In the present paper we prove that the isolated differences of r. e. degrees are dense in the r. e. degrees.

Examining various kinds of isolation phenomena in the Turing degrees, I show that there are, for every n>0, (n+1)-c.e. sets isolated in the n-CEA degrees by n-c.e. sets below them. For n≥1 such phenomena arise below any computably enumerable degree, and conjecture that this result holds densely in the c.e. degrees as well. Surprisingly, such isolation pairs also exist where the top set has high degree and the isolating set is low, although the complete situation for jump classes remains unknown.

We examine the randomness and triviality of reals using notions arising from martingales and prefix-free machines.

We examine the effective categoricity of equivalence structures via Ershov's difference hierarchy. We explore various kinds of categoricity available by distinguishing three different notions of isomorphism available in this hierarchy. We prove several results relating our notions of categoricity to computable equivalence relations: for example, we show that, for such relations, computable categoricity is equivalent to our notion of weak ω-c.e. categoricity, and that $\Delta _2^0 $ -categoricity is equivalent to our notion of graph-ω-c.e. categoricity.

We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.

Given two incomparable c.e. Turing degrees a and b, we show that there exists a c.e. degree c such that c = (a ⋃ c) ⋂ (b ⋃ c), a ⋃ c | b ⋃ c, and c < a ⋃ b.

We construct a $\Delta^0_2$ degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.

We construct a Δ 0 2 degree which fails to be computably enumerable in any computably enumerable set strictly below $\emptyset'$.

Are historians storytellers? Is it possible to tell true stories about the past? These are just a couple of the questions raised in this comprehensive collection of texts about philosophy, theory, and methodology of writing history. Drawing together seminal texts from philosophers and historians, this volume presents the great debate over the narrative character of history from the 1960s onwards. The History and Narrative Reader combines theory with practice to offer a unique overview of this debate and illuminates the practical (...) implications of these philosophical debates for the writing of history. The editor's introduction offers a succinct survey of the subject to support the readings, which explore the role of narrative in everything from historical understanding and human action to linguistics and the practice of history. Including the work of F. R. Ankersmit, David Carr, Hayden White, W. H. Dray, and Frederick Olafson; a detailed bibliography; and a glossary of key concepts, this collection will prove an invaluable resource for students of historical theory and methodology. (shrink)

The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, (...) and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives. (shrink)

In this carefully researched, thought-provoking book, Geoffrey Hughes examines the trajectory of political correctness and its impact on public life.

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)

After some metatheoretic preliminaries on questions of justification and rational reconstruction, we lay out some key desiderata for foundational frameworks for mathematics, some of which reflect recent discussions of pluralism and structuralism. Next we draw out some implications (pro and con) bearing on set theory and category and topos therory. Finally, we sketch a variant of a modal-structural core system, incorporating elements of predicativism and the systems of reverse mathematics, and consider how it fares with respect to the desiderata highlighted (...) earlier. Overall, we are making a case for "foundations with modest, welltempered foundationalism". (shrink)

Two kinds of theoretical framework for syntax are encountered in current linguistics. One emerged from the mathematization of proof theory, and is referred to here as generative-enumerative syntax (GES). A less explored alternative stems from the semantic side of logic, and is here called model-theoretic syntax (MTS). I sketch the outlines of each, and give a capsule summary of some mathematical results pertaining to the latter. I then briefly survey some diverse types of evidence suggesting that in some ways MTS (...) seems better suited to theorizing about the relevant linguistic phenomena. (shrink)

