Logical positivism

2. Relativistic physics

Albert Einstein’s special (1905) and general (1916) theories of relativity entered this volatile intellectual situation as a revelation (see Einstein, A.; General relativity, philosophical responses to; Relativity theory, philosophical significance of). And the relativistic revolution in physics directly stimulated Schlick, Reichenbach and Carnap to initiate a parallel revolution in scientific philosophy. All three thinkers agreed that relativity – especially through the general relativistic description of gravitation via a (four-dimensional) geometry of variable curvature – definitively refutes the Kantian idea that Euclidean geometry is synthetic a priori. Moreover, relativity arises from critical reflection on the empirical significance of spatiotemporal concepts in physics (in particular, the concept of simultaneity and the concept of motion) and thus demonstrates the fruitfulness of Mach’s basic point of view. At the same time, however, through its use of sophisticated abstract mathematics, relativity also illustrates the limitations of Machian empiricism (according to which even mathematical concepts have an empirical origin). All three thinkers therefore attempted to formulate an intermediate position that would do justice to both Machian empiricism and the continued importance of a priori mathematical elements in physics. Poincaré’s concept of convention came to play a central role.

Schlick, Reichenbach and Carnap first pursued rather different paths. Whereas Schlick emphasized from the outset that the Kantian synthetic a priori has no place at all in the new relativistic context, Reichenbach and Carnap initially attempted to salvage important aspects of Kantianism. Reichenbach began by distinguishing the idea of necessary and unrevisable truth from the idea of necessary presupposition of a given scientific conceptualization of nature. For Reichenbach, relativity refuted the former but embodied the latter. Kant was right that the necessary presuppositions of Newtonian physics included Euclidean geometry and the laws of motion. In moving to relativistic physics, however, these are replaced by fundamentally new presuppositions. We thus end up with a relativized version of the Kantian a priori (as constituting the presuppositions of a particular theory). Carnap, by contrast, began by distinguishing metrical from topological features of physical space. The latter are indeed synthetic a priori as Kant thought (they even depend on a kind of pure intuition), but the former – as general relativity has shown – essentially involve the behaviour of empirically given bodies. We thus end up with a weakening of the Kantian a priori (from metrical to topological features).

These early attempts to salvage aspects of the synthetic a priori did not survive, however. For Schlick’s view that relativity is simply incompatible with Kant eventually won the day. Although the distinction between Poincaré’s conventionalism and Helmholtzian empiricism was not entirely clear (and Reichenbach, in particular, preferred to associate his later viewpoint with Helmholtz rather than Poincaré), both Reichenbach and Carnap soon came to replace the Kantian notion of the a priori with Poincaré’s concept of convention. Yet this form of conventionalism (unlike Poincaré‘s) was forged in the crucible of a revolutionary new physics and thus demonstrated the vitality and relevance of a new philosophy.