We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

We obtain several game characterizations of Baire 1 functions between Polish spaces _X_, _Y_ which extends the recent result of V. Kiss. Then we propose similar characterizations for equi-Bare 1 families of functions. Also, using related ideas, we give game characterizations of Baire measurable and Lebesgue measurable functions.

This interdisciplinary study introduces readers to Friedrich Schleiermacher’s diverse pathways of reflection and creative practice that are related to the field of translation. By drawing attention to Schleiermacher’s various writings on a range of subjects (including philology, criticism, hermeneutics, dialectics, rhetoric and religion), the author makes it clear that the frequently cited lecture Über die verschiedenen Methoden des Übersetzens (On the Different Methods of Translating) represents but a fraction of Schleiermacher’s contributions to modern-day insights into translation. The analysis of Schleiermacher’s (...) various pathways of reflection on translation presented in this book leads to the conclusion that translation is part of the essence of the world, as it is a fundamental tool of our cognition and a foundation of our existence. In Schleiermacher’s works, transfer, translation, mediation, and communication underpin our very existence in the world and our self-awareness. At the same time, they represent fundamental categories for a project that focuses on the consolidation and assimilation – through translation – of that which is foreign, different, diverse. (shrink)

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)

We study a strengthening of the notion of a perfectly meager set. We say that a subset A of a perfect Polish space X is countably perfectly meager in X, if for every sequence of perfect subsets $\{P_n: n \in \mathbb N\}$ of X, there exists an $F_\sigma $ -set F in X such that $A \subseteq F$ and $F\cap P_n$ is meager in $P_n$ for each n. We give various characterizations and examples of countably perfectly meager sets. We prove (...) that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszyński. (shrink)

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a group scheme action.

In the paper, several data reduction techniques for machine learning from big datasets are discussed and evaluated. The discussed approach focuses on combining several techniques including stacking, rotation, and data reduction aimed at improving the performance of the machine classification. Stacking is seen as the technique allowing to take advantage of the multiple classification models. The rotation-based techniques are used to increase the heterogeneity of the stacking ensembles. Data reduction makes it possible to classify instances belonging to big datasets. We (...) propose to use an agent-based population learning algorithm for data reduction in the feature and instance dimensions. For diversification of the classifier ensembles within the rotation also, alternatively, principal component analysis and independent component analysis are used. The research question addressed in the paper is formulated as follows: does the performance of a classifier using the reduced dataset be improved by integrating the data reduction mechanism with the rotation-based technique and the stacking? (shrink)

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative Hasse–Schmidt derivations [13] and about Galois actions [14]. As an application of our methods, we obtain a new model complete theory of actions of a finite group on fields of finite imperfection degree.

This paper offers a critical review of the notion of a “singular cognitive role”, which is central to some recent theories of singular thought. According to those theories, whether a thought is singular depends on the role it plays in the subject’s cognitive activity. We compare the two most developed accounts of this type: Crane’s :21–43 2011, The Objects of Thought2013) and Jeshion’s. Both theories aim to capture the notion of a singular cognitive role in terms of mental files. We (...) argue that Jeshion’s theory is much more promising as it provides a more detailed and non-circular characterization of the mental files responsible for singular thinking. We examine the prospects for enhancing that account in light of three major concerns about it present in the literature. First, we discuss whether the weakest aspect of the whole proposal, i.e. the condition for the initiation of mental files, can be replaced without debilitating the rest of the theory. Second, we examine Goodman’s : 437–461 2014, The Philosophical Quarterly2015) argument against mental file theories of singular thought and show that it does not affect Jeshion’s account. Third, we argue against Sawyer :264–283 2012) that Jeshion’s notion of a singular cognitive role is in strong opposition to acquaintance-based theories of singular thought and cannot be incorporated into any of them. Thus, the paper concludes that Jeshion’s proposal, despite its shortcomings, is currently the most promising account of a singular cognitive role. (shrink)

The doctrine of the Intelligent Design offers an intuitive explanation of why the ordering in the Universe is authored by an intentional agency. Due to its appeal to common-sense perception, this doctrine is endorsed even by scientifically literate circles despite of its obvious contradiction with the discoveries of science. In this article, an attempt to apply the tools of the cognitive science of religion to the appraisal of the methodological and epistemic status of the ID doctrine is presented. It is (...) concluded that the ID doctrine may serve as means of the real-time metaphorical reassurance of the creative power of God while it cannot give grounds to any literal inferences on the nature of the Divine action. (shrink)

