The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

In this paper I first briefly outline the difficulty of maintaining a realistic interpretation of religious discourse in the context of religious pluralism. Then I present two attempts to reconcile religious realism and pluralism. The first is John Hick’s proposal, the second the 'internalist pluralism' developed by Victoria Harrison on the basis of Putnam's internal realism. I point out the weaknesses of these theories. Finally, I outline my own proposal, based on a slightly different interpretation of internal realism than Harrison’s (...) internalist pluralism, namely by using the pragmatic aspects of Putnam's thought. He argues that pragmatic-realistic pluralism avoids the weaknesses of Hick’s and Harrison’s conceptions while at the same time sharing their strengths. (shrink)

The paper revises the biographical data about Michel Foucault’s stay in Poland in 1958-1959. The main inspiration comes from the recent very well documented literary reportage book by Remigiusz Ryziński, Foucault in Warsaw. Ryziński’s aim is to present the data and tell the story, not to analyse the data within the context of Foucault’s work. This paper fulfills this demand by giving additional hypotheses as to why Polish authorities expelled Foucault from Poland and what the relation was between communism and (...) homosexuality. The Polish experience, the paper compels, might have been inspiring for many of Foucault’s ideas in his Madness and Civilization, Discipline and Punish, and The History of Sexuality. On the other hand the author points to the fact that Foucault recognized the difference between the role of the intellectual in the West and in communist countries but did not elaborate on it. In this paper the main argument deals with the idea of sexual paranoia as decisive, which is missing in Foucault's works, although it is found in e.g. Guy Hocquenghem. (shrink)

A calculus of names is a logical theory describing relations between names. By a pure calculus of names we mean a quantifier-free formulation of such a theory, based on classical propositional calculus. An axiomatisation of a pure calculus of names is presented and its completeness is discussed. It is shown that the axiomatisation is complete in three different ways: with respect to a set theoretical model, with respect to Leśniewski's Ontology and in a sense defined with the use of axiomatic (...) rejection. The independence of axioms is proved. A decision procedure based on syntactic transformations and models defined in the domain of only two members is defined. (shrink)

The aim of the paper is to point out the modelling choices that lead to different systems of deontic action logic. A kind of a roadmap is presented. On the one hand it can help the reader to find the deontic logic appropriate for an intended application relying on the information considering the way in which a deontic logic represents actions and how it characterises deontic properties in relation to (the representation of) actions. On the other hand it is a (...) guideline how to build a deontic action logic which satisfies the desired properties. (shrink)

Some subfamilies of κ, for κ regular, κ λ, called -semimorasses are investigated. For λ = κ+, they constitute weak versions of Velleman's simplified -morasses, and for λ > κ+, they provide a combinatorial framework which in some cases has similar applications to the application of -morasses with this difference that the obtained objects are of size λ κ+, and not only of size κ+ as in the case of morasses. New consistency results involve existence of nonreflecting objects of singular (...) sizes of uncountable cofinality such as a nonreflecting stationary set in κ, a nonreflecting nonmetrizable space of size λ, a nonreflecting nonspecial tree of size λ. We also characterize possible minimal sizes of nonspecial trees without uncountable branches. (shrink)

