Answering a question in the reverse mathematics of combinatorial principles, we prove that the thin set theorem for pairs ) implies the diagonally noncomputable set principle over the base axiom system $\mathrm{RCA}_{0}$.

We examine the reverse mathematical strength of a variation of Hindman’s Theorem (HT) constructed by essentially combining HT with the Thin Set Theorem to obtain a principle that we call thin-HT. This principle states that every coloring c:N→N has an infinite set S⊆N whose finite sums are thin for c, meaning that there is an i with c(s)≠i for all nonempty sums s of finitely many distinct elements of S. We show that there is a computable instance (...) of thin-HT such that every solution computes ∅′, as is the case with HT, as shown by Blass, Hirst, and Simpson (1987). In analyzing this proof, we deduce that thin-HT implies ACA0 over RCA0+IΣ20. On the other hand, using Rumyantsev and Shen’s computable version of the Lovász Local Lemma, we show that there is a computable instance of the restriction of thin-HT to sums of exactly 2 elements such that any solution has diagonally noncomputable degree relative to ∅′. Hence there is a computable instance of this restriction of thin-HT with no Σ20 solution. (shrink)

The thin set theorem for n-tuples and k colors states that every k-coloring of $[\mathbb {N}]^n$ admits an infinite set of integers H such that $[H]^n$ avoids at least one color. In this paper, we study the combinatorial weakness of the thin set theorem in reverse mathematics by proving neither $\operatorname {\mathrm {\sf {TS}}}^n_k$, nor the free set theorem imply the Erdős–Moser theorem whenever k is sufficiently large. Given a problem $\mathsf {P}$, a computable instance of $\mathsf {P}$ (...) is universal iff its solution computes a solution of any other computable $\mathsf {P}$ -instance. It has been established that most of Ramsey-type problems do not have a universal instance, but the case of Erdős–Moser theorem remained open so far. We prove that Erdős–Moser theorem does not admit a universal instance. (shrink)

Abstract.In this paper, we construct, by effective induction, a ∏11 equivalence relation E on ωω for which there is no largest E-thin E-invariant ∏11 subset of ωω by effective induction. This result answers a problem asked by Kechris in [1].

Are there objects that are “thin” in the sense that their existence does not make a substantial demand on the world? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. This book attempts to (...) develop the needed explanations by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. (shrink)

A free ultrafilter $\mathcal{U}$ on $\omega$ is called a $T$-point if, for every countable group $G$ of permutations of $\omega$, there exists $U\in\mathcal{U}$ such that, for each $g\in G$, the set $\{x\in U:gx\ne x, gx\in U\}$ is finite. We show that each $P$-point and each $Q$-point in $\omega^*$ is a $T$-point, and, under CH, construct a $T$-point, which is neither a $P$-point, nor a $Q$-point. A question whether $T$-points exist in ZFC is open.

The Thin Red Line is the third feature-length film from acclaimed director Terrence Malick, set during the struggle between American and Japanese forces for Guadalcanal in the South Pacific during World War Two. It is a powerful, enigmatic and complex film that raises important philosophical questions, ranging from the existential and phenomenological to the artistic and technical. This is the first collection dedicated to exploring the philosophical aspects of Malick’s film. Opening with a helpful introduction that places the film (...) in context, five essays, four of which were specially commissioned for this collection, go on to examine the following: the exploration of Heideggerian themes – such as being-towards-death and the vulnerability of Dasein’s world – in The Thin Red Line how Malick’s film explores and cinematically expresses the embodied nature of our experience of, and agency in, the world Malick’s use of cinematic techniques, and how the style of his images shapes our affective, emotional, and cognitive responses to the film the role that images of nature play in Malick’s cinema, and his ‘Nietzschean’ conception of human nature. The Thin Red Line is essential reading for students interested in philosophy and film or phenomenology and existentialism. It also provides an accessible and informative insight into philosophy for those in related disciplines such as film studies, literature and religion. Contributors: Simon Critchley, Hubert Dreyfus and Camilo Prince, David Davies, Amy Coplan, Iain Macdonald. (shrink)

Let E be a Σ1 1 equivalence relation for which there does not exist a perfect set of inequivalent reals. If 0# exists or if V is a forcing extension of L, then there is a good ▵1 2 well-ordering of the equivalence classes.