In the paper, several data reduction techniques for machine learning from big datasets are discussed and evaluated. The discussed approach focuses on combining several techniques including stacking, rotation, and data reduction aimed at improving the performance of the machine classification. Stacking is seen as the technique allowing to take advantage of the multiple classification models. The rotation-based techniques are used to increase the heterogeneity of the stacking ensembles. Data reduction makes it possible to classify instances belonging to big datasets. We (...) propose to use an agent-based population learning algorithm for data reduction in the feature and instance dimensions. For diversification of the classifier ensembles within the rotation also, alternatively, principal component analysis and independent component analysis are used. The research question addressed in the paper is formulated as follows: does the performance of a classifier using the reduced dataset be improved by integrating the data reduction mechanism with the rotation-based technique and the stacking? (shrink)

An operation on inferential rules, called H-operation, is used to minimize the axiom basis for classical logic.

Kategoria integralności może być różnie rozumiana. Autorzy tekstów zamieszczonych w tomie opierają się na koncepcji Kena Wilbera AQAL. Głównymi jej składowymi są koncepcja Czterech Ćwiartek, ujmująca w sposób systemowy rzeczywistość i pozwalająca analizować związki między różnymi jej fenomenami, oraz Dynamika Spiralna, dotycząca rozwoju kulturowego, systemów i świadomości człowieka. Perspektywa integralna znalazła wyraz w ich publikacjach począwszy od 2005 roku, wcześniej – w praktyce akademickiej, a zwieńczeniem tego wstępnego etapu poszukiwań wilberowskich była konferencja naukowa „Ciało – Edukacja – Umysł” (2008) i (...) monografia pod tym samym tytułem (2010). Koncepcja Wilbera wzbudziła zainteresowanie w środowisku pedagogicznym akademickim i wśród praktyków. Między innymi Marzanna Bogumiła Kielar w monografii Integralna wizja Kena Wilbera i jej zastosowanie w edukacji (2012) dokonała rekonstrukcji koncepcji Wilbera, Zbigniew Kwieciński nawiązał do niej w wystąpieniu otwierającym VIII Zjazd Pedagogiczny w 2013 roku. Na UMK odbyły się też studia podyplomowe „Dyrektor jako lider oświaty”, których treści zostały skonstruowane na podwalinach koncepcji AQAL Wilbera. Do tej pory ukazały się następujące nasze monografie, w których AQAL zastosowano jako narzędzie opisu i wyjaśniania: P. Błajet, Ciało w kulturze współczesnej (2006), B. Przyborowska, P. Błajet, Szkice o wychowaniu agonistycznym (2008), P. Błajet, Miłość. Rozwój. Wychowanie (2010), P. Błajet, Od edukacji sportowej do olimpijskiej (2012), B. Przyborowska, Pedagogika innowacyjności: między teorią a praktyką (2013), P. Błajet, (Nie)przypadkowa edukacja (2016). „Kategoria integralności w edukacji” stanowi pokłosie licznych spotkań i dyskusji z myśleniem Wilbera w tle lub jako wątkiem wiodącym, stanowi rozszerzenie i pogłębienie, autorski wkład, a czasami krytyczną analizę myśli tego autora. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical analogies (...) and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

Współczesne dylematy filozofii i kultury powstały z inicjatywy pracowników Zakładu Filozofii Współczesnej, Myśli Społecznej i Ontologii UWM w Olsztynie. Jednak miały one stanowić przyczynek do zintegrowania badań nie tylko środowiska naukowego tegoż zakładu czy Instytutu Filozofii Uniwersytetu Warmińsko-Mazurskiego (jego kadry, doktorantów i absolwentów). Celem niniejszego projektu było bowiem zawiązanie ściślejszej współpracy pomiędzy naukowcami Wydziału Humanistycznego, która mogłaby w przyszłości zaowocować wyznaczeniem wspólnych celów, kierunków i ram badawczych czy choćby interdyscyplinarnymi spotkaniami, konferencjami i publikacjami. Przyjęliśmy, że wątkiem łączącym dociekania naukowe w (...) przestrzeni humanistyki jest jeden wspólny temat – kultura. I nie ma w tym nic odkrywczego, bowiem przedmiotem badań nauk humanistycznych jest człowiek – jej twórca, uczestnik i twór, dlatego też podstawowe w jego poznaniu okazuje się zrozumienie całokształtu jego duchowego i materialnego dorobku kulturowego. I tak filozofia (nie tylko filozofia kultury, ale i filozofia polityki, filozofia życia gospodarczego, historiozofia), literaturoznawstwo, estetyka, politologia, socjologia, historia i wiedza o stosunkach międzynarodowych stają się naukami o kulturze. (shrink)

