We investigate strong versions of enumeration reducibility, the most important one being s-reducibility. We prove that every countable distributive lattice is embeddable into the local structure $L(\mathfrak D_s)$ of the s-degrees. However, $L(\mathfrak D_s)$ is not distributive. We show that on $\Delta^{0}_{2}$ sets s-reducibility coincides with its finite branch version; the same holds of e-reducibility. We prove some density results for $L(\mathfrak D_s)$ . In particular $L(\mathfrak D_s)$ is upwards dense. Among the results about reducibilities that are stronger than s-reducibility, (...) we show that the structure of the $\Delta^{0}_{2}$ bs-degrees is dense. Many of these results on s-reducibility yield interesting corollaries for Q-reducibility as well. (shrink)

Let A be an infinite $\Delta _{2}^{0}$ set and let K be creative: we show that K ≤Q A if and only if K ≤Q1 A. (Here ≤Q denotes Q-reducibility, and ≤Q1 is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x) ∩ Wf(y) = ∅, if x ≠ y.) Using this result we prove that A is hyperhyperimmune if and only if no $\Delta _{2}^{0}$ subset B of A is (...) s-complete. i.e., there is no $\Delta _{2}^{0}$ subset B of A such that K̄ ≤s B, where ≤s denotes s-reducibility, and K̄ denotes the complement of K. (shrink)

We prove that if $A$, $B$ are noncomputable c.e. sets, $A<_{sQ_{1}}B$ and [($B$ is not simple and $A\oplus B\leq _{sQ_{1}}B$) or $B\equiv _{sQ_{1}}B\times \omega $], then there exist infinitely many pairwise $sQ_{1}$-incomparable c.e. sets $\{C_{i}\}_{i\in \omega }$ such that $A<_{sQ_{1}}C_{i}<_{sQ_{1}}B$, for all $i\in \omega $. We also show that there exist infinite collections of $sQ_{1}$-degrees $\{\boldsymbol {a_{i}}\}_{i\in \omega }$ and $\{\boldsymbol {b_{i}}\}_{i\in \omega }$ such that for every $i, j,$ (1) $\boldsymbol {a_{i}}<_{sQ_{1}}\boldsymbol {a_{i+1}}$, $\boldsymbol {b_{j+1}}<_{sQ_{1}}\boldsymbol {b_{j}}$ and $\boldsymbol {a_{i}}<_{sQ_{1}}\boldsymbol {b_{j}}$; (...) (2) every c.e set in $\boldsymbol {a_{i}}$ is a maximal set; and (3) every c.e. set in $\boldsymbol {b_{j}}$ is a non-maximal hyperhypersimple set. We prove that a noncomputable c.e. $sQ$-degree contains either only one or infinitely many c.e. $sQ_{1}$-degrees. The $sQ_{1}$-degrees of c.e. cylinders are dense upper semilattice. (shrink)

Let A be an infinite Δ₂⁰ set and let K be creative: we show that K≤Q A if and only if K≤Q₁ A. (Here ≤Q denotes Q-reducibility, and ≤Q₁ is the subreducibility of ≤Q obtained by requesting that Q-reducibility be provided by a computable function f such that Wf(x)∩ Wf(y)=∅, if x \not= y.) Using this result we prove that A is hyperhyperimmune if and only if no Δ⁰₂ subset B of A is s-complete, i.e., there is no Δ⁰₂ subset (...) B of A such that \overline{K}≤s B, where ≤s denotes s-reducibility, and \overline{K} denotes the complement of K. (shrink)

We show that if M is an r‐maximal set, A is a major subset of M, B is an arbitrary set and, then. We prove that the c.e. ‐degrees are not dense. We also show that there exist infinite collections of ‐degrees and such that the following hold: (i) for every i, j,, and,(ii) each consists entirely of r‐maximal sets, and(iii) each consists entirely of non‐r‐maximal hyperhypersimple sets.

We prove that a computably enumerable set A is effectively speedable (effectively levelable) if and only if there exists a splitting (A₀,A₁) of A such that both A₀ and A₁ are effectively speedable (effectively levelable). These results answer two questions raised by J. B. Remmel.

