We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...) are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations. (shrink)

An algebra is effective if its operations are computable under some numbering. When are two numberings of an effective partial algebra equivalent? For example, the computable real numbers form an effective field and two effective numberings of the field of computable reals are equivalent if the limit operator is assumed to be computable in the numberings . To answer the question for effective algebras in general, we give a general method based on an algebraic analysis of approximations by elements of (...) a finitely generated subalgebra. Commonly, the computable elements of a topological partial algebra are derived from such a finitely generated algebra and form a countable effective partial algebra. We apply the general results about partial algebras to the recursive reals, ultrametric algebras constructed by inverse limits, and to metric algebras in general. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)

The period in the foundations of mathematics that started in 1879 with the publication of Frege's Begriffsschrift and ended in 1931 with Gödel's Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I can reasonably be called the classical period. It saw the development of three major foundational programmes: the logicism of Frege, Russell and Whitehead, the intuitionism of Brouwer, and Hilbert's formalist and proof-theoretic programme. In this period, there were also lively exchanges between the various schools culminating in (...) the famous Hilbert-Brouwer controversy in the 1920s. -/- The purpose of this anthology is to review the programmes in the foundations of mathematics from the classical period and to assess their possible relevance for contemporary philosophy of mathematics. What can we say, in retrospect, about the various foundational programmes of the classical period and the disputes that took place between them? To what extent do the classical programmes of logicism, intuitionism and formalism represent options that are still alive today? These questions are addressed in this volume by leading mathematical logicians and philosophers of mathematics. (shrink)

Mircea Eliade has contributed immense scholarship to the study of religion. His theories have been analyzed, utilized, and critiqued by many. This paper will apply Eliade’s concept of axis mundi in an interpretation of the North Indian classical dance form of Kathak. A foundational understanding of axis mundi will be established before applying the theory in interpreting Kathak. The foundation will be built by defining terms and ideas integral in Eliade’s writings and by examining his interpretation of Barabudur as an (...) axis mundi. By discussing the consecration of space, the positioning of the body, the intention of the performer, and the role of the art form in society, this paper will argue that a Kathak dancer also functions as an axis mundi—a point of communication between the profane and the Divine. While acknowledging various critiques of Eliade’s approach, this paper will also address the need for practitioner perspectives in developing a multi-faceted interpretation of religious phenomena. (shrink)

Previous studies of auditory expectation have focused on the expectedness perceived by listeners retrospectively in response to events. In contrast, this research examines predictive uncertainty —a property of listeners' prospective state of expectation prior to the onset of an event. We examine the information-theoretic concept of Shannon entropy as a model of predictive uncertainty in music cognition. This is motivated by the Statistical Learning Hypothesis, which proposes that schematic expectations reflect probabilistic relationships between sensory events learned implicitly through exposure. Using (...) probability estimates from an unsupervised, variable-order Markov model, 12 melodic contexts high in entropy and 12 melodic contexts low in entropy were selected from two musical repertoires differing in structural complexity (simple and complex). Musicians and non-musicians listened to the stimuli and provided explicit judgments of perceived uncertainty (explicit uncertainty). We also examined an indirect measure of uncertainty computed as the entropy of expectedness distributions obtained using a classical probe-tone paradigm where listeners rated the perceived expectedness of the final note in a melodic sequence (inferred uncertainty). Finally, we simulate listeners' perception of expectedness and uncertainty using computational models of auditory expectation. A detailed model comparison indicates which model parameters maximize fit to the data and how they compare to existing models in the literature. The results show that listeners experience greater uncertainty in high-entropy musical contexts than low-entropy contexts. This effect is particularly apparent for inferred uncertainty and is stronger in musicians than non-musicians. Consistent with the Statistical Learning Hypothesis, the results suggest that increased domain-relevant training is associated with an increasingly accurate cognitive model of probabilistic structure in music. (shrink)

In this article we refine the design ofcontext shifting experiments, which play a central role in contextualist debates, and we subject a large number of scenarios involving different types of expressions of interest to contextualists, including ‘know’ and color adjectives like ‘green’, to experimental investigation. Our experiment (i) reveals an effect of changing contexts on the evaluation of uses of the sentences that we examine, thereby overturning the absence of results reported in previous experimental studies (so‐callednull results), (ii) uncovers evidence (...) for a ‘truth bias' in favor of positive over negative sentences, and (iii) reveals previously unnoticed distinctions between the strength of the contextual effects displayed by scenarios involving knowledge ascriptions and scenarios concerning color and other miscellaneous scenarios. (shrink)

