Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.

A real x is -Kurtz random if it is in no closed null set . We show that there is a cone of -Kurtz random hyperdegrees. We characterize lowness for -Kurtz randomness as being -dominated and -semi-traceable.

We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event [Formula: see text] such that if [Formula: see text] then X has an infinite subset Y such that no element of [Formula: see text] is Turing computable from Y.

This is a review of The Turing Guide (2017), written by Jack Copeland, Jonathan Bowen, Mark Sprevak, Robin Wilson, and others. The review includes a new sociological approach to the problem of computability in physics.

Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of nontrivial automorphisms of the Turing degrees are indicated.

We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that such sets cannot be weakly 2-random. We also study the class $superhigh^\diamond$ and show that it contains some, but not all, of the noncomputable K-trivial sets.

We show that Carmo and Jones’ condition 5 conflicts with the other conditions on their models for contrary-to-duty obligations. We then propose a resolution to the conflict.

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle . The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in λ . While the Hippocratic approach is in general much more restrictive, there are cases where the (...) two coincide. The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Löf randomness and the measure λ is a Bernoulli measure, classical randomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity. (shrink)

In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure λ, a choice needs to be made. One approach is to allow randomness tests to access the measure λ as an oracle. The other approach is the opposite one, where the randomness tests are completely effective and do not have access to the information contained in λ. While the Hippocratic approach is in general much more restrictive, there are cases where the two coincide. (...) The first author showed in 2010 that in the particular case where the notion of randomness considered is Martin-Löf randomness and the measure λ is a Bernoulli measure, classical randomness and Hippocratic randomness coincide. In this paper, we prove that this result no longer holds for other notions of randomness, namely computable randomness and stochasticity. (shrink)

Is there a nontrivial automorphism of the Turing degrees? It is a major open problem of computability theory. Past results have limited how nontrivial automorphisms could possibly be. Here we consider instead how an automorphism might be induced by a function on reals, or even by a function on integers. We show that a permutation of ω cannot induce any nontrivial automorphism of the Turing degrees of members of 2ω, and in fact any permutation that induces the trivial automorphism must (...) be computable.A main idea of the proof is to consider the members of 2ω to be probabilities, and use statistics: from random outcomes from a distribution we can compute that distribution, but not much more. (shrink)

The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this theorem. We also show thatthe set of indices of computable lattices that are complete is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete;the set of indices of computable lattices that are algebraic is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete;the set of compact elements of a computable (...) lattice is Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document} and can be Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^1_1$$\end{document}-complete; andthe set of compact elements of a distributive computable lattice is Π30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{0}_{3}$$\end{document}, and there is an algebraic distributive computable lattice such that the set of its compact elements is Π30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^0_3$$\end{document}-complete. (shrink)

We divide the class of infinite computable trees into three types. For the first and second types, 0' computes a nontrivial self-embedding while for the third type 0'' computes a nontrivial self-embedding. These results are optimal and we obtain partial results concerning the complexity of nontrivial self-embeddings of infinite computable trees considered up to isomorphism. We show that every infinite computable tree must have either an infinite computable chain or an infinite Π01 antichain. This result is optimal and has connections (...) to the program of reverse mathematics. (shrink)

We consider two axioms of second-order arithmetic. These axioms assert, in two different ways, that infinite but narrow binary trees always have infinite paths. We show that both axioms are strictly weaker than Weak König's Lemma, and incomparable in strength to the dual statement (WWKL) that wide binary trees have paths.

We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, $\scr{D}_{h}$ . In fact, we prove that every sublattice of any hyperarithmetic lattice (and so, in particular, every countable, locally finite lattice) is isomorphic to an initial segment of $\scr{D}_{h}$ . Corollaries include the decidability of the two quantifier theory of $\scr{D}_{h}$ and the undecidability of its three quantifier theory. The key tool in the proof is a (...) new lattice representation theorem that provides a notion of forcing for which we can prove a version of the fusion lemma in the hyperarithmetic setting and so the preservation of $\omega _{1}^{CK}$ . Somewhat surprisingly, the set theoretic analog of this forcing does not preserve ω₁. On the other hand, we construct countable lattices that are not isomorphic to any initial segment of $\scr{D}_{h}$. (shrink)

In Reverse Mathematics, the axiom system DNR, asserting the existence of diagonally non-recursive functions, is strictly weaker than WWKL0.

Cooperation is fundamentally moderated by the form of relationship between the actors involved, as is normative resource distribution. We argue that possessions are likely treated differently across different types of cooperative relationships. Whereas Boyer's computational model might in principle account for this, the theory would benefit from a specification of how different cooperative contexts can shape the representation of ownership.

