We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for pairs (...) (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

In this paper we investigate computable models of -categorical theories and Ehrenfeucht theories. For instance, we give an example of an -categorical but not -categorical theory such that all the countable models of except its prime model have computable presentations. We also show that there exists an -categorical but not -categorical theory such that all the countable models of except the saturated model, have computable presentations.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Theater of Nature: Jean Bodin and Renaissance Science by Ann BlairPeter DearAnn Blair. The Theater of Nature: Jean Bodin and Renaissance Science. Princeton: Princeton University Press, 1997. Pp. xiv + 382. Cloth, $45.00.Jean Bodin’s Universae naturae theatrum (1596) is the least celebrated of all the major publications by this outstanding figure of the French renaissance. It lacks the apparent political, historiographical, and philosophical relevance of Bodin’s well-known (...) earlier works (the Methodus ad facilem historiarum cognitionem of 1566, Les six livres de la République of 1576, and De la démonomanie des sorciers of 1580, all receiving much more attention then as now). Ann Blair focuses our attention on the Theatrum, as a text whose significance for her book exists on at least three interrelated levels: there is its relation to Bodin’s views in the more famous texts; its advantage as a treatise on natural philosophy about whose author we know much more (intellectually) than those of most such works; and in connection with the last, there is above all its value as a distinguished representative of a genre of natural philosophical writings that was prominent in the late sixteenth and early seventeenth centuries.It is the third consideration that motivates Blair’s book most centrally. She declares her wish to enrich our view of the history of science with works, like the Theatrum, that were not made by subsequently regarded stars such as Galileo or Descartes; the very typicality of its genre makes the Theatrum, she argues, a valuable window on contemporary understandings of what natural knowledge was and should be about. Bodin’s enterprise possessed a religious core: natural philosophy was for him a tool to be used in shoring up broadly irenical positions (of the kind associated with the Colloquium heptaplomeres, usually attributed, as here, to Bodin). This kind of “natural theology” avant la lettre characterized a good number of different thinkers and writers on natural philosophy in this period, many of them German (besides their discussion here, Blair is considering such people, and their project of pia philosophia, more fully in her current work). It is a subject that, more than anything, stands at the heart of her study.Bodin, rather conventionally, tried to establish a close liaison between natural philosophy and religious knowledge—that is, between those things to be inferred from experience of the natural world and the central dogmas of faith. Less conventionally, he attempted to demonstrate on occasion truths that were far from orthodox. Regardless of whether Bodin was “really” a Catholic or a Protestant (and Blair observes the great interest in the Theatrum shown by German Calvinists in the first few decades after its original publication), his general religious stance was one of accommodation. Thus good philosophizing could demonstrate (in the weak, rhetorical sense of that term) such doctrines as the existence and providence of God; contentious issues, such as the correct interpretation of the Eucharist, were left aside. Nonetheless, Bodin also argued, at such length and with such vigor as to have the propositions condemned by the Catholic church, that human souls and angels (as well as, more usually, demons) were corporeal beings. The importance to Bodin of this position stemmed from its sociopolitical implications: in particular, if human souls were incorporeal, it became unclear how rewards and punishments—necessary sanctions for restoring the social order threatened by the Wars of Religion—could be meted out after death. Curiously, such a view seems to imply that pleasure and pain are inextricably connected to bodies alone. [End Page 363]Among the historiographical strands informing Blair’s approach is recent literature on the “history of the book,” best known through the work of Roger Chartier. Accordingly, Blair discusses the vicissitudes of production of Bodin’s book in its various editions and emissions, and carefully considers, along with the likely reading practices by the aid of which Bodin came to compose it, the various uses to which its first readers put it. Her major interpretive trope is that of the commonplace book. While acknowledging the lack of direct material evidence for Bodin’s use of such a technique as his chief means of... (shrink)

The erosion of the three interlocking dimensions of nature, society and self is the consequence of what Felix Guattari referred to as integrated world capitalism (IWC). In South Africa the erosion of nature, society and self is also the consequence of centuries of colonialism and decades of apartheid. In this paper I wish to explore how the African philosophy of ubuntu (humanness), which appears to be anthropocentric, might be invoked to contribute to the healing of the three ecologies—how healing of (...) the social might transversally effect healing of nature and the self. My theoretical exploration has relevance to education in South Africa, given that a mandate of national curriculum policy is that indigenous knowledge systems form part of the discursive terrains of all school learning areas/subjects. (shrink)

