We study the connection between factors of the Medvedev lattice and constructive logic. The algebraic properties of these factors determine logics lying in between intuitionistic propositional logic and the logic of the weak law of the excluded middle (also known as De Morgan, or Jankov, logic). We discuss the relation between the weak law of the excluded middle and the algebraic notion of join-reducibility. Finally we discuss autoreducible degrees.

ABSTRACT In the work of Ernesto Laclau, populism is treated as a hegemonic challenge. Hegemony describes the usurpation of the image of society as a totality by a particular and underdetermined social imaginary. Seen through the lens of what Johann P. Arnason terms “post-transcendental phenomenology”, this concerns the way in which a society sees and experiences both itself and the world it inhabits. This article suggests that hegemonic social imaginaries are built into a society’s public spaces, and are in turn (...) experienced by citizens moving through these spaces, meaning that the built environment is central to the development of populist imaginaries. The article discusses how the neoliberal city exemplifies the way social imaginaries are inscribed into the physical landscape by highlighting three moments in the city; the institution of a certain imaginary as dominant; its sedimentation within the urban fabric over time; and finally, the re-activation of the original moment of institution, which opens up the possibility for new beginnings to overwrite the imaginaries encoded in the city. These three moments describe how physical, built spaces make concrete the power relations and horizons of possibility of the hegemonic imaginary—making possible and encouraging certain ways of being while discouraging (and hiding) others. This hegemonic logic of occupying a public space in the name of a particular subset of the population is a not only parallel to the form of populist politics, but populist sentiment is—at least in part—provoked by the experiences of inhabiting these spaces. (shrink)

Various questions arise in semantic analysis concerning the nature of types. These questions include whether we need types in a semantic theory, and if so, whether some version of simple type theory (STT, Church 1940) is adequate or whether a richer more flexible theory is required to capture our semantic intuitions. Propositions and propositional attitudes can be represented in an essentially untyped first-order language, provided a sufficiently rich language of terms is adopted. In the absence of rigid typing, care needs (...) to be taken to avoid the paradoxes, for example by constraining what kinds of expressions are to be interpreted as propositions (Turner 1992). But the notion of type is ontologically appealing. In some respects, STT seems overly restrictive for natural language semantics. For this reason it is appropriate to consider a system of types that is more flexible than STT, such as a Curry-style typing (Curry & Feys 1958). Care then has to be taken to avoid the logical paradoxes. Here we show how such an account, based on the Property Theory with Curry Types (PTCT, Fox & Lappin 2005), can be formalised within Typed Predicate Logic (TPL, Turner 2009). This presentation provides a clear distinction between the classes of types that are being used to (i) avoid paradoxes (ii) allow predicative polymorphic types. TPL itself provides a means of expressing PTCT in a uniform language. (shrink)

We investigate the structure of the Medvedev lattice as a partial order. We prove that every interval in the lattice is either finite, in which case it is isomorphic to a finite Boolean algebra, or contains an antichain of size $2^{2^{\aleph }0}$ , the size of the lattice itself. We also prove that it is consistent with ZFC that the lattice has chains of size $2^{2^{\aleph }0}$ , and in fact these big chains occur in every infinite interval. We also (...) study embeddings of lattices and algebras. We show that large Boolean algebras can be embedded into the Medvedev lattice as upper semilattices, but that a Boolean algebra can be embedded as a lattice only if it is countable. Finally we discuss which of these results hold for the closely related Muchnik lattice. (shrink)

The relation between Hume’s constructive and skeptical aims has been a central concern for Hume interpreters. Hume’s two definitions of ‘cause’ in the Treatise and first Enquiry apparently represent an important constructive achievement, but this paper argues that the definitions must be understood in terms of Hume’s skepticism. The puzzle I address is simply that Hume gives two definitions rather than one. I use Don Garrett’s interpretation as a foil to develop my alternative skeptical interpretation. Garrett claims the definitions exhibit (...) a general susceptibility to two kinds of definition that all “sense-based concepts” share. Against Garrett, I argue that the definitions express an imperfection Hume finds only in our concept of causation. That imperfection is absent from other sense-based concepts, and prompts skeptical sentiments in Hume’s conclusion to the Treatise’s Book 1. I close by comparing my interpretation with those of Helen Beebee, Stephen Buckle, Galen Strawson and Paul Russell. (shrink)

We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals.