Dieser Beitrag bietet eine umfassende Diskussion des Textes “Humanismus und Christentum” (1950) des dänischen Philosophen und Theologen Knud E. Løgstrup. Er verortet den Text in seinem geistesgeschichtlichen Kontext und analysiert seine wichtigsten Argumente wie auch seine zentrale These, der zufolge Humanismus und Christentum einen entscheidenden Grundsatz teilen, insofern beide die Ethik als “stumm“ oder “unausgesprochen“ verstehen. Darüber hinaus wird dargelegt, wie Løgstrups Text zentrale Überlegungen in dessen späteren Publikationen, besonders in dem Hauptwerk Die ethische Forderung (1956), vorwegnimmt.

Dieser Beitrag bietet eine umfassende Diskussion des Textes “Humanismus und Christentum” (1950) des dänischen Philosophen und Theologen Knud E. Løgstrup. Er verortet den Text in seinem geistesgeschichtlichen Kontext und analysiert seine wichtigsten Argumente wie auch seine zentrale These, der zufolge Humanismus und Christentum einen entscheidenden Grundsatz teilen, insofern beide die Ethik als “stumm“ oder “unausgesprochen“ verstehen. Darüber hinaus wird dargelegt, wie Løgstrups Text zentrale Überlegungen in dessen späteren Publikationen, besonders in dem Hauptwerk Die ethische Forderung (1956), vorwegnimmt.

The degree of doxastic revision required in response to evidence of disagreement is typically thought to be a function of our beliefs about (1) our interlocutor’s familiarity with the relevant evidence and arguments, and their intellectual capacities and virtues, relative to our own, or (2) the expected probability of our interlocutor being correct, conditional on our disagreeing. While these two factors are typically used interchangeably, I show that they have an inverse correlation in cases of disagreement about politically divisive propositions. (...) This presents us with a puzzle about the epistemic impact of disagreement in these cases. The most significant disagreements on (1) are the least significant disagreements on (2), and vice versa. I show that assessing the epistemic status of an interlocutor by reference to either (1) or (2) has uncomfortable consequences in these cases. I then argue that this puzzle cannot be escaped by claiming that we usually have dispute-independent reason to reject the significance of politically charged disagreement altogether. (shrink)

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it (...) is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical , provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional. (shrink)

This is the first English edition of a major work by the Danish philosopher and theologian K. E. Løgstrup (1905-81). It is the culmination of his critical engagement with Kierkegaardianism, which had begun almost 20 years earlier. In this text, Løgstrup focuses on four main themes in Kierkegaard: his understanding of Christ and thus of Christianity; his understanding of suffering in human existence; Christian vs. secular ethics; and Platonistic influences on Kierkegaard's position, which Løgstrup characterises as nihilistic. Løgstrup presents his (...) own alternative conception in response: that Christ revealed universal ontological ethical structures that put Christians and non-Christians on a par; that suffering is a basic human experience and so there is no such thing as a particular Christian suffering; that sovereign expressions of life such as trust, sincerity, and compassion are the fundamental phenomena of ethics that enable our lives to function, and are thus given as a gift of creation, not of faith; and finally that human existence as created is meaningful and holds value and so is not a Kierkegaardian 'nothingness' of mere relativity. As well as offering a classic and yet controversial critique of Kierkegaard, this text also develops Løgstrup's conception of the sovereign expressions of life, which was to become central to his later ethics, further deepening his distinctive understanding of the human condition. Here translated in full for the first time, it will now be possible for English-speaking readers to explore the issues that drew Løgstrup into his controversion with Kierkegaard. (shrink)

In this article we discuss what we call the deliberative division of epistemic labor. We present evidence that the human tendency to engage in motivated reasoning in defense of our beliefs can facilitate the occurrence of divisions of epistemic labor in deliberations among people who disagree. We further present evidence that these divisions of epistemic labor tend to promote beliefs that are better supported by the evidence. We show that promotion of these epistemic benefits stands in tension with what extant (...) theories in epistemology take rationality to require in cases of disagreement. We argue that the epistemic benefits that result from the deliberative division of epistemic labor can provide epistemic reason to maintain confidence in cases of disagreement. We then show that the deliberative division of epistemic labor constitutes a distinct kind of epistemic dependence. (shrink)

This article argues that anthropology may represent untapped perspectives of relevance to social theory. The article starts by critically reviewing how anthropology has come to serve as the ‘Other’ in various branches of social theory, from Marx and Durkheim to Parsons to Habermas, engaged in a hopeless project of positing ‘primitive’ or ‘traditional’ society as the opposite of modernity. In contemporary debates, it is becoming increasingly recognized that social theory needs history, back to the axial age and beyond. The possible (...) role of anthropology in theorizing modernity receives far less attention. That role should go much beyond representing a view from ‘below’ or a politically correct appreciation of cultural diversity. It involves attention to key theoretical concepts and insights developed by maverick anthropologists like Arnold van Gennep, Marcel Mauss, Victor Turner and Gregory Bateson, concepts that uniquely facilitate an understanding of some of the underlying dynamics of modernity. (shrink)

We answer a question of Ambos-Spies and Kuˇcera in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests.

