What remains of probability?

This paper offers some reflections on the concepts of objective and subjective probability and Lewis' Principal Principle

Sofic groups and direct finiteness

We construct an analogue of Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic groups.Comment: 9 pages, a shortened proof of the main resul

On the formal statement of the special principle of relativity

The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality

How to move an electromagnetic field?

As a first principle, it is the basic assumption of the standard relativistic formulation of classical electrodynamics (ED) that the physical laws describing the electromagnetic phenomena satisfy the relativity principle (RP). According to the standard view, this assumption is absolutely unproblematic, and its correctness is well confirmed, at least in a hypothetico-deductive sense, by means of the empirical confirmation of the consequences derived from it. In this paper, we will challenge this customary view as being somewhat simplistic. The RP is actually used in exceptional cases satisfying some special conditions. As we will see, however, it is quite problematic how the RP must be understood in the general case of a coupled particles + electromagnetic field system