A mass problem is a set of functions $\omega \to \omega $. For mass problems ${\mathcal {C}}, {\mathcal {D}}$, one says that ${\mathcal {C}}$ is Muchnik reducible to ${\mathcal {D}}$ if each function in ${\mathcal {C}}$ is computed by a function in ${\mathcal {D}}$. In this paper we study some highness properties of Turing oracles, which we view as mass problems. We compare them with respect to Muchnik reducibility and its uniform strengthening, Medvedev reducibility.For $p \in [0,1]$ let ${\mathcal {D}}$ (...) be the mass problem of infinite bit sequences y such that for each computable bit sequence x, the bit sequence $ x {\,\leftrightarrow\,} y$ has asymptotic lower density at most p = y$ ). We show that all members of this family of mass problems parameterized by a real p with $0 p$ for each computable set x. We prove that the Medvedev complexity of the mass problems ${\mathcal {B}}$ is the same for all $p \in $, by showing that they are Medvedev equivalent to the mass problem of functions bounded by ${2^{2}}^{n}$ that are almost everywhere different from each computable function.Next, together with Joseph Miller, we obtain a proper hierarchy of the mass problems of type $\text {IOE}$ : we show that for any order function g there exists a faster growing order function $h $ such that $\text {IOE}$ is strictly above $\text {IOE}$ in the sense of Muchnik reducibility.We study cardinal characteristics in the sense of set theory that are analogous to the highness properties above. For instance, ${\mathfrak {d}} $ is the least size of a set G of bit sequences such that for each bit sequence x there is a bit sequence y in G so that $\underline \rho >p$. We prove within ZFC all the coincidences of cardinal characteristics that are the analogs of the results above. (shrink)

We give two new characterizations of K-triviality. We show that if for all Y such that Ω is Y-random, Ω is -random, then A is K-trivial. The other direction was proved by Stephan and Yu, giving us the first titular characterization of K-triviality and answering a question of Yu. We also prove that if A is K-trivial, then for all Y such that Ω is Y-random, ≡LRY. This answers a question of Merkle and Yu. The other direction is immediate, so (...) we have the second characterization of K-triviality.The proof of the first characterization uses a new cupping result. We prove that if A≰LRB, then for every set X there is a B-random set Y such that X is computable from Y⊕A. (shrink)

PIERRE-YVES MONIN. — Que dit la chanson?JULIETTE. — La chanson ne dit rien. Et la chanson peut tout dire. Cela doit dépendre de la bouche qui la fredonne et l’invente. Elle reflète peut-être le monde, la société qui l’a vue naître. Elle reflète peut-être aussi la Vérité, la vraie, celle qui sort, toute nue, de son puits. Mais elle...

The infinite pigeonhole principle for 2-partitions asserts the existence, for every set A, of an infinite subset of A or of its complement. In this paper, we study the infinite pigeonhole pr...

We investigate the role of continuous reductions and continuous relativization in the context of higher randomness. We define a higher analogue of Turing reducibility and show that it interacts well with higher randomness, for example with respect to van Lambalgen’s theorem and the Miller–Yu/Levin theorem. We study lowness for continuous relativization of randomness, and show the equivalence of the higher analogues of the different characterizations of lowness for Martin-Löf randomness. We also characterize computing higher [Formula: see text]-trivial sets by higher (...) random sequences. We give a separation between higher notions of randomness, in particular between higher weak 2-randomness and [Formula: see text]-randomness. To do so we investigate classes of functions computable from Kleene’s [Formula: see text] based on strong forms of the higher limit lemma. (shrink)

If lay theories associate moral intuitions with deeply held values, people should feel uncomfortable relying on deliberative thinking when judging violations of personal taboos. In two preliminary studies, participants with siblings of the opposite sex were particularly troubled when evaluating a sibling incest scenario under instructions to think slowly and rationally, or when the scenario was presented in a hard-to-read font forcing them to employ deliberative processing. This suggests that we may be intuitive intuitionists, and opens the door for investigations (...) of people’s preferred modes of moral judgment. (shrink)

There exist two main notions of typicality in computability theory, namely, Cohen genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of typicality, and show that many basis theorems apply to partition genericity. More precisely, we prove that every co-hyperimmune set and every Kurtz random is partition generic, and that every partition generic set admits weak infinite subsets, for various notions of weakness. In particular, (...) we answer a question of Kjos-Hanssen and Liu by showing that every Kurtz random admits an infinite subset which does not compute any set of positive effective Hausdorff dimension. Partition genericity is a partition regular notion, so these results imply many existing pigeonhole basis theorems. (shrink)

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

We study genericity and randomness with respect to ITTMs, continuing the work initiated by Carl and Schlicht. To do so, we develop a framework to study randomness in the constructible hierarchy. We then answer several of Carl and Schlicht’s question. We also ask a new question one the equality of two classes of randoms. Although the natural intuition would dictate that the two classes are distinct, we show that things are not as simple as they seem. In particular we show (...) that the categorical analogues of these two classes coincide, in contradiction with the natural intuition. Even though we are not able to answer the question for randomness in this article, we delineate and sharpen its contour and outline. (shrink)