The book presents five philosophical and axiological studies devoted to the relationship between aesthetics and politics. It shows this relationship throughout the works of some avant-gardists, pragmatists, and postmodernists. It is also a voice in the discussion about the meaning of the fine arts and aesthetics in the context of the political aims and norms. This voice claims that the political dimension of art and aesthetics should be studied much more seriously than it has been till today, and needs more (...) courageous re-interpretations and re-readings. (shrink)

The aim of this paper is to analyze the implications flowing from adopting methodological naturalism in science, with special emphasis on the relation between science and religion. Methodological naturalism, denying supernatural and teleological explanations, influences the content of scientific theories, and in practice leads to vision of science as compatible with ontological naturalism and in opposition to theism. Ontological naturalism in turn justifies the acceptance of methodological naturalism as the best method to know the reality. If we accept realistic interpretation (...) of scientific theories, then methodological naturalism conflicts science with religion. Theistic evolution does not seem to be a proper way to reconcile Darwinism and methodological naturalism with theism. Many of such propositions are boiled down to deism. Although evolution can be interpreted theistically, it is not the way in which majority of modern scientists and respectable scientific institutions understand it. (shrink)

In this paper, we present a reinterpretation of Roman Ingarden's theory of intentional objects. There are four types of intentional objects in Ingarden's ontology, we offer a detailed analyses of an intentional object that is a correlate of a text. Such an object is characterised by Ingarden as a two-sided and schematised formation. We focus on the notion of schematism. We classify different interpretations of schematism and propose our own definition of schematism of a purely intentional object.

Music and noise can be considered as a collection of vibrational events which may impinge upon the body and the mind. As such they can induce beneficial or harmful bodily and psychological reactions. Much contemporary music production and consumption, however, produces sensory saturation and/or overload with sounds being manipulated in terms of spectrum and dynamic range. Such manipulation is not harmful by definition, but the manipulations may increase the potential for harm. Much research has been devoted to the risk of (...) auditory overstimulation, but the topic is still relevant as listening to music is a significant form of leisure noise exposure. Listening habits and attitudes toward loud music may even promote behaviors that could cause harm to listeners, both in a direct and indirect way. Listening to loud music, in fact, may be damaging to the cochlea (and possibly also the auditory nuclei and the auditory pathway), and may cause both temporary or permanent hearing loss. On the other hand, loud music may have benefits for us, particularly in terms of social integration and an enhanced sense of wellbeing and fun. Several questions can therefore be raised. What are the physical effects of sound as transferable and vibrational energy? Are there constraints and biases that shape and modify our reactions to the sounds? What are the perceptual and associated behavioral aspects? What are the psychological mechanisms for liking loud music? What are the social factors that contribute to increased preferences for loud music? And how can we assess the beneficial and harmful effects of sounds that are outside of the optimal range of stimulation? (shrink)

In this paper we show that the field of the real numbers is an intentional object in the sense specified by Roman Ingarden in his Das literarische Kunstwer and Der Streit um die Existenz der Welt. An ontological characteristics of a classic example of an intentional object, i.e. a literary character, is developed. There are three principal elements of such an object: the author, the text and the entity in which the literary character forms the content. In the case of (...) the real numbers the triad consists of Richard Dedekind, his work Steitigkeit und irratinale Zahlen, and the intentional object determined by this work. Showing that we are indeed faced with the inten-tional object we analyse three moments: two-sidedness of the formal structure of the intentional object, the moment of its existentional derivation, and schematism of the intentional object. Since there are many constructions of the real numbers known in mathematics, we show what relation obtains between Dedekind's and Cantor's constructions of the real numbers as these are taken as intentional objects. Moreover, we show what relation obtains between Dedekind's construction and the axiomatic characteristics of the real numbers. (shrink)

