We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time generalization of the (...) countable Borel equivalence relations, a key subclass of the Borel equivalence relations, and again show that several key properties carry over to the larger class. Lastly, we collect together several results from the literature regarding Borel reducibility which apply also to absolutely $\Delta^1_2$ reductions, and hence to the infinite time computable reductions. (shrink)

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.

Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank strictly increases in complexity with the rank. Subsequently, Thomas proved that the complexities of the classification problems for p-local torsion-free abelian groups of fixed rank n are pairwise incomparable as p varies. We prove that if 3≤m (...) torsion-free abelian groups of rank n. (shrink)

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to (...) the splitting number coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics. (shrink)

We show that for any countable homogeneous ordered graph G, the conjugacy problem for automorphisms of G is Borel complete. In fact we establish that each such G satisfies a strong extension property called ABAP, which implies that the isomorphism relation on substructures of G is Borel reducible to the conjugacy relation on automorphisms of G.

We introduce the computable FS-jump, an analog of the classical Friedman–Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable FS-jump is proper with respect to computable reducibility. We then study the effect of the computable FS-jump on computably enumerable equivalence relations (ceers).

We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group [Formula: see text] we introduce the [Formula: see text]-jump. We study the elementary properties of the [Formula: see text]-jumps and compare them with other previously studied jump operators. One of our main results is to establish that for many groups [Formula: see text], the [Formula: see text]-jump is proper in the sense that for any Borel equivalence relation [Formula: see text] the [Formula: see (...) text]-jump of [Formula: see text] is strictly higher than [Formula: see text] in the Borel reducibility hierarchy. On the other hand, there are examples of groups [Formula: see text] for which the [Formula: see text]-jump is not proper. To establish properness, we produce an analysis of Borel equivalence relations induced by continuous actions of the automorphism group of what we denote the full [Formula: see text]-tree, and relate these to iterates of the [Formula: see text]-jump. We also produce several new examples of equivalence relations that arise from applying the [Formula: see text]-jump to classically studied equivalence relations and derive generic ergodicity results related to these. We apply our results to show that the complexity of the isomorphism problem for countable scattered linear orders properly increases with the rank. (shrink)

We study the complexity of the classification problem for countable models of set theory (). We prove that the classification of arbitrary countable models of is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of.

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above \ in complexity.

In a recent book and an article, Carl Craver construes the relations between different levels of a mechanism, which he also refers to as constitutive relations, in terms of mutual manipulability (MM). Interpreted metaphysically, MM implies that inter-level relations are symmetrical. MM thus violates one of the main desiderata of scientific explanation, namely explanatory asymmetry. Parts of Craver’s writings suggest a metaphysical interpretation of MM, and Craver explicitly commits to constitutive relationships being symmetrical. The paper furthermore explores the option of (...) interpreting MM epistemologically, as a means for individuating mechanisms. It is argued that MM then is redundant. MM should therefore better be abandoned. (shrink)

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

Many take Kantian ethics to founder when it comes to our duties to animals. In this paper, I advocate a novel approach to this problem. The paper is divided into three sections. In the first, I canvass various passages from Kant in order to set up the problem. In the second, I introduce a novel approach to this problem. In the third, I defend my approach from various objections. By way of preview: I advocate rejecting the premise that nonhuman animals (...) are nonrational. (shrink)

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow us (...) to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

The controversy over the equivalence of continuous sedation until death (CSD) and physician-assisted suicide/euthanasia (PAS/E) provides an opportunity to focus on a significant extended use of CSD. This extension, suggested by the equivalence of PAS/E and CSD, is designed to promote additional patient autonomy at the end-of-life. Samuel LiPuma, in his article, “Continuous Sedation Until Death as Physician-Assisted Suicide/Euthanasia: A Conceptual Analysis” claims equivalence between CSD and death; his paper is seminal in the equivalency debate. Critics contend that sedation (...) follows proportionality protocols for which LiPuma’s thesis does not adequately account. Furthermore, sedation may not eliminate consciousness, and as such LiPuma’s contention that CSD is equivalent to neocortical death is suspect. We not only defend the equivalence thesis, but also expand it to include additional moral considerations. First, we explain the equivalence thesis. This is followed by a defense of the thesis against five criticisms. The third section critiques the current use of CSD. Finally, we offer two proposals that, if adopted, would broaden the use of PAS/E and CSD and thereby expand options at the end-of-life. (shrink)

