Several investigations in probability theory and the theory of expert systems show that it is important to search for some reasonable generalizations of fuzzy logics (e.g. Łukasiewicz, Gödel or product logic) having a non-associative conjunction. In the present paper, we offer a non-associative fuzzy logic L CBA having as an equivalent algebraic semantics lattices with section antitone involutions satisfying the contraposition law, so-called commutative basic algebras. The class (variety) CBA of commutative basic algebras was intensively studied in several recent papers (...) and includes the class of MV-algebras. We show that the logic L CBA is very close to the Łukasiewicz one, both having the same finite models, and can be understood as its non-associative generalization. (shrink)

Individual eschatological images are rarely a research subject that applies in-depth interviews and qualitative methods of analysis. Due to the use of simple questionnaire measures, knowledge about possible variations in personal images of heaven or hell is very poor. Furthermore, data concerning any connection between personality and eschatological images is scarce. The research project presented in the article was an attempt to apply a narrative method and to combine qualitative and simple quantitative methods to describe the wide variety of individual (...) views of heaven, hell, and purgatory. The relationship between individual eschatological images, denominational culture, and the chosen dimension of personality—i.e., hope understood in Erik Erikson's terms as a relatively stable conviction that the world is meaningful, ordered and friendly towards people—was also explored. The research was conducted among religiously engaged Christians from two denominational groups: Catholics and Lutherans. (shrink)

Zaproponowano, by Quine’a kryterium istnienia (teoria zakłada istnienie zmiennych związanych) rozszerzyć na matematyczne struktury. W duchu tego kryterium każdą matematyczną strukturę można uważać za oddzielny świat, w którym istnieją tylko te byty, bez zakładania których struktura straciłaby sens. Niektóre matematyczne światy są używane przez fizyków do modelowania rzeczywistego świata. W takiej sytuacji ontologia danej struktury matematycznej przenosi się na fizyczny świat. Mówiąc bardziej prozaicznie, niektóre matematyczne struktury interpretuje się jako struktury fizycznego świata. Cud rozumienia świata sprowadza się do cudu tej (...) interpretacji. (shrink)

Physics is inseparably connected with western philosophy. From the seventieth century, physics began to play the role similar to that of ontology. Moreover, many notions and problems moved from philosophy to physics. That way it came into being something that is now called „philosophy in physics”. It means that some traditional philosophical questions, like for example the problem of individualization, emerge in physics in a new, exact and mathematical form. Therefore, physics will in the future become gradually philosophy.

Space, time and probabilities not only form the arena of many physical theories, but also the arena of our everyday life. Therefore, the problem of their ontological status becomes even more interesting. It seems that this problem cannot be solved before we have the final physical theory ("theory of everything"). However, various methods of looking for such a theory lead to converging results, and are able to elucidate the problem in question. We analyze noncommutative algebraic methods, and show that, when (...) applied to model the fundamental level, they suggest a nonlocal regime in which there is no space and no time, in their usual sense, and which is essentially probabilistic (in a generalized sense). In the noncommutative approach there are many probabilistic measures (not just one "probability" as in macroscopic physics), and none of them seems to be distinguished in any way. The tentative conclusion is that space, time and probability are not "absolute categories", but rather aspects of the world structure emergent from the fundamental level. One should expect that the ultimate theory will be well off our traditional philosophical categories. This shows that our mind has a peculiar property allowing it to reach far beyond its usual limitations. (shrink)

Various anniversaries encourage historical reflection. Although 40th anniversary is not a common reason for excessive celebration, in the case of a scientific journal, however, it is already long enough that it deserves a brief moment of thought.

Noncommutative geometry is quickly developing branch of mathematics finding important application in physics, especially in the domain of the search for the fundamental physical theory. It comes as a surprise that noncommutative generalizations of probabilistic measure and dynamics are unified into the same mathematical structure, i.e., noncommutative von Neumann algebra with a distinguished linear form on it. The so-called free probability calculus and the Tomita-Takesaki theorem, on which this unification is based, are briefly presented. It is argued that the unitary (...) evolution, known from quantum mechanics, could be a trace of noncommutativity on a deeper level. Philosophical significance of these results is also discussed. (shrink)

Our present knowledge in the field of dynamical systems, information theory, probability theory and other similar domains indicates that the human brain is a complex dynamical system working in a strong chaotic regime in which random processes play important roles. In this environment our mental life develops. To choose a logically ordered sequence from a random or almost random stream of thoughts is a difficult and energy consuming task. The only domain in which we are able to do this with (...) a full success is mathematics. Leibniz’s life ambition was to extend this success, with the help of what he called _characteristica universalis_, to other areas of human activity. The belief that this is possible lies at the basis of Leibniz’s rationalist system. Reasoning within his system, Leibniz claimed that also fundamental laws of physics can be deduced from the “first principles”. Just as linguistic or conceptual units are at the basis of the _charactersistica universalis_, his monads are responsible for physical activity of material bodies. When this rationalistic strategy is applied to the philosophy of space and time, it leads to their radically relational conception. Leibniz’s rationalistic approach to philosophy and science arouses out sympathy but it was Newton’s mathematical-empirical method that turned out to be effective in human endeavour to understand the functioning of the physical world. Successes of the Newtonian method compel us to revise our concept of rationality. (shrink)