Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we provide structure results for chains having less than continuum many isomorphism classes of equimorphic chains. We deduce as a corollary that any chain has either a single isomorphism class of equimorphic chains or infinitely many.

Shelah, S., C. Laflamme and B. Hart, Models with second order properties V: A general principle, Annals of Pure and Applied Logic 64 169–194. We present a general framework for carrying out the construction in [2-10] and others of the same type. The unifying factor is a combinatorial principle which we present in terms of a game in which the first player challenges the second player to carry out constructions which would be much easier in a generic extension of (...) the universe, and the second player cheats with the aid of ♦. Section 1 contains an axiomatic framework suitable for the description of a number of related constructions, and the statement of the main theorem 1.9 in terms of this framework. In Section 2 we illustrate the use of our combinatorial principle. The proof of the main result is then carried out in Sections 3–5. (shrink)

We give a new characterization of the cardinal invariant $\mathfrak {d}$ as the minimal cardinality of a family $\mathcal {D}$ of tall summable ideals such that an ultrafilter is rapid if and only if it has non-empty intersection with all the ideals in the family $\mathcal {D}$. On the other hand, we prove that in the Miller model, given any family $\mathcal {D}$ of analytic tall p-ideals such that $\vert \mathcal {D}\vert <\mathfrak {d}$, there is an ultrafilter $\mathcal {U}$ which (...) is an $\mathscr {I}$ -ultrafilter for all ideals $\mathscr {I}\in \mathcal {D}$ at the same time, yet $\mathcal {U}$ is not a rapid ultrafilter. As a corollary, we obtain that in the Miller model, given any analytic tall p-ideal $\mathscr {I}$, $\mathscr {I}$ -ultrafilters are dense in the Rudin–Blass ordering, generalizing a theorem of Bartoszyński and S. Shelah, who proved that in such model, Hausdorff ultrafilters are dense in the Rudin–Blass ordering. This theorem also shows some limitations about possible generalizations of a theorem of C. Laflamme and J. Zhu. (shrink)

We prove several theorems about the cardinal $\mathfrak{g}$ associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps fromω toω, all families of size $< \mathfrak{g}$ are below all unbounded families. With respect to a natural ordering of filters onω, all filters generated by $< \mathfrak{g}$ sets are below all non-feeble filters. If $\mathfrak{u}< \mathfrak{g}$ then $\mathfrak{b}< \mathfrak{u}$ and $\mathfrak{g} = \mathfrak{d} = \mathfrak{c}$ . (The definitions of these cardinals are recalled in the introduction.) Finally, (...) some consequences deduced from $\mathfrak{u}< \mathfrak{g}$ by Laflamme are shown to be equivalent to $\mathfrak{u}< \mathfrak{g}$. (shrink)

Reviewed Works:Tomek Bartoszynski, Marion Scheepers, Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13-15, 1992, April 10-11, 1993, March 25-27, 1994, Boise State University, Boise, Idaho.R. Aharoni, A. Hajnal, E. C. Milner, Interval Covers of a Linearly Ordered Set.Eyal Amir, Haim Judah, Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets.Tomek Bartoszynski, Ireneusz Reclaw, Not Every $\gamma$-Set is Strongly Meager.Andreas Blass, Reductions Between Cardinal Characteristics of the Continuum.Claude Laflamme, Filter Games and Combinatorial Properties of Strategies.R. Daniel Mauldin, (...) Analytic non-Borel Sets Modulo Null Sets.Janusz Pawlikowski, Laver's Forcing and Outer Measure.Marion Scheepers, Meager Sets and Infinite Games.Saharon Shelah, On Some Problems in General Topology.Saharon Shelah, Remarks on $\aleph_1$-CWH not CWH First Countable Spaces.Juris Steprans, Cardinal Invariants Associated with Hausdorff Capacities. (shrink)