This book explores the differences and similarities between Sartrean existentialism and French poststructuralism.

A selection of his more important writings.

The management and mismanagement of Roman groves was a serious matter, and intentional and unintentional violations of these spaces could be severely punished. In spite of this, groves remained loosely defined by Romans and their boundaries were commonly misunderstood, a confusion that has continued into modern scholarship, where groves are understood as either a clearing in a wood or a dark space lit by artificial lighting. This article takes up this discussion, and explores the nature of an ancient grove as (...) a well-attested space under forest management that influences later conversations on the nature of wooded spaces in more recent periods. (shrink)

The author argues that our best hope for addressing world problems (from climate change to violence, to poverty) is to teach critical thinking through the study of language and all symbol systems. This means removing disciplinary boundaries so that we can focus more effectively on solving common problems. Human survival also depends upon our critical analysis of electronic media and our wise uses of technology. Critical thinking via all symbol systems is more likely to generate humane actions. Therefore, education—not governments (...) or armies or institutions or private corporations—is our best hope. (shrink)

In this study, we examine the influence of senior leadership on firms’ corporate social responsibility. We integrate upper echelons research that has investigated either the influence of the CEO or the top management team on CSR. We contend that functional experience complementarity between CEOs and TMTs in formulating and implementing CSR strategy may underlie differentiated strategies in CSR. We find that when CEOs who have predominant experience in output functions are complemented by TMTs with a lower proportion of members who (...) have experience in output functions, there is a pronounced effect on the community, product, and diversity dimensions of CSR. In turn, when output-oriented CEOs are complemented by output-oriented TMTs, we observe an effect on the employee relations dimension of CSR. Interestingly, we find no influence of CEO-TMT complementarity on the environment dimension of CSR. In general, our empirical results support the relevance of the interaction between CEOs and their TMTs in defining their firms’ CSR profile. (shrink)

Simpson introduced the lattice of Π0 1 classes under Medvedev reducibility. Questions regarding completeness in are related to questions about measure and randomness. We present a solution to a question of Simpson about Medvedev degrees of Π0 1 classes of positive measure that was independently solved by Simpson and Slaman. We then proceed to discuss connections to constructive logic. In particular we show that the dual of does not allow an implication operator (i.e. that is not a Heyting algebra). We (...) also discuss properties of the class of PA-complete sets that are relevant in this context. (shrink)

In this study, we examine the influence of senior leadership on firms’ corporate social responsibility. We integrate upper echelons research that has investigated either the influence of the CEO or the top management team on CSR. We contend that functional experience complementarity between CEOs and TMTs in formulating and implementing CSR strategy may underlie differentiated strategies in CSR. We find that when CEOs who have predominant experience in output functions are complemented by TMTs with a lower proportion of members who (...) have experience in output functions, there is a pronounced effect on the community, product, and diversity dimensions of CSR. In turn, when output-oriented CEOs are complemented by output-oriented TMTs, we observe an effect on the employee relations dimension of CSR. Interestingly, we find no influence of CEO-TMT complementarity on the environment dimension of CSR. In general, our empirical results support the relevance of the interaction between CEOs and their TMTs in defining their firms’ CSR profile. (shrink)