Science and technology have vastly expanded the realm of medicine. The numbers of and knowledge about diseases has greatly increased, and we can help more people in many more ways than ever before. At the same time, the extensive expansion has also augmented harms, professional responsibility, and ethical concerns. While these challenges have been studied from a wide range of perspectives, the problems prevail. This article adds value to previous analyses by identifying how the moral imperative of medicine has expanded (...) in three ways: (1) from targeting experienced phenomena, such as pain and suffering, to non-experienced phenomena (paraclinical signs and indicators); (2) from addressing present pain to potential future suffering; and (3) from reducing negative wellbeing (pain and suffering) to promoting positive wellbeing. These expansions create and aggravate problems in medicine: medicalization, overdiagnosis, overtreatment, risk aversion, stigmatization, and healthism. Moreover, they threaten to infringe ethical principles, to distract attention and responsibility from other competent agents and institutions, to enhance the power and responsibility of professionals, and to change the professional-beneficiary relationship. In order to find ways to manage the moral expansion of medicine, four traditional ways of setting limits are analyzed and dismissed. However, basic asymmetries in ethics suggest that it is more justified to address people’s negative wellbeing (pain and suffering) than their positive wellbeing. Moreover, differences in epistemology, indicate that it is less uncertain to address present pain and suffering than future wellbeing and happiness. Based on these insights the article concludes that the moral imperative of medicine has a gradient from pain and suffering to wellbeing and happiness, and from the present to the future. Hence, in general present pain and suffering have normative priority over future positive wellbeing. (shrink)

There is a tendency in the business ethics literature to think of ethics in restrictive terms: what one should not do, and how to control this. Drawing on Lawrence Kohlberg''s theory of moral development, the paper focuses on, and draws attention to, another more positive aspect of ethics: the capacity of ethics to inspire and empower individuals, as well as groups. To understand and facilitate such empowerment, it is argued that it is necessary to move beyond Kohlberg''s justice reasoning so (...) as to appreciate the value and importance of feeling and care. Accordingly, we draw upon case study material to review the meaning of Kohlberg''s higher stages — 5, 6 and 7 — to question the meaning of ethical reasoning. With such deeper understanding of particular ethical codes or practices, it is thought that members of organisations may come closer to thespirit, as opposed to the letter, of ethical conduct in organisations. This, we argue, is consistent with the degree of trust and integrity demanded by leaner, post-bureaucratic ways of organizing and conducting business as well as being personally beneficial to the people involved. (shrink)

Liminality and the Modern offers a comprehensive introduction to this concept, discussing its development and laying out a conceptual and experiential framework for thinking about change in terms of liminality. Applying this framework to questions surrounding the implosion of ‘non-spaces’, the analysis of major historical periods and the study of political revolution, the book also explores its possible uses in social science research and its implications for our understanding of the uncertainty and contingency of the liquid structures of modern society.

This book is an introduction to and interpretation of the philosophy of language devised by Donald Davidson over the past 25 years. The guiding intuition is that Davidson's work is best understood as an ongoing attempt to purge semantics of theoretical reifications. Seen in this light the recent attack on the notion of language itself emerges as a natural development of his Quinian scepticism towards "meanings" and his rejections of reference-based semantic theories. Linguistic understanding is, for Davidson, essentially dynamic, arising (...) only through a continuous process of theory construction and reconstruction. The result is a conception of semantics in which the notion of interpretation and not the notion of knowing a language is fundamental. In the course of his book Bjorn Ramberg provides a critical discussion of reference-based semantic theories, challenging the standard accounts of the principle of charity and elucidating the notion of radical interpretation. The final chapter on incommensurability ties in with the discussions of Kuhn's work in the philosophy of science and suggests certain links between Davidson's analytic semantics and hermeneutic theory. (shrink)

In the debate on conscientious objection in healthcare, proponents of conscience rights often point to the imperative to protect the health professional’s moral integrity. Their opponents hold that the moral integrity argument alone can at most justify accommodation of conscientious objectors as a “moral courtesy”, as the argument is insufficient to establish a general moral right to accommodation, let alone a legal right. This text draws on political philosophy in order to argue for a legal right to accommodation. The moral (...) integrity arguments should be supplemented by the requirement to protect minority rights in liberal democracies. Citizens have a right to live in accordance with their fundamental moral convictions, and a right to equal access to employment. However, this right should not be unconditional, as that would unduly infringe on the rights of other citizens. The right must be limited to cases where the moral basis is more fundamental in a sense that all reasonable citizens in a liberal democracy should accept, such as the constitutive role of the inviolability of human life in liberal democracies. There should be a legal, yet circumscribed, right to accommodation for conscientious objectors refusing to provide healthcare services that they reasonably consider to involve the intentional killing of a human being. (shrink)