We show that the _sQ_-degree of a hypersimple set includes an infinite collection of \(sQ_1\) -degrees linearly ordered under \(\le _{sQ_1}\) with order type of the integers and each c.e. set in these _sQ_-degrees is a hypersimple set. Also, we prove that there exist two c.e. sets having no least upper bound on the \(sQ_1\) -reducibility ordering. We show that the c.e. \(sQ_1\) -degrees are not dense and if _a_ is a c.e. \(sQ_1\) -degree such that \(o_{sQ_1}, then there exist (...) infinitely many pairwise _sQ_-incomputable c.e. _sQ_-degrees \(\{c_i\}_{i\in \omega }\) such that \((\forall \,i)\;(a. (shrink)

We show: for every noncomputable c.e. incomplete c-degree, there exists a nonspeedable c-degree incomparable with it; The c-degree of a hypersimple set includes an infinite collection of \-degrees linearly ordered under \ with order type of the integers and consisting entirely of hypersimple sets; there exist two c.e. sets having no c.e. least upper bound in the \-reducibility ordering; the c.e. \-degrees are not dense.

We use certain strong Q-reducibilities, and their corresponding strong positive reducibilities, to characterize the hyperimmune sets and the hyperhyperimmune sets: if A is any infinite set then A is hyperimmune (respectively, hyperhyperimmune) if and only if for every infinite subset B of A, one has \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\rm ss} B}$$\end{document} (respectively, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}\not\le_{\overline{\rm s}} B}$$\end{document}): here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm (...) s}}}$$\end{document} is the finite-branch version of s-reducibility, ≤ss is the computably bounded version of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\le_{\overline{\rm s}}}$$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{K}}$$\end{document} is the complement of the halting set. Restriction to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} sets provides a similar characterization of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^0_2}$$\end{document} hyperhyperimmune sets in terms of s-reducibility. We also show that no \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \geq_{\overline{\rm s}}\overline{K}}$$\end{document} is hyperhyperimmune. As a consequence, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\deg_{\rm s}(\overline{K})}$$\end{document} is hyperhyperimmune-free, showing that the hyperhyperimmune s-degrees are not upwards closed. (shrink)

Brain functions are stochastic processes without intentionality whereas mind emerges from brain functions as a Hegelian “change from quantity”, that is, on the order of 1012 profusely interconnected neurons, “into a new quality”: the collective phenomenon of the brain's self-experience. This self-referential and self-observing quality we have in mind is capable of (recursively) observing its self-observations, i.e., interpreting change that is meaningful in relation to itself. The notion of self-interpretation embodies the idea of a “hermeneutic circle”, that is, (in interpretation (...) theory) the treatment of the whole in relation to its parts. (shrink)

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q1-degrees linearly ordered under \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\leq_{Q_1}}$$\end{document} with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q1-degrees are not an upper semilattice. The main result of this paper is that the Q1-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi_1^0}$$\end{document}s1-degrees. (shrink)

This volume describes the current "main contenders," including neo-Piagetian, neo-connectionist, neo-innatist and sociocultural models.

We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus} A\equiv{}_{Q_{1,N}}M_{2}{\setminus} B}$$\end{document}, then M1\A≡mM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}{\setminus}A\equiv{}_{m}M_{2}{\setminus} B}$$\end{document}. If M1 and M2 are r-maximal sets and M10,M11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0},\,M_{1}^{1}}$$\end{document} and M20,M21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{2}^{0},\,M_{2}^{1}}$$\end{document} are nontrivial splittings of M1 and M2, respectively, then M10≡Q1,NM20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{Q_{1,N}}M_{2}^{0}}$$\end{document} if and only if M10≡1M20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_{1}^{0} \equiv{}_{1}M_{2}^{0}}$$\end{document}. From this result follows that if A and B are Friedberg splitting of an r-maximal set, then the Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degree of A contains only one c.e. 1-degree. (shrink)

Drawing on mostly ignored texts, this book thoroughly reassesses Marx and Engels's engagement with theology.