This article explores the influence of Spinozism on the deep ecology movement and on new materialism. It questions the stance of supporters of the DEM because their ecosophies unwittingly anthropomorphise the more-than-human-world. It suggests that instead of humanising the ‘natural’ world, morality should be naturalised, that is, that the object of human expression of ethics should be the more-than-human world. Moreover, the article discusses Deleuze’s Spinozism that informs new materialism and argues that stripping the human of its ontological privilege does (...) not deprive the human animal from its ethico-normative distinctiveness. Implications of the discussion for an education aimed at cultivating human sensibilities are explored. (shrink)

The importance of a healthy mentoring relationship, and how to go about achieving one, has been explored in several disciplines, including psychology. However, little of this work has focused specifically on unique ethical issues that may arise while mentoring undergraduate students. The authors provide a definition of mentoring in the context of undergraduate education that takes into account undergraduates' status as emerging adults. We delineate both similarities and differences between mentoring undergraduate students and graduate students. Ethical issues that may arise (...) while mentoring undergraduates, especially around themes of vocation, autonomy and influence, boundaries, power, the priority of the protg's needs, the mentor's motives, and accessibility, are spotlighted. We argue that although there is considerable overlap between mentoring graduate students and mentoring undergraduates, there are issues and concerns unique to working with undergraduates that require explication so that they can be appropriately addressed to the benefit of both protg and mentor. (shrink)

We examined how children’s strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34 - 18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were more (...) likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems. (shrink)

We provide three new results about interpolating 2-r.e. or 2-REA degrees between given r.e. degrees: Proposition 1.13. If c h are r.e. , c is low and h is high, then there is an a h which is REA in c but not r.e. Theorem 2.1. For all high r.e. degrees h g there is a properly d-r.e. degree a such that h a g and a is r.e. in h . Theorem 3.1. There is an incomplete nonrecursive r.e. A (...) such that every set REA in A and recursive in 0′ is of r. e. degree. The first proof is a variation on the construction of Soare and Stob . The second combines highness with a modified version of the proof strategy of Cooper et al. . The third theorem is a rather surprising result with a somewhat unusual proof strategy. Its proof is a 0‴ argument that at times moves left in the tree so that the accessible nodes are not linearly ordered at each stage. Thus the construction lacks a true path in the usual sense. Two substitute notions fill this role: The true nodes are the leftmost ones accessible infinitely often; the semitrue nodes are the leftmost ones such that there are infinitely many stages at which some extension is accessible. Another unusual feature of the construction is that it involves using distinct priority orderings to control the interactions of different parts of the construction. (shrink)

The notion of Befindlichkeit in Heidegger’s phenomenological way. Heidegger’s phenomenology of Befindlichkeit and the different kinds of affection was initiated still before Being and Time, and developed in its essential features till the end of the 1930’s. The current paper argues that, since its very origins in a philosophical framework, back to the translation of the affectiones in Augustine, the notion of Befindlichkeit sets the beginning of a structural understanding of existence - displayed both at the ontological levei of Grundstimmungen (...) (such as anguish, boredom or reservedness), and at the ontic level of different factual Stimmungen. Any comprehensive analysis of those affections counts on a tripie background with a Wovor, a Worum and the full-fledged exercise (Vollzug) of such and such affective understanding. In Being and Time this analysis is dedicated to fear, in its different nuances. But this phenomenon was already dealt with in Heidegger’s Lectures on Augustine (1921) and will reoccur in the Beiträge (1936-38). A reading of this conceptual evolution will here ground a defense of the phenomenological character of Heidegger’s way of thinking. (shrink)

In (Fund Math 60:175–186 1967), Wolk proved that every well partial order (wpo) has a maximal chain; that is a chain of maximal order type. (Note that all chains in a wpo are well-ordered.) We prove that such maximal chain cannot be found computably, not even hyperarithmetically: No hyperarithmetic set can compute maximal chains in all computable wpos. However, we prove that almost every set, in the sense of category, can compute maximal chains in all computable wpos. Wolk’s original result (...) actually shows that every wpo has a strongly maximal chain, which we define below. We show that a set computes strongly maximal chains in all computable wpo if and only if it computes all hyperarithmetic sets. (shrink)

Appropriate enablers are essential for management of intellectual capital. Through the use of structural equation modeling, we investigate whether organic renewal environments, interactive behaviors, and trust are conducive to intellectual capital management processes, as they each depend upon the establishment of a climate emphasizing mutual respect. Owing to a lack of clarity in the literature, we tested the ordering of the variables and found statistical significance for two ordering alternatives. However, the sequence presented in this article provides the best statistical (...) fit: an organic renewal environment provides a foundation for interactive behaviors, which leads to trust, and thus is consistent with the development of intellectual capital management pro- cesses within the organization. (shrink)

