This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. (...) Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

Ageing populations are a major consideration for socio-economic development in the early twenty first century. This demographic change is mainly seen as a threat rather than as an opportunity to improve the quality of human life, especially in Europe, where ageing has resulted in a reduction in economic competitiveness. Economic Foundations for Creative Ageing Policy mixes the silver economy, the creative economy, and the social economy to construct positive solutions for an ageing population. Klimczuk covers theoretical analyses and case study (...) descriptions of good practices to suggest strategies that could be internationally popularized. Contents: Foreword by Harry R. Moody Foreword by Kathrin Komp Introduction 1. Old Age as a Stage in the Life Course and the Life Cycle 2. Forms of Older People’s Capital 3. Creativity and Ageing: Concepts and Controversies 4. Mixed Economy and Multisectoral Approach to Population Ageing 5. Silver, Creative, and Social Economies as Positive Responses to Population Ageing 6. Benefits at the Interface Between Economic Systems Conclusion Afterword by Lukasz Tomczyk. (shrink)

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

Listening and polyphony lead us directly to reflection on the musical form of the fugue. Starting with M. Heidegger’s considerations about the juncture of beyng, we will phe-nomenologically ask about the essence of the fugue, and the musical work put under analysis will be The Art of Fugue by J.S. Bach. The article aims to show the convergence between Heidegger’s philosophy and the essence of the musical form of fugue as an artis-tic mode of the essential occurrence of beyng as (...) an event. (shrink)

This article addresses the subject of the ekphrastic description of experiencing music. It shows the main differences between ekphrasis and commonly used analysis in music theory and musicology. In approaching the problem of ekphrasis with what is called pure music, I emphasize its ancient understanding, thus differing from Lydia Goehr (2010) and Siglind Bruhn (2000, 2001, 2019). The ekphrastic analysis of the first movement of Arnold Schoenberg’s Six Little Piano Pieces Op. 19 conducted in this article uses the methodology developed (...) by Gottfried Boehm (2014) and Georges Didi-Huberman (2005, 2015, 2017, 2018) in the discipline of art history. This article aims to delineate a new way of researching the art of music, an essential feature of which is the combination of the traditions of analytic philosophy and phenomenology. (shrink)

By the classical mereology I mean a theory of mereological structures in the sense of [10]. In [7] I proved that the class of these structures is not elementarily axiomatizable. In this paper a new version of this result is presented, which according to my knowledge is the first such presentation in English. A relation of this result to a certain Hsing-chien Tsai’s theorem from [13] is emphasized.

This book introduces the English-speaking reader to the thought of Stanislaw Brzozowski (1878-1911), the outstanding Polish philosopher and literary critic. Although practically unknown in the West, Brzozowski is an important but neglected forerunner of the intellectual tradition of `Western Marxism', most commonly associated with Georg Lukács and Antonio Gramsci. -/- Concentrating first on the early phase of Brzozowski's thought, Professor Walicki goes on to analyse his ideas on the working class and its relation to the intelligentsia and contemporary working-class ideologies. (...) Finally he deals with aspects of his thought which go beyond the Marxian problematic and round off the intellectual portrait of the man. -/- Brzozowski's anti-naturalistic approach resulted in a radical reinterpretation of Marxism which dealt with many of the problems of the revolt against positivism in European philosophy. Professor Walicki argues that the retrieval of the philosophical and humanist aspect of Marxism, and its separation from the Engels-inspired `scientific Marxism', was the achievement of Brzozowski and not, as frequently assumed, of Lukács, who came to similar conclusions only some ten years later. -/- By placing Brzozowski within the cross-currents of the various philosophical, sociological, literary, and political streams of Western and Eastern European thought in which Marxism was situated, Professor Walicki produces a fascinating study of an early East European challenge to orthodox Marxism. (shrink)