Model transfer refers to the observation that particular model structures are used across multiple distinct scientific domains. This paper puts forward an account to explain the inter-domain transfer of model structures. Central in the account is the role of validation criteria in determining whether a model is considered to be useful by practitioners. Validation criteria are points of reference to which model correctness for a particular purpose is assessed. I argue that validation criteria can be categorized as being mathematical, theoretical (...) or phenomenological in nature. Model transfer is explained by overlap in validation criteria between scientific domains. Particular emphasis is placed on overlap between phenomenological criteria. Overlap in phenomenological criteria can be explained through the notion of universal patterns. Universal patterns are abstract structures that can be made to refer to multiple distinct phenomena when coupled with phenomena-specific empirical content. I present the case study of the Yule Process, in which universal patterns play a crucial role in explaining model transfer. This paper provides an account of model transfer that stays close to modelling practice and expands existing accounts by introducing the notion of universal patterns. (shrink)

"-Barbara Ehrenreich, Mother Jones "This book represents the expression of a particular feminist perspective made all the more compelling by Keller's evident commitment to and understanding of science.

Augustine is the person from the ancient world about whom we know most. He is the author of an intimate masterpiece, the Confessions, which continues to delight its many admirers. In it he writes about his infancy and his schooling in the classics in late Roman North Africa, his remarkable mother, his sexual sins ('Give me chastity, but not yet,' he famously prayed), his time in an outlawed heretical sect, his worldly career and friendships and his gradual return to God. (...) His account of his own eventual conversion is a classic study of anguish, hesitation and what he believes to be God's intervention. It has inspired philosophers, Christian thinkers and monastic followers, but it still leaves readers wondering why exactly Augustine chose to compose a work like none before it. Robin Lane Fox follows Augustine on a brilliantly described journey, combining the latest scholarship with recently found letters and sermons by Augustine himself to give a portrait of his subject which is subtly different from older biographies. Augustine's heretical years as a Manichaean, his relation to non-Christian philosophy, his mystical aspirations and the nature of his conversion are among the aspects of his life which stand out in a sharper light. For the first time Lane Fox compares him with two contemporaries, an older pagan and a younger Christian, each of whom also wrote about themselves and who illumine Augustine's life and writings by their different choices. More than a decade passed between Augustine's conversion and his beginning the Confessions. Lane Fox argues that the Confessions and their thinking were the results of a long gestation over these years, not a sudden change of perspective, but that they were then written as a single swift composition and that its final books are a coherent consummation of its scriptural meditation and personal biography. This exceptional study reminds us why we are so excited and so moved by Augustine's story. Praise for Pagans and Christians 'This open-hearted and learned book is one that any scholar of the ancient world and of early Christianity would be proud to have written... Lane Fox has opened his pages to let in an entirely new world.' Peter Brown, New York Review of Books 'A work of generous humanity and recondite erudition... of consuming interest to all of us who want to know and understand the consequences of the ancient world.' Henry Chadwick, Financial Times Praise for The Unauthorised Version 'I don't know where one would turn for an account of the Bible so clear, so lively and, in many respects, so just.' Frank Kermode, Guardian 'Magnificent... delivered with authority and verve. Learned but never pedantic, he is an unfailingly incisive, thought-provoking, humane, courteous, and often entertaining guide.' Economist. (shrink)

In the context of his theory of numberings, Ershov showed that Kleene's recursion theorem holds for any precomplete numbering. We discuss various generalizations of this result. Among other things, we show that Arslanov's completeness criterion also holds for every precomplete numbering, and we discuss the relation with Visser's ADN theorem, as well as the uniformity or nonuniformity of the various fixed point theorems. Finally, we base numberings on partial combinatory algebras and prove a generalization of Ershov's theorem in this context.

This volume follows shifting conceptions of decadence in art and society at various moments in British literature. The decline from a higher standard, social malaise, aesthetic ennui -- all of these ideas presume certain facts about the past, the present, and time's linear nature. To reject the past as a given and to relish the subtleties of present nuance is the beginning of decadence. This study explores the inherent conflict between society's moral contempt toward purportedly decadent artists and the artist's (...) belief that the stranglehold society maintained on individual interpretation was true decadence. (shrink)

This Is A New Release Of The Original 1899 Edition.

Name der Zeitschrift: Wittgenstein-Studien Jahrgang: 5 Heft: 1 Seiten: 57-88.

