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Space, Time and Falsifiability Critical Exposition and Reply to “A Panel Discussion of Grünbaum's Philosophy of Science”

Published online by Cambridge University Press:  14 March 2022

Adolf Grünbaum
Adolf Grünbaum*
Affiliation:
University of Pittsburgh
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Abstract

Prompted by the “Panel Discussion of Grünbaum's Philosophy of Science” (Philosophy of Science 36, December, 1969) and other recent literature, this essay ranges over major issues in the philosophy of space, time and space-time as well as over problems in the logic of ascertaining the falsity of a scientific hypothesis.

The author's philosophy of geometry has recently been challenged along three main distinct lines as follows : (i) The Panel article by G. J. Massey calls for a more precise and more coherent account of the Riemannian conception of an intrinsic as opposed to an extrinsic metric, which the author has invoked as his basis for the distinction between non-conventional and convention-laden ascriptions of metrical equality and inequality; (ii) the latter distinction has been claimed to suffer from the liabilities of the so-called “standard conception” of scientific theories [36]; and (iii) pursuant to H. Putnam's “An Examination of Grünbaum's Philosophy of Geometry” [56], J. Earman [16, 17] and R. Swinburne [65] have contended that the difference between intrinsic and extrinsic metrics is scientifically unilluminating, and that the associated distinction between non-conventional and convention-laden metrical comparisons does not have the kind of relevance to extant scientific theories that the author has claimed for it.

The essay consists of two installments. The present installment, comprising the Introduction and Part A, is devoted to the clarification, correction and further development of the author's prior writings on the philosophy of geometry. Its main objective is constructive elaboration rather than offering polemics. But rebuttals to Earman, [16, 17], Swinburne [65] and Demopoulos [13] are included, because their inclusion conduced to clarity in giving the new exposition. Part B is to appear in a subsequent issue and will be devoted to replies to critiques contained in the Panel Discussion and in other recent literature. It will range over issues in the philosophy of geometry and in the logic of ascertaining the falsity of a scientific hypothesis.

By way of merely elliptical anticipation of much more precise statements given in Part A, section 3(ii), the Introduction dissociates the notion of convention-ladenness developed in Part A from the quite different notion integral to the so-called “standard conception” of scientific theories. Thereby, the Introduction prepares the ground for seeing, as a corollary to Part A, section 3(ii), that the notion advocated in the present essay has nothing to fear from the following fact, noted by C. G. Hempel ([36]; cf. also his 1970 Carus Lectures): “even though a sentence may originally be introduced as true by stipulation, it soon joins the club of all other member-statements of the theory and becomes subject to revision in response to further empirical findings and theoretical developments.”

Part A, which begins with a fairly detailed table of contents, endeavors to meet the aforementioned three-fold challenge to the author's philosophy of geometry. Massey's call for the provision of clear and detailed characterizations of intrinsic and extrinsic metrics is answered with the invaluable aid rendered personally by Massey himself. These characterizations are shown to permit a precise explication of the portions of Riemann's Inaugural Dissertation relevant to (1) Riemann's brilliant anticipation of Einstein's dynamical conception of physical geometry, and (2) the author's philosophical characterization of the metrics and geometries of space, time, and space-time {section 2(c)}.

A byproduct of the analysis is to raise two major philosophical doubts concerning Clifford's sketch of a so-called “space-theory of matter” as elaborated in J. A. Wheeler's relativistic geometrodynamics. That theory's vision of understanding matter as a manifestation of empty curved space is questioned in regard to (1) the existence of an intra-geometrodynamic basis for individuating the metrically homogeneous world points of its space-time manifold {section 1(a)}, and (2) the compatibility of the theory with the Riemannian metrical philosophy apparently espoused by its proponents {section 2(c) (i)}.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 4 , December 1970 , pp. 469 - 588
Copyright
Copyright © 1970 by The Philosophy of Science Association