This paper investigates properties of \(\sigma \) -closed forcings which generate ultrafilters satisfying weak partition relations. The Ramsey degree of an ultrafilter \({\mathcal {U}}\) for _n_-tuples, denoted \(t({\mathcal {U}},n)\), is the smallest number _t_ such that given any \(l\ge 2\) and coloring \(c:[\omega ]^n\rightarrow l\), there is a member \(X\in {\mathcal {U}}\) such that the restriction of _c_ to \([X]^n\) has no more than _t_ colors. Many well-known \(\sigma \) -closed forcings are known to generate ultrafilters with finite Ramsey degrees, (...) but finding the precise degrees can sometimes prove elusive or quite involved, at best. In this paper, we utilize methods of topological Ramsey spaces to calculate Ramsey degrees of several classes of ultrafilters generated by \(\sigma \) -closed forcings. These include a hierarchy of forcings due to Laflamme which generate weakly Ramsey and weaker rapid p-points, forcings of Baumgartner and Taylor and of Blass and generalizations, and the collection of non-p-points generated by the forcings \({\mathcal {P}}(\omega ^k)/\mathrm {Fin}^{\otimes k}\). We provide a general approach to calculating the Ramsey degrees of these ultrafilters, obtaining new results as well as streamlined proofs of previously known results. In the second half of the paper, we calculate pseudointersection and tower numbers for these \(\sigma \) -closed forcings and their relationships with the classical pseudointersection number \({\mathfrak {p}}\). (shrink)

The notion that our society, its education system and its intellectual life, is characterised by a split between two cultures – the arts or humanities on one hand and the sciences on the other – has a long history. But it was C. P. Snow's Rede lecture of 1959 that brought it to prominence and began a public debate that is still raging in the media today. This fiftieth anniversary printing of The Two Cultures and its successor piece, A Second (...) Look features an introduction by Stefan Collini, charting the history and context of the debate, its implications and its afterlife. The importance of science and technology in policy run largely by non-scientists, the future for education and research, and the problem of fragmentation threatening hopes for a common culture are just some of the subjects discussed. (shrink)

One of the very few accounts in English of German idealism, this ambitious work advances and revises our understanding of both the history and the thought of the classical period of German philosophy. As he traces the structure and evolution of idealism as a doctrine, Frederick Beiser exposes a strong objective, or realist, strain running from Kant to Hegel and identifies the crucial role of the early romantics—Hölderlin, Schlegel, and Novalis—as the founders of absolute idealism.

Is there such a thing as natural knowledge of God? C. Stephen Evans presents the case for understanding theistic arguments as expressions of natural signs in order to gain a new perspective both on their strengths and weaknesses. Three classical, much-discussed theistic arguments - cosmological, teleological, and moral - are examined for the natural signs they embody. At the heart of this book lie several relatively simple ideas. One is that if there is a God of the kind accepted by (...) Christians, Jews, and Muslims, then it is likely that a 'natural' knowledge of God is possible. Another is that this knowledge will have two characteristics: it will be both widely available to humans and yet easy to resist. If these principles are right, a new perspective on many of the classical arguments for God's existence becomes possible. We understand why these arguments have for many people a continued appeal but also why they do not constitute conclusive 'proofs' that settle the debate once and for all. Touching on the interplay between these ideas and contemporary scientific theories about the origins of religious belief, particularly the role of natural selection in predisposing humans to form beliefs in God or gods, Evans concludes that these scientific accounts of religious belief are fully consistent, even supportive, of the truth of religious convictions. (shrink)

