Abstract
Lorenzen rejects ontological commitments of relativity. Realism of physical geometry already breaks down with Poincaré’s arguments. Lorenzen agrees with Poincaré, but offers a constructive account: space is not an empirical entity described by means of conventions , but a purely constructive entity constituted by the norms of spatial measurement . This space however, as Lorenzen argues, is Euclidean. In this paper, we shall analyse Lorenzen arguments and explicate how they relate to arguments from empiricism and neo-kantianism. It will be shown that the originality of Lorenzen’s position consists in systematically accounting for the role of measurement and measurement instruments.
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Notes
- 1.
Cf. Reichenbach’s critique of Kraus: “On the basis of an apriorist philosophy, he wants to assert something about the behaviour of physical things; he wants to deduce physics from philosophy”, in Reichenbach (1978, Vol. II, 8).
- 2.
In his Vorwort to Dingler’s Aufbau der exakten Fundamentalwissenschaften, Lorenzen presented Dinglers philosophy as a continuation of the Kantian transcendental philosophy after its collapse in the face of empiricist attacks in nineteenth century (Lorenzen 1964, p. 10). As an interpretation of Dingler’s philosophy this may be regarded as too benevolent. As a characterization of his own point of view it may however be accepted. In particular it is evident from this that Lorenzen’s concept of a priori is closely related to Reichenbach’s “relative a priori ” in being constitutive but not apodictic.
- 3.
As is known, Kant considered the regress of splitting matter to be infinite. I agree with Wilhelm Wundt that this assumption rests on a mistake and that in effect every regress is indefinite—cf. Wundt (1910, pp. 82–83).
- 4.
As a straightforward presentation of this issue cf. Leibniz’ letter to de l’Hospital, in Leibniz (2004, pp. 616–625).
- 5.
This is the—very plausible—interpretation of Freudenthal (1999).
- 6.
Of course inertia does not figure in Newton’s Mathematical Principles of Natural Philosophy as an explanatory baseline, but is (in definition III) attributed to matter as a faculty, the potentia resistendi. Nevertheless, this does not change the functional role of inertia in the science of mechanics.
- 7.
- 8.
As Michael Wolff recently has shown (Wolff 2001), Kant’s notion of geometry corresponds perfectly to the idea of a theory of forms. The straight line for example is defined by Kant in purely qualitative terms as a self-similar line, i.e. as a line whose parts are similar both to each other and to the whole line. The quantitative archimedean property of being the shortest line connecting two points is inferred from this definition in a synthetical way, presenting thus a synthetic a priori judgment. Also Bertrand Russell (1896, p. 38) stressed that the straight line, “if it is to serve as the basis of metrical properties, has to be defined without reference to this properties” and thus in a purely qualitative way.
- 9.
Lorenzen’s Elementrageometrie in fact fails to give a non-circular criterion of rigidity. Nevertheless this failure was not due to the strategy developed there. For a more promising realisation of this program cf. Janich (1976).
- 10.
For more details on the notion of projective geometry and its use by Russell cf. Torretti (1978, pp. 303–307).
- 11.
Walter (2009, pp. 194–195), is thus wrong in counting Couturat among the neo-Kantians.
- 12.
As regards the role of rational principles in Couturat, cf. Bowne (1966).
- 13.
- 14.
Lorenzen’s point of view obviously is closely related to the revival of the Lorentzian approach to relativity in the recent work of Harvey Brown (1995). For a comparison of Lorenzen and Brown, both of them referring to Lorentz, it should be noted the they used the notion of kinematics in a quite different way: For Brown kinematics includes the comparison of different frames of reference while for Lorenzen it is restricted to movements in a single frame. Brown shows that Lorentz’s approach still holds when the existence of the ether is denied—which is indeed a precondition of its reevaluation. More interesting for the present purpose is the reason of its reinvestigation. Brown links the discussion of the interpretation of the effects deduced from Lorentz-transformations directly to the concept of explanation. He suggests that an explanation must always be given in terms of a mechanism (Brown 1995, pp. 8, 24), a coupling (Brown 1995, p. 24), or an interaction (Brown 1995, p. 140), and thus that space-time is ruled out as an explanans—at least in special relativity for particles have no “space-time feelers” (Brown 1995, p. 24). In the case of general relativity Brown revises his opinion because here particles and the space-time-structure indeed interact (Brown 1995, p. 150).
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Schlaudt, O. (2014). Geometry as a Measurement-Theoretical A Priori: Lorenzen’s Defense of Relativity Against the Ontology of Its Proponents. In: Rebuschi, M., Batt, M., Heinzmann, G., Lihoreau, F., Musiol, M., Trognon, A. (eds) Interdisciplinary Works in Logic, Epistemology, Psychology and Linguistics. Logic, Argumentation & Reasoning, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-03044-9_3
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