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References

REFERENCES

[1] Adler, R., Bazin, M., and Schiffer, M., Introduction to General Relativity, McGraw-Hill, New York, 1965.Google Scholar
[2] Anderson, J. L., Principles of Relativity Physics, Academic Press, New York, 1967.CrossRefGoogle Scholar
[3] Arzeliès, H., Relativistic Kinematics, Pergamon Press, New York, 1966.Google Scholar
[4] Bergmann, P. G., “The General Theory of Relativity,” in Handbuch der Physik, vol. IV (ed. Flügge, S.), Springer, Berlin, 1962, pp. 203–272.Google Scholar
[5] Bondi, H., Cosmology, 2nd ed., Cambridge University Press, Cambridge, 1961.Google Scholar
[6] Bourbaki, N., Éléments d'Histoire des Mathématiques, Hermann, Paris, 1969.Google Scholar
[7] Bridgman, P. W., “Some implications of Recent Points of View in Physics,” Revue Internationale de Philosophie, vol. III, No. 10 (1949).Google Scholar
[8] Cech, E., Point Sets, Academic Press, New York, 1969.Google Scholar
[9] Clifford, W. K., The Common Sense of the Exact Sciences, Dover Publications, New York, 1955.Google Scholar
[10] Clifford, W. K., “On the Space Theory of Matter,” in The World of Mathematics, vol. 1 (ed. Newman, J. R.), Simon and Schuster, New York, 1956, pp. 568–569.Google Scholar
[11] Crombie, A. C., Robert Grosseteste and the Origins of Experimental Science, Oxford University Press, Oxford, 1953.Google Scholar
[12] d'Abro, A., The Evolution of Scientific Thought from Newton to Einstein, Dover Publications, New York, 1950.Google Scholar
[13] Demopoulos, W., “On the Relation of Topological to Metrical Structure,” in Minnesota Studies in the Philosophy of Science, vol. 4 (eds. M. Radner and S. Winokur), 1971.Google Scholar
[14] Earman, J., “Irreversibility and Temporal Asymmetry,” Journal of Philosophy, vol. 64 (1967), pp. 543–549.CrossRefGoogle Scholar
[15] Earman, J., “The Anisotropy of Time,” Australasian Journal of Philosophy, vol. 47 (1969), pp. 273–295.CrossRefGoogle Scholar
[16] Earman, J., “Are Spatial and Temporal Congruence Conventional?” (forthcoming).Google Scholar
[17] Earman, J., “Who is Afraid of Absolute Space?”, Australasian Journal of Philosophy, December, 1970.CrossRefGoogle Scholar
[18] Eddington, A. S., The Mathematical Theory of Relativity, Cambridge University Press, Cambridge, Mass. 1952.Google Scholar
[19] Einstein, A., “The Foundations of the General Theory of Relativity,” in The Principle of Relativity, A Collection of Original Memoirs, Dover Publications, New York, 1952.Google Scholar
[20] Einstein, A., “Geometry and Experience,” in Readings in the Philosophy of Science (eds. Feigl, H. and Brodbeck, M.), Appleton-Century-Crofts, New York, 1953, pp. 189–194.Google Scholar
[21] Eisenhart, L. P., Riemannian Geometry, Princeton University Press, Princeton, 1949.Google Scholar
[22] Feinberg, G., “Pulsar Test of a Variation of the Speed of Light with Frequency,” Science, vol. 166 (1969), pp. 879–881.CrossRefGoogle ScholarPubMed
[23] Grünbaum, A., “Geometry, Chronometry, and Empiricism,” in Minnesota Studies in the Philosophy of Science, vol. III (eds. Feigl, H. and Maxwell, G.), University of Minnesota Press, Minneapolis, 1962, pp. 405–526.Google Scholar
[24] Grünbaum, A., Philosophical Problems of Space and Time, Alfred Knopf, New York, 1963, and Routledge and Kegan Paul Ltd., London, 1964.Google Scholar
[25] Grünbaum, A., “The Falsifiability of a Component of a Theoretical System,” in Mind, Matter and Method: Essays in Philosophy and Science in Honor of Herbert Feigl (eds. Feyerabend, P. K. and Maxwell, G.), University of Minnesota Press, Minneapolis, 1966, pp. 273–305.Google Scholar
[26] Grünbaum, A., Modern Science and Zeno's Paradoxes, Wesleyan University Press, Middletown, Conn., 1967. A revised edition is listed next.Google Scholar