This book is the first part of a comprehensive study of Wittgenstein's conception of language description. Describing language was no pastime occupation for the philosopher. It was hard work and it meant struggle. It made for a philosophy that required Wittgenstein's full attention and half his life. His approach had always been working on himself, on how he saw things. The central claim of this book is that nothing will come of our exegetical efforts to see what Wittgenstein's later philosophy (...) amounts to if his work on describing language is not given the place and concern it deserves. The book shows what his philosophy might begin to look like in the light of critical questions around his interest to see the end of the day with descriptions, and these things only. (shrink)

Recently there has been a renewed interest in moral inquiry among American scholars in a variety of disciplines. This collection of accessible essays by scholars in philosophy, political theory, psychology, history, literary studies, sociology, religious studies, anthropology, and legal studies affords a view of the current state of moral inquiry in the American academy, and it offers fresh departures for ethically informed, interdisciplinary scholarship. Seeking neither to reduce values to facts nor facts to values, these essays aim to foster discussion (...) about inquiry and moral judgment, and demonstrate that moral inquiry need not be either dispassionate and value-free or moralistic and preachy. (shrink)

For every partial combinatory algebra, we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca’s, i.e., the smallest ordinals where these relations become equal. We show that the closure ordinal of Kleene’s first model is ${\omega _1^{\textit {CK}}}$ and that the closure ordinal of Kleene’s second model is $\omega _1$. We calculate the exact complexities of the extensionality relations in Kleene’s first model, showing that they exhaust the hyperarithmetical hierarchy. We also discuss embeddings of (...) pca’s. (shrink)

The essays included here represent Fox Keller's attempts to integrate the insights of feminist theory with those of her contemporaries in the history and philosophy of science.

Clinical bioethics is big business. There are now hundreds of people who bioethics in community and university hospitals, nursing homes, rehabilitation and home care settings, and some who play the role of clinical ethics consultant to transplant teams, managed care companies, and genetic testing firms. Still, there is as much speculation about what clinically active bioethicists actually do as there was ten years ago. Various commentators have pondered the need for training standards, credentials, exams, and malpractice insurance for ethicists engaged (...) in clinical consultation. Much of the discussion seems to accept an implicit presumption that all clinical ethics consultation practices look pretty much alike. But is this accurate? What do clinical ethicists do, how and where do they do it, and what kind of clinical ethics is useful in the hospital and in other settings? (shrink)

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.

In 1986, philosopher-bioethicist Samuel Gorovitz published an essay entitled “Baiting Bioethics,” in which he reported on various criticisms of bioethics that were “in print, or voiced in and around … the field” at that time, and set forth his assessment of their legitimacy. He gave detailed attention to what he judged to be the particularly fierce and “irresponsible attacks” on “the moral integrity” and soundness of bioethics contained in two papers: “Getting Ethics” by philosopher William Bennett and “Medical Morality Is (...) Not Bioethics,” coauthored by us. Gorovitz attributed some of the criticisms that bioethics was eliciting to the fact that this new, rapidly rising, and increasingly visible field had brought “scholars and practitioners together who otherwise would have little exposure to one another's disciplines. Their interactions are mutually enriching at times,” he declared, “but mutually baffling and even infuriating at other times.” In this latter regard, he suggested that “perhaps” Fox and Swazey's characterization of bioethics in the article he dissected “reflects a general revulsion at endeavors they see as inadequately like the social sciences or insufficiently respectful of them.” He went on to say that despite his objections to our “complaints” about bioethics—especially to our claim that “autonomy [had] been an unduly emphasized value” in the field—he had “a lingering sense” that there might be “a grain of truth” in them. Gorovitz ended his essay with an affirmation about the “benefit” that bioethics can derive from “responsible” and even from “irresponsible” criticism. “The unexamined discipline invites the philosopher's critical scrutiny no less than the unexamined life,” he aphoristically concluded. a. (shrink)

We investigate the initial segments of the Medvedev lattice as Brouwer algebras, and study the propositional logics connected to them.