By and large, Inferential Erotetic Logic (IEL, for short) is an approach to the logic of questions which puts in the centre of attention inferential aspects of questioning. IEL is not an enterprise of the last few years only. The idea originates from the late 1980s. It evolved through time. Initially, the stress was put on the phenomenon of question raising. This changed gradually, as some forms of reasoning that involve questions have appeared to be analyzable by means of the (...) conceptual apparatus developed. In this essay I present the basics of IEL and comment on them. Most, though not all, of the ideas discussed here have been scattered across my earlier publications. The invitation from the organizers of the Asking and Answering workshop (Greifswald, September 2020) resulted in an attempt of presenting the themes of IEL in a concise but, as I hope, also comprehensible way. (shrink)

We examine some extensions of the constructive propositional logic with strong negation in the setting of varieties of $\mathcal{N}$ -lattices. The main aim of the paper is to give a description of all pretabular, primitive and preprimitive varieties of $\mathcal{N}$ -lattices.

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

We continue investigations of reasonable ultrafilters on uncountable cardinals defined in previous work by Shelah. We introduce stronger properties of ultrafilters and we show that those properties may be handled in λ-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal λ with generating systems of size less than $2^\lambda$ . We also show how ultrafilters generated by small systems can be killed by forcing notions which have enough (...) reasonable completeness to be iterated with λ-supports. (shrink)

The studies of health care systems are conducted intensively on various levels. They are important because the systems suffer from numerous pathologies. The health care is analyzed, first of all, in economic aspects but their functionality in the framework of systems theory is studied, as well. There are also attempts to work out some general values on which health care systems should be based. Nevertheless, the aforementioned studies, however, are fragmentary ones. In this paper holistic approach to the philosophical basis (...) of health care is presented. The levels on which the problem can be considered are specified explicitly and relations between them are analyzed, as well. The philosophical basis on which the national health care systems could be based is proposed. Personalism is the basis for the proposal. First of all, the values, that are derived from the personalistic philosophy, are specified as the basic ones for health care systems. Then, general organizational and functional properties of the system are derived from the assumed values. The possibility of adaptation of solutions from other fields of social experiences are also mentioned. The existing health care systems are analyzed within the frame of the introduced proposal. (shrink)

The approach to analysing population ageing and its impacts on the economy has evolved in recent years. There is increasing interest in the development and use of products and services related to gerontechnology as well as other social innovations that may be considered as central parts of the "silver economy." However, the concept of silver economy is still being formed and requires detailed research. This article proposes a typology of models of the silver economy in the European Union at the (...) national and regional levels. This typology was created by comparing the Active Ageing Index to the typology of varieties and cultures of capitalism and typology of the welfare states. Practical recommendations for institutions of the EU and directions for further research are discussed. (shrink)

This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ + (for a strongly inaccessible cardinal λ).

The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.

W artykule proponuje się aksjomatyzację fragmentu klasycznej logiki zdań, który zostaje nazwany logiką niesymplifikacyjną. Nazwa pochodzi stąd, że unika się w nim, jak przypuszcza pewna ilość badaczy – wskazanych w tekście – paradoksalnych własności klasycznej implikacji i równoważności. Twierdzenie o niewyprowadzalności tez paradoksalnych nie jest jeszcze definitywnie udowodnione. Ale cały bieg myśli wydaje się interesujący z filozoficznego punktu widzenia ze względu na możliwość odróżnienia kilku rodzajów implikacji i równoważności.

Embodied cognition: assumptions, theses and challenges: The paper aims at providing a concise presentation of the concept of embodied cognition that emerged in the cognitive sciences a few decades ago and has gained great popularity among empirically and philosophically informed researchers. The term “embodied cognition” is used by the author in two senses. The narrow sense implies that the body plays an important role in the process of cognition. In the broad sense “embodied cognition” is to characterize the general tendency (...) within cognitive science which finds its articulation in the 4E perspective on cognition. The working hypothesis of the 4E perspective is that cognition depends on the characteristics of the agent’s body and its interaction with the physical and social environment. It emphasizes that cognition is: embodied, embedded, enacted, extended. After reconstructing the key concepts and basic assumptions the author offers a brief appraisal of the views under discussion. He claims that the characteristics of such a trend are incomplete and not homogeneity since the perspective encompasses at least a few related and partly overlapping views on cognition. The author concludes that “embodied cognition” serves as a label for a variety of research programs within cognitive science rather than a strictly defined and well-established research tradition or a new paradigm. (shrink)

Using two distinct membership symbols makes possible to base set theory on one general axiom schema of comprehension. Is the resulting system consistent? Can set theory and mathematics be based on a single axiom schema of comprehension?