[27] Grünbaum, A., Modern Science and Zeno's Paradoxes, Allen and Unwin Ltd., London, 1968.Google Scholar
[28] Grünbaum, A., Geometry and Chronometry in Philosophical Perspective, University of Minnesota Press, Minneapolis, 1968.Google Scholar
[29] Grünbaum, A., “Are Physical Events Themselves Transiently Past, Present and Future? A Reply to H. A. C. Dobbs,” The British Journal for the Philosophy of Science, vol. 20 (1969), pp. 145–162.CrossRefGoogle Scholar
[30] Grünbaum, A., “Can We Ascertain the Falsity of a Scientific Hypothesis?” Studium Generale, vol. 22 (1969), pp. 1061–1093. This essay will also appear (revised) in Observation and Theory in Science, Johns Hopkins Press, 1971.Google Scholar
[31] Grünbaum, A., “Reply to Hilary Putnam's ‘An Examination of Grünbaum's Philosophy of Geometry’,” in Boston Studies in the Philosophy of Science, vol. V (eds. Cohen, R. S. and Wartofsky, M. W.), Reidel Publishing, Holland, 1969, pp. 1–150.Google Scholar
[32] Grünbaum, A., “Simultaneity by Slow Clock Transport in the Special Theory of Relativity,” Philosophy of Science, vol. 36 (1969), pp. 5–43.CrossRefGoogle Scholar
[33] Grünbaum, A., Salmon, W. C., van Fraassen, B. C., and Janis, A. I., “A Panel Discussion of Simultaneity by Slow Clock Transport in the Special and General Theories of Relativity,” Philosophy of Science, vol. 36 (Mar., 1969), pp. 1–81.CrossRefGoogle Scholar
[34] Halmos, P. R., Measure Theory, Van Nostrand, New York, 1950.CrossRefGoogle Scholar
[35] Hasse, H. and Scholz, H., Die Grundlagenkrisis der griechischen Mathematik, Pan-Verlag, Charlottenburg, 1928.CrossRefGoogle Scholar
[36] Hempel, C. G., “On the ‘Standard Conception’ of Scientific Theories,” in the Eisenberg Memorial Lecture Series, 1965-66 (ed. Suter, R.), Michigan State University Press, East Lansing, 1970.Google Scholar
[37] Heyting, A., Axiomatic Projective Geometry, North-Holland Publishing, Amsterdam, 1963.Google Scholar
[38] Hobson, E. W., The Theory of Functions of a Real Variable, vol. I, Dover Publications, New York, 1957.Google Scholar
[39] Huntington, E. V., “Inter-Relations Among the Four Principal Types of Order,” in Transactions of the American Mathematical Society, vol. 38 (1935), pp. 1–9.CrossRefGoogle Scholar
[40] Huntington, E. V., The Continuum and Other Types of Serial Order, 2nd ed., Harvard University Press, Cambridge, 1942.Google Scholar
[41] Hurewicz, W. and Wallman, H., Dimension Theory, Princeton University Press, Princeton, 1941.Google Scholar
[42] James, and James, , Mathematics Dictionary, 3rd ed., Van Nostrand, Princeton, 1968.Google Scholar
[43] Janis, A. I., “Synchronism by Slow Transport of Clocks in Noninertial Frames of Reference,” Philosophy of Science, vol. 36 (Mar., 1969), pp. 74–81.CrossRefGoogle Scholar
[44] Landau, L. and Lifschitz, E., The Classical Theory of Fields, Addison-Wesley Press, Cambridge, Mass., 1951.Google Scholar
[45] Leonard, H. S. and Goodman, N., “The Calculus of Individuals and Its Uses,” Journal of Symbolic Logic, vol. 5 (1940), pp. 45–55.CrossRefGoogle Scholar
[46] Lipschutz, S., General Topology, Schaum Publishing, New York, 1965.Google Scholar
[47] Luria, S., “Die Infinitesimaltheorie der antiken Atomisten,” Quellen und Studien zur Geschichte der Mathematik, Astronomie, und Physik, Abteilung B, Studien II, Berlin, 1933.Google Scholar
[48] Marzke, R. F. and Wheeler, J. A., “Gravitation as Geometry—I: The Geometry of Space-Time and the Geometrodynamical Standard Meter,” in Gravitation and Relativity (eds. Chin, H. and Hoffman, W. F.), W. A. Benjamin, New York, 1964.Google Scholar
