Online research in philosophy

In modern physics, the constant “c” plays a twofold role. On the one hand, “c” is the well known velocity of light in an empty Minkowskian space–time, on the other hand “c” is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space–time intervals. We ask for the interrelations between these two, at first sight different meanings of “c”. The conjecture that the value of “c” has any influence on the structure (...) of space–time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space–time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space–time can be reconstructed already on the basis of a restricted classical ontology (Mittelstaedt, Philosophie der Physik und der Raum-Zeit, Mannheim: BI-Wissenschaftsverlag, 1988 and Mittelstaedt, Kaltblütig: Philosophie von einem rationalen Standpunkt, Stuttgart: S. Hirzel Verlag, pp. 221–240, 2003 ), and that without any reference to the propagation of light. However, the space–time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with “c” but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of “c” and for a dualism of space–time and matter. (shrink)

The main goal of quantum logic is the bottom-up reconstruction of quantum mechanics in Hilbert space. Here we discuss the question whether quantum logic is an empirical structure or a priori valid. There are good reasons for both possibilities. First, with respect to the possibility of a rational reconstruction of quantum mechanics, quantum logic follows a priori from quantum ontology and can thus not be considered as a law of nature. Second, since quantum logic allows for a reconstruction of quantum (...) mechanics, self-referential consistency requires that the empirical content of quantum mechanics must be compatible with the presupposed quantum ontology. Hence, quantum ontology contains empirical components that are also contained in quantum logic. Consequently, in this sense quantum logic is also a law of nature. (shrink)

Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can (...) be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or “formulas”—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant’s theory of addition as a form of synthetic operation. (shrink)

The principle of excluded middle is the logical interpretation of the law V A v in an orthocomplemented lattice and, hence, in the lattice of the subspaces of a Hilbert space which correspond to quantum mechanical propositions. We use the dialogic approach to logic in order to show that, in addition to the already established laws of effective quantum logic, the principle of excluded middle can also be founded. The dialogic approach is based on the very conditions under which propositions (...) can be confirmed by measurements. From the fact that the principle of excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, we conclude that this principle is inherited by all finite compound propositions. For this proof it is essential that, in the dialog-game about a connective, a finite confirmation strategy for the mutual commensurability of the subpropositions is used. (shrink)

The logic of quantum physical propositions can be established by means of dialogs which take account of the general incommensurability of these propositions. Investigated first are meta-propositions which state the formal truth of object-propositions. It turns out that the logic of these meta-propositions is equivalent to ordinary logic. A special class of meta-propositions which state the material truth of object-propositions may be considered as quantum logical modalities. It is found that the logic of these modalities contains all the quantum logical (...) restrictions and thus differs essentially from the modal calculi of ordinary logic. (shrink)