Introduction to Engineering Ethics provides the background for discussion of the basic issues in engineering ethics. Emphasis is given to the moral problems engineers face in the corporate setting. It places those issues within a philosophical framework, and it seems to exhibit both their social importance and their intellectual challenge. The primary goal is to stimulate critical and responsible reflection on moral issues surrounding engineering practice and to provide the conceptual tools necessary for pursuing those issues. As per new ABET (...) 2000 guidelines, more and more introductory engineering courses cover engineering ethics as part of their instruction. Students preparing to function within the engineering profession need to be introduced to the basic issues in engineering ethics. This book places those issues within a wider philosophical framework than has been customary in the past and aims to stimulate critical and responsible reflection on the moral issues surrounding engineering practice and to provide the conceptual tools necessary for pursuing those issues. (shrink)

Une approche philosophique de la prière à des fins politiques est possible dans le cas où les deux substantifs sont mis en relais inconditionnel. Le premier élément responsable de cette filature des liens c’est la présence de l’autre. Prier et faire de la politique sont deux activités humaines trop humaines qui exigent l’ouverture à l’autre, pour l’autre comme pour l’édification de sa propre identité individuelle et collective. Comme les rites et les cultes, la liturgie, notamment la prière collective, a un (...) effet thérapeutique, et pédagogique, disons didactique et sociopolitique. Elle calme les esprits, la volonté, apaise l’angoisse et solidifie les liens sociaux. L'Eglise, par exemple, est née du rassemblement du peuple de Dieu en prière et c'est dans son sein que toute célébration liturgique trouve perpétuellement son accomplissement aussi bien que sa régénération dans l’invocation du nom du Christ-Vérité, Rédempteur, Fondateur, Roi et Prêtre. La présente étude sur « Vérité et Royauté » focalise l’attention sur l’essence même du politique qui se nourrit du religieux tout en lui fournissant gloire, pouvoir et moyens d’existence. (shrink)

The experimental philosophy movement advocates the use of empirical methods in philosophy. The methods most often discussed and in fact employed in experimental philosophy are appropriated from the experimental paradigm in psychology. But there is a variety of other (at least partly) empirical methods from various disciplines that are and others that could be used in philosophy. The paper explores the application of corpus analysis to philosophical issues. Although the method is well established in linguistics, there are only a few (...) tentative attempts of philosophers to utilise it. Examples are introduced and the merit of corpus analysis is compared to that of using general internet search engines and questionnaires for similar purposes. (shrink)

Roland Reichenbach; On Irritation and Transformation: A–teleological Bildung and its Significance for the Democratic Form of Living, Journal of Philosophy of Ed.

Roland Reichenbach; On Irritation and Transformation: A–teleological Bildung and its Significance for the Democratic Form of Living, Journal of Philosophy of Ed.

The 2015 Disneyland outbreak of measles in the US unequivocally brought to light what had been brewing below the surface for a while: a slow but steady decline in vaccination rates resulting in a rising number of outbreaks. This can be traced back to an increasing public questioning of vaccines by an emerging anti-vaccination movement. This article argues that, in the face of diminishing vaccination rates, childhood vaccinations should not be seen as part of the domain of parental choice but, (...) instead, as a non-negotiable legal obligation. The first part of the article formulates and defends two arguments in favour of unqualified mandatory childhood vaccination laws. First, government should not permit parents to put their children at avoidable risk of death and suffering; second, government should guard the common good of herd immunity to protect vulnerable persons. The second part rejects legal and pragmatic objections against such mandatory vaccination laws. (shrink)

Contrary to received opinion among philosophers, psychologists, and neuroscientists, conscious duality as a principle of brain organization is neither incoherent nor demonstrably false. The present paper begins by reviewing the history of the theory and its anatomical basis and defending it against the claim that it rests upon an arbitrary decision as to what constitutes the biological substratum of mind or person.

Supposons qu'il soit possible de transplanter les centres de Ia douleur de Jones dans le cerveau de Smith. A mi-chemin pendant!'operation, on teste ces centres de Ia douleur en les stimulant électriquement in vitro. Y aurait-il de Ia douleur? L'argument de cet article est qu'il n'y en aurait pas, parce que Ia douleur doit avoir un possesseur. Sinon, il ne peut arriver que les centres de Ia douleur se déchargeant dans un cerveau soient en eux-mêmes Ia douleur. On peut logiquement (...) transférer le mécanisms de Ia douleur, mais non Ia douleur elle-mêmes. Ainsi le materialisme est faux.Suppose we live in a very advanced age of neurosurgical skills. We have a patient, Jones, with intractable pain. We have a second patient, Smith, with a long history of unintentional self-injury due to congenital absence of pain centres. So we decide to do double service by transplanting Jones's pain centres into Smith's brain. (shrink)