[49] Massey, G. J., The Philosophy of Space, unpublished doctoral dissertation, Princeton University, 1963.Google Scholar
[50] Massey, G. J., “Toward a Clarification of Grünbaum's Concept of Intrinsic Metric,” Philosophy of Science, vol. 36 (1969), pp. 331–345.CrossRefGoogle Scholar
[51] Massey, G. J., Understanding Symbolic Logic, Harper and Row, New York, 1970.Google Scholar
[52] Massey, G. J., “Is ‘Congruence’ a Peculiar Predicate ?” in Boston Studies in the Philosophy of Science (Proceedings of the 1970 {2nd} Biennial Congress of the Philosophy of Science Association), (eds. R. C. Buck, and R. S. Cohen), to be published by Reidel, Holland.CrossRefGoogle Scholar
[53] Menger, K., Dimensionstheorie, B. G. Teubner, Leipzig, 1928.CrossRefGoogle Scholar
[54] M⊘ller, C., The Theory of Relativity, Oxford University Press, Oxford, 1952.Google Scholar
[55] Newton, I., Principia (ed. Cajori, F.), University of California Press, Berkeley, 1947.Google Scholar
[56] Putnam, H., “An Examination of Grünbaum's Philosophy of Geometry,” in Philosophy of Science, The Delaware Seminar, vol. 2 (ed. Baumrin, B.), Interscience, New York, 1963, pp. 205–255.Google Scholar
[57] Reichenbach, H., Philosophie der Raum-Zeit-Lehre, Walter de Gruyter and Co., Berlin, 1928.CrossRefGoogle Scholar
[58] Reichenbach, H., The Philosophy of Space and Time, Dover Publications, New York, 1958.Google Scholar
[59] Reichenbach, H., Axiomatization of the Theory of Relativity, University of California Press, Berkeley, 1969.Google Scholar
[60] Riemann, B., Gesammelte Mathematische Werke und Wissenschaftlicher Nachlass, 2nd ed. (ed. Weber, H.), Dover Publications, New York, 1953.Google Scholar
[61] Riemann, B., “On the Hypotheses Which Lie at the Foundations of Geometry,” in A Source Book in Mathematics, vol. II (ed. Smith, D. E.), Dover Publications, New York, 1959, pp. 411–425.Google Scholar
[62] Russell, B., “Sur les Axiomes de la Géométrie,” Revue de Métaphysique et de Morale, vol. VII (1899), pp. 684–707.Google Scholar
[63] Russell, B., The Foundations of Geometry, Dover Publications, New York, 1956.Google Scholar
[64] Schrödinger, E., Expanding Universes, Cambridge University Press, Cambridge, 1956.CrossRefGoogle Scholar
[65] Swinburne, R., Review of A. Grünbaum's Geometry and Chronometry in Philosophical Perspective in The British Journal for the Philosophy of Science, vol. 21 (1970) pp. 308–311.CrossRefGoogle Scholar
[66] Synge, J. L., Relativity: The Special Theory, North-Holland Publishing, Amsterdam, 1956.Google Scholar
[67] Tarski, A., “What is Elementary Geometry?”, in The Axiomatic Method (eds. Henkin, L., Suppes, P. and Tarski, A.), North-Holland Publishing, Amsterdam, 1959.Google Scholar
[68] van Fraassen, B., “On Massey's Explication of Grünbaum's Conception of Metric,” Philosophy of Science, vol. 36 (1969), pp. 346–353.CrossRefGoogle Scholar
[69] Veblen, O., “The Foundations of Geometry,” in Modern Mathematics (ed. Young, J. W. A.), Dover Publications, New York, 1955, pp. 3–51.Google Scholar
[70] Weatherburn, C. E., Riemannian Geometry and the Tensor Calculus, Cambridge University Press, Cambridge, Mass., 1957.Google Scholar
[71] Weyl, H., Space-Time-Matter, Dover Publications, New York, 1950.Google Scholar
[72] Wheeler, J. A., “Gravitation as Geometry—II,” in Gravitation and Relativity (eds. Chin, H. and Hoffman, W. F.), W. A. Benjamin, New York, 1964.Google Scholar
[73] Wheeler, J. A., Geometrodynamics, Academic Press, New York, 1962.Google Scholar
[74] Wheeler, J. A., Einsteins Vision, Springer-Verlag, Berlin, 1968.10.1007/978-3-642-86531-2CrossRefGoogle Scholar
[75] Wheeler, J. A., “Particles and Geometry,” in Relativity (eds. Carmeli, M., Fickler, S. I., and Witten, L.), Plenum Press, New York, 1970.Google Scholar