification of the result that is invented. Second, the scientific result is an aesthetically critical target. And there is an aesthetically critical vocabulary or lexicon. For example, according to this aesthetic principle of simplicity Poincaré criticized the Lorentz’s electronic theory, because it introduces too many ad hoc hypothesis (Li 1983, pp.136-144). Einstein's revealed it at the beginning of the special theory of relativity that Maxwell's electrodynamics causes the asymmetry, which is not inherent of the phenomenon self, to explain relative motion of the conductor and magnet. Moreover, he always pays attention to scrutinizing and criticizing the existing theory in terms of aesthetics all the time (see Einstein 1977, p.124). We have already involved people's aesthetic appraisal on scientific result, theory of relativity and quantum mechanics many times in the front, which is undoubtedly another effective evidence of proving our view conclusively.
In the scientific practice, to judge the degree of empirical adequacy of theories, most scientists are content to use empirical criteria such as internal consistency and consistency with extant empirical data, which is rational and normal. But, as scientists are aware, where are cases in which empirical criteria for theory evaluation fail to reveal a theory’s true degree of empirical adequacy. These Cases may be classified as false negative, in which empirical data appear to cast doubt on a theory that is true, and false positives, in which data appear to corroborate a theory that is false. For Duhem-Quine thesis’s existence (Li 1996, pp.323-377), whether to accept or refuse a given high-level theory can be evaluated only from non-empirical view, especially by aesthetic standard. Dirac said:
Suppose a discrepancy had appeared, well confirmed and substantiated, between the theory and observations…. Should one then consider the theory wrong? … I would say that the answer to the last questions emphatically No…. Anyone who appreciates the fundamental harmony connecting the way Nature runs and general mathematical principles must feel that a theory with the beauty and elegance of Einstein’s theory has to be substantially correct. If a discrepancy should appear in some application of the theory, it must be caused by some secondary feature relating to this application, which has not been adequately taken into account, and not by a failure of the general principles of the theory.
Similarly, A. M. Taylor wrote: “The elegant beauty of the theoretical edifice [of general relativity] is thought sufficient reason for believing it to be true.” If aesthetical judgment were able reveal a theory true or close to the truth, it would solve the problem of detecting the false negatives obtained in the empirical evaluation of theories. About false positives, since there is a valid argument from false premises to some true conclusion, it is possible for any scientific theory that is false to make predictions that accord with empirical findings. Therefore, it may be that some theories that have passed all empirical tests to which they have been subjected are nevertheless distant from the truth. If there are no more discriminating empirical tests to which they can be subjected, such theories may be identified only, if at all, by appeal to non-empirical criteria. Which non-empirical criteria can reveal the falsity of an empirically successful theory? Dirac suggests that aesthetic criteria has this power: theories that are aesthetically displeasing are likely to be distinct from the true even if they have track record of empirical success. (McAllister 1996, pp.93-94) Wechsler provides the annotation explanatory note of different class: When the scientist reviews their job, development of concept and expounding theory in detail, they think intuition and aesthetics guide their feeling of "this is it must be ", i.e. their feeling to accuracy. In fact, if we believe science and reality have single and only relations and assume it and truth are synonymous, the aesthetic idea seems to be the idea on the changeable or edge idea in science judgment or cognition. People can still recognize that the scientific result is beautiful (truth equals to beauty). However, if people regard science as the attempt with tangible convergence, submit to the experiment, must not submit to verify, then we have freedom of taking action: People can imagine, the hypothesis suitable for choosing obeys the aesthetic factor.
Therefore is easy to see, which is more important of experience standard and aesthetics standard do not have a unified model answer. We should treat specifically to the concrete case. Here, there are not available rule and procedure that can be applied mechanically, which need is that Poincaré’s so-called “intuition” and Duhem’s so-called “good sense”. When Duhem discussed the good sense is the judge of a theory or a hypothesis, which ought to be abandoned, he said: When certain consequences of a are struck by experiment contradiction, we learn that this theory should be modified but we are not told by the experiment what must be changed. It leaves the to the physicist the task of finding out the weak spot that impairs the whole system. No absolute principle directs this inquiry, which different physicists may conduct in very different ways without having the right to accuse one another of illogicality. For instance, one may be obliged to safeguard certain fundamental which he tries to reestablish harmony between the consequences of the theory and the facts by complicating the schematism in which these hypotheses are applied, by invoking various causes of error, and by multiplying corrections. The next physicist, disdainful of these complicated artificial procedures, may decide to change some one of the essential assumptions supporting the entire system. The first physicist does not have the right to condemn in advance boldness of the second one, nor does the latter have the right to treat the timidity of the first physicist as absurd. The methods they follow are justifiable only by experiment, and if they both succeed in satisfying the requirements of each is logically permitted to declare himself content with the work that he has accomplished. Now,
It may be good sense that permits us to decide between two physicists. It may be that we do not approve of the haste with which the second one upsets the principle of a vast and harmoniously constructed theory whereas a modification of detail, a slight correction, would have sufficed to put these theories in accord with the facts. On the other hand, it may be that we may find it childish and unreasonable for the first physicist to maintain obstinately at any cost, at the price of continual repairs and many tangled-up stays, the worm-eaten columns of a building tottering in every part, when by razing these columns it would be possible to construct a simple, elegant, and solid system.(Duhem 1954, pp.216-217)
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