A set of integers A is computably encodable if every infinite set of integers has an infinite subset computing A. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this article, we extend this notion of computable encodability to subsets of the Baire space, and we characterize the Π10-encodable compact sets as those which admit a nonempty Σ11-subset. Thanks to this equivalence, we prove that weak weak König’s lemma is not strongly computably reducible to (...) Ramsey’s theorem. This answers a question of Hirschfeldt and Jockusch. (shrink)

Quantification has been constitutive of psychology since its inception and is core to its scientific status. The adoption of qualitative methods eschewing inferential statistics is therefore unlikely to obtain. Rather than discarding useful tools because of improper use, we recommend highlighting how inferential statistics can be more thoughtfully applied.

For Knobe, observers evaluate mental states by comparing agents' statements with the attitudes they are expected to hold. In our analysis, Knobe's model relies primarily on what agents should think, and little on expectancies of what they would think. We show the importance and complexity of including descriptive and prescriptive norms if one is to take expectancies seriously.

This book offers an introduction to the Sophists of fifth-century Athens and a new overall interpretation of their thought. Since Plato first animadverted on their activities, the Sophists have commonly been presented as little better than intellectual mountebanks - a picture which Professor Kerferd forcefully challenges here. Interpreting the evidence with care, he shows them to have been part of an exciting and historically crucial intellectual movement. At the centre of their teaching was a form of relativism, most famously expressed (...) by Protagoras as 'Man is the measure of all things', and which they developed in a wide range of views - on knowledge and argument, virtue, government, society, and the gods. On all these subjects the Sophists did far more than simply provoke Plato to thought. Their contributions were substantial and serious; they inaugurated the debate on many central philosophical questions and decisively shifted the focus of philosophical attention from the cosmos to man. (shrink)

"First published by Oxford University Press, 1916."--Title page verso.

Various U.S. laws, such as the Clean Air Act and the Food Quality Protection Act, require additional protections for susceptible subpopulations who face greater environmental health risks. The main ethical rationale for providing these protections is to ensure that environmental health risks are distributed fairly. In this article, we (1) consider how several influential theories of justice deal with issues related to the distribution of environmental health risks; (2) show that these theories often fail to provide specific guidance concerning policy (...) choices; and (3) argue that an approach to public decision making known as accountability for reasonableness can complement theories of justice in establishing acceptable environmental health risks for the general population and susceptible subpopulations. Since accountability for reasonableness focuses on the fairness of the decision-making process, not the outcome, it does not guarantee that susceptible subpopulations will receive a maximum level of protection, regardless of costs or other morally relevant considerations. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, as (...) proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

In recent years, scholars have come to understand emotions as dynamic and socially constructed—the product of interdependent cultural, relational, situational, and biological influences. While researchers have called for a multilevel theory of emotion construction, any progress toward such a theory must overcome the fragmentation of relevant research across various disciplines and theoretical frameworks. We present affect control theory as a launching point for cross-disciplinary collaboration because of its empirically grounded conceptualization of social mechanisms operating at the interaction, relationship, and cultural (...) levels, and its specification of processes linking social and individual aspects of emotion. After introducing the theory, we illustrate its correspondence with major theories of emotion construction framed at each of four analytical levels: cultural, interactional, individual, and neural. (shrink)

This chapter first surveys general issues in the epistemic internalism / externalism debate: what is the distinction, what motivates it, and what arguments can be given on both sides. -/- The second part of the chapter will examine the internalism / externalism debate as regards to the specific case of the epistemology of memory belief.

volume 1. Developing institutional theory -- volume 2. New research agendas -- volume 3. Applying institutional theory.

The acquisition of a new skill usually proceeds through five stages, from novice to expert, with a sixth stage of mastery available for highly motivated performers. In this chapter, we re-state the six stages of the Dreyfus Skill Model, paying new attention to the transitions and interrelations between them. While discussing the fifth stage, expertise, we unpack the claim that, “when things are proceeding normally, experts don’t solve problems and don’t make decisions; they do what normally works” (Dreyfus & Dreyfus, (...) 1988, pp. 30 – 31). This leads us to offer an account of the “perspectival deliberation” that arises for experts and masters and that is distinct from the calculative deliberation characteristic of the lower stages of skillfulness. (shrink)