When Kuhn first published his _Structure of Scientific Revolutions_ he was accused of promoting an “irrationalist” account of science. Although it has since been argued that this charge is unfair in one aspect or another, the early criticism still exerts an influence on our understanding of Kuhn. In particular, normal science is often characterized as dogmatic and uncritical, even by commentators sympathetic to Kuhn. I argue not only that there is no textual evidence for this view but also that normal (...) science is much better understood as being based on _epistemically justified_ commitment to a paradigm and as _pragmatic_ in its handling of anomalies. I also argue that normal science is an example of what I call Kuhn’s program of _revisionary rational reconstruction_. (shrink)

The allocation of scarce health care resources such as flu treatment or organs for transplant presents stark problems of distributive justice. Persad, Wertheimer, and Emanuel have recently proposed a novel system for such allocation. Their “complete lives system” incorporates several principles, including ones that prescribe saving the most lives, preserving the most life-years, and giving priority to persons between 15 and 40 years old. This paper argues that the system lacks adequate moral foundations. Persad and colleagues' defense of giving priority (...) to those between 15 and 40 leaves them open to the charge that they discriminate unfairly against children. Second, the paper contends that the complete lives system fails to provide meaningful practical guidance in central cases, since it contains no method for balancing its principles when they conflict. Finally, the paper proposes a new method for balancing principles of saving the most lives and maximizing life-years. (shrink)

In his discussion of the duty of benevolence in §27 of the Metaphysics of Morals, Kant argues that agents have no obligation to promote their own happiness, for ‘this happens unavoidably’ (MS, AA 6:451). In this paper I argue that Kant should not have said this. I argue that Kant should have conceded that agents do have an obligation to promote their own happiness.

In this paper, I argue that Kant gives a philosophically plausible derivation of the general duty of benevolence and that this derivation can be used to show how to derive other general duties of commission with the universalizability tests. The paper is divided into four sections. In the first, I explain Kant’s notion of a general duty. In the second, I introduce the universalizability tests. In the third, I examine and argue against an account in the secondary literature of how (...) to derive general duties from these tests. In the fourth, I look at Kant’s derivation of the duty of benevolence in the Metaphysics of Morals, and I suggest how this reasoning can be extended to other duties. (shrink)

In this article, I provide an interpretation of Heidegger’s critique of Hegel. Hegel’s ability to provide a presuppositionless metaphysics is often taken to be the core strength of his Logic. In his critique of Hegel, Heidegger attempts to show that Hegel in fact smuggles in a decisive presupposition concerning being. Building on the recent work of Robert Pippin, I argue that we can understand this critique by situating it in terms of their common understanding of problems of first principles. Once (...) we do, we can fully appreciate a point that Pippin misses, that Heidegger develops his methodology and concept of ground in order to avoid the problems that he locates in Hegel. The upshots of my interpretation are that it (1) allows us to appreciate the systematicity and radicality of Heidegger’s mature ontology, and (2) forces those sympathetic to Hegel to reevaluate Hegel’s ability to provide a presuppositionless metaphysics. (shrink)

This book examines the evidential status and use of linguistic intuitions, a topic that has seen increased interest in recent years. Linguists use native speakers' intuitions - such as whether or not an utterance sounds acceptable - as evidence for theories about language, but this approach is not uncontroversial. The two parts of this volume draw on the most recent work in both philosophy and linguistics to explore the two major issues at the heart of the debate. Chapters in the (...) first part address the 'justification question', critically analysing and evaluating the theoretical rationale for the evidential use of linguistic intuitions. The second part discusses recent developments in the domain of experimental syntax, focusing on the question of whether formal and systematic models of gathering intuitions are epistemically and methodologically superior to the informal methods that have traditionally been used. -/- The volume provides valuable insights into whether and how linguistic intuitions can be used in theorizing about language, and will be of interest to graduate students and researchers in linguistics, philosophy, and cognitive science. (shrink)

This article is divided into three sections. In the first and second, I examine Sartorio’s account of the causal structure of the famous Thirsty Traveler thought experiment. I argue that this account does not withstand critical scrutiny. In the third, I turn to a novel kind of moral luck that Sartorio uses the Thirsty Traveler to expose. I expand the scope of my argument to look also at other recently proposed categories of moral luck. I argue that these proposals are (...) overhasty. (shrink)

