The aim of the paper is to introduce the concept of adaptive logics (AL) or rather adaptive logical approach. In the introduction, a motivation and an emergence of AL are briefly discussed. In the second part of the paper, specifics of AL are analysed – especially nonmonotonic character, internal and external dynamics, as well as the structure of AL, namely the distinction between upper limit logic and lower limit logic. In this part, the dynamic proof is also described. Applications of (...) AL are presented in the third part. Three illustrations from three different branches of philosophy are presented. First one is an illustration of description of science – a traditional application of AL. Second one is an illustration of solving a deontic conflict – this is a new direction within in AL which has recently been researched. Third one is an illustration of analyses of metaphors – an example of an unusual application of AL. In the conclusion of the paper, contemporary results of AL are critically evaluated with respect to some problems of the project of AL. (shrink)

Následující text si klade za cíl představit koncepci adaptivních logik (dále AL), či lépe adaptivně logický přístup. Úvodní oddíl textu stručně pojednává o vzniku AL a o motivacích pro tento přístup. Druhý oddíl následně rozebírá specifika AL, především jejich nemonotónní charakter, interní a externí dynamiku, dále pak jejich strukturu, tedy rozlišení mezi upper limit logic a lower limit logic, a představuje pojetí dynamického důkazu. Třetí oddíl ilustruje vybrané aplikace AL ve třech oblastech – v tradiční, totiž při popisu vědy, v (...) moderní, při řešení deontických konfliktů, a v nezvyklé, při analýze metafor. V závěru práce jsou zhodnoceny dosavadní výsledky v rámci celého projektu AL a je poukázáno na některé problémy, které jsou s tímto projektem spjaty. (shrink)

Just as the accuracy of scientific theories is best tested in extreme physical conditions, it is advisable to verify the accuracy of a recognized conception of language on its extreme parts. Mathematical statements meet this role, thanks to the notion of truth and proof. Michael Dummett’s anti-realism is an enterprise that has attempted on this basis to question the notion of the functioning of language-based primarily on the principle of bivalence, the truth-condition theory of meaning, and the notion that the (...) speaker must be able to demonstrate his knowledge of meaning publicly. In common language practice, one can observe assertions that we can neither verify nor refute in principle. On these so-called undecidable statements, Dummett tried to show that if we apply the traditional description to them, we inevitably reach paradoxical conclusions. Mathematical statements referring to an infinite number may be examples of these assertions. In the submitted paper, I will present Dummett’s position resulting primarily in a manifestation and acquisition argument, according to which it should not be possible to understand undecidable statements at all. In conclusion, however, I will show that his intention – despite many valuable comments – fails, i.e. that there is a way to avoid both arguments while preserving the realistic description of the language in general. Key words: anti-realism, mathematical statements, meaning, Michael Dummett, truth, truth-condition theory of meaning. (shrink)

Recenze knihy:Luca Incurvati, Conceptions of Set and the Foundations of Mathematics. Cambridge University Press, 2020, 238 s.

This paper aims to describe and examine Alfred Tarski's famous semantic conception of truth as well as some of the critiques presented against it. The first part of this paper is divided into five segments: criteria imposed upon every adequate definition of truth are discussed in the first segment; the second is dedicated to Tarski’s Convention T; distinction between object language and metalanguage, as well as Tarski’s attitude toward formalized and colloquial languages, is described in the third segment; fourth segment (...) is devoted to Tarski’s definition of truth using the notion of “satisfaction”; the last segment is the evaluation of Tarski’s solution of paradoxes. In the second part of this paper the selected objections against Tarski’s conception are presented with emphasis on their diversity. (shrink)