Notice that this paper has not claimed that all natural languages are CFL's. What it has shown is that every published argument purporting to demonstrate the non-context-freeness of some natural language is invalid, either formally or empirically or both.18 Whether non-context-free characteristics can be found in the stringset of some natural language remains an open question, just as it was a quarter century ago.Whether the question is ultimately answered in the negative or the affirmative, there will be interesting further questions (...) to ask. If it turns out that natural languages are indeed always CFL's, it will be reasonable to ask whether this helps to explain why speakers apparently recognize so quickly whether a presented utterance corresponds to a grammatical sentence or not, and to associate structural and semantic details with it. It might also be reasonable to speculate about the explanation for the universally context-free character of the languages used by humans, and to wonder whether evolutionary biological factors are implicated in some way (Sampson (1979) could be read in this light). And naturally, it will be reasonable to pursue the program put forward by Gazdar (1981, in press) to see to what extent CFL-inducing grammatical devices can be exploited to yield insightful descriptions of natural languages that capture generalizations in revealing ways.If a human language that is not a CFL is proved to exist, on the other hand, a different question will be raised: give the non-context-free character of human languages in general, why has this property been so hard to demonstrate that it has taken over twenty-five years to bring it to light since the issue was first explicitly posed? If human languages do not have to be CFL's, why do so many (most?) of them come so close to having the property of context-freeness? And, since the CFL's certainly constitute a very broad class of mathematically natural and computationally tractable languages, what property of human beings or their communicative or cognitive needs is it that has caused some linguistic communities to reach beyond the boundaries of this class in the course of evolving a linguistic system?Either way, we shall be interested to see our initial question resolved, and further questions raised. One cautionary word should be said, however, about the implications (or lack of them) that the answer will have for grammatical studies. Chomsky has repeatedly stated that he does not see weak generative capacity as a theme of central importance in the theory of grammar, and we agree. It is very far from being the case that the recent resurgence of interest in exploring the potential of CF-PSG or equivalent systems will, or should, be halted dead in its tracks by the discovery (if it is ever forthcoming) that some natural language is not a CFL. In the area of parsing, for instance, it seems possible that natural languages are not only parsed on the basis of constituent structure such as a CF-PSG would assign, but are parsed as if they were finite state languages (see Langendoen (1975) and Church (1980) for discussion along these lines). That is, precisely those construction-types that figure in the various proofs that English is not an FSL appear to cause massive difficulty in the human processing system; the sentences crucial to the proofs are for the most part unprocessable unless they are extremely short (yet the arguments for English not being and FSL only go through if length is not an issue). This means that in practice properties of finite state grammars are still of great potential importance to linguistic theory despite the fact that they do not provide the framework for defining the total class of grammatical sentences. The same would almost certannly be true of CF-PSG's if they were shown to be inadequate in a similar sense. It is highly unlikely that the advances made so far in far in phrase structure description could be nullified by a discovery about weak generative capacity. Moreover, there are known to be numerous ways in which the power of CF-PSG's can be marginally enhanced to permit, for example, xx languages to be generated without allowing anything like the full class of recursively enumerable or even context-sensitive languages (see Hopcroft and Ullmann (1979), Chapter 14) for an introduction to this topic, noting especially Figure 14.7 on p. 393. The obvious thing to do if natural languages were ever shown not to be CFL's in the general case would be to start exploring such minimal enhancements of expressive power to determine exactly what natural languages call for in this regard and how it could be effectively but parsimoniously provided in a way that closely modelled human linguistic capacities.In the meantime, it seems reasonable to assume that the natural languages are a proper subset of the infinite-cardinality CFL's until such time as they are validly shown not to be. (shrink)

matter of knowing that -- that injustice is wrong, courage is valuable, and care is As a result, what I'll be doing is primarily defending in general -- and due. Such knowledge is embodied in a range of capacities, abilities, and skills..

Words like you, here, and tomorrow are different from other expressions in two ways. First, and by definition, they have different kinds of meanings, which are context-dependent in ways that the meanings of names and descriptions are not. Second, their meanings play a different kind of role in the interpretations of the utterances that contain them. For example, the meaning of you can be paraphrased by a description like "the addressee of the utterance." But an utterance of (1) doesn't say (...) the same thing as an utterance of (2). (shrink)

I assess a number of connected ideas about temporal experience that are introspectively plausible, but which I believe can be argued to be incorrect. These include the idea that temporal experiences are extended experiential processes, that they have an internal structure that in some way mirrors the structure of the apparent events they present, and the idea that time in experience is in some way represented by time itself. I explain how these ideas can be developed into more sharply defined (...) views, and then argue that these views are inconsistent with certain empirical facts about how time is represented in the brain. These facts instead support a kind of atomic view, on which temporal experiences are temporally unstructured atoms. (shrink)