Andrew Samuels is one of the best known figures internationally in the fields of psychotherapy, Jungian analysis, relational psychoanalysis and counselling and in academic studies in those areas. His work is a blend of the provocative and original together with the reliable and scholarly. His many books and papers figure prominently on reading lists on clinical and academic teaching contexts. This self-selected collection, Passions, Persons, Psychotherapy and Politics, brings together some of his major writings at the interface of politics and (...) therapy thinking. In this volume, he includes chapters on the market economy, prospects for eco-psychology and environmentalism; the role of the political Trickster, particularly the female Trickster; chapters on the father; on relations between women and men and his celebrated and radical critique of the Jungian idea of 'the feminine principle'. Clinical material consists of his work on parents and on the therapy relationship. The book concludes with his seminal and transparent work on Jung and anti-semitism and an intriguing account of the current trajectory of the Jungian field.Samuels has written a highly personal and confessional introduction to the book. Each chapter also has its own topical introduction, written in a clear and informal style. There is also much that will challenge long-held beliefs of many working in politics and in the social sciences. This unique collection of papers will be of interest to psychotherapists, Jungian analysts, psychoanalysts and counsellors--as well as those undertaking academic work in those areas. (shrink)

Folk is an analog foundation in a digital world. Phenomenology is a big word about a small, impossible task: trying to imagine the real. This book describes this task in relation to its foundation. Most of all, 'Folk phenomenology' is a defense of the integrity and sufficiency of art--thinking, feeling, living, dying. In short, being in love."--Back cover.

Thinking About Stories is a fun and thought-provoking introduction to philosophical questions about narrative fiction in its many forms, from highbrow literature to pulp fiction to the latest shows on Netflix. Written by philosophers Samuel Lebens and Tatjana von Solodkoff, it engages with fundamental questions about fiction, like: What is it? What does it give us? Does a story need a narrator? And why do sad stories make us cry if we know they aren’t real? The format of the (...) book emulates a lively, verbal exchange: each chapter has only one author while the other appears spontaneously in pop-up boxes in the text along the way, raising questions and voicing criticisms, and inviting responses from their co-author. This unique format allows readers to feel like they are a part of the conversation about the philosophical foundations of some of the fictions in their own lives. (shrink)

In Improvisation, Samuel Wells defines improvisation in the theater as "a practice through which actors seek to develop trust in themselves and one another in order that they may conduct unscripted dramas without fear." Sounds a lot like life, doesn't it? Building trust, overcoming fear, conducting relationships, and making choices--all without a script. Wells establishes theatrical improvisation as a model for Christian ethics, a matter of "faithfully improvising on the Christian tradition." He views the Bible not as a "script" (...) but as a "training school" that shapes the habits and practices of the Christian community. Drawing on scriptural narratives and church history, Wells explains six practices that characterize both improvisation and Christian ethics. His model of improvisation reinforces the goal of Christian ethics--to teach Christians to "embody their faith in the practices of discipleship all the time."--Publisher description. (shrink)

Morality can hardly perform a function, which is discussed in this chapter, unless it offers directives that not only can but frequently do differ from those of self-interest itself. The idea of potential congruence asserts that the relation between morality and the interests of the individual agent is characterized by a high degree of mutual accommodation, so that the frequency and severity of conflict between these two perspectives is significantly reduced. Conflicts are nevertheless possible in principle, but the extent to (...) which they arise in practice is not fixed or immutable. Instead, the frequency of conflict depends to a considerable degree on the character of the prevailing social and political institutions. Achieving convergence between morality and self-interest is in part a social and political task. The account of the “priority” of morality developed by Thomas Scanlon in his book What We Owe to Each Other is similar in a number of respects to this chapter's account of potential congruence. (shrink)

New and experienced psychotherapists alike can find themselves overwhelmed by an ethical quandary where there doesn't seem to be an easy solution. This book presents positive ethics as a means to overcome such ethical challenges. The positive approach focuses on not just avoiding negative consequences, but reaching the best possible outcomes for both the psychotherapist and the client. The authors outline a clear decision-making process that is based on three practical strategies: the ethics acculturation model to help therapists incorporate personal (...) ethics into their professional roles, the quality enhancement model for dealing with high-risk patients who are potentially harmful, and ethical choice-making strategies to make the most ethical decision in a situation where two ethical principles conflict. Throughout the decision-making process, psychotherapists are encouraged to follow four basic guidelines: Focus on overarching ethical principles Consider intuitive, emotional, and other nonrational factors Accept that some problems have elusive solutions Solicit input from colleagues and consultation groups Numerous vignettes illustrate how to apply positive ethics to many different ethical challenges that psychotherapists will likely encounter in practice. (shrink)

