The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the (...) new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic. (shrink)

część I. [without special title] -- część II. [without special title ]-- część III. [without special title] -- część IV. Geneza życia biologicznego.

It appears that we know surprisingly little about how judges frame linguistically the rationale behind their decisions and how such texts are structured. Using the concept of rhetorical moves, this paper adopts a genre-based approach to examine the rhetorical structure of legal justifications provided in the decisions of the Polish Constitutional Court. The goal of the study is to verify the claim that the way justifications are drafted is becoming more and more uniform and conventional. The results show that there (...) is a common core of rhetorical structure realized by means of recurrent functional segments of text. This paper proposes a prototypical move structure of a Constitutional Tribunal justification and it argues that that the way justifications are drafted are subject to very concrete, even if not explicitly stated constraints. (shrink)

Contacts of the two logicians are listed, and all Gödel's written mentions of Tarski's work are quoted. Why did Gödel almost never mention Tarski's definition of truth in his notes and papers? This puzzle of Gödel's silence, proposed by Feferman, is not merely biographical or psychological but has interesting connections to Gödel's philosophical views.No satisfactory answer is given by the three “standard” explanations: no need to repeat the work already done; Tarski's achievement was obvious to Gödel; Gödel's exceptional caution. In (...) fact, , Tarski had done the work, but Gödel almost never mentioned the achievement; , the obviousness is no explanation for the omission of Tarski's work in contexts in which an application of the definition of satisfaction was useful, and even necessary; , the point was not just caution: if Gödel had felt the need to mention the program of scientific semantics he could easily have done that in his manuscripts, or in conversations.Three ideas, detectable in Gödel's approach, can help us understand Gödel's silence: the idea of truth as the intuitive provability in the most general sense; defining it set-theoretically would contribute nothing. the idea of truth as an inexhaustible idea in the sense of Kant; “truth in general” is a category that must be applicable to all kinds of sentential expressions; also, while for Gödel language was secondary, Tarski's definition is focused on language. the idea of logic as the universal language, in Hintikka's sense, as opposed to the perception of logic as a reinterpretable calculus; hence the thesis that semantics is inexpressible. Gödel always remains a Platonist who asks a natural question: what does really happen in the realm of abstract objects? (shrink)

Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest (...) a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent. (shrink)

In the initial part of the article texts of some authors are analyzed concerning material implication. In the further part of the article the proposition is justified that the operator of material implication differs in quality from other truth-functional operators. The final part of the article is devoted to considerations aiming at presenting what the thesis of the classical propositional calculus, in which the main operator is the operator of material implication, denote.

Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.

Artykuł składa się z trzech części. W pierwszej części pod uwagę brana jest możliwość, że ludzie, a być może także wszystkie inne skończone podmioty poznające, które dysponują zdolnością do formułowania ocen moralnych, podlegają uniwersalnemu złudzeniu co do hierarchizacji wartości moralnych, według których działają, a więc że mają odwrócone spektrum aksjologiczne. W części drugiej jest uzasadniana teza, że jedynym środkiem, pozwalającym wykluczyć możliwość podlegania radykalnej iluzji aksjologicznej przez skończone podmioty poznające, jest odwołanie się do metafizycznego pojęcia Boga, rozumianego jako pojęcie istoty (...) najdoskonalszej, i do Jego wiedzy na temat tego, co jest dobre, a co jest złe. Kwestia istnienia Boga oraz wskazanie, w jaki sposób należałoby religijnie konkretyzować pojęcie Boga, nie są podejmowane. Do przeprowadzenia prezentowanej w artykule argumentacji wystarczy, że Bóg będzie rozumiany jako osoba dysponująca atrybutem wszechwiedzy. Część trzecia jest poświęcona uwagom na temat relatywizmu moralnego, zagadnieniu tzw. dylematów moralnych oraz pojęciu istoty dobra moralnego. (shrink)

The paper seeks to present a conception of the didactics of logic according to Jean Alexis Borrelly, the author of among others Plan de réformations des etudes élémentaires and a textbook for logic Elémens de l’art de penser, ou la logique, réduite à ce qu’elle a d’utile. The legacy of Borrelly summarises the tendencies typical of the Enlightenment with regard to 1) reforms of education, 2) redefining values in the didactics of philosophy, and 3) modification in the then logic. The (...) presentation has a twofold structure. In part one I present some specific characteristics of Borrelly’s didactic plan against the background of school reforms. Part two is devoted to the teaching of logic: 1) the nature of logic in the didactic curriculum, 2) its realization in Borrelly’s textbook for logic, and that against the background of modern tendencies in reforming a conception of this discipline. This is in particular with regards to the theory and practice of the didactics of logic in Polish school reforms contemporary to Borrelly’s accomplishments. It has been pointed out that both at the declarative level and in the textbooks Borrelly’s conception is an example of eclectic achievements typical of the Enlightenment. They come to terms with the radical solutions, hostile to formal logic, with school requirements, a fact that makes Borrelly’s solution to be one of the standards characteristic, for instance, of the popular Logic of Port-Royal by A. Arnauld and P. Nicole. (shrink)

This article covers the traditional problems of the philosophy of law: the controversies between realism and normativism, on the one hand, and positivism and non-positivism, on the other. The author, adopting the ontological perspective of the artefactual theory of law, attempts to attain two research aims. First, he argues that artefactual theory of law paves the way towards a moderate position overcoming realism-normativism duality. Second, he advocates the thesis that the supposedly ontological difference between positivist and non-positivist views might be (...) dispelled and described as merely conceptual. Therefore, the opposite points of view could be considered as metaphysically equivalent ways of grasping the same social reality. According to the crucial premise of the argument law is a meliorative thick concept. The essay was inspired by an analogy between the philosophy of law and the philosophy of science first discussed by Lon L. Fuller. (shrink)

The article presents Moore’s concept of the naturalistic fallacy, with particular reference to two interpretations of the term: According to the interpretation, the naturalistic fallacy consists in identifying the quality of „goodness” with any other qualities, while according to the second, naturalistic fallacy would consist in identifying „good” with the natural qualities. Further, distinction is made between the naturalistic fallacy and its consequences which are sometimes confused with the fallacy itself by some authors.

The subject of the article is a description of a certain version of fanaticism represented by spokesmen of family planning. The author first presents some definitions of fanaticism. Next he discusses the world’s demographic problems linking demography with the question of good life. He calls the standpoints that do not notice the negative effect of the demographic explosion fanatical.

Eduard Spranger ujął program swojego życia w następujących słowach: „zgłębiać siły duchowe i uwarunkowania człowieka, które drzemią w jego wnętrzu, pragnąc je chronić i próbować je kształtować". Sam przyznaje, że stoi on jakby pomiędzy trzema dyscyplinami naukowymi: filozofią, psychologią i pedagogiką. Biorąc jednak pod uwagę jego wkład w rozwój tych trzech dyscyplin, należałoby wymienić je w odwrotnej kolejności.