Chomsky’s highly influential Syntactic Structures ( SS ) has been much praised its originality, explicitness, and relevance for subsequent cognitive science. Such claims are greatly overstated. SS contains no proof that English is beyond the power of finite state description (it is not clear that Chomsky ever gave a sound mathematical argument for that claim). The approach advocated by SS springs directly out of the work of the mathematical logician Emil Post on formalizing proof, but few linguists are aware of (...) this, because Post’s papers are not cited. Chomsky’s extensions to Post’s systems are not clearly defined, and the arguments for their necessity are weak. Linguists have also overlooked Post’s proofs of the first two theorems about effects of rule format restrictions on generative capacity, published more than ten years before SS was published. (shrink)

In a Special Issue of Discourse Studies titled ‘The Epistemics of Epistemics’, contributing authors criticize Heritage’s research on participants’ orientations to, and management of, the distribution of knowledge in conversation. These authors claim that the analytic framework Heritage developed for analyzing epistemic phenomena privileges the analysts’ over the participants’ point of view, and rejects standard methods of conversation analysis ; that and are adopted in developing and defending the use of abstract analytic schemata that offer little purchase on either the (...) specific actions speakers accomplish or the understanding others display of them; and that, by virtue of these deficiencies, claims about the systematic relevance of epistemic phenomena for talk-in-interaction breach long-standing norms regarding the relationship between data analysis and generalizing claims. Using a collection of excerpts bearing on the import of epistemics for action formation and action sequencing, I demonstrate that these claims are patently false and suggest that they reflect the authors’ effort to recast CA as a kind of fundamentalist enterprise. I then consider excerpts from a second collection to illustrate how the form of social organization described by Heritage can be used to explicate other phenomena that depend on systematic alterations to its basic features. In conclusion, I suggest that CA’s success in enhancing our grasp of the organization of talk-in-interaction derives from its unique commitment to both generalization and context specificity, collections and single cases, findings plus a continual openness to the ‘something more’ that each particular case can provide. (shrink)

Neuroscientists have long sought to study the dynamic activity of the human brain—what's happening in the brain, that is, while people are thinking, feeling, and acting. Ideally, an inside look at brain function would simultaneously and continuously measure the biochemical state of every cell in the central nervous system. While such a miraculous method is science fiction, a century of progress in neuroimaging technologies has made such simultaneous and continuous measurement a plausible fiction. Despite this progress, practitioners of modern neuroimaging (...) struggle with two kinds of limitations: those that attend the particular neuroimaging methods we have today and those that would limit any method of imaging neural activity, no matter how powerful.In this essay, I consider the liabilities and potential of techniques that measure human brain activity. I am concerned here only with methods that measure relevant physiologic states of the central nervous system and relate those measures to particular mental states. I will consider in particular the preeminent method of functional neuroimaging: BOLD fMRI. While there are several practical limits on the biological information that current technologies can measure, these limits—as important as they are—are minor in comparison to the fundamental logical restraints on the conclusions that can be drawn from brain imaging studies. (shrink)

Geoffrey Leech stresses the contribution of semantics to the understanding of practical problems of communication and concept-manipulation in modern society.

We examine an argument for the non-context-freeness of English that has received virtually no discussion in the literature. It is based on adjuncts of the form 'X or no X', where X is a nominal. The construction has been held to exemplify unbounded syntactic reduplication. We argue that although the argument can be made in a mathematically valid form, its empirical basis is not secure. First, the claimed unbounded syntactic identity between nominals does not always hold in attested cases, and (...) second, an understanding of the semantics of the construction removes the necessity of making reference to any syntactic reduplication. (shrink)

This extraordinary book offers a clear and compelling biography of Jacques Derrida along with one of Derrida's strangest and most unexpected texts. Geoffrey Bennington's account of Derrida leads the reader through the philosopher's familiar yet widely misunderstood work on language and writing to the less familiar themes of signature, sexual difference, law, and affirmation. In an unusual and unprecedented "dialogue," Derrida responds to Bennington's text by interweaving Bennington's text with surprising and disruptive "periphrases." Truly original, this dual and dueling (...) text opens new dimensions in Derrida's thought and work. "Bennington is a shrewd and well-informed commentator whose book should do something to convince the skeptics... that Jacques Derrida's work merits serious attention."—Christopher Norris, _New Statesman & Society_ "Geoffrey Bennington and Jacques Derrida have presented a fascinating example of what might be called post-structuralist autobiography."—Laurie Volpe, _French Review_ "Bennington's account of what Derrida is up to is better in almost all respects—more intelligent, more plausible, more readable, and less pretentious—than any other I have read."—Richard Rorty, _Contemporary Literature_. (shrink)