'The problem of the twentieth-century is the problem of the color-line.' Originally published in 1903, The Souls of Black Folk is a classic study of race, culture, and education at the turn of the twentieth century. With its singular combination of essays, memoir, and fiction, this book vaulted W. E. B. Du Bois to the forefront of American political commentary and civil rights activism. The Souls of Black Folk is an impassioned, at times searing account of the situation of African (...) Americans in the United States. Du Bois makes a forceful case for the access of African Americans to higher education, memorably extols the achievements of black culture (above all the spirituals or 'sorrow songs'), and advances the provocative and influential argument that due to the inequalities and pressures of the 'race problem', African American identity is characterized by 'double consciousness'. This edition includes a valuable appendix of other writing by Du Bois, which sheds light on his attitudes and intentions. ABOUT THE SERIES: For over 100 years Oxford World's Classics has made available the widest range of literature from around the globe. Each affordable volume reflects Oxford's commitment to scholarship, providing the most accurate text plus a wealth of other valuable features, including expert introductions by leading authorities, helpful notes to clarify the text, up-to-date bibliographies for further study, and much more. (shrink)

In February 54b.c. Cicero concludes a missive to his brother with a passing and – for us – tantalizing remark:Lucreti poemata ut scribis ita sunt, multis luminibus ingeni, multae tamen artis. sed cum veneris. virum te putabo si Sallusti Empedoclea legeris; hominem non putabo. Quintus had, it seems, readDe rerum natura, or at least parts thereof, just before he left Rome for an undisclosed location nearby, and he shared his enthusiasm with his brotherper codicillos. Meanwhile, he was corresponding with Julius (...) Caesar, whose staff in Gaul he was about to join. When, a few months later, he was stationed with Caesar, he was involved in another literary affair, this time concerning his brother who wrote to him, inquiring about his autobiographicalDe temporibus suis:quo modo nam, mi frater, de nostris versibus Caesar? nam primum librum se legisse scripsit ad me ante, et prima sic ut neget se ne Graeca quidem meliora legisse; reliqua ad quendam locum ῥᾳθυμότερα (hoc enim utitur verbo). dic mihi verum: num aut res eum aut χαρακτὴρ non delectat?(Q.fr.2.15.5). (shrink)

We presuppose a position of scientific realism to the effect (i) that the world exists and (ii) that through the working out of ever more sophisticated theories our scientific picture of reality will approximate ever more closely to the world as it really is. Against this background consider, now, the following question: 1. Do the empirical theories with the help of which we seek to approximate a good or true picture of reality rest on any non-empirical presuppositions? One can answer (...) this question with either a 'yes' or a 'no'. 'No' is the preferred answer of most contemporary methodologists -- Murray Rothbard is one distinguished counterexample to this trend -- who maintain that empirical theories are completely free of non-empirical ('a priori') admixtures and who see science as a matter of the gathering of pure 'data' obtained through simple observation. From such data scientific propositions are then supposed to be somehow capable of being established. (shrink)

What are the most fundamental features of the world? Do minds stand outside the natural order? Is a unified picture of mental and physical reality possible? The Mind in Nature provides a staunchly realist account of the world as a unified system incorporating both the mental and the physical. C. B. Martin, an original and influential exponent of 'ontologically serious' metaphysics, echoes Locke's dictum that 'all things that exist are only particulars', and argues that properties are powerful qualities. He also (...) spells out the implications of this view for philosophical conceptions of causation, intentionality, consciousness, and the mind-body problem. Martin emphasizes the importance of non-conscious 'vegetative' systems, which provide clear examples of intentionality in the form of representational use. The slide from representational use to consciousness involves a change in the material of use, but not the form of representation. A concluding chapter provides an argument for the view that an ontology of particular substances and properties leads ineluctably to monism: the bus we board with Locke takes us directly to the world of Spinoza and Einstein. Along the way, we are led to understand the nature of minds and conscious states of mind in a way that avoids both reductionism and dualism. (shrink)

On the doctrines of Madhva, 13th century exponent of the Dvaita school in Hindu philosophy.

In this concise yet powerful book, one of the twentieth century's most respected political philosophers presents a controversial reassessment of the political ideas and intellectual legacy of Edmund Burke. A practicing politician and powerful writer, full of ideas, Burke was intent on getting those ideas translated into government policies. But he was too much the impatient practitioner to set out his principles in a single book in the manner of Locke or Hume, leaving both admirers and opponents ample scope to (...) reinterpret his work in different ways. Macpherson, however, finds Burke's views on political economy to be the one consistent factor in his thinking. Today Burke is often viewed as one of modern conservatism's founding lights, and in an era of global capitalism unfettered by national borders, Macpherson's reassessment of Burke's ideas is perhaps more timely than ever. (shrink)

Fifty adults who had made monetary contributions to political campaigns were interviewed to determine differences between liberals and conservatives in terms of personality, child-rearing attitudes, and birth order/sex variables. Study 1 found liberals to favor nonrestrictive controls both on self and on children, while conservatives tended to favor the opposite. Women were more likely than men to be liberals, and all first-born females were liberals. In Study 2, the sample as a whole was high in self-esteem and autonomy, and there (...) were no significant differences between liberals and conservatives. Although saying that liberals are Democrats and conservatives are Republicans is accurate to some extent, it misses the fact that many do not identify with either party but consider themselves to be independents. (shrink)