,Etwa zwei Monate vor dem Tode sagte Husserl:,Man solle seine Vergangenheit nicht trivialisieren. ' "1 Die Herausforderung dieser Worte lieB sich nur schwer abschatzen, als ich dem Stifter des Husserl-Archivs, meinem Freund Pater Van Breda, im Januar I974- zwei Monate vor seinem unzeitigen Hingang- den von ihm so sehr begruBten und geforderten EntschluB, eine Husserl-Bio­ graphie zu schreiben, naher erlauterte. Mancherlei ware darin ein­ zubringen gewesen: Ubersicht uber die Geschicke des Bismarck­ Staates und das aufkommende Hitler-Reich, Vertrautheit mit Stifter und (...) Hofmannsthal, Kenntnis der Theorie mathematischer Funktionen wie der Psychologie der Wurzburger Schule, Einsicht in die Einfuhlungslehre von Lipps wie auch Heideggers Seins­ frage. Aber solche Absicht erwies sich hauptsachlich deswegen als undurchfiihrbar, weil es derzeit noch am Notigsten fehlt: an einer verlaBlichen Durcharbeitung von Husserls Denken und seiner Entwicklung, wie sie sich in den veroffentlichten Werken, vor al­ lem aber im Meer bewahrter Manuskripte niederschlug. Hier galt es, da viel bisher im Dunkeln liegt, die Materialien zu einer Bio­ graphie erst einmal bereitzustellen und, wenn auch oft nur um­ riBhaft, fur die Zukunft sicherzustellen. Ergebnis dieser Beschei­ dung ist die vorliegende Chronik. GewiB, Husserl ware selbst der befugteste interpres sui gewe­ sen. Doch was er unterm 20. Juni rg2r an den Meiner Verlag schrieb - der,Stand seiner Lebensarbeit" erlaube es ihm zur Zeit nicht, zu der in diesem Verlag erscheinenden Reihe von Selbstdarstellungen einen Beitrag zu liefern (F I r8/r + 25) -, galt, wie gerade unsere Chronik deutlich macht, fur ihn zeitlebens. (shrink)

The concept of innateness has historically exerted an influence in many regions of biology and it continues to play a significant role in cognitive science especially, developmental psychology and linguistics. This chapter provides an overview of some recent efforts to empirically study the innateness concept, both as deployed in folk contexts and among scientists. It considers whether this research really bolsters the standard criticism. The chapter describes research by Paul Griffiths and his collaborators, which seeks to assess whether the folk (...) concept of innateness is a manifestation of the folk biology. It reviews further research, largely due to Josh Knobe and Richard Samuels, on folk innateness judgments. The chapter describes how this research was extended in order to explore the issue of whether scientists’ innateness judgments rely on a distinctly scientific innateness concept, or whether they merely redeploy the folk concept. (shrink)

Subtle-body practices are found particularly in Indian, Indo-Tibetan and East Asian societies, but have become increasingly familiar in Western societies, especially through the various healing and yogic techniques and exercises associated with them. This book explores subtle-body practices from a variety of perspectives, and includes both studies of these practices in Asian and Western contexts. The book discusses how subtle-body practices assume a quasi-material level of human existence that is intermediate between conventional concepts of body and mind. Often, this level (...) is conceived of in terms of an invisible structure of channels, associated with the human body, through which flows of quasi-material substance take place. Contributors look at how subtle-body concepts form the basic explanatory structure for a wide range of practices. These include forms of healing, modes of exercise and martial arts as well as religious practices aimed at the refinement and transformation of the human mindbody complex. By highlighting how subtle-body practices of many kinds have been introduced into Western societies in recent years, the book explores the possibilities for new models of understanding which these concepts open up. It is a useful contribution to studies on Asian Religion and Philosophy. (shrink)

One of the more interesting philosophical debates in the seventeenth century concerned the nature and explanation of qualities. In order to understand these debates, it is important to place them in their proper historical-philosophical context. This book chapter starts with theoretical background in the work of Aristotle and the atomists, and then moves on to survey various theories of motion and rest, light, color, and sound, as well as the distinction between primary and secondary qualities, as represented in the work (...) of such figures as Berkeley, Boyle, Charleton, Cordemoy, Descartes, Desgabets, Galileo, Gassendi, Hobbes, Locke, Malebranche, Newton, Régis, Rohault, and Sennert. (shrink)