The aim of the paper is to provide a presentation and evaluation of Kazimierz Twardowski's conception, the subject matter and contents of which is delimited, roughly by (Twardowski 1965a). Since there is no separate problematization of the notion of action in Twardowski, it is maintained that the conception in question should be characterized rather as a conception of "products of actions" (hence the term "Twardowski's conception of products of actions") and not as a conception of "actions and products" - contrary (...) to what is suggested by the title of the above mentioned Twardowski's paper. Twardowski's conception of products of actions includes a conception which has the general notion of products of actions as its central notion, and which belongs to philosophy of action. This conception has been called "Twardowski's general conception of products of actions". It is supplemented by some conceptions which can be characterised, roughly, as based on it (I.3.). Among the theses that belong to the general conception are the theses that make together what has been called in the paper "the conception of nonpermanent products as events" (II.7.). There is also a thesis to the effect that each action has but one product (II.1.), and a thesis which eliminates the material of actions from their products (II.11.). As for the conceptions which are based on Twardowski's general conception of products of actions, all but one belong to the logic of language and semiotics. They include Twardowski's conception of meaning and, within its confines, his conception of proposition as the product of judgement. The presentation and evaluation of Twardowski's conception of products of actions often requires preparatory considerations of a purely ontological, epistemological and/or methodological character. A separate section (II.8.) is devoted entirely to some ontological problems of complexity with the question of "empty" parts as the question in focus. Twardowski's conception of products of actions has to be seen as making a contribution to the research on the ontological foundations of philosophy of action and philosophy of mind. If the objections that have been raised against it are correct, the importance of its contribution to this research may be questioned (IV.1.). Such is f.e. the import of the objections raised against Twardowski's conception of meaning: while this conception seems at first sight to substantially widen our perspectives in respect of the ontic status of meanings, the corrections proposed as a result of its critical appraisal reduce all that can have a claim to originality to a variant of the thesis to the effect that meanings are defective in respect of ontic autonomy (III.2.6.). The results presented in the paper have some bearing on the question of Twardowski's attitude towards psychologism, as well as his contribution to the battle against it: on the one hand there seems to be no reason to question Twardowski's position as a consistent antipsy. (shrink)

In the paper the methodological status of the partial definitions of dispositional predicates is considered. The problem of conservativeness, analyticity and of a pragmatic role of such definitions is analyzed.

In my paper I'm going to present and evaluate position that science and religion (Christianity) do not contradict each other and that they rather answer different kinds of questions and solve different problems. Even if they both claim anything about the origin of Universe or human their claims are made from various, independent perspectives. Advocates of complementarity of science and religion state that science is a search for empirical data while religion refers to the domain of values and meaning. In (...) effect they are complementary to each other and their connection gives richer and consistent picture of reality. I agree that there are many problems and questions that are not common to scientific and religious domains, but I'm also going to show that meaning of many religious claims - also the crucial ones - is dependent upon existence of some facts in empirical world included to realm of science. I will also argue that the thesis of complementarity of science and religion is based on discredited neopositivistic picture of science as free from any philosophical commitments. (shrink)

The article covers the problem of testability of intelligent design theory. The objection that intelligent design theory does not correspond to principle of methodological naturalism is discussed. I show that recognizing intelligent causes is commonly applied in science. I present the "specification-complexity" criterion, an attempt to generalize the criteria used to define the problem in particular sciences. This criterion - together with the concept of explanatory filter - is to guarantee the testability of intelligent design theory. The irreducible complexity criterion, (...) which is to recognize design in biology, is brought forward. The problem of progressiveness of intelligent design theory is also reported. The analysis leads to the conclusion that functioning in intelligent design theory criterion of design recognition belongs to probability and complexity theory and that theory discussed is empirically testable. (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)

A calculus of properties due to Żabski [1982] is outlined and criticised. Some of its theorems are claimed to fail to account for the relevant onotological intuitions and some to fail to be true. The argument in its favour from co-extensional nonidentical properties is challenged. In conclusion, the need for a calculus of properties in general is doubted.

"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)

An attempt at moral interpretation of Hegelian ‘struggle for recognition’. The Author shows how the Hegelian figures of ‘Lord’ and ‘Bondsman’ (from The Phenomenology of Spirit) can be used to explain social role and importance of the idea of tolerance in the context of (intolerant) group moralities and the universal morality. The text is built of three parts: (1) the author sketches the connection of the traditional idea of tolerance and sociological understanding of morality on the basis of Hegel’s understanding (...) of recognition (Anerkennung). In the second step (2), he gives an outline of Hegelian two accounts of mutual recognition, finally (3) the author shows the moral dimension of recognition, as referred to the idea of tolerance and universalistic morality. (shrink)

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.

(2001). Associo‐deliberative democracy and qualitative participation. Critical Review of International Social and Political Philosophy: Vol. 4, Associative Democracy: The Real Third Way, pp. 71-84. doi: 10.1080/13698230108403338.

The paper considers whether virtue ethics should be regarded as excluding duty ethics or any of its essential elements. The argument suggested here consists of two steps: (1) an argument that there are two different versions of virtue ethics (moderate and strong) and that moderate virtue ethics does not exclude the duty ethics; (2) an analysis of various difficulties with the strong version of virtue ethics, which shows that moderate virtue ethics is more plausible because of its capacity to avoid (...) these difficulties. This capacity makes moderate virtue ethics more attractive as an ethical theory because it covers the entire range of moral phenomena described both by strong versions of virtue ethics and by duty ethics without the attendant difficulties. (shrink)