It is critically important for emerging professionals in education to be sensitised to the ethical and moral responsibilities of their practice throughout their training and beyond. There is a wide disparity in contemporary practice in this regard, which points to a need for greater clarity and consistency in our thinking about ethics within education. Ethics in Education attempts to meet this need, and will be a valuable resource for students, teachers and researchers in education, health and social sciences. Most significantly, (...) the increasing awareness of the importance of ethics, diversity and social pedagogy in the teacher education curriculum will ensure that this book becomes essential reading or recommended reading for initial teacher education and CPD courses in education. The Editors have gathered together an exciting and dynamic group of contributors across many fields of English education, and asked them to help rethink the role of ethics in education in the 21st century. The types of questions that we address include: Do we have a shared view of ethical practice? What are the values that underpin ethical practice? What are our ethical responsibilities as pedagogues? (shrink)

I give an account of the difference between "Holistic" and "Atomistic" views of conscious experience. On the Holistic view, we enjoy a unified "field" of awareness, whose parts are mere modifications of the whole, and therefore owe their existence to the whole. There is some tendency to saddle those who reject the Holistic field model with a (perhaps) implausible "building block" view. I distinguish a number of different theses about the parts of an experience that are suggested by the "building (...) block" metaphor, but which can be rejected by those who also reject the holistic field view. (shrink)

"The book's major parts, one on polarity and the other on analogy, introduce the reader to the patterns of thinking that are fundamental not only to Greek philosophy but also to classical civilization as a whole. As a leading classicist in his own right, Lloyd is an impeccable guide. His sophistication in adducing anthropological parallels to Greek models of polarity and analogy broadens his perspective, making him a forerunner in the study of what we are now used to calling semiotics. (...) A striking example of Lloyd's approach is his re-examination of the dichotomy of Olympian and chthonian gods in ancient Greek world view, which surpasses the reductionist and pseudo-historical models of sky-gods and earth-goddesses that are still commonly invoked to account for polarities in Greek pantheon. "In the second part, dealing with analogy, three crucial metaphorical models for the universe turn out to be basis for a dazzlingly wide variety of scientific and philosophical perspectives. Each model is tested in the whole spectrum of Greek artistic, philosophical and scientific thought. This work is a treasure-house of insights for experts and non experts alike." --Gregory Nagy, Harvard University. (shrink)

Sir Geoffrey Lloyd presents a cross-disciplinary exploration of the unity and diversity of the human mind. He discusses cultural variations with regard to ideas of colour, emotion, health, the self, agency and causation, reasoning, and other fundamental aspects of human cognition. He draws together scientific, philosophical, anthropological, and historical arguments in showing how our evident psychic diversity can be reconciled with our shared humanity.

This essay draws on the work of Jacques Derrida and Angela Y. Davis towards a philosophical resistance to the death penalty in the U.S. I find promise in Derrida’s claim that resistance to the death penalty ought to contest a political structure that founds itself on having the power to decide life and death, but I move beyond Derrida’s desire to consider the abolition of the death penalty without engaging with the particular histories and geographies of European colonialism. I offer (...) a critique of Derrida’s recently published work on the death penalty by engaging with the work of Davis and argue that discussions of state violence in nations that inherit European forms of sovereignty must take seriously the racist violence on which those sovereign powers rely. (shrink)

During the Standing Rock protests in North Dakota, USA/Turtle Island, a group of military veterans knelt in front of Oceti Sakowin Elders asking forgiveness for centuries of settler colonial military ventures in Oceti Sakowin Territory. Leonard Crow Dog forgave them and immediately demanded respect for Native Nations throughout the U.S. Lacking such respect, he said, Native people will cease paying taxes. Crow Dog’s post-forgiveness remarks speak to the political context of the military veterans’ request: They seek collective forgiveness amidst ongoing (...) occupation and harms committed by the collective they represent. In this chapter, I examine this case study and argue that ongoing harm undermines requests for forgiveness on behalf of collectives. I look to the work of Glen Coultard, Waziyatawin, and Leanne Simpson to consider what a responsible request for collective forgiveness would entail. (shrink)