The thin red line ( TRL ) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the ‘actual future’, even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God’s omniscience. In the modern branching time setting, the theory of the TRL is widely (...) regarded to suffer from several fundamental problems. In this paper we propose several new TRL semantics, each with differing degrees of success. This leads up to our final semantics, which is a cross between the TRL and supervaluationism. We discuss the notions of truth, validity and semantic consequence which result from our final semantics, and demonstrate some of its pleasing results. This account, we believe, answers the main objection in the literature, and thus places the TRL on the same level as any other competing semantics for future contingents. (shrink)

Cenzer, D., R. Downey, C. Jockusch and R.A. Shore, Countable thin Π01 classes, Annals of Pure and Applied Logic 59 79–139. A Π01 class P {0, 1}ω is thin if every Π01 subclass of P is the intersection of P with some clopen set. Countable thin Π01 classes are constructed having arbitrary recursive Cantor- Bendixson rank. A thin Π01 class P is constructed with a unique nonisolated point A and furthermore A is of degree 0’. It (...) is shown that no set of degree ≥0” can be a member of any thin Π01 class. An r.e. degree d is constructed such that no set of degree d can be a member of any thin Π01 class. It is also shown that between any two distinct comparable r.e. degrees, there is a degree that contains a set which is of rank one in some thin Π01 class. It is shown that no maximal set can have rank one in any Π01 class, while there exist maximal sets of rank 2. The connection between Π01 classes, propositional theories and recursive Boolean algebras is explored, producing several corollaries to the results on Π01 classes. For example, call a recursive Boolean algebra thin if it has no proper nonprincipal recursive ideals. Then no thin recursive Boolean algebra can have a maximal ideal of degree ≥0”. (shrink)

Body image research focuses almost exclusively on women or overweight and obesity or both. Yet, body image concerns among thin men are common and can result, at least in part, from mixed messages in society around how men qua men should dress and behave in order to look good and feel good. Stand-alone interventions to meet these different messages tend to provide men with little therapeutic relief. This conceptual paper draws on literature from the medical humanities; gender and body (...) image studies; the social psychology of clothing; and the author’s own lived experience to address this contemporary problem. The paper embraces visual culture as a resource that can frame discussion of how two sets of ‘performativity’ might reduce male anxiety about thinness. First, thin men could choose repeatedly to wear masculine-looking clothing, which could create their masculinity as a personal aesthetic that strengthens the confidence to harness masculine traits in healthy ways. Secondly, health and allied health service providers could promote and reinforce such dress behavior by offering advice that integrates aesthetic and functional aspects of clothing. Empirical studies are needed to test this dual model of performativity. (shrink)

The fundamental standard of health care is health. Theories of health affect how we conceive of good health, ill health, Good patients, and Good providers. They also profoundly affect how we go about attempting to solve health problems once we’ve identified them. In this chapter, I argue that the way health care providers, bioethicists, and public health experts approach health relies on ideal theory despite the heavy knowledge that this world will never be ideal. We need a conception of health (...) that accounts for this. I outline the weakness of ideal theory in general and with respect to theories of health, and argue in favor of a nonideal approach to health that is rooted in intersubjectivity, empiricism, inclusivity, contextual specificity, and reflexivity which are not entrusted to any one set of knowers. Throughout, I use the example of how we approach fatness, and medicalize obesity, to illustrate where we’ve gone wrong and to chart a path toward how we can go right. (shrink)

“Thin concepts” are dubious entities. Careful analysis of the usual examples of thick and thin raises serious doubts about both their conceptuality and their thinness. Confusions aside, there is little obvious use for them in ethics or metaethics. The very idea that there could be a naturally-occurring purely evaluative moral concept, with no descriptive content, no cultural setting, and no capacity for distanced or ironic use, is as chimerical as any other ahistorical illusion. Our concentration on thick and (...) thin has distracted us from thinking about other interesting and important ethical distinctions—evidential/ verdictive, evaluative/ prescriptive, determinable/ determinate, Zangwill’s because-relation, Anscombe’s brute-relative-to relation—which have something genuine and non-illusory on both sides of them. (shrink)

Abstract: Presentism is the view that whatever exists presently exists. Without defending Presentism, I argue first that Presentists should be Time-Free Presentists – Presentists whose views do not imply that there exist irreducible times. Second, I argue that Presentists should accept Limited Thick Presentism, the view that 'the present' has some extension and is thereby neither durationlessly thin nor unlimitedly 'thick'. Third, before addressing several objections to Limited Time-Free Thick Presentism [LTFTP], I argue that defenders of LTFTP should accept (...) that 'temporal becoming' involves an overlapping succession of present entities, not a 'skipping' from one set of present entities to the next discrete set. (shrink)