Christianity finds itself in a new situation, one that resembles its first‐century experience in that it will be shaped by a new dominant world culture. This culture is marked by three factors‐the economy, the multireligious situation, and science. The author's discussion deals with the issues that arise in this engagement with culture under three rubrics: dialogue between science and religion, globalization of the religious encounter, and interreligious dialogue in a globalized world. The major assertions are: (1) Science and religions must (...) avoid restrictive and expansionist relationships and work for reciprocal interaction. (2) Globalization is an unavoidable, but ambiguous, historical development; religions should reject responses of “ethnification” and “primitivism” and rather engage in strategies that encourage both productive encounter and critical distance. (3) Interreligious dialogue includes dialogues of life, of intellectual exchange, of religious experience, of common action, and of confrontation; this dialogue will seek to embrace truth (which involves science) and wisdom (which includes the various religious traditions) in the reciprocal interaction that is marked by love. (shrink)

In an introduction to tbe tbeology and moral pbilosopby of tbe Danisb tbinker, K. E. Legstrup, tbe starting point ist taken in bis on pbenomenological basis developed pbilosopby of creation. Tbe vibrant discussion in Denmark in tbe fifties between K. E. Legstrup an N. H. See conceming a specific cbristian etbics is evaluated and it is sbown bow Legstcups etbical tbinking developed in two directions. On tbe one band be expands bis pbilosopby of creation into metapbysical reflections in order to (...) substantiate bis solution to tbe problern of tbe foundations of etbics. On tbe otber band be anticipates a development towards applied etbics. (shrink)

During the past decades, research collaboration between researchers from different disciplines has become more frequent. However, there is a need to look into the generic modalities and challenges. The article explores a series of potential obstructions to cross-disciplinary collaboration of methodological and epistemological nature. Furthermore, a number of contextual, inhibiting factors are outlined. As means of overcoming the obstacles, the importance of mutual knowledge, allocation of adequate time and conducive research management is emphasised. New teams may benefit from tutoring by (...) facilitators, who can help to make problem areas explicit and negotiate solutions. Owing to the training background of the author, most of the examples are drawn from the interface between biomedicine/natural science and applied medical anthropology. However, the issues raised basically apply to all sorts of cross-disciplinary research collaboration in various combinations. (shrink)

Existing research on the formation of employee ethical climate perceptions focuses mainly on organization characteristics as antecedents, and although other constructs have been considered, these constructs have typically been studied in isolation. Thus, our understanding of the context in which ethical climate perceptions develop is incomplete. To address this limitation, we build upon the work of Rupp to develop and test a multi-experience model of ethical climate which links aspects of the corporate social responsibility, ethics, justice, and trust literatures and (...) helps to explain how employees’ ethical climate perceptions form. We argue that in forming ethical climate perceptions, employees consider the actions or characteristics of a complex web of actors. Specifically, we propose that employees look outward at how communities are impacted by their organization’s actions, upward to make inferences about the ethicality of leaders in their organizations, and inward at their own propensity to trust others as they form their perceptions. Using a multiple-wave field study conducted at a privately held US corporation, we find substantial evidence in support of our model. (shrink)

This chapter contains sections titled: The Problem of Definition Problems of Interpretation Nature and Convention Transcendence Death and the Afterlife Problems of Evil Fatalism and Free Will? Divine Command Theory Piety and Divine Simplicity Works cited.

This essay aims to outline in what ways Kierkegaard’s thinking of existence not only brings into view a concept of existence, but, more fundamentally, enables one to locate an opening to questioning anew the relation of thinking and existence. This thinking of existence does not seek to dissolve existence into knowledge but aims at intensifying the question of a thinking grounded not in the conclusion made in “an external relation between a knower and a non-knower” of which non-knowledge is the (...) negative determination of knowledge, but rather of a thinking grounded in existence. (shrink)

As moral injury is a still-emerging concept within the area of military mental health, prevalence estimates for moral injury and its precursor, potentially morally injurious events (PMIEs), remain unknown for many of the world’s militaries. The present study sought to estimate the prevalence of PMIEs in the Canadian Armed Forces (CAF), using data collected from CAF personnel deployed to Afghanistan, via logistic regressions controlling for relevant sociodemographic, military, and deployment characteristics. Analyses revealed that over 65% of CAF members reported exposure (...) to at least one event that would be considered a PMIE. The most commonly PMIEs individuals reported included seeing ill or injured women and children they were unable to help (48.4%), being unable to distinguish between combatants and non-combatants (43.6%), and finding themselves in a threatening situation where they were unable to respond due to the rules of engagement under which they were required to operate (35.4%). These findings provide support for both the presence of exposure to PMIEs in CAF members and the need for formal longitudinal data collection regarding PMIE exposure and moral injury development. (shrink)