On the base of the classical logic the connectives of necessity and possibility have the equivalent positions in this sense that each of them is definable by the other one. The consequence of this fact is the possibility to define of the both modalities using the connective of identity. Thus, the connective of propositional identity defining the congruence of the propositional language has become the base of the reconstruction of necessity operator in some modal systems. Already in 1957 Greniewski [9] (...) obtained system S5 on the base of the propositional calculus with identity. Next, Cresswell [3], [4] reconstructed S4 and S5 in a similar way. Systematic investigations of this problem were undertaken by Suszko within the broader frame of SCI programme [16], [17], [18]. The connections between modal connectives and the connective of identity settle some philosophical sense of both modalities. Something is necessary, if it is identical with a logical truth. If something is different from the negation of some logical truth, it is possible. It is however, the “ontological” characteristics typical for modalities defined on the base of the classical logic. The settling of similar connections between intuitionistic identity and intuitionistic modalities uncover the philosophical sense of the “epistemic” necessity and possibility. Unfortunately, the symmetry between the classical and intuitionistic case is not entire. The acceptance of both equalities: = ¬ ¬ and = ¬ ¬, in the intuitionistic logic yields the classical versions of both modalities . Thus, there is a problem with defining the connective of intuitionistic possibility by the connective of identity. In Sections 2 and 3 two “partial” solutions of the mentioned problem are presented. They are “partial” because the connective of possibility has undesirable properties. The second solution yields the strengthening of the necessity connective, too. The main aim of this paper is obtained in Section 5, where a definition of the intuitionistic possibility is given. This definition uses the new connective of nonidentity, presented in Section 4. The new approach bases on the idea that some connectives like implication, negation, identity, necessity are “Heyting's” ones. The case of possibility is different. Together with coimplication, weak negation, and nonidentity, possibility belongs to the so-called “Brouwerian” connectives. The connectives of the first kind have such property that in Kripke's style semantics their interpretations in each point of this semantics are related to the interpretations in next points. In the case of the “Brouwerian” connectives the interpretations in each point depend on the interpretations in previous points. In this sense, “Heyting's” connectives are interpreted from the point of view of the future, while the interpretations of the “Brouwerian” connectives are from the point of view of the past. The relations between nonidentity and possibility connectives allow to say that in temporal semantics something is possible in the moment a, if before a there was such moment b in which it was different from the contradiction. Thus, “something is possible” does not mean that it held once in the past. A broader philosophical remarks about the nature of intuitionistic possibility are contained in two Comments in the last Section. (shrink)

Autor mówił o roli dziennikarza muzycznego i DJ-a w radiu publicznym. Podzielił swoje obowiązki na pięć kategorii: granie audycji DJ-skich, przygotowywanie programów autorskich, programów publicystycznych, prezentowanie bloków muzycznych oraz oprawę muzyczną.

In this text I take into account Roman Ingarden's theory of general objects. Polish phenomenologist avoided most of paradoxes implied by traditional theories of universals pointing out the difference between two kinds of form inherent in general object, namely form of subject of properties and form of whole and parts. Every idea has twofold construction: as an idea (qua idea) it is a subject of peculiar properties and on the other hand it has a content consisted of so called constants (...) and variables. The content of the idea has a whole-parts form. This however is inconsistent with other analyses of whole-parts form and of the character of constants and variables given by Roman Ingarden. In the consequence I claim that a third form, unique for general object, is needed. I also point out difficulty of indicating positive characteristic of general object (i.e. other than negation of properties of individuals). (shrink)

Epistemicism seems to be the most dominating approach to vagueness in the recent twenty years. In the logical and philosophical tradition, e.g. Peirce, vagueness does not depend on human knowledge. Epistemicists deny this fact and contend that vagueness is merely the result of our imperfect mind, our dearth of knowledge, sort of phantom, finally, that it simply does not exist. In my opinion, such a stance not only excludes vagueness comprehended in terms of human knowledge, but which is worse, stems (...) from spurious logical arguments. The part of arguments called Sorensen’s Arguments or even Proofs were the subject of my analysis in the book Paradoksy and in the paper “Epistemicism and Roy Sorensen Arguments” published in the Bulletin of the Section of Logic. Here I shall only briefly refer to these works and focus mainly on the arguments launched by Tymothy Williamson. One of them is to uncover why we are not able to recognize the alleged sharp boundary between positive and negative extensions of any vague predicates. Williamson’s reasoning is based on his margin for error principle. Another argumentation of Williamson aims at the refutation of the principle I know that I know. It should be emphasized that all the aforementioned arguments are fundamental for epistemicism and all of them are fallacious because of either formal or false-premise fallacy. There is the circumstance that we cannot deem epistemicism logical. Finally, we show that within the epistemic frame the following thesis is valid: if what epistemicism states is the case, then what epistemicism states is not the case. This immediately implies → ¬p’) that it is not the case what epistemicism states. So, either epistemicism or logic. (shrink)