The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards objects, whereas nominalists such as Field (...) have asserted that these apparent ontological commitments should not be taken at face value. In this article I argue for an intermediate position which upholds the legitimacy of ascribing a reference to abstract singular terms in an attenuated sense relative to the more robust ascription of reference applicable to names denoting concrete entities. In so doing I seek to clear up some confusions regarding the ramifications of such a thin notion of reference for ontological claims about mathematical objects. (shrink)

Most significant policy issues facing humanity reach across national borders. Consequential political decisions with cross-national effects are frequently made by states, non-state organisations, and corporations. Under these circumstances, it is widely acknowledged that it is important to conduct deliberation at the global level. Below this shallow agreement, however, lies deep disagreement about a crucial question: how, if at all, is it morally permissible for deliberation to result in a set of international laws and rules that are imposed on a world (...) population which is deeply pluralistic in its moral and political attitudes? When the equivalent question is asked within the confines of a political community, one prominent answer is by reference to a standard of public reason. While there is a large literature about public reason at the domestic level, the literature on global public reason is comparatively underdeveloped. The paper addresses this lacuna in two ways. First, it motivates the global public reason project, and conceptualises the nature of the challenge that accounts of global public reason face. Second, it demonstrates that, by their own evaluative standards, existing accounts of global public reason are unable to satisfy both desiderata simultaneously, being either too ‘thick’ or too ‘thin’. (shrink)

An effectively closed set, or ${\Pi^{0}_{1}}$ class, may viewed as the set of infinite paths through a computable tree. A numbering, or enumeration, is a map from ω onto a countable collection of objects. One numbering is reducible to another if equality holds after the second is composed with a computable function. Many commonly used numberings of ${\Pi^{0}_{1}}$ classes are shown to be mutually reducible via a computable permutation. Computable injective numberings are given for the family of ${\Pi^{0}_{1}}$ classes and (...) for the subclasses of decidable and of homogeneous ${\Pi^{0}_{1}}$ classes. However no computable numberings exist for small or thin classes. No computable numbering of trees exists that includes all computable trees without dead ends. (shrink)

We present the resistive switching characteristics of Metal-Insulator-Metal devices based on amorphous Al2O3which is deposited by Atomic Layer Deposition. A maximum processing temperature for this memory device is 300°C, making it ideal for Back-End-of-Line processing. Although some variations in the forming, set, and reset voltages are obtained for many of the measured MIM devices, thememristoreffect has been obtained after cyclicI-Vmeasurements. These resistive transitions in the metal oxide occur for bothbipolarandunipolarconditions, while theIOFF/IONratio is around 4–6 orders of magnitude and is formed (...) at gate voltages ofVg<4 V. In unipolar mode, a gradual reduction inVSETis observed and is related to combined incomplete dissolution of conductive filaments which leaves some residuals and thickening of chemically reduced Al2O3during localized Joule heating. This is important because, by analyzing the macroscopic resistive switching behavior of this MIM structure, we could indirectly relate it to microscopic and/or nanoscopic phenomena responsible for the physical mechanism upon which most of these devices operate. (shrink)

The value of psychology as a science has been challenged in phenomenology and in other epistemological trends. The main objective of this book is to draw the attention of students of human and animal behaviour to important achievements in phenomenological psychology and comparative physiology which are mostly overlooked, although they offer a genuine approach to subjective experience in relation to behavioural regulations. The work of Brentano, Stumpf, Husserl, Politzer, Katz, Michotte, Buytendijk and many others is analysed from this epistemological standpoint. (...) The significance of the phenomenological approach for the biology of behaviour is discussed. The meaning of Sherrington's physiology of the behavioural field is evaluated in the same framework. Basic reading for students of experimental psychology, comparative psychology and ethology, this book will appeal particularly to those interested in the philosophy of psychology and biology. Originally published in 1977. (shrink)

