Abstract
In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms (conceptual conventions), the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities (coordinative definitions), and conventions that are made possible by possible revisions to theory (the thesis of empirical underdetermination). I claim that it is not possible to interpret the Principle of Relativity as based on one of these three types of convention. This renders the conventionalist interpretation of the Principle of Relativity untenable. The paper is part of a larger project that aims to understand the philosophical significance of the Principle of Relativity.
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Notes
In the following I use “positivism” as a broad term, involving an overall commitment to the verificationist theory of meaning. Early proponents of logical positivism adopted a narrow interpretation of the verificationist theory of meaning, according to which theoretical statements are logically reducible to observation statements. In contradistinction, Logical Empiricists adopted a looser verificationist principle. According to their approach, theoretical statements are only indirectly or partially verifiable using observation statements. I refer to the distinction between Positivism and Logical Empiricism only in contexts where the distinction is relevant.
I will exclude discussion of epistemological approaches to geometry that take intuitions about infinitesimal parts of space to be guiding our construction of geometric knowledge. Such approaches are prevalent among thinkers who were involved in the development of group-theoretical concepts, such as Lie, Klein and Weyl. See Ryckman (1994, 2005) for an examination of these approaches as contextual alternatives to conventionalist accounts of the General PR. See also Darrigol (forthcoming) for a modern attempt at reviving such an approach.
Ben Menahem (2006) distinguishes between two kinds of conventionalist claims: the first is the thesis that scientific theory is underdetermined by the evidence, the second is the notion that fundamental scientific propositions are reducible to conventions because of their foundational roles. According to Ben-Menahem these two theses are often run together in the literature. In this paper, I further argue that commentators often conflate conceptual and coordinative definitions, which are distinct types of convention.
Stump (2015, Chapter 3) argues that there is a difference between the types of conventionalism endorsed by Poincaré in relation to geometry and mechanical principles. He pegs this difference on Poincaré commitment to the relational nature of space, which then explains the more radical conventionalism Poincaré holds with regards to geometry. But I think a simpler explanation exists for Poincaré’s varying attitudes towards geometry and mechanical principles; namely, that mechanical principles do not presupposes coordinative definitions between bodies described by the axiomatic system and bodies described by a physical science.
For a modern Neo-Kantian revival of Reichenbach’s early views see Holland (1992).
See Padovani (2011) for the distinction between various kinds of axioms of coordination.
The correspondence can be accessed in http://quantum-history.mpiwg-berlin.mpg.de/eLibrary/sources/ms-hr/hr-ms. In the following I will refer to the Schlick Reichenbach correspondence as the SRC.
Friedman (1991, 1994) and Howard (1994) explain the positivist critique of synthetic à priori principles as one of the central motivations for the logical positivist school in general. It seems that Einstein himself was influenced by Schlick’s writings during the period of 1915–1918. See Howard (1984).
In the discussion here I do not attend to the confusion in Reichenbach’s thinking between coordinate systems and reference frames, a confusion that was initially present in Einstein’s thinking as well. Reichenbach assumed that general covariance is directly related to a conventionalism about reference frames, but this was famously shown to be a mistaken assumption by Kretschmann (1917). Furthermore, I do not consider the problems of articulating the thesis of geometric conventionalism in the context of the GTR. Weatherall and Manchak (2014) argue that Reichenbach’s general outline for articulating the conventionalist thesis cannot be used to define alternative force-fields via conventional choices of the metric \(G_{\mu \nu }\). These issues are mostly irrelevant to the general argument of this paper, namely, that there is a further conflation in Reichenbach’s thought between conceptual and coordinative definitions.
See also Reichenbach’s letter to Schlick from 29.11.2020 in the SRC.
In Tal (2013) we see a critique of conventionalist epistemology, which for him, makes it seem as if once the convention is selected, one relies on laws of nature and empirical observations to see what follows from the convention. Tal objects to this view because it fails to see the iterative process, occurring for example, in setting standards for the measurement of time. The iterative process of correction and idealization results in an intricate relation between the conventional and empirical elements of measurement, which involves revising the conventional element of measurement standards both prior to and posterior to experiments.
See Reichenbach (1938, 14–15).
For the appropriation of Hilbert by the logical-positivists see Majer (2002).
The situation becomes different when we use the Kelvin scale, since the value zero of this particular scale is not given arbitrarily, and negative numbers have no meaning on the scale.
This is why Minkowski’s (1952) account of space-time, as having symmetries analogous to the symmetries of Euclidean space, forms a better explanation for the equivalence between inertial references frames. The account explains the equivalence as a mathematical symmetry, not an equivalence between different applications of the theory.
References
Balashov, Y., & Janssen, M. (2003). Critical notice: Presentism and relativity. British Journal for the Philosophy of Science, 54, 327–346.
Ben Menahem, Y. (2006). Conventionalism. Cambridge: Cambridge University Press.
Brown, H. R. (2005). Physical relativity: Space-time structure from a dynamical perspective. Oxford: Oxford University Press.
Carnap, R. (1936). Testability and meaning. Philosophy of Science, 3, 419–471.
Carnap, R. (1937a). Testability and meaning—Continued. Philosophy of Science, 4, 1–40.
Carnap, R. (1937b). The logical syntax of language. London: Routledge & Kegan Paul.