This article challenges conventional readings of Michel Foucault by examining his fascination with neoliberalism in the late 1970s. Foucault did not critique neoliberalism during this period; rather, he strategically endorsed it. The necessary cause for this approval lies in the broader rehabilitation of economic liberalism in France during the 1970s. The sufficient cause lies in Foucault's own intellectual development: drawing on his long-standing critique of the state as a model for conceptualizing power, Foucault concluded, during the 1970s, that economic liberalism, (...) rather than “discipline,” was modernity's paradigmatic power form. Moreover, this article seeks to clarify the relationship between Foucault's philosophical antihumanism and his assessment of liberalism. Rather than arguing that Foucault's antihumanism precluded a positive appraisal of liberalism, or that the apparent reorientation of his politics in a more liberal direction in the late 1970s entailed a partial retreat from antihumanism, this article contends that Foucault's brief, strategic, and contingent endorsement of liberalism was possible precisely because he saw no incompatibility between antihumanism and liberalism—but only liberalism of the economic variety. Economic liberalism alone, and not its political iteration, was compatible with the philosophical antihumanism that is the hallmark of Foucault's thought. (shrink)

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and (...) conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area. (shrink)

C W Evers, J C Walker; Knowledge, Partitioned Sets and Extensionality: a refutation of the forms of knowledge thesis, Journal of Philosophy of Education, Volume.

The arguments for redistribution of wealth, and for prohibiting certain transactions such as price-gouging, both are based in mistaken conceptions of exchange. This paper proposes a neologism, “euvoluntary” exchange, meaning both that the exchange is truly voluntary and that it benefits both parties to the transaction. The argument has two parts: First, all euvoluntary exchanges should be permitted, and there is no justification for redistribution of wealth if disparities result only from euvoluntary exchanges. Second, even exchanges that are not euvoluntary (...) should generally be permitted, because access to market exchange may be the only means by which people in desperate circumstances can improve their position. (shrink)

C. S. Lewis sets out to persuade his audience of the importance and relevance of universal values such as courage and honor in contemporary society.

The Holocaust marks a decisive moment in modern suffering in which it becomes almost impossible to find meaning or redemption in the experience. In this study, C. Fred Alford offers a new and thoughtful examination of the experience of suffering. Moving from the Book of Job, an account of meaningful suffering in a God-drenched world, to the work of Primo Levi, who attempted to find meaning in the Holocaust through absolute clarity of insight, he concludes that neither strategy works well (...) in today's world. More effective are the day-to-day coping practices of some survivors. Drawing on testimonies of survivors from the Fortunoff Video Archives, Alford also applies the work of Julia Kristeva and the psychoanalyst Donald Winnicot to his examination of a topic that has been and continues to be central to human experience. (shrink)

Most whistleblowers talk as if they never had a choice about whether to blow the whistle. This doesn't mean they acted suddenly, or impulsively, only that they believe they could not have done otherwise. Trying to make sense of this near universal answer to the question "Why did you do it?" the essay draws on narrative theory. Narrative theory distinguishes between actant and sender—that is, between actor and his or her values. This distinction helps to explain what it means to (...) face a difficult choice over something about which one feels one never had a choice. (shrink)

This book reveals the rational basis for historians' descriptions, interpretations and explanations of past events. C. Behan McCullagh defends the practice of history as more reliable than has recently been acknowledged. Historians, he argues, make their accounts of the past as fair as they can and avoid misleading their readers. He explains and discusses postmodern criticisms of history, providing students and teachers of history with a renewed validation of their practice. McCullagh takes the history debate to a new stage with (...) bold replies to the major questions historians face today. (shrink)

This essay is about the ethical propriety and practical efficacy of a range of policy undertakings which, in the last twenty years, has come to be referred to as “affirmative action.” These policies have been contentious and problematic, and a variety of arguments have been advanced in their support. Here I try to close a gap, as I see it, in this “literature of justification” which has grown up around the practice of preferential treatment. My principal argument along these lines (...) is offered in the next section. I then consider how some forms of argument in support of preferential treatment, distinctly different from that offered here, not only fail to justify the practice but, even worse, work to undermine the basis for cooperation among different ethnic groups in the American democracy. Finally, I observe that as a practical matter the use of group preference can, under circumstances detailed in the sequel, produce results far different from the egalitarian objectives which most often motivate their adoption. It may seem fatuous in the extreme to raise as a serious matter, in the contemporary United States, the question “Why should we care about group inequality?” Is not the historical and moral imperative of such concern self-evident? Must not those who value the pursuit of justice be intensely concerned about economic disparities among groups of persons? The most obvious answer to the title question would seem, then, to be: “We should care because such inequality is the external manifestation of the oppression of individuals on the basis of their group identity.”. (shrink)