Let A and B be subsets of the reals. Say that A κ ≥ B, if there is a real a such that the relation "x ∈ B" is uniformly Δ 1 (a, A) in L[ ω x,a,A 1 , x,a,A]. This reducibility induces an equivalence relation $\equiv_\kappa$ on the sets of reals; the $\equiv_\kappa$ -equivalence class of a set is called its Kleene degree. Let K be the structure that consists of the Kleene degrees and the induced partial order (...) K ≥. A substructure of K that is of interest is P, the Kleene degrees of the Π 1 1 sets of reals. If sharps exist, then there is not much to P, as Steel [9] has shown that the existence of sharps implies that P has only two elements: the degree of the empty set and the degree of the complete Π 1 1 set. Legrand [4] used the hypothesis that there is a real whose sharp does not exist to show that there are incomparable elements in P; in the context of V = L, Hrbacek has shown that P is dense and has no minimal pairs. The Hrbacek results led Simpson [6] to make the following conjecture: if V = L, then p forms a universal homogeneous upper semilattice with 0 and 1. Simpson's conjecture is shown to be false by showing that if V = L, then Godel's maximal thin Π 1 1 set is the infimum of two strictly larger elements of P. The second main result deals with the notion of jump in K. Let A' be the complete Kleene enumerable set relative to A. Say that A is low-n if A (n) has the same degree as $\varnothing^{(n)}$ , and A is high-n if A (n) has the same degree as $\varnothing^{(n + 1)}$ . Simpson and Weitkamp [7] have shown that there is a high (high-1) incomplete Π 1 1 set in L. They have also shown that various other Π 1 1 sets are neither high nor low in L. Legrand [5] extended their results by showing that, if there is a real x such that x # does not exist, then there is an element of P that, for all n, is neither low-n nor high-n. In § 2, ZFC is used to show that, for all n, if A is Π 1 1 and low-n then A is Borel. The proof uses a strengthened version of Jensen's theorem on sequences of admissible ordinals that appears in [7, Simpson-Weitkamp]. (shrink)

Recent studies support a model in which the progeny of SOX9+ epithelial progenitors at the distal tip of lung branches undergo cell allocation and differentiation sequentially along the distal‐to‐proximal axis. Concomitant with the elongation and ramification of lung branches, the descendants of the distal SOX9+ progenitors are distributed proximally, express SOX2, and differentiate into cell types in the conducting airways. Amid subsequent sacculation, the distal SOX9+ progenitors generate alveolar epithelial cells to form alveoli. Sequential cell allocation and differentiation are integrated (...) with the branching process to generate a functional branching organ. This review focuses on the roles of SOX9+ cells as precursors for new branches, as the source of various cell types in the conducting airways, and as progenitors of the alveolar epithelium. All of these processes are controlled by multiple signaling pathways. Many mouse mutants with defective lung branching contain underlying defects in one or more steps of cell allocation and differentiation of SOX9+ progenitors. This model provides a framework to understand the molecular basis of lung phenotypes and to elucidate the molecular mechanisms of lung patterning. It builds a foundation on which comparing and contrasting the mechanisms employed by different branching organs in diverse species can be made. (shrink)

This study elucidates the nursing of undernourished patients as experienced by eight registered clinical nurses and five nursing assistants by using content analysis. The participants' narratives describe the inner perspective of caring for undernourished patients, known in Sweden as `the thin ones'. Categories identified were: frustration in nursing, joy in nursing and that undernourishment is taboo. The taboo was narrated as feelings of guilt and shame. Frustration in nursing could be seen as feeling stressed, exposed, lonely, powerless, helpless, and (...) being torn between demands and needs. Joy in nursing was experienced when creating a trusting relationship, promoting pleasure in the meal situation and working with respect for each individual's life-style and context of life. Understanding staff members' views is important when implementing guidelines as well as in the teaching situation in order to identify where staff stand with regard to knowledge and attitudes. (shrink)

O objetivo deste artigo é apresentar a analogia básica entre arquitetura e retórica antiga a partir dos tratados De Architectura, de Vitrúvio, e o De Oratore, de Cícero. A analogia se verifica na definição do artífice, dos gêneros e partes das técnicas e dos fins de cada uma delas. Para tanto, tomaram-se como referência as fontes do tratado vitruviano, que menciona a influência de Varrão na gramática, de Lucrécio na filosofia e de Cícero no método oratório. A analogia com Cícero (...) serve tanto para conferir autoridade ao modelo de arquiteto vitruviano quanto para diferenciar a arquitetura das demais ciências, sobretudo a filosofia, objeto de debate na obra ciceroniana. (shrink)

Study, with text of the Yogasūtra of Patañjali, text on Yoga philosophy.

