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The Weight of Simplicity in the Construction and Assaying of Scientific Theories

Published online by Cambridge University Press:  14 March 2022

Mario Bunge
Mario Bunge*
Affiliation:
University of Pennsylvania
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Extract

One of the most difficult and interesting problems of rational decision is the choice among possible diverging paths in theory construction and among competing scientific theories—i.e., systems of accurate testable hypotheses. This task involves many beliefs—some warranted and others not as warranted—and marks decisive crossroads. Suffice to recall the current conflict between the general theory of relativity and alternative theories of gravitation (e.g., Whitehead's) that account for the same empirical evidence, the rivalry among different interpretations of quantum mechanics (e.g., Bohr-Heisenberg's, de Broglie-Bohm's, and Landé's), and the variety of cosmological theories (e.g., Tolman's cyclical model and the steady-state theory). They all account for the same observed facts although they may predict different kinds of as yet unknown facts; they are consequently, up to now, empirically equivalent theories even though they are conceptually different and may even involve different philosophical views—i.e., they are conceptually inequivalent.

Type
A Panel Discussion of Simplicity of Scientific Theories
Information
Philosophy of Science , Volume 28 , Issue 2 , April 1961 , pp. 120 - 149
Copyright
Copyright © Philosophy of Science Association 1961

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Footnotes

∗

With leave of absence from the Universidad de Buenos Aires.

References

1 Cf. Mario Bunge, “The Complexity of Simplicity”, presented to the international Congress for Logic, Methodology, and Philosophy of Science (Stanford, 1960), Jour. Phil. (forthcoming).

2 Adolphe Lindenbaum, “Sur la simplicité formelle des notions”, Actes du Congrès International de Philosophie Scientifique (Paris: Hermann, 1936), VII, 28. Nelson Goodman, The Structure of Appearance (Cambridge, Mass.: Harvard University Press, 1951), ch. iii, and “Axiomatic Measure of Simplicity”, Jour. Phil., 52, 709 (1955). John G. Kemeny, “Two Measures of Complexity”, Jour. Phil., 52, 722 (1955). Horst Kiesow, “Anwendung eines Einfachheitsprinzip auf die Wahrscheinlichkeitstheorie”, Archiv. f. Math. Logik u. Grundlagenforschung, 4, 27 (1958).

3 Dorothy Wrinch and Harold Jeffreys, “On Certain Fundamental Principles of Scientific Inquiry”, Phil. Mag., 42, 369 (1921); Harold Jeffreys, Theory of Probability, 2nd. ed.(Oxford: Clarendon Press, 1948), p. 100. Karl R. Popper, The Logic of Scientific Discovery (1935; London: Hutchinson, 1959), secs 44 to 46, and *Appendix VIII. John G. Kemeny, “The Use of Simplicity in Induction”, Phil. Rev., 62, 391 (1953).

4 Mario Bunge, reference 1.

5 William Craig, “Replacement of Auxiliary Expressions”, Phil. Rev., 65, 38 (1956).

6 Cf. Wilhelm Ostwald, Grundriss der Naturphilosophe (Leipzig: Reclam, 1908), p. 127: simple formulas to express laws of nature can be found only when the conceptual analysis of phenomena is quite advanced.

7 Cf. Ernst Cassirer, Determinismus und Indeterminismus in der modernen Physik (Göteborg: Elanders, 1937), p. 88, being no. 3, vol. XLII, of Göteborgs Högskolas Årsskrift (1936).

8 Cf. Patrick Suppes, Introduction to Logic (Princeton: Van Nostrand, 1957), p. 169.

9 Nelson Goodman, references 2, has argued most persuasively in favor of this thesis.

10 Cf. H.J. Eysenck, Uses and Abuses of Psychology (London: Penguin, 1953), ch. 12. Ernest Nagel, “Methodological Issues in Psychoanalytic Theory”, in S. Hook (ed.), Psycho-analysis, Scientific Method, and Philosophy (New York: New York University Press, 1959), ch. 2.

11 Karl R. Popper, The Logic of Scientific Discovery (1935; London: Hutchinson, 1959), sections 44 to 46, and *Appendix VIII.

12 Cf. Hermann Weyl, Philosophy of Mathematics and Natural Science (1927; Princeton: Princeton University Press, 1949), p. 156, and Popper, reference 11.

13 Alfred Tarski, “The Semantic Conception of Truth”, Phil. and Phenom. Res., 4, 341 (1944).

14 Mario Bunge, Causality (Cambridge, Mass.: Harvard University Press, 1959), pp. 290-1.

15 Cf. Mario Bunge, “Levels: A Semantical Preliminary”, Rev. Metaphys., 13, 396 (1960), and “On the Connections Among Levels”, Proc. XIIth Intern. Congr. Phil. (in press).

16 The compatibility of astronomy with physics was as essential to Copernicus as was the “saving of appearances”, as E. Rosen rightly notes in his Introduction to Three Copernican Treatises, 2nd. ed. (New York: Dover, 1959), p. 29. “What Copernicus desired was not merely a simpler system, as Burtt thought, but a more reasonable one” (loc. cit.). The unification of astronomy and terrestrial mechanics was also an unfulfilled dream of Averroes and the main drive for Galileo and Newton.

17 See, e.g., George R. Price, “Science and the Supernatural”, Science, 122, 359 (1955). On the other hand C. D. Broad, in “The Relevance of Psychical Research to Philosophy”, Philosophy, 24, 291 (1949), accepted ESP while acknowledging that it would require a radical upheaval in psychology, biology, physics, and philosophy.

