The Wadge hierarchy was originally defined and studied only in the Baire space. Here we extend the Wadge hierarchy of Borel sets to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g., several Hausdorff–Kuratowski -type theorems in quasi-Polish spaces. In fact, many results hold not (...) only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q. (shrink)

A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $\mathbf {0}'$ -computable low $_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $n\geq 2$, there exists a Polish space $X_n$ such that exactly the high $_{n}$ -degrees are required to present the homeomorphism type of $X_n$. (...) Along the way we investigate the computable aspects of Čech homology groups. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. (shrink)

Attempts to extend the classical Hausdorff difference hierarchy to the case of partitions of a space to k > 2 subsets lead to non‐equivalent notions. In a hope to identify the “right” extension we consider the extensions appeared in the literature so far: the limit‐, level‐, Boolean and Wadge hierarchies of k ‐partitions. The advantages and disadvantages of the four hierarchies are discussed. The main technical contribution of this paper is a complete characterization of the Wadge degrees of Δ02‐measurable k (...) ‐partitions of the Baire space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

The wedge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). Here we extend the Wadge hierarchy of Borel sets to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g. several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, (...) many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q. (shrink)

We establish some results on the Borel and difference hierarchies in φ-spaces. Such spaces are the topological counterpart of the algebraic directed-complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non-collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question of (...) characterizing the ω-ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (shrink)

It is well known that any finitary operation is recursive in a suitable total numeration. A. Orlicki showed that there is an ω-operation not recursive in any total numeration. We will show that any ω-operation is recursive in a partial numeration.

We state some general facts on r.e. structures, e.g. we show that the free countable structures in quasivarieties are r.e. and construct acceptable numerations and universal r.e. structures in quasivarieties. The last facts are similar to the existence of acceptable numerations of r.e. sets and creative sets. We state a universality property of the acceptable numerations, classify some index sets and discuss their relation to other decision problems. These results show that the r.e. structures behave in some respects better than (...) the recursive structures. (shrink)

We prove that for any k≥3 each element of the h-quasiorder of finite k-labeled forests is definable in the ordinary first order language and, respectively, each element of the h-quasiorder of countable k-labeled forests is definable in the language Lω1ω, in both cases provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we characterize the automorphism groups of both structures and show that the structure of finite k-forests is atomic. Similar results hold true for two other relevant (...) structures: the h-quasiorder of finite k-labeled trees and of finite k-labeled trees with a fixed label of the root element. (shrink)

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache & Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in various (...) real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation. (shrink)

For long time, especially in the West, there is old paradigm that is strong separation between science and theology/religion matters. Especially, such a diverging path started from Galileo persecution, and also other patterns where religious authority seem to hold the last word on scientific issues. Other area of this World, seems to not hold such a diverging path, for instance it can be read in the works of physicist turned to religious philosopher, for instance Pavel Florensky and Nesteruk. That is (...) why we also discuss shortly about those scientists in this book. In the last chapter, we discuss about eureka, an experience which for a long time was attributed to divine spark or “God’s favor to an artist or to a scientist, such luminaries like Newton, Pascal, Leibniz etc.” Nonetheless, new methodology appears to be able to be generated once we accept balanced brain approach, where left brain and right brain hemispheres of humans can work together. (shrink)

As such "Essay on Exoticism" is essential reading for both cultural theorists or those with an interest in the politics of difference and diversity.

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical (...) wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space. (shrink)

Contributed articles presented at a National seminar.

Contributed articles presented at a National Seminar on "Teaching Philosophy in India: a Vision for the Twenty-First Century Education", held at Andhra University, during 9-11 March 1998 and sponsered by Indian Council of Philosophical Research, New Delhi.

The book outlines the contribution of passivity to the constitution of phenomena as diverse as temporal syntheses, perceptual associations, memory fulfillment and cross-cultural communication.

We consider fine hierarchies in recursion theory, descriptive set theory, logic and complexity theory. The main results state that the sets of values of different Boolean terms coincide with the levels of suitable fine hierarchies. This gives new short descriptions of these hierarchies and shows that collections of sets of values of Boolean terms are almost well ordered by inclusion. For the sake of completeness we mention also some earlier results demonstrating the usefulness of fine hierarchies.