There is an infinite set T of Turing-equivalent completions of Peano Arithmetic such that whenever M and N are nonisomorphic countable, arithmetically saturated models of PA and Th, Th∈T, then Aut≇Aut.

Several notions of computability-theoretic reducibility between [Formula: see text] principles have been studied. This paper contributes to the program of analyzing the behavior of versions of Ramsey’s Theorem and related principles under these notions. Among other results, we show that for each [Formula: see text], there is an instance of RT[Formula: see text] all of whose solutions have PA degree over [Formula: see text] and use this to show that König’s Lemma lies strictly between RT[Formula: see text] and RT[Formula: see (...) text] under one of these notions. We also answer two questions raised by Dorais, Dzhafarov, Hirst, Mileti, and Shafer on comparing versions of Ramsey’s Theorem and of the Thin Set Theorem with the same exponent but different numbers of colors. Still on the topic of the effect of the number of colors on the computable aspects of Ramsey-theoretic properties, we show that for each [Formula: see text], there is an [Formula: see text]-coloring [Formula: see text] of [Formula: see text] such that every [Formula: see text]-coloring of [Formula: see text] has an infinite homogeneous set that does not compute any infinite homogeneous set for [Formula: see text], and connect this result with the notion of infinite information reducibility introduced by Dzhafarov and Igusa. Next, we introduce and study a new notion that provides a uniform version of the idea of implication with respect to [Formula: see text]-models of RCA0, and related notions that allow us to count how many applications of a principle [Formula: see text] are needed to reduce another principle to [Formula: see text]. Finally, we fill in a gap in the proof of Theorem 12.2 in Cholak, Jockusch, and Slaman. (shrink)

We propose a new method for constructing Turing ideals satisfying principles of reverse mathematics below the Chain–Antichain (CAC) Principle. Using this method, we are able to prove several new separations in the presence of Weak König’s Lemma (WKL), including showing that CAC+WKL does not imply the thin set theorem for pairs, and that the principle “the product of well-quasi-orders is a well-quasi-order” is strictly between CAC and the Ascending/Descending Sequences principle, even in the presence of WKL.

In Thin Objects: An Abstractionist Account, Linnebo offers what he describes as a “simple and definitive” solution to the bad company problem facing abstractionist accounts of mathematics. “Bad” abstraction principles can be rendered “good” by taking abstraction to have a predicative character. But the resulting predicative axioms are too weak to recover substantial portions of mathematics. Linnebo pursues two quite different strategies to overcome this weakness in the case of set theory and arithmetic. I argue that neither infinitely iterated (...) abstraction nor abstraction on possible specifications fully resolves the bad company problem. (shrink)

This is an introduction to the most primitive form of the new Boolean relation theory, where we work with only one function and one set. We give eight complete classifications. The thin set theorem (along with a slight variant), and the complementation theorem are the only substantial cases that arise in these classifications.

Applying social contract theory to business ethics is a relatively new idea, and perhaps nobody has pursued this direction better than Thomas Donaldson and Thomas W. Dunfee. Their "Integrative Social Contracts Theory" manages to combine culturally sensitive decision making capacities with trans-cultural norms by setting up a layered system of social contracts. Lurking behind their work is a concern with the problems of relativism. They hope to alleviate these problems by introducing three concepts important to the ISCT: "authentic norms," which (...) clarify culturally specific norms, "priority rules," which determine the rules of engagement when authentic norms clash, and "hypernorms," which measure the value of authentic norms against a thin set of universally upheld values. This paper traces the genealogy of these hypernorms and challenges their value for the ISCT. It argues that well-conceived priority rules can do everything hypernorms can, and can do so more simply. (shrink)

In addition to thin concepts like the good, the bad and the ugly, our evaluative thought and talk appeals to thick concepts like the lewd and the rude, the selfish and the cruel, the courageous and the kind -- concepts that somehow combine evaluation and non-evaluative description. Thick concepts are almost universally assumed to be inherently evaluative in content, and many philosophers claimed them to have deep and distinctive significance in ethics and metaethics. In this first book-length treatment of (...) thick concepts, Pekka Väyrynen argues that all this is mistaken. Through detailed attention to the language of thick concepts, he defends a novel theory on which the relationship between thick words and evaluation is best explained by general conversational and pragmatic norms. Drawing on general principles in philosophy of language, he argues that many prominent features of thick words and concepts can be explained by general factors that have nothing in particular to do with being evaluative. If evaluation is not essential to the sort of thinking we do with thick concepts, claims for the deep and distinctive significance of the thick are undermined. The Lewd, the Rude and the Nasty is a fresh and innovative treatment of an important topic in moral philosophy and sets a new agenda for future work. It will be essential reading to anyone interested in the analysis and the broader philosophical significance of evaluative and normative language. (shrink)