18 See F.C.S. Schiller, “Hypothesis”, in C. Singer (ed.), Studies in the History and Method of Science (Oxford: Clarendon Press, 1921), II, p. 442.

19 The term serendipity (lucky accident) was coined by Horace Walpole and revived by Walter Cannon, The Way of an Investigator (New York: Norton, 1945), ch. iv, and by Robert K. Merton, Social Theory and Social Structure, rev. ed. (Glencoe, 111.: Free Press, 1957), ch. ii.

20 Further reasons are given in Mario Bunge, reference 14, ch. 12.

21 Henry Margenau, The Nature of Physical Reality (N. York: McGraw Hill, 1950), p. 90.

22 Freeman J. Dyson “Invention in Physics”, Sci. American, 199, n° 3, p. 80 (1958)

23 Some variables regarded as observable in nonrelativistic quantum mechanics are no longer observable in the relativistic theory, and conditions of observability, such as reality (hermiticity), are open to criticism. It can be shown that a nonhermitian operator may represent, in a number of cases, a pair of observables. Cf. Andrés J. Kálnay, “Sobre los observables cuánticos y el requisito de la hermiticidad” (forthcoming).

24 Karl R. Popper, The Logic of Scientific Discovery (1935; London: Hutchinson, 1959), ch. iv.

25 The legitimity of such irrefutable statements, rejected by Popper, is defended in Mario Bunge, “Kinds and Criteria of Scientific Laws”, Philosophy of Science (to appear).

26 Mario Bunge, “The Place of Induction in Science”, Phil. Sci., 27, 262 (1960).

27 Mario Bunge, Metascientific Queries (Springfield, Ill.: Charles Thomas, 1959), ch. 4.

28 Cf. Mario Bunge, Intuition, Intuitionism, and Science (forthcoming).

29 Carl G. Hempel, “The Concept of Cognitive Significance: A Reconsideration”, Proc. Amer. Acad. Arts and Sciences, 80, 61 (1951). Arthur Pap, “Are Physical Magnitudes Operationally Definable ?”, in C. West Churchman and P. Ratoosh (eds.), Measurement: Definitions and Theories (N. York: Wiley, 1959), ch. 9.

30 Mario Bunge, Causality (Cambridge, Mass.: Harvard University Press, 1959).

31 According to general relativity, the paths of bodies are determined by the gravitational field, and the latter is in turn determined by the mass distribution. The field strength being proportional to the quantity of matter (as given, e.g., by the nuclear particles), it is not possible to find a coordinate system in which the sun's field turns out to be weaker than the earth's so that the latter might be regarded as stationary and the sun as revolving around it. Gravitational fields are equivalent to accelerations, and the latter can be transformed away by means of suitable coordinate transformations, within differential spacetime volumes alone; e.g., Einstein's elevator must start from a place within the earth's field, and it finally crashes. For a criticism of the erroneous belief that general relativity permits to transform every acceleration away, see V. A. Fock, “Lesystème de Ptolomée et le système de Copernic à la lumière de la théorie générale de la rélativité”, in Questions scientifiques (Paris: Ed. de la Nouvelle Critique, 1952), I, 149.

32 For the kinematical and dynamical inequivalence of the geocentric and the Copernican reference axes according to the general theory of relativity, see G. Giorgi and A. Cabras, “Questioni relativistiche sulle prove della rotazione terrestre”, Rendic. Accad. Naz. Lincei, IX, 513 1929).

33 J. L. Synge, “Orbits and Rays in the Gravitational Field of a Finite Sphere According to the Theory of A. N. Whitehead”, Proc. Roy. Soc. Lond. A, 211, 303 (1952).

34 R. V. Pound and G. A. Rebka, Jr., “Apparent Weight of Photons”, Phys. Rev. Letters, 4, 337 (1960).

35 For a protest against the complexities of general relativity, see P. W. Bridgman, The Nature of Physical Theory (New York: Dover, 1936), pp. 89 ff.

36 For an analysis of the logical status of the parity conservation law and other metanomological statements, see Mario Bunge, “Laws of Physical Laws” (forthcoming).

37 See, e.g., W. Stanley Jevons, The Principles of Science, 2nd. ed. (1877; New York: Dover, 1958), p. 510; Pierre Duhem, La théorie physique, 2nd. ed. (Paris: Rivière, 1914), p. 26; see, however, p. 259, where he admits that simplicity is not a sign of certainty.

38 An early recognition of the multiplicity of requiremants is found in Heinrich Hertz, The Principles of Mechanics (1894; N. York: Dover, 1956), Introduction. Hertz listed the following: (1) logical possibility, or compatibility with the “laws of thought”; (2) predictive power; (3) maximum number of “essential relations of the object” (what I have called depth); (4) “the smaller number of superfluous or empty relations”. Haif a century elapsed before another scientist-philosopher dared to add non-empirical requirements: Henry Margenau, The Nature of Physical Reality (New York: Mc Graw-Hill, 1950), ch. 5, lists the following “metaphysical requirements on constructs”: (1) logical fertility, (2) multiple connections, (3) permanence or stability, (4) extensibility, (5) causality, (6) simplicity and elegance. See also Mario Bunge, Metascientific Queries (Springfield, Ill.: Charles Thomas, 1959), pp. 79 ff., and Karl R. Popper, “The Idea of Truth and the Empirical Character of Scientific Theories”, presented to the International Congress for Logic, Methodology, and Philosophy of Science (Stanford, 1960). In this paper Popper grants that one of the requirements for a good theory is that it “should succeed with at least some of its new predictions”-i.e., that it should be confirmed.

39 William Craig, reference 5.