Chalmers' (2018) meta-problem of consciousness emphasizes unexpected common ground between otherwise incompatible positions. We argue that the materialist should welcome discussion of the meta-problem. We suggest that the core of the metaproblem is the seeming arbitrariness of subjective experience. This has an unexpected resolution when one moves to an interventionist account of scientific explanation: the same interventions that resolve the hard problem should also resolve the meta-problem.

The present paper is an extract from a thesis concerning the debate between bradley and russell on the nature of relations. it concerns only the most general points of interaction - the positive influence of bradley upon russell with respect to psychologism, logic, and constructions; the negative influence: russell's work seen as a reaction to bradley. the intention is to show that bradley was an extremely strong influence in russell's development hardly worthy of the disregard which russell showed him.

C. K. Grant; X*—On a Definition of Knowledge, Proceedings of the Aristotelian Society, Volume 73, Issue 1, 1 June 1973, Pages 157–166, https://doi.org/10.1093/a.

C A Wringe; Pupils’ Rights, Journal of Philosophy of Education, Volume 7, Issue 1, 30 May 2006, Pages 103–115, https://doi.org/10.1111/j.1467-9752.1973.tb00475.

Arthur Danto is the Johnsonian Professor Emeritus of Philosophy at Columbia University and the most influential philosopher of art in the last half century. As an art critic for The Nation for 25 years and frequent contributor to other widely read outlets such as the New York Review of Books, Danto also has become one of the most respected public intellectuals of his generation. He is the author of some two dozen important books, along with hundreds of articles and reviews (...) which have been the center of both controversy and discussion. In this volume Danto offers his intellectual autobiography and responds to essays by 27 of the keenest critics of his thought from the worlds of philosophy and the arts. The book includes 16 pages of color art reproductions. Danto is the author dozens of books on art, philosophy, the philosophy of art, and art criticism. He is a rare philosopher who is also a public intellectual. (shrink)

Монографія "Функціональність релігії: український контекст".

In the first and shorter part of this essay I comment on Wittgenstein's general influence on the practice of philosophy since his time. In the second and much longer part I discuss aspects of his work which have had a more particular influence, chiefly on debates about meaning and mind. The aspects in question are Wittgenstein's views about rule-following and private language. This second part is more technical than the first.

