This paper compares Cassirer´s and Bohr´s views on symbolic knowledge in quantum physics. Although both of them consider quantum physics as symbolic knowledge, for Cassirer this amounts to a complete renunciation to intuition in quantum physics, while according to Bohr only spatio-temporal images may provide the mathematical formalism of the theory with physical reference. We show the Kantian roots of Bohr´s position and we claim that his Kantian concept of symbol enables Bohr to account for the sensible content of quantum theory as well as for its systematic relation to classical physics.
This paper compares Cassirer´s and Bohr´s views on symbolic knowledge in quantum physics. Although both of them consider quantum physics as symbolic knowledge, for Cassirer this amounts to a complete renunciation to intuition in quantum physics, while according to Bohr only spatio-temporal images may provide the mathematical formalism of the theory with physical reference. We show the Kantian roots of Bohr´s position and we claim that his Kantian concept of symbol enables Bohr to account for the sensible content of quantum theory as well as for its systematic relation to classical physics.
Je me propose dans ce travail de comparer la fonction épistémologique que Cassirer assigne à l'intuition sensible dans la physique quantique à celle qui lui est attribuée par Bohr. Je montrerai que tous deux coïncident sur l'impossibilité de considérer les représentations spatio-temporelles comme des exhibitions directes d'objets et de processus atomiques dans l?intuition. En ce sens, tout autant Cassirer que Bohr considèrent que notre connaissance du domaine quantique est une connaissance symbolique. Cependant, alors que pour Cassirer ceci implique que les images spatio-temporelles ne jouent aucun rôle dans la physique quantique, Bohr soutient que ce sont ces images qui apportent une référence physique au formalisme mathématique de la théorie. Au lieu de se réjouir comme Cassirer d'un soi-disant abandon des représentations sensibles en physique atomique, Bohr soutient que celles-ci doivent être conservées pour que les objets et les processus quantiques soient exhibés indirectement dans l'intuition. Je montrerai qu'avec cette position, Bohr adopte un concept de symbole plus proche de celui de Kant que celui que propose le néokantien Cassirer dont les caractéristiques sont, dans un certain sens, plutôt leibniziennes. À la lumière de cette analyse, nous verrons que, pour Cassirer, ce n'est qu'à travers un renoncement complet aux représentations sensibles en physique quantique qu'il est possible d'atteindre une systématicité dans la connaissance physique. Je soutiendrai que Bohr, au contraire, est capable de rendre compte aussi bien de la référence empirique de la théorie quantique, que de sa relation systématique avec la physique classique.
In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed how we conceive our knowledge of the world. Face to this new situation, what was changed in our classical reason? However, if the transcendental point of view is adopted, in the specific case of quantum mechanics, we have to wonder about the general conditions of this theory that make possible such knowledge, which predictive value is much more accurate than the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support to a transcendental pragmatic position in the analysis of science.
Abstract: In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed how we conceive our knowledge of the world. Face to this new situation, what was changed in our classical reason? However, if the transcendental point of view is adopted, in the specific case of quantum mechanics, we have to wonder about the general conditions of this theory that make possible such knowledge, which predictive value is much more accurate than the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support to a transcendental pragmatic position in the analysis of science.
According to Kant, intuition is a non-logical mental form of representation, one that serves partly to idealize conceptual contents and partly to render them concrete. In performing this task, intuition fulfills the semantic function of giving sense and significance to formal concepts. With reference to Kant, Bohr and Heisenberg demand that abstract quantum theory be interpreted intuitively by means of complementary classical descriptions of phenomena. This interpretation rests on Bohr’s correspondence principle, which gives sense and significance to abstract quantum theory. Since today’s physics does not have consistent axiomatic foundations, Bohr’s principle is required as a bridge principle, in order to give a physical interpretation of quantum mechanical states with recourse to classical magnitudes. In the case of the Feynman diagrams of quantum field theory, by contrast, intuition merely has the function of making a complex theoretical calculus comprehensible by means of iconic representation.
A draft of a possible comparison between the use made of mathematics in classical field theories and in quantum mechanics is presented. Hilbert’s space formalism, although not only elegant and powerful but intuitive as well, does not give us a spatio-temporal representation of physical events. The picture of the electromagnetic field as an entity which is real in itself – i.e., as a wave without support – fostered by the emergence of special relativity can be seen as the first step, favored by many physicists and philosophers, of a gradual “escape” from intuition into a purely mathematical representation of the external world. After the introduction, in recent theoretical physics, of fiber bundle formalism the classical notion of field acquires a new spatio-temporal intuitiveness. This intuitiveness is clearly foreshadowed in the Kantian and Meinongian analysis of the notion of magnitude. At the end of the paper we show that, contrary to what happens in quantum mechanics, mathematics plays a truly explicative role in general relativity, without any loss of spatio-temporal intuitiveness.
Determinismus und Indeterminismus in der modernen Physik (DI) is one of Cassirer’s least known and studied works, despite his own assessment as “one of his most important achievements” (Gawronsky 1949, 29). A prominent theme locates quantum mechanics as a yet further step of the tendency within physical theory towards the purely functional theory of the concept and functional characterization of objectivity. In this respect DI can be considered an “update”, like the earlier monograph Zur Einsteinschen Relativitätstheorie: Erkenntnistheoretische Betrachtungen (1921), to Substanzbegriff und Funktionsbegriff (1910), a seminal work considering only classical and pre-relativistic physics. But how does DI cohere with the three volumes of The Philosophy of Symbolic Forms (1923–29) providing a systematic survey of symbolic meanings in diverse aspects of culture, each with its own mode of “objectification” via self-created signs and images? Cassirer’s “phenomenology of cognition” via distinct types of symbolic form locates Dirac’s Principles of Quantum Mechanics (1930) as an exemplar within physical theory of purely symbolic thought, a realm of pure relations and their correlated meanings. In particular, Dirac’s characterization of the new notion of “physical state” in quantum mechanics by a “symbolic algebra of observables” severed from particular representations points to a limiting pole of the Bedeutungsfunktion, the third and highest mode of symbolic formation.