This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group:,,, ⌜∨ ☐q⌝,and for any n > 0 a formula ⌜ ∨ ⌝, where has not the atom ‘q’, and and have no common atom. We generalize Pollack’s result from [12],where (...) he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities. (shrink)

The shaping of creative economy is particularly important for development of cities and regions. This process can be analyzed in conjunction with changes in work and leisure time and their place in the human life cycle. This article aims to approximate the main features of: contemporary position of elderly people, creative ageing policy, benefits from seniors creativity and controversies linked to this concept. This essay also indicates the patterns of recommendations and activities in development of services for older people which (...) may be the subject of further in-depth research. These examples exist in: documents and strategic programs, the activities of network organizations and the activities of urban cultural and artistic institutions. (shrink)

The objective of the paper is a presentation and an interpretation of Władysław Stróżewski’s views on aesthetics. Built upon the foundation provided by classical metaphysics, Stróżewski’s aesthetics is simultaneously a continuation of the tradition of phenomenological interpretation of art. Stróżewski extends Roman Ingarden’s aesthetic theory by including the idea of numinous concretion, largely inspired by the works of Rudolf Otto. As a result, this new phenomenological perspective transcends the narrowly understood ‘aesthetics’ of the work of art towards the inherent dimension (...) of the sacred. Moreover, Stróżewski’s scrutiny of the aspect of art that goes beyond the aesthetic reveals an important relationship obtaining between his insights and the theological aesthetics of Hans Urs von Balthasar. Thus Stróżewski’s ideas turn out to be of significance to contemporary aesthetic and theological debates. In particular, he shows the movement of beauty from aesthetic to transcendental, and ultimately towards the sacred, where numinosum is manifested as Mystery. (shrink)

We prove that the Sacks forcing collapses the continuum onto ${\frak d}$ , answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses $\omega_2$ then it forces $\diamondsuit_{\omega_{1}}$.

We continue developing the general theory of forcing notions built with the use of norms on possibilities, this time concentrating on ccc forcing notions and classifying them.

There are inferences from a sentence or a set of sentences to a question. The relation between the premises and conclusions of such inferences is sometimes called arising.

The article attempts to define the concept of “post-neo-Kantianism” based on the nature of its relationship to the concept of “neo-Kantianism”. Concerning this matter, the author poses the following tasks: to characterize the phenomenon of neo-Kantianism, to point out the problems of its definition, to identify the relevance of the term “post-neo-Kantianism” and its relation to the philosophy of I. Kant in particular. The author emphasizes the need to introduce this term in the classification of philosophy of the XX century (...) with the appropriateness of building the model of “Kantianism - Neo-Kantianism - Neo-Neo-Kantianism - Post-Neo-Kantianism”, where each new stage is determined by the nature of the reflection of thinkers of a certain period over the fundamental philosophical problems articulated in Kant's “Critics”. Among the post-Neo-Kantians, A. Noras names thinkers traditionally considered to be german phenomenologists, such as E. Husserl and M. Heidegger: it is from the philosophical concept of Husserl that one can speak of the emergence of post-Neo-Kantianism, and the semantically correct interpretation of Heidegger, according to author, is most clearly understood in the framework of Baden Neo-Kantianism. Investigating the phenomenon of post-Neo-Kantianism, the need is established for answering a question regarding the preceding Neo-Kantian tradition, within which there is still a number of contradictions unresolved in the history of philosophy regarding the classification of Neo-Kantian schools and the distinction between the two periods of Neo-Kantianism: early and late. Neo-Kantianism shows the relevance of Kantian philosophy, highlighting the ongoing debate about understanding the Kantian “Critique of Pure Reason”. Post-Neo-Kantianism plays an important role in terms of the perspectives of modern Kant studies, which include Gottfried Martin, Manfred Brelage, or Hans-Michael Baumgartner. (shrink)