This article attempts to rehabilitate the concept of fetishism and to contribute to the debate on the social role of objects as well as to fashion theory. Extrapolating from Michel Serres’ theory of the quasi-objects, I distinguish two phenomenologies possessing almost opposite characteristics. These two phenomenologies are, so I argue, essential to quasi-object theory, yet largely ignored by Serres’ sociological interpreters. They correspond with the two different theories of fetishism found in Marx and Durkheim, respectively. In the second half of (...) the article, I introduce the fashion object as a unique opportunity for studying the interchange between these two forms of fetishism and their respective phenomenologies. Finally, returning to Serres, I briefly consider the theoretical consequences of introducing the fashion object as a quasi-object. (shrink)

This book is an introduction to and interpretation of the philosophy of language devised by Donald Davidson over the past 25 years. The guiding intuition is that Davidson's work is best understood as an ongoing attempt to purge semantics of theoretical reifications. Seen in this light the recent attack on the notion of language itself emerges as a natural development of his Quinian scepticism towards "meanings" and his rejections of reference-based semantic theories. Linguistic understanding is, for Davidson, essentially dynamic, arising (...) only through a continuous process of theory construction and reconstruction. The result is a conception of semantics in which the notion of interpretation and not the notion of knowing a language is fundamental. In the course of his book Bjorn Ramberg provides a critical discussion of reference-based semantic theories, challenging the standard accounts of the principle of charity and elucidating the notion of radical interpretation. The final chapter on incommensurability ties in with the discussions of Kuhn's work in the philosophy of science and suggests certain links between Davidson's analytic semantics and hermeneutic theory. (shrink)

This article presents and evaluates arguments supporting that an approval procedure for genome-edited organisms for food or feed should include a broad assessment of societal, ethical and environmental concerns; so-called non-safety assessment. The core of analysis is the requirement of the Norwegian Gene Technology Act that the sustainability, ethical and societal impacts of a genetically modified organism should be assessed prior to regulatory approval of the novel products. The article gives an overview how this requirement has been implemented in the (...) regulatory practice, demonstrating that such assessment is feasible and justified. Even in situations where genome-edited organisms are considered comparable to non-modified organisms in terms of risk, the technology may have—in addition to social benefits—negative impacts that warrant assessments of the kind required in the Act. The main reason is the disruptive character of the genome editing technologies due to their potential for novel, ground-breaking solutions in agriculture and aquaculture combined with the economic framework shaped by the patent system. Food is fundamental for a good life, biologically and culturally, which warrants stricter assessment procedures than what is required for other industries, at least in countries like Norway with a strong tradition for national control over agricultural markets and breeding programs. (shrink)

This article argues that we must abandon the still predominant view of modernity as based upon a separation between the secular and the religious - a “separation” which is allegedly now brought into question again in “postsecularity”. It is more meaningful to start from the premise that religion and politics have always co-existed in various fields of tension and will continue to do so. The question then concerns the natures and modalities of this tension, and how one can articulate a (...) publically grounded reason with reference to it. It will first be argued that this question cannot be articulated, let alone fully answered, from the position developed by John Rawls. A different approach will then be developed, building on the writings of Eric Voegelin. This involves a much more serious engagement with the classical tradition in thought and philosophy than found in Rawls. It also implies much more than a “pragmatic” recognition of religion as a possible source for overlapping consensus, since for Voegelin a true, balanced rationality can only depart from an experientially grounded encounter with the transcendent. (shrink)

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...) I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed λ-calculus, whose λ-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context. (shrink)

The article seeks to develop a new conceptual framework suitable for analysing the ageing processes of objects in modern culture. The basic intuition is that object experience cannot be analysed separately from collective participation. The article focuses on the question of the ‘timeless’ nature of modernist design and seeks to understand why modernist objects age more slowly than other objects. First, inspired by the late Durkheim’s account of symbolism, I turn to the experiential effects of collective embeddedness. Second, I enter (...) the field of architectural practices and architectural theory. Visiting early modernist ideologue Adolf Loos, I seek to understand the modernist attitude as a direct response to experiences of the acceleration of ageing processes characteristic of modern culture. I then try to show how Loos’s explicit awareness of the collective dimension is ignored by the subsequent modernist movement and by architectural theory. Finally, I try to assess the consequences of this neglect. (shrink)

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence (...) class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology. (shrink)