This paper seeks to understand Heidegger’s phenomenological analysis of the time experience in Sein und Zeit, from the formal point of view of the Care-structure, and in the Seminars of Zollikon, where time is described as world-time in its fullness. Aimed is to show that the early anthropological reception of his major work of 1927 by some of his pupils, like Löwith, who detected similarities with Psychoanalysis, is somehow strengthed by Heidegger himself later on, as he comes with Medard Boss (...) to develop Daseynsanalysis as a metaonlogical understanding of humans life in health and pathology. Illness as privation of health will be seen as the failure of inauthentic existence. And the full, ecstatical experience of time will be shown as the proper or authentic one, being-in-the-world as well as within the psychoanalytical session and interpretation. (shrink)

Heidegger’ s Prolegomena zur Geschichte des Zeitbegriff offers what could be called a phenomenology of Phenomenology itself, that is: an investigation of its history. The husserlian discovery of the “categorial intuition” appears as the second moment of this history, after Brentano’s “intentionality” and before Heidegger’s own discovery of the “original sense of the a priori”, which constitutes the third moment. Our paper seeks to understand this sequence as a way to answer the leading question of how it may be possible (...) that “to be a intentional object can have any relationship with the being itself”. Or, to put it in another formulation: how is intentionality itself ontologically possible? (shrink)

‘Quiet’ and ‘Disquiet’ are terms which express ways of accounting for time-experience, besides being equally open for a rendering as emotional states. Starting from three existential moods – stress, boredom, and the joy of the present moment – this inquiry aims to put into evidence the structuring features of our existential experience of time itself, both in the daily exercise of our being-in-the-world, and at the level of our being or not being in possession of oneself in such exercise and (...) in its potentially pathological derivates. In this context, which finds its theoretical roots in the Heideggerian analysis of the being-in, quiet and disquiet reveal their paradoxical character in terms of the mutual belonging and tension each of them, respectively, presupposes. At the same time, and with such a basis, we will find the way of understanding ‘quiet’ as a correlate of time as a ‘duration’. (shrink)

In his quest to let language speak, Heidegger explored thoroughly the possibilities of meaning of factical language, in its phenomenological and poietic dimensions. He thereby came to characterize Being and Time as a way, a path which must be followed until it ends. He later understood it as a wandering and, finally, as a dead end (Holzweg). The idea of the walker, in conversation with himself, accompanies this entire journey. The present essay seeks to uncover the main moments of Heidegger’s (...) retrospective and self-interpreting way, based on recent publications of the Gesamtausgabe (in particular GA 82 and 70.1), which he himself wanted to see, generally speaking, as the edition of his Wege, nicht Werke. (shrink)

If postmodernism is/was a condition and poststructuralism an academic theory associated with it, then one might ask what condition characterizes contemporary life and what emerging theories might b...

Currently, global society is delicately poised on a civilisational threshold similar to that of the feudal era. This is a time when outmoded institutions, values, and systems of thought and their associated dogmas are ripe for transcendence by more relevant systems of organization and knowledge (Davidson, 2000). The foundations of the modern era (including modern educational institutions) are under sharp scrutiny; the fragmentation of nature, society and self is evidence of the cracks in the foundations. In times of crises old (...) questions often come to the fore. For example, as environmental problems reach unprecedented levels the perennial existential question of how we should live is emerging once more. So too are educational questions such as what and how we should learn. But, times of crises also present new opportunities, create fresh imaginings and alternative meanings, metaphors and languages.In this paper I wish to appraise sustainability (and its epithets such as development) as a new discourse that emerged in the late 20th century in response to the psycho-socio-environmental crises of the time. I shall also examine the (in)capacity of disciplinary knowledge and traditional scholarship to respond to the complex and pressing problems of contemporary society. Finally, I will critically discuss the role that new modes of knowledge production, an expanded view of scholarship and alternative metaphors might play in (re)imagining the university's role in sustainability education. (shrink)

This article explores an understanding of organizational management developed from the metaphorical application of complexity science to the field of organizational development. It focuses on the insights that fractality triggers in relation to an alternative way of examining and appreciating organizational hierarchy, and the subsequent implications to liberating creativity, ingenuity and potentiality of individuals working within the organization. Sites where such a fractal-hierarchy mindset appears to be evident are discussed, and the effects on productivity noted.