This new Encyclopedia of Postmodernism is structured with biographical entries on all the key contributors to the postmodernism debate, including Mikhail Bakhtin, Pierre Bourdieum, Jacques Derrida, Jurgen Habermas and Wittgenstein. Providing an all-encompassing and welcome addition to the field, the Encyclopedia contains entries on foundational concepts of postmodernism which have revolutionized thinking in every intellectual discipline. This new Encyclopedia is the first to provide comprehensive A-Z coverage of the key individuals and concepts of postmodernism. The 300+ entries include: * African (...) American studies * Roland Barthes * binary opposition * Buddhism * comparative literature * cyberculture * death of God * Gilles Deleuze * desire * digital culture * end of history * globalization * grand narrative * improvisation * jouissance * logocentrism * metalanguage * sadism * theatre arts * trope * visuality * Cornell West * and much more. Fully cross-referenced and indexed, with suggestionsfor further reading. (shrink)

Excerpt from Les Sceptiques Grecs Enfin le doute lui-meme n'est pas le scepticisme. C'est du doute seulement qu'on pourrait dire qu'il est a peu pres contem porain de la pensee humaine; car, pour un esprit qui reflechit, la decouverte de la premiere erreur suffit a inspirer une certaine defiance de soi; et combien de temps a-t-il fallu a des esprits un peu attentifs pour s'apercevoir qu'ils s'etaient plus d'une fois trompee? About the Publisher Forgotten Books publishes hundreds of thousands of (...) rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Etnofiction essay, between anthropology and philosophy.

Research on collective emotion spans social sciences, psychology and philosophy. There are detailed case studies and diverse theories of collective emotion. However, experimental evidence regarding the universal characteristics, antecedents and consequences of collective emotion remains sparse. Moreover, current research mainly relies on emotion self-reports, accounting for the subjective experience of collective emotion and ignoring their cognitive and physiological bases. In response to these challenges, we argue for experimental research on collective emotion. We start with an overview of theoretical frameworks to (...) identify a set of three characteristics of collective emotion. Based on research in cognitive and affective sciences, we then examine the corresponding candidate mechanisms. Finally, we highlight outstanding questions, review experimental evidence, and suggest ideas for future experimental research. (shrink)

Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...) argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers. (shrink)

to be or not to be ethically neutral, in a world of decieve and calculation.

The article reviews the concepts of the multi-author book Society. National Strategy. War: Political and Strategic Lessons of the First World War. This collective research is notable for rich original scientific apparatus and methodological proficiency. Thus, the analysis of participating countries is conducted according to a single template, which includes: the state of pre-war society in all participating countries ; goals of engaging in war and expectations of the powerful and financial elites for the war ; assessment of how did (...) different strata of society find the war; the evolution of the morale of the people during the war; problems that arose during the war ; the evolution of women’s position in society during the war, the development of a broad segment of women-workers, the extension of emancipation as one of the positive results of the war; the outcome of the war for the country. Special attention is drawn to the pacifist nature of the ideology of the reviewed research, demonstration of deprivation and suffering of people in all countries. The book’s authors identify the main causes of the First World War: ambitions and inefficiency of the world’s elites, the lack of a coherent strategy. As the result, the USA, thanks to their strategy, received the maximum dividends with minimal participation. At the same time, it is noted that the context of research on the nature of war should be expanded to take into account the general competition of countries and civilizations. The authors comprehensively analyze the informational and propaganda activities of the participating countries and conclude that England’s activities in this field were the most effective. Based on the methodology of this collective research, the nature of a future world war, its potential participants and their goals can be considered. (shrink)

In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

Recently, several scholars have argued in support of the idea that folk psychology involves a primary capacity for regulating our mental states and patterns of behavior in accordance with a bunch of shared social norms and routines :259–281, 2015; Zawidzki, Philosophical Explorations 11:193–210, 2008; Zawidzki, Mindshaping: A new framework for understanding human social cognition, MIT Press, Cambridge, 2013). This regulative view shares with the classical Dennettian intentional stance its emphasis on the normative character of human socio-cognitive capacities. Given those similarities, (...) it makes sense to assess the regulative view by considering some of the classical arguments against the normative nature of the intentional stance :76–100, 1985; Stich, Philosophical Topics 12:39–62, 1981; Stich, The fragmentation of reason: Preface to a pragmatic theory of cognitive evaluation, MIT Press, Cambridge, 1990). The aim of this paper is to argue that the priority that the regulative view lays on the pluralistic and regulative character of folk psychology leaves the theory well-placed to resist these arguments. In this sense, the regulative view possesses better theoretical options to defend the normative character of human social cognition. (shrink)