Publication Details

Abstract

The present paper represents a philosophical analysis of the attempts of Birkhoff, Neumann, Fevrier, Weizsäcker, Reichenbach, Kuznecov etc. to build up the logic of quantum mechanics. In quantum mechanics special genetic structures are being unveiled which are not known in classical physics: at the potential level of reality, they act as the co-existence of possibilities which — at the actual level of realiy — disjoin as incommensurable aspects of the same object, mutually completing each other. To express such a structure, they need a theoretical language in which mathematical equations are constructed which are observationally meaningless (Bohr-Heisenberg), undecidable (Weizsäcker) or indeterminate (Reichenbach). By means of reduction, complementary statements are obtained from them; these statements describe the wave-corpuscular duality. The incorporation of such a structure into the theories of a certain type is a necessary condition of the preservation of their logical non-contradicoriness. The language of such theories requires a richer logical system than the classical (Boolian) logic. It is noted for the incorporation of new, non-classical, extralogical constants which represent new forms of thought. The attempts to build it start either from the invalidity of distributive laws, or from the invalidity (or limited validity) of the law of tercium non datur. The present author points out a whole range of signs in which the given genetic structure agrees with the contradictory structure analysed by Marx in The Capital. The analogy is evident, especially at the phenomenological level and in the differentiation of the outer incommensurability (duality) and the inner co-existence of possibilities. The concept proper of the ,,co-existing possibilities" is not yet clear in quantum mechanics.