Un-conventional wisdom: theory-specificity in Reichenbach's geometric conventionalism

https://doi.org/10.1016/j.shpsb.2004.04.005Get rights and content

Abstract

The standard account portrays Hans Reichenbach's argument for geometric conventionalism as based upon general epistemological concerns of verifiability. As such, his version of conventionalism ought to be equally well applicable to all theories that posit a geometric structure to space–time. But when Reichenbach's writings from the period between the publication of Relativitätstheorie und Erkenntnis Apriori and Axiomatik der Raum-Zeit-Lehre, i.e., between 1920 and 1924, are examined, a very different picture emerges. The argument for the conventionality of geometry that appears in these writings is tied to discussions of the theory of general relativity and Reichenbach explicitly argues that geometry in Minkowski space–time is not conventional once the definition of simultaneity is put in place. In light of this, the received interpretation of Reichenbach's position needs to be replaced with a theory-specific picture of geometric conventionalism. This change has interesting consequences for both the standard arguments against Reichenbach's view and for questions in Reichenbach scholarship.

Section snippets

The standard interpretation and refutation of Reichenbach's geometric conventionalism

The received view of Reichenbach's geometric conventionalism connects the argument from universal forces in Philosophie der Raum-Zeit-Lehre (Reichenbach, 1928) back to the pre-relativistic discussions of Henri Poincaré.1 Poincaré (1902) argued that all statements concerning physical geometry are necessarily entangled with statements about physical interactions of bodies and this grants us a degree of epistemological freedom in

Friedman and Coffa on the emergence of Reichenbach's conventionalist doctrine

It is pointed out that Reichenbach was not always a geometric conventionalist. Indeed in his first book, he explicitly argues that the use of Riemannian geometry in the general theory of relativity (GTR) undercuts Poincaré's claims of geometric conventionality (Reichenbach, 1920a, p. 4 fn. 1).2

The wissenschaftsanalytische methode

Both Friedman's and Coffa's accounts are based on the supposition that the move to geometric conventionalism signals a foundational change in Reichenbach's approach between 1920 and 1924. While these depictions are both of great importance in shedding light on Reichenbach's intellectual trajectory, they fail to fully note the coherence of his work in that period. If (1920a) is examined in terms of epistemological methodology—his so-called wissenschaftsanalytische Methode—and the limited goal of

Theory-dependence in Reichenbach's early writings

What is striking about Reichenbach's writings between 1920 and 1924, indeed as far forward as 1928, the year of publication of Philosophie der Raum-Zeit-Lehre—the supposed hallmark of positivist conventionalism—is the lack of discussions about the conventional nature of physical geometry. Reichenbach's articles on relativity, space, time, and motion in this period are devoted primarily to issues of time, focusing largely on refuting proposed means of determining an absolute non-local

Geometric conventionalism and the general theory of relativity

Reichenbach's geometric conventionalism first appears in (1922a).10 Here we see the notion of universal forces appear as “forces of type X” (forces d’espèce X) in an early version of the well-known argument from empirical underdetermination. But the full context of this discussion is something quite different from the presentation in the standard interpretation.

Reichenbach begins the piece with a discussion of the special theory and absolute simultaneity.

Reichenbach's mature conventionalist doctrine

So what then ought we make of the discussion of universal forces in the opening section of Philosophie der Raum-Zeit-Lehre? Certainly, this discussion does not occur in the context of an axiomatic treatment of the GTR and looks clearly to be based upon general concerns of verifiability. Did the view change between 1924 and 1928? It did not.

Philosophie der Raum-Zeit-Lehre was a victim of its own success. Its praises are sung by the most notable names in the history of field. In addition to

References (31)

  • T. Ryckman

    Weyl, Reichenbach, and the epistemology of geometry

    Studies in the History and Philosophy of Science

    (1994)
  • J. Coffa

    The semantic traditionFrom Kant to Carnap

    (1990)
  • Einstein, A. (1905). On the electrodynamics of moving bodies. In The principle of relativity (pp. 35–65). New York:...
  • Einstein, A. (1921). Geometry and experience. In Sidelights on relativity (pp. 25–56). New York:...
  • M. Friedman

    Foundations of space–time theories

    (1983)
  • M. Friedman

    Geometry, convention, and the relativized a prioriReichenbach, Schlick and Carnap

  • M. Friedman

    Logical positivism reconsidered

    (1999)
  • C. Glymour

    Theory and evidence

    (1980)
  • Grünbaum, A. (1973). Philosophical problems of space and time. In Boston studies in the philosophy of science, Vol....
  • D. Howard

    Realism and conventionalism in Einstein's philosophy of scienceThe Einstein–Schlick correspondence

    Philosophia Naturalis

    (1984)
  • H. Poincaré

    Science and hypothesis

    (1902)
  • H. Poincaré

    The value of science

    (1905)
  • Reichenbach, H. (1920a). Relativitätstheorie und Erkenntnis Apriori. Berlin: Julius Springer. Translated as Theory of...
  • H. Reichenbach

    Die Einsteinsche Raumlehre

    Die Umschau

    (1920)
  • H. Reichenbach

    Bericht über eine Axiomatik der Einsteinsche Raum-Zeit-Lehre

    Physikalische Zeitschrift

    (1921)
  • Cited by (1)

    View full text