Carnap, R. (1956). The methodological character of theoretical concepts. In H. Feigl & M. Scriven (Eds.), The foundations of science and the concepts of psychology and psychoanalysis, volume 1 of Minnesota studies in the philosophy of science (pp. 38–76). Minneapolis: University of Minnesota Press.
Darrigol, O. (forthcoming). Constitutive principles versus comprehensibility conditions in post-Kantian physics. Synthese.
Einstein, A. (1952). On the electrodynamics of moving bodies. In The principle of relativity, (pp. 37–65). Dover.
Friedman, M. (1983). Foundations of space-time theories. Cambridge: MIT Press.
Friedman, M. (1991). The re-evaluation of logical positivism. The Journal of Philosophy, 88, 505–519.
Friedman, M. (1994). Geometry, convention, and the relativized a priori: Reichenbach, Schlick, and Carnap. In W. C. Salmon & G. Wolters (Eds.), Logic, language, and the structure of scientific theories. Pittsburgh: University of Pittsburgh Press.
Friedman, M. (1999). Reconsidering logical positivism. Cambridge: Cambridge University Press.
Grünbaum, A. (1963). Philosophical problems of space and time. New York: Knopf.
Hilbert, D. (1950). Foundations of geometry. Chicago: Open Court.
Holland, R. (1992). Kant, Reichenbach, and aprioricity. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 66, 209–233.
Howard, D. (1984). Realism and conventionalism in Einstein’s philosophy of science: The Einstein–Schlick correspondence. Philosophia Naturalis, 21, 616–629.
Howard, D. (1994). Einstein, Kant, and the origins of logical empiricism. In W. C. Salmon & G. Wolters (Eds.), Logic, language, and the structure of scientific theories (pp. 45–105). Pittsburgh: University of Pittsburgh Press.
Janssen, M. (2009). Drawing the line between kinematics and dynamics in special relativity. Studies in History and Philosophy of Modern Physics, 40, 26–52.
Kretschmann, E. (1917). Über den physikalischen Sinn der Relativitätpostulate, A. Einsteins neue und seine ursprünglische Relativitätstheorie. Annalen der Physik, 53, 575–614.
Majer, U. (2002). Hilbert’s program to axiomatize physics (in analogy to geometry) and its impact on Schlick, Carnap and other members of the Vienna Circle. In H. Sadler (Ed.), History of philosophy and science (Vol. 9, pp. 213–224). Kluwer.
Maudlin, T. (2012). Philosophy of physics: Space and time. Princeton: Princeton University Press.
Minkowski, H. (1952). Space and time. In the principle of relativity. New York: Dover.
Mühlhölzer, F. (1991). Equivalent descriptions. Erkenntnis, 35, 77–97.
Nerlich, G. (1976). The shape of space. Cambridge: Cambridge University Press.
Norton, J. (1994). Science and certainty. Synthese, 99, 3–22.
Padovani, F. (2011). Relativizing the relativized a priori: Reichenbach’s axioms of coordination divided. Synthese, 181, 41–62.
Poincaré, H. (1905). Science and hypothesis. London: Walter Scott Publishing.
Putnam, H. (1983). Equivalence. In Philosophical papers, volume 3: Realism and reason (pp. 26–45). Cambridge University Press.
Reichenbach, H. (1928). The philosophy of space and time. New York: Dover.
Reichenbach, H. (1938). Experience and prediction: An analysis of the foundation and the structure of knowledge. Chicago: University of Chicago Press.
Reichenbach, H. (1959). The philosophical significance of the theory of relativity. In P. A. Schilpp (Ed.), Albert Einstein: Philosopher scientist (Vol. I, pp. 289–311). New York: Harper.
Reichenbach, H. (1965) [1920]. The theory of relativity and a priori knowledge. University of California Press.
Reichenbach, H. (1969) [1924]. Axiomatization of the theory of relativity. University of California Press.
Ryckman, T. (1994). Weyl, Reichenbach and the epistemology of geometry. Studies in History and Philosophy of Science, 25, 831–870.
Ryckman, T. (2005). The reign of relativity, philosophy in physics 1915–1925. Oxford: Oxford University Press.
Schlick, M. (1978). The philosophical significance of relativity. In H. L. Mulder & B. F. B. Van De Velde-Schlick (Eds.), Moritz Schlick: Philosophical papers. Volume 1: (1909–1922) (pp. 153–189). Dordrecht: D. Reidel Publishing Company.
Schlick, M. (1979). Are natural laws conventions? In B. V. D. Velde-Schlick & H. L. Mulder (Eds.), Moritz Schlick: Philosophical papers (Vol. 2, pp. 437–445). Dordrecht: Reidel.
Schlick, M. (1985). General theory of knowledge. Chicago: Open Court.
Schlick, M. (2005). Space and time in contemporary physics: An introduction to the theory of relativity and gravitation. New York: Dover.
Stump, D. J. (2015). Conceptual change and the philosophy of science: Alternative interpretations of the a priori. London: Routledge.
Tal, E. (2013). Old and new problems in philosophy of measurement. Philosophy Compass, 8, 1159–1173.
Weatherall, J. O., & Manchak, J. B. (2014). The geometry of conventionality. Philosophy of Science, 81, 233–247.
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Funding was supported by the Israel Science Foundation (Grant No. 992/19).
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Belkind, O. Conventionalism in Early Analytic Philosophy and the Principle of Relativity. Erkenn 87, 827–852 (2022). https://doi.org/10.1007/s10670-020-00220-9
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DOI: https://doi.org/10.1007/s10670-020-00220-9