Whether copyrights should exist in content generated by an artificial intelligence is a frequently discussed issue in the legal literature. Most of the discussion focuses on economic rights, whereas the relationship of artificial intelligence and moral rights remains relatively obscure. However, as moral rights traditionally aim at protecting the author’s “personal sphere”, the question whether the law should recognize such protection in the content produced by machines is pressing; this is especially true considering that artificial intelligence is continuously further developed (...) and increasingly hard to comprehend for human beings. This paper first provides the background on the protection of moral rights under existing international, U.S. and European copyright laws. On this basis, the paper then proceeds to highlight special issues in connection with moral rights and content produced by artificial intelligence, in particular whether an artificial intelligence itself, the creator or users of an artificial intelligence should be considered as owners of moral rights. Finally, the present research discusses possible future solutions, in particular alternative forms of attribution rights or the introduction of related rights. (shrink)

To each computable enumerable (c.e.) set A with a particular enumeration {As}s∈ω, there is associated a settling function mA(x), where mA(x) is the last stage when a number less than or equal to x was enumerated into A. One c.e. set A is settling time dominated by another set B (B >st A) if for every computable function f, for all but finitely many x, mB(x) > f(m₄(x)). This settling-time ordering, which is a natural extension to an ordering of the (...) idea of domination, was first introduced by Nabutovsky and Weinberger in [3] and Soare [6]. They desired a sequence of sets descending in this relationship to give results in differential geometry. In this paper we examine properties of the <st ordering. We show that it is not invariant under computable isomorphism, that any countable partial ordering embeds into it, that there are maximal and minimal sets, and that two c.e. sets need not have an inf or sup in the ordering. We also examine a related ordering, the strong settling-time ordering where we require for all computable f and g, for almost all x, mB(x) > f(mA(g(x))). (shrink)

We consider the set of jumps below a Turing degree, given by JB={x':x≤a}, with a focus on the problem: Which recursively enumerable degrees a are uniquely determined by JB? Initially, this is motivated as a strategy to solve the rigidity problem for the partial order R of r.e. degrees. Namely, we show that if every high2 r.e. degree a is determined by JB, then R cannot have a nontrivial automorphism. We then defeat the strategy—at least in the form presented—by constructing (...) pairs a0, a1 of distinct r.e. degrees such that JB=JB within any possible jump class {x:x'=c}. We give some extensions of the construction and suggest ways to salvage the attack on rigidity. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

In this paper we analyze the relative effectiveness of the moment of contact between a brand and an individual consumer. The concept of effectiveness is made operational through the use of both attitude and awareness measures. The main research uses a 4x4 Latin square confounded within subjects factorial design with different touch points and brands. The appropriate stimuli were identified in a preliminary study. The results indicate that, overall, TV advertising and print advertisements – the traditional media channels – are (...) significantly more effective than the internet, a non-traditional media channel. (shrink)

Este estudio examina las relaciones entre política, poder, comunicación y cultura y el impacto de las nuevas tecnologías en esas relaciones. En él se destaca la función de la universidad en la producción de conocimiento útil al ciudadano en sus prácticas político-sociales, en la interpretación del m..

The political discourse of Rafael Caldera and Carlos Andrés Pérez is here analyzed. Thess leaders share features in exercising power as presidents of Venezuela, and in their being members of the traditional political parties that ruled the country in the second half of the XXth century. A crit..

We investigate the relationship of the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low 2.

Last year (1998) saw the celebration of the 50th Anniversaryof the British National Health Service (NHS). One ofthe few completely nationalised systems of health carein the world, the NHS is seen by many as a moralbeacon of what it means to provide equitable medicaltreatment to all citizens on the basis of need andneed alone. However, others argue that it has failedto achieve the overall goals for which it was created.Because of scarce resources, some urgently needed careis not available at all, (...) while that which is receivedis sometimes second class. For these reasons, it isclaimed that the NHS should be scrapped and replacedby other systems of health care delivery.This paper outlines the history of the NHS,indicating some of the problems and innovations whichhave led to its current organization and structure.The philosophical foundations of the NHS are then articulated and defended on the grounds that it stillrepresents a morally coherent and economicallyefficient approach to the delivery of health care.Scarce resources are the key problem facing the NHS,making rationing inevitable and it is shown thatthis is not incompatible with the moral foundations ofthe service. However, there can be little doubt thatthe NHS is now becoming dangerously under-funded. Thepaper concludes with arguments about why this is soand what might be done about it. (shrink)

Drawing on feminist philosophical accounts of reproduction and initial data acquired through research with migrant mothers in London, this article argues that the role and place of reproduction remains under-theorized within scholarly accounts of women's role in migration processes. Working with an expanded concept of reproduction that includes not only childbirth and motherhood, but also the work of reproducing heritage, culture and structures of belonging, it argues that feminist migration scholars can draw on valuable theoretical resources in order to tell (...) more complicated stories about the place of reproduction in migration, and challenge the often problematic gendered distinctions between travelling and staying put, change and repetition that continue to underpin some of the narrative structures operative in migration studies. (shrink)