"I define the Neutral as that which outplays the paradigm, or rather I call Neutral everything that baffles paradigm." With these words, Roland Barthes describes a concept that profoundly shaped his work and was the subject of a landmark series of lectures delivered in 1978 at the Collège de France, just two years before his death. Not published in France until 2002, and appearing in English for the first time, these creative and engaging lectures deepen our understanding of (...) class='Hi'>Roland Barthes's intellectual itinerary and reveal his distinctive style as thinker and teacher. The Neutral (_le neutre_), as Barthes describes it, escapes or undoes the paradigmatic binary oppositions that structure and produce meaning in Western thought and discourse. These binaries are found in all aspects of human society ranging from language to sexuality to politics. For Barthes, the attempt to deconstruct or escape from these binaries has profound ethical, philosophical, and linguistic implications. _The Neutral_ is comprised of the prewritten texts from which Barthes lectured and centers around 23 "figures," also referred to as "traits" or "twinklings," that are possible embodiments of the Neutral (sleep, silence, tact, etc.) or of the anti-Neutral (anger, arrogance, conflict, etc.). His lectures draw on a diverse set of authors and intellectual traditions, including Lao-tzu, Tolstoy, German mysticism, classical philosophy, Rousseau, Baudelaire, Walter Benjamin, and John Cage. Barthes's idiosyncratic approach to his subjects gives the lectures a playful, personal, and even joyous quality that enhances his rich insights. In addition to his reflections on a variety of literary and scholarly works, Barthes's personal convictions and the events of his life shaped the course and content of the lectures. Most prominently, as Barthes admits, the recent death of his mother and the idea of mourning shape several of his lectures. (shrink)

Although postmodernist thought has become prominent in some educational circles, its influence on science education has until recently been rather minor. This paper examines the proposal of Michalinos Zembylas, published earlier in this journal, that Lyotardian postmodernism should be applied to science educational reform in order to achieve the much sought after positive transformation. As a preliminary to this examination several critical points are raised about Lyotard's philosophy of education and philosophy of science which serve to challenge and undermine Zembylas’ (...) project. Subsequently, the three main theses of Lyotard that Zembylas considers beneficial and wishes to transpose onto science classrooms and pedagogy are scrutinized and found to be more of a hindrance than a help to curriculum reformers. (shrink)

Supposons qu'il soit possible de transplanter les centres de Ia douleur de Jones dans le cerveau de Smith. A mi-chemin pendant!'operation, on teste ces centres de Ia douleur en les stimulant électriquement in vitro. Y aurait-il de Ia douleur? L'argument de cet article est qu'il n'y en aurait pas, parce que Ia douleur doit avoir un possesseur. Sinon, il ne peut arriver que les centres de Ia douleur se déchargeant dans un cerveau soient en eux-mêmes Ia douleur. On peut logiquement (...) transférer le mécanisms de Ia douleur, mais non Ia douleur elle-mêmes. Ainsi le materialisme est faux.Suppose we live in a very advanced age of neurosurgical skills. We have a patient, Jones, with intractable pain. We have a second patient, Smith, with a long history of unintentional self-injury due to congenital absence of pain centres. So we decide to do double service by transplanting Jones's pain centres into Smith's brain. (shrink)

Although postmodernist thought has become prominent in some educational circles, its influence on science education has until recently been rather minor. This paper examines the proposal of Michalinos Zembylas, published earlier in this journal, that Lyotardian postmodernism should be applied to science educational reform in order to achieve the much sought after positive transformation. As a preliminary to this examination several critical points are raised about Lyotard's philosophy of education and philosophy of science which serve to challenge and undermine Zembylas’ (...) project. Subsequently, the three main theses of Lyotard that Zembylas considers beneficial and wishes to transpose onto science classrooms and pedagogy are scrutinized and found to be more of a hindrance than a help to curriculum reformers. (shrink)

This book presents one of the first systematic assessments of aesthetic insights into world politics. It examines the nature of aesthetic approaches and outlines how they differ from traditional analysis of politics. The book explores the potential and limits of aesthetics through a series of case studies on language and poetics"--Provided by publisher.