In the first part of his magnum opus Hans Urs von Balthasarpresents his project of theological aesthetics where the experience of art becomes an entrance to a religious act and an ennobling way leading to the contemplation of God. Defining the essence of being human as a spiritual being directed towards God bears a deep ethical meaning in this consideration. H.U. von Balthasar’s reflection over the religious dimension of the essence of art is shaped within theology but at the same (...) time in the opposition to aesthetic theology which is de-scribed as ‘aesthetisation’ of the Mystery of Revelation. The art of music occupies a particular place in this reflection. For this reason Mass in B Minor BWV 232 by Johann Sebastian Bach, which is an emblematic example of the revelation of the glory of the Lord (Herrlichkeit), will be analysed not only from the perspective of philosophical or musicological aesthetics, but also theological aesthetics. This article outlines characteristic features of theological aesthetics specifically developed from traditional philosophical aesthetics whose range was extended by the human being’s relation to God. (shrink)

In 'The Work of Music and the Problem of Its Identity' by Roman Ingarden we are presented with a philosophical theory of the structure of the musical work. The author includes melody, rhythm and harmony among the primary elements of the musical work while dynamics, tempo and colouration (sonoristics) are classified as its secondary elements. The elements designated by the score constitute a schematic prescription for creating a particular work. Still, the scheme also includes numerous gaps and indeterminacies which can (...) be filled in only through performance which makes the work an individualized concretum. However, it is puzzling why the list of the elements of the musical work does not include articulation. In this article I claim that the absence of articulation in the theory of the structure of the musical work indicates its omnipresence, thus the broader we understand the term articulation, the better it penetrates into the remaining elements of the musical work, preserving its distinctiveness at the same time. (shrink)

Roman Ingarden has exerted an immense influence on the development of aesthetics, and his texts in this field continue to inspire in-depth studies on art, despite the passage of several decades since the publication of his major works. At the same time, however, phenomenology – especially in France – brought about crucial changes during the second half of the twentieth century with regard to thinking about art, undermining its own methodological principles and tenets, as well as redefining fundamental phenomenological concepts. (...) In this article, I address the question of the continued relevance of Roman Ingarden’s approach to the musical work within the context of current phenomenological research, in particular that which concerns the subject of aesthetic concretisation. (shrink)

A work of music as an artefact is a particular acoustic material. However, the sounds are not identical with music since they only constitute the external appearance of a musical work and its most explicit layer, while aesthetic perception is certainly not limited to the superficial perception of sounds. Contemporary research in the field of fine arts by Gottfried Boehm and Georges Didi-Huberman showed new possibilities of revealing the hidden inner phenomenality of a work of art. Yet, is it possible (...) to apply the methodology of research on the invisible visuality of a painting to the field of non-acoustic sound of a musical work? What kind of additional research problems does a work of music cause, taking into account the fact that it is not only created by its author-composer, but it also requires a re-creational performance to phenomenally exist? The article provides the critical analysis of Roman Ingarden’s views on the subject of a musical work and indicates the need to expand the research horizon as regards the issue of nonsounding elements of music. The article aims mainly at bringing new research perspectives on a work of music in the light of contemporary phenomenology. (shrink)

Phenomenological reflection on the essence of art goes towards the revelation of its ultimate Source, which is also the Source of spirituality of a man and, finally, of artistic works. Art occupies a prominent place in the works of Martin Heidegger, Hans Urs von Balthasar and Michel Henry, and what they have in common is pointing out the ability of transcending artistic work towards beyond-aesthetic and over-aesthetic dimensions. For those philosophers the work of art is a ‘way’ which may lead (...) human spirit towards Transcendence (the Absolute, God), but also towards the inner self. In this article the reflection over a religious dimension of the essence of art is extended by the analysis of St John Passion, BWV 245 by Johann Sebastian Bach, as a particular example of an artistic realization of phenomenologically rooted philosophical and theological reflection. (shrink)

We continue investigations of reasonable ultrafilters on uncountable cardinals defined in Shelah [8]. We introduce a general scheme of generating a filter on λ from filters on smaller sets and we investigate the combinatorics of objects obtained this way.