The paper is devoted to the history of considerations on the denotation of propositions, or on that which is denoted, or described by propositions. In the first part of the paper, aside to the views of ancient authors (Plato, Aristotle, Stoics) concerning this issue, the debate about the existence and nature of the denotation of propositions has been presented. It was alive especially in the later scholastic philosophy (two objectivistic standpoints – among others – Gregory of Rimini, and one subjectivistic). The second part of the paper discusses the position of modern and contemporary authors, i.e. two ways with which the question of the denotation of propositions was reconstructed in the 19th century, the so-called Brentano’s schools (Twardowski, Meinong), Frege’s thought and his followers. The texts of many authors have been analysed in order to present (and compare) all the more important views in the question of the denotation of propositions, starting from antiquity until the contemporary times.

The paper presents several attempts to express intuition concerning the understanding of knowledge and conviction by means of the conceptual apparatus of many-valued logic. J. Łoś’s pioneer system has been presented here, the system constructed by Ngoc Duc Ho, in which the internal logic in this system is used by the knowing subject as the three-valued logic of Łukasiewicz and the third logical value is understood as “unjustified”, and the four-valued system of N. Belnap, the system that allows for the occurrence of propositions which are evaluated both as true and false.

In the paper I discuss some premises of “quantum mechanics” with regard to the thesis that the time arrow does (not) exist. In this context I consider above all the famous Einstein-Podolsky-Rosen’s experiment (EPR-experiment). I also indicate Schrödinger’s interpretation of wave function “symmetrical” towards time (nomological isotropy) and the peculiar understanding of the pair particle-antiparticle, assuming that the direction of time can be reversed. Eventually, I discuss the issue of measurement in quantum mechanics with which the existence of time arrow (anisotropy) is often linked. If it comes to the interpretations of quantum mechanics, from the point of which I consider the issues in question, then in principle I limit myself to two: the so-called Copenhagen interpretation and David Bohm’s conception of “hidden parameters.” I arrive at a conclusion that the premises of quantum mechanics that are at issue here cannot be sufficient grounds for a conclusive recognition of the reversibility (non--existence) of time arrow.

The paper brings a critical analysis of the assumptions on which K. Ajdukiewicz (1934) based his considerations concerning the theory of meaning and proposes to look at these problems from a new research perspective. The considerations sought to analyse the modes of accepting propositions which call for a contact with empirical reality, therefore to apply some empirical procedures (observations, tests, experiments).