The idea of belief revision is strictly connected with the notion of contraction given by the set of postulates formulated by Alchourrón, Gärdenfors and Makinson. In the present paper expansion and contraction are defined by Tarski's consequence relation and Tarski-like elimination relation. The logic of falsehood (i.e. a logic dual in Wójcicki's sense to the given logic of truth) plays a key role for defining the elimination relation. A decision of adding or refusing of some sentences is arbitrary and depends (...) on our wish only. This decision cannot be logical and logic cannot justify it. In our approach logic is a tool for faultless and precise realization of extension or reducing of the set of our beliefs. Step forward extends the set of our beliefs and it is used when some new belief appears. Step backward reduces the set of our beliefs and it is used when we reject from some previously accepted belief. But why some "initial" sentences should be added or refused depends on extralogical reasons. The logic for the back-reasoning uses the class of models adequate for the logic extending the set of our beliefs. However, the class is used in a specific i.e. dual form. That is why the step forward (expansion) and the step backward (contraction) constitute the one whole. Procedure of contraction satisfies the well known AGM postulates. We limit our considerations to first six conditions for contraction. Satisfaction of almost every postulate is a good sign that our approach is reasonable. The only exception we make for the controversial fifth postulate. (shrink)

A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” . The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. Both procedures taken (...) together were successfully verified by using so-called AGM , postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson . Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: non-formal examples for nonmonotonicity and formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point and almost none belonging to satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them. (shrink)

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show that any (...) formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members. (shrink)

Since ontology is to be the science which studies that what exists, every ontological enterprise has to be preceded by an agreement as to what „existence” means. This is best done by giving a definition of existence. In the article the author examines definitions of existence that are used, or could be used, in various ontologies. To this aim he introduces a systematics of the possible definitions and with its help studies definitions of existence given by various authors. Definitions that (...) he consid-ers have the form „ ”, where „p” is a sentence (it is also possible to treat existence as an undefined primary term, but such a treatment in the context of ontology in which it is used may be regarded as a contextual definition). Thus, in fact the subject of the analysis is what is understood by the expression of the form „x exists”. (shrink)

"This is a full original version of Makowski's work on Aristotelian dunamis (shortened & revised version has been previously published as "Metaphysics of Practical Philosophy" paper). The author presents the Aristotelian conception of capacity/potentiality (dunamis) – one of the most important in Aristotle’s metaphysics. A closer inspection allows to draw conclusion, that the concept of capacity is an important link between ‘theory’ and ‘practice’ (metaphysics on the one side, and practical – ethical, rhetorical, political – skills, on the other). A (...) picture of the connection between theory and practice is based on the most important parts of Metaphysics (books delta and theta), it relates metaphysical definitions to an essential element of Aristotelian practical philosophy – the concept of virtue (aretê). In the practical works of Aristotle, we can find different definitions of aretê: in Nicomachean Ethics Aristotle defines aretê using the notion of disposition (hexis), but in Rhetoric he formulates a definition based on the concept of capacity. Distinctive analysis of this inconsistency shows the significance of capacity in The Stagirite’s philosophy.". (shrink)

Philippa Foot once said: I'm not clever at all. I have a certain insight into philosophy, cost I think. But I'm not clever, I don't find complicated arguments easy to follow. Foot's cleverness enticed many thinkers to take these Gombrowiczian lines seriously.

The paper seeks to understand the proper motivation of John McDowell’s interest in both Kant and Hegel. It reconstructs his arguments in favour of the Hegelian notion of conceptualized experience, and shows how it affects his reading of Kant’s transcendental philosophy. It concludes with a comparison of McDowell’s position on experience with Hegel’s by pointing out the most important difference regarding the notion of factivity.

The aim of the thesis is to provide the foundations for a representation-based theory of meaning, i.e. a theory of meaning that encompasses the psychological level of cognitive representations. This is in opposition to the antipsychologist goals of the Fregean philosophy of language and represents the results of a joint analysis of multiple philosophical problems in contemporary philosophy of language, which, as argued in the tesis, stem from the lack of recognition of a cognitive level in language. In the thesis, (...) I first provide and argue a definition of cognitive/mental representations based on results in developmental psychology as well as theoretical considerations. Then, I use the definition to build upon it a richer theory of concepts and apply it to various philosophical conundra. The problems tackled include the problem of proper names (for which a solution is proposed that respects the post-Kripkean criticism), a unified meaning postulate for modalities and the epistemology and ontology of mathematical terms. The thesis concludes with a proposed application of the newly acquired framework to select social aspects of language use. (shrink)