The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

The choice of connectives for many valued propositional logics suitable for theoretical and applicational interests in most cases is an open problem up to now. We will not offer a general solution here, but support the point of view of some recent developments in fuzzy set theory that the triangular norms – t-norms for short – of Schweizer/Sklar [3] and the ϕ-operators of Pedrycz [2] represent quite general classes of connectives at least for many valued logics with truth value set (...) the real interval [0,1] . Special classes of t-norms and general properties of them have been discussed in some papers just recently, e.g. by Dombi [1], Weber [4], Yager [5] to mention only a few of them. (shrink)

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.

The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people’s performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based (...) on computational requirements for solving a problem. According to the EPO framework, current methods for improving probabilistic reasoning are of two kinds: First, reduction of Bayesian problems to a type of probabilistic problems requiring less conceptual and procedural competencies. Second, enhancing people’s utilization competence by fostering the application of quantitative inference schemas. The approach suggests new applications, including the teaching of probabilistic reasoning, using analogical problem solving in probabilistic reasoning, and new methods for analyzing errors in probabilistic problem solving. (shrink)

Dispositional essentialism is a non-Humean view about the essences of certain fundamental or natural properties that looms large in recent metaphysics , not least because it promises to explain neatly the natural modalities such as laws of nature, counterfactuals, causation and chance. In the current paper, however, several considerations are presented that indicate a serious tension between its essentialist core thesis and natural “metaphysical” interpretations of its central explanatory claims.

In this paper, we argue that the popular claim that laws of nature explain their instances creates a philosophical puzzle when it is combined with the widely held requirement that explanations need to be underpinned by ‘wordly’ relations. We argue that a “direct solution” to the puzzle that accounts for both explanatory laws and explanatory realism requires endorsing at least a radical metaphysics. Then, we examine the ramifications of a “skeptical solution”, i.e., dissolving it by giving up at least one (...) of these two claims, and argue that adopting it is more favorable to Humean reductionists than to anti-reductionists about laws of nature. (shrink)

In an overview of developments spanning the past seventy years, Siegfried Zielinski discusses how the means of technology-based communication assumed a systemic character and how theory, art, and criticism were operative in this process. [... After the Media] advocates for a distinction to be made between online existence and offline being.