La traduction de l'epistrophe grecque en conversio latine a pu laisser entendre une continuite entre le retour des philosophies grecques neoplatoniciennes et l'evenement religieux proprement chretien de la conversion. Le paradigme en serait le passage de Plotin a Augustin. Mais peut-on oublier que les grecques classiques n'ont pas d'ethique du repentir et que, sans ce rapport au temps de la faute, la constitution de soi n'a ni le meme sens ni le meme lieu? C'est le travail du Centre A.J. Festugiere (...) de Paris X-Nanterre sur les entrecroisements et reprises entre philosophie et religion qui est a l'origine des etudes rassemblees en cet ouvrage. Que nous voyions apparaitre aujourd'hui une nouvelle forme de repentir publique convie a mieux distinguer deux modeles de constitution de soi qui se reconnaissent en ce que l'accent porte tantot sur l'etre et tantot sur le temps. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:diacritics 30.1 (2000) 106-123 [Access article in PDF] The (Mis)Uses of Cannibalism in Contemporary Cultural Critique C. Richard King At least since 1979, when W. Arens demystified what he termed "the man-eating myth," cannibalism, once a fundamental feature of the anthropological imagination and a primary trope for interpreting cultural difference, has become subject to serious debate and lingering doubt [see Osborne]. Even as some anthropologists have sought to recuperate (...) anthropophagy as a tangible symbolic, ideological, and ritual complex [Brown and Tuzin; Conklin, "'Thus are our Bodies'"; Forsyth; Harris, Good to Eat 199-234; Sanday], a constellation of scholarly projects and popular works has complicated cannibalism by relocating it in the West. Perhaps most visibly, Hollywood cinema has reclaimed cannibalism. Although a handful of films have revived well-worn clichés of dark-skinned savages preparing to consume Westerners, as in King Solomon's Mines and Crocodile Dundee, others have cast the Western subject as cannibal to grapple with the horrors of reluctant cannibalism, as in Alive! [see Fiddes 121-31], to work through the transgressive and terrifying desires associated with psychopathic cannibalism, as in The Silence of the Lambs [Fuss; Halberstam], and importantly to parody the normative beliefs and behaviors of white, middle-class, heterosexual EuroAmericans, as in Eating Raoul and Parents. At the same time, an array of scholars, artists, and activists have invoked cannibalism to fashion critical perspectives on Western cultural practices. In his film Cannibal Tours (1987), Dennis O'Rourke encourages his audiences to think critically about tourists who travel to the Sepik River Valley to encounter reformed cannibals, asking implicitly who the cannibals are, the Melanesians who formerly (were thought to/claim to have) practiced anthropophagy or the tourists who travel to New Guinea to consume them [see Bruner]. Others have pushed the metaphor. Michael Ames, borrowing explicitly from O'Rourke, uses the cannibal to reframe ethnographic museums and their practices. Similarly, Jane Tompkins asserts that "Museums are a form of cannibalism made safe for polite society" [533]. More generally, Crystal Bartolovich playfully glosses consumerism as the cultural logic of the late cannibalism; bell hooks speaks of the EuroAmerican desires for and incorporation of things ethnic as "eating the other"; and Rosalind Morris suggests that cannibalism is the essential metaphor for late capitalism. More telling, however, are a set of overlapping critical projects that offer detailed theorizations [End Page 106] [Begin Page 108] of contemporary anthropophagy. Here, I will examine three that have had an important impact on discussions of tourism, museums, cultural appropriation, and consumption. Dean MacCannell, in an exciting exploratory review of the documentary Cannibal Tours, makes explicit what O'Rourke left unsaid: we are cannibals, and contemporary capitalism is neocannibalism. Perhaps more radically, Jack Forbes argues that Western civilization fosters cannibalism as an embodied, psychosocial condition or psychosis rooted in exploitation and consumption. Inspired at least in part by Forbes, Deborah Root rethinks Western civilization as cannibal culture.Although I am terribly sympathetic with these perspectives, particularly their political commitments and theoretical creativity, I am disturbed by the practices and effects that animate them. Indeed, as powerful as this critical field promises to be, it is at the same time troubling and dangerous. Although it defamiliarizes practices of cultural production and consumption, it does not enhance understanding of the contexts in which individuals and institutions deploy them and does less to effectively challenge or undermine them. In reframing beliefs and behaviors to accentuate productivity and power, it reinstates and reaffirms binaries and, worse, often turns on the same forms of appropriation.* * *Arguably, flesh eating has always promoted the elaborations of differences. Works central to the Western canon mobilize cannibalism to make (sense of) the world. Herodotus offers an early anthropophagic distinction:These Scythian husbandmen then occupy the country eastward for three days' journey.... Beyond this region the country is desert for a great distance; and beyond the desert Androphagi dwell.... The Androphagi have the most savage customs of all men; they pay no regard to justice, nor make use of any established law. They are nomads and wear a dress like a Scythian; they... (shrink)

C Evers; Epistemology and the Structure of Educational Theory: some reflections on the O'Connor-Hirst debate, Journal of Philosophy of Education, Volume 21, Iss.