Autocatalytic networks have been used to model the emergence of self‐organizing structure capable of sustaining life and undergoing biological evolution. Here, we model the emergence of cognitive structure capable of undergoing cultural evolution. Mental representations (MRs) of knowledge and experiences play the role of catalytic molecules, and interactions among them (e.g., the forging of new associations) play the role of reactions and result in representational redescription. The approach tags MRs with their source, that is, whether they were acquired through social (...) learning, individual learning (of pre‐existing information), or creative thought (resulting in the generation of new information). This makes it possible to model how cognitive structure emerges and to trace lineages of cumulative culture step by step. We develop a formal representation of the cultural transition from Oldowan to Acheulean tool technology using Reflexively Autocatalytic and Food set generated (RAF) networks. Unlike more primitive Oldowan stone tools, the Acheulean hand axe required not only the capacity to envision and bring into being something that did not yet exist, but hierarchically structured thought and action, and the generation of new MRs: the concepts EDGING, THINNING, SHAPING, and a meta‐concept, HAND AXE. We show how this constituted a key transition toward the emergence of semantic networks that were self‐organizing, self‐sustaining, and autocatalytic, and we discuss how such networks replicated through social interaction. The model provides a promising approach to unraveling one of the greatest anthropological mysteries: that of why development of the Acheulean hand axe was followed by over a million years of cultural stasis. (shrink)

Abstract Do the central aims of epistemology, like those of moral philosophy, require that we designate some important place for those concepts located between the thin-normative and the non-normative? Put another way, does epistemology need "thick" evaluative concepts and with what do they contrast? There are inveterate traditions in analytic epistemology which, having legitimized a certain way of viewing the nature and scope of epistemology's subject matter, give this question a negative verdict; further, they have carried with them a (...) tacit commitment to what we argue to be an epistemic analogue of the reductionistic centralist thesis which Bernard Williams, in our view, successfully repudiates in ethics. In this essay, we challenge the epistemic analogue of the traditional but mistaken thesis. In offering an alternative to it which provides a comfortable home for the epistemic normativity which attends thick evaluative concepts, we align ourselves with what has been recently called the Value Turn in epistemology. From this perspective, we defend that, contrary to tradition, as influenced by centralist assumptions, epistemology does need thick evaluative concepts. Further, the sort of theories that will be able to give thick evaluative concepts an irreducible role in both belief and agent evaluation are adequately social epistemologies. What loosely refer to as second-wave of virtue epistemology is the widespread interest to provide a comfortable home for the role of thick normativity, as it is connected both with epistemic evaluation, and guidance. We recognize that, in breaking from centralism, there is a worry that a resulting anti-centralist theory will be reductionistic in the other direction, making the thick primary. We contend however that second-wave virtue epistemologies take different sources of social and epistemic value into account; they seek the 'right thickness' to ride with conception of epistemology and a field which due in part to virtue theory's resurgence, is today normative, diverse and expansive than was the traditional set of problems from which it emerged. (shrink)

Given resource constraints in healthcare, demands justice and equity require the constant development of material principles for resource distribution. In many cases, such material principles are formulated as mid-level principles, well-adapted to handle healthcare distribution but suffering from aspects outside the healthcare context that affect their application. In healthcare, factors outside the healthcare system will sometimes affect patients’ equal opportunity to receive treatment and achieve health. Examples of such factors might include an individual’s economic means, the cost of drugs, geography, (...) etc. This article explores whether the formal equality principle could help us address such problems. It is argued that the traditional (thin) formal equality principle can aid in priority setting, both as a heuristic tool to aid in consistency and also in handling under-determined cases. However, it appears to be too ‘thin’ to handle problems caused by factors outside the healthcare context. In the article, I explore a more robust version of the formal equality principle and argue that such a principle can be used to address such cases. However, even a more comprehensive formal equality principle will need to consider whether some other actors have a moral responsibility to address the problem or whether the issue could be solved more effectively by others. Furthermore, such a principle needs to consider whether the opportunity cost of achieving ‘thick’ formal equality is acceptable, given the material principles of distribution. (shrink)