Logical positivism

1. Historical background

Immanuel Kant, in the positivists’ eyes, had made a lasting contribution to scientific philosophy – particularly in his rejection of the possibility of supersensible metaphysical knowledge and his reorientation of theoretical philosophy around the two questions ‘how is pure mathematics possible?’ and ‘how is pure natural science possible?’ In answering these questions Kant developed his famous defence of synthetic a priori knowledge – knowledge independent of sensible experience yet nonetheless substantively applicable to the empirical world. For Kant, the mathematical physics of Newton paradigmatically exemplified such synthetic a priori knowledge through its reliance on Euclidean geometry and fundamental laws of motion such as the law of inertia. Kant’s theory of a priori faculties of the mind – the faculty of pure intuition or sensibility and the faculty of pure understanding – was then intended to explain the origin of synthetic a priori knowledge and thus make philosophically comprehensible the possibility of Newtonian mathematical physics.

After the intervening dominance of post-Kantian idealism, a number of German-speaking philosophers renewed the call for a scientific, epistemological and non-metaphysical form of philosophy. But these Neo-Kantian philosophers also had to face an important new challenge to the Kantian synthetic a priori: the nineteenth-century development of non-Euclidean geometry by Gauss, Bolyai, Lobachevskii, Riemann and Klein (see Geometry, philosophical issues in §§1, 3). Although some Neo-Kantians attempted to defend the uniqueness and apriority of Euclidean geometry nonetheless, others – especially those of the Marburg School such as Paul Natorp and Ernst Cassirer – aimed to generalize the synthetic a priori beyond its particular embodiment in classical Euclidean–Newtonian mathematical physics (see Neo-Kantianism). This latter tendency was similar in important respects to ideas the logical positivists were to elaborate.

But the most important nineteenth-century predecessors of logical positivism were Hermann von Helmholtz, Ernst Mach and Henri Poincaré. Through their efforts to comprehend the radical changes sweeping through nineteenth-century science, these three thinkers initiated a new style of scientific philosophy later taken up and systematized by the positivists. The changes in question included the rise of non-Euclidean geometry, the formulation of the conservation of energy and general thermodynamics, and the beginnings of scientific physiology and psychology. Helmholtz made fundamental contributions to all three areas. He based geometry on the postulate of ‘free mobility’ of rigid bodies, and, since all classical geometries of constant curvature – negative, positive or zero (Euclidean) – satisfy this postulate, he opposed the Kantian commitment to the aprioricity of geometry: whether space is Euclidean or non-Euclidean is an empirical question about the actual behaviour of rigid bodies. In physiology, Helmholtz articulated a general principle of psycho-physical correlation whereby our sensations correspond to – but are in no way pictures or images of – processes in the external physical world. These processes consist, in the end, of microscopic atoms interacting via central forces, and, on this basis, Helmholtz developed his famous interpretation of the conservation of energy.

Mach and Poincaré can be seen as reacting, in diverse ways, to Helmholtz. Mach attacked especially atomism and the idea of a psychophysical correlation between two incommensurable realms, and he advanced a programme for the unity of science based on immediately perceptible ‘elements’ or ‘sensations’. The task of science consists solely in seeking correlations among such elements (as in phenomenological thermodynamics), and all dualistic and atomistic tendencies are to be purged as metaphysical via historico-critical analysis. This Machian empiricism exerted a decisive influence on the logical positivists. Poincaré, on the other hand, influenced the positivists primarily through his philosophy of geometry. He agreed with Helmholtz’s emphasis on the free mobility of rigid bodies but disagreed with Helmholtz’s empiricism. According to Poincaré, the idea of a rigid body is an idealization that cannot be straightforwardly instantiated in the physical world. By freely choosing one of the three classical geometries as, so to speak, a definition of rigidity, we then first make it possible to carry out empirical investigations with real physical bodies. Physical geometry is thus neither synthetic a priori nor empirical: it is ‘conventional’ (see Conventionalism).