The traditional distinction between basic and applied science has been much criticized in recent decades. The criticism is based on a combination of historical and systematic epistemic argument. The present paper is mostly concerned with the historical aspect. I argue that the critics impose an understanding at odds with the way the distinction was understood by its supporters in debates on science education and science policy in the nineteenth and twentieth centuries. And I show how a distinction that refers to (...) difference on several epistemic and social dimensions makes good sense of representative historical cases. If this argument is tenable it suggests more continuity in the epistemology and politics of science than has been claimed by a new paradigm of science studies and politics during recent decades. (shrink)

In recent decades there has been increasing demand for and considerable efforts to conduct cross-disciplinary research. However, assessment of research quality in such endeavours still is often based on mono-disciplinary criteria and not seldom carried out by reviewers without strong cross-disciplinary experience. The authors suggest a two-pronged approach to cross-disciplinary research evaluation. One part should comprise an individual review of all the disciplines involved based on their mono-disciplinary sets of criteria. The other part should be a separate evaluation of the (...) cross-disciplinary aspects based on the review of “problem formulation”, “integration and scope of the disciplines”, “parts and the whole”, “practical managerial aspects” and “the applied aspects”. The pros and cons of implementing this approach in a stepwise manner or simultaneously is discussed. It is suggested that funding agencies develop more fair sets of review procedures for cross-disciplinary research and show willingness to allocate extra funds and time to such forms of research that sometimes are regarded as relatively more “risky” than conventional mono-disciplinary types. (shrink)

In this essay I will examine the various ways in which the concept of decision emerges in the writings of Kierkegaard focusing mainly on the Philosophical Fragments and the Postscript. This prepares the way for revisiting Kierkegaard’s concept of decision. Doing so indicates the radical way in which Kierkegaard connects the concept of decision to an aporia. The crucial existential concept of decision not only concerns the difficulty, or even the impasse, pertaining to knowledge, but also relates to the question (...) of how the singular finds his or her own way through existence. (shrink)

When faced with the threat of negative reputation spillover from an alliance partner accused of environmental misconduct, the focal firm must decide whether to adopt a supportive or non-supportive response. We argue that this decision denotes a commitment escalation dilemma, but that factors previously found to increase escalation tendencies lead to de-escalation in our crisis contagion context. Specifically, we derive four hypotheses from this reverse effect proposition, and test these using a policy-capturing survey targeting Norwegian CEOs. We found that firms (...) are more likely to select an adversary response when the alliance is of high strategic importance and has high termination costs. Conversely, firms are more likely to select an advocacy response when the alliance is of low strategic importance and has low termination costs and when the CEO was not involved in the formation of the alliance. Overall, our study answers a call for a more nuanced understanding of commitment escalation and the theory’s boundary conditions by introducing reputation spillover crisis as a contextual influencer of escalation behavior. It also extends the reputation literature and provides new evidence that reputation concerns can instigate ethical decision-making. (shrink)

A method of supervaluation for Kripke’s theory of truth is presented. It differs from Kripke’s own method in that it employs trees; results in a compositional semantics; assigns the intuitively correct truth values to the sentences of a particularly tricky example of Gupta’s; and – it is argued – is acceptable as an explication of the correspondence theory of truth.

Judges and jurors must make decisions in an environment of ignoranceand uncertainty for example by hearing statements of possibly unreliable ordishonest witnesses, assessing possibly doubtful or irrelevantevidence, and enduring attempts by the opponents to manipulate thejudge''s and the jurors'' perceptions and feelings. Three importantaspects of decision making in this environment are the quantificationof sufficient proof, the weighing of pieces of evidence, and therelevancy of evidence. This paper proposes a mathematical frameworkfor dealing with the two first aspects, namely the quantification ofproof (...) and weighing of evidence. Our approach is based on subjectivelogic, which is an extension of standard logic and probability theory,in which the notion of probability is extended by including degrees ofuncertainty. Subjective Logic is a framework for modelling humanreasoning and we show how it can be applied to legalreasoning. (shrink)

There is theoretical and empirical evidence that firms’ environmental performance has ramifications for their appeal to various stakeholders. Yet, we know little about how this plays out in the context of strategic alliance formation. Stated differently, research is lacking on how ‘green’ prospective alliance partners are estimated by the initiating firm. This article employs strong environmental reputation as a proxy for high environmental performance and explores implications for the well-established alliance formation trust-based mechanism, under the strategic cognition perspective. The ensuing (...) hypotheses are subjected to empirical scrutiny through an experimental method. A random sample of 138 CEOs and top managers of Norwegian manufacturing firms completed a scenario-based questionnaire. The results show that two out of three trust dimensions are affected and, moreover, that two out of three—but not the same—trust dimensions influence partner attractiveness. Several theoretical and managerial implications, and future research opportunities, are derived from the findings. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 10.1 (2003) 57-62 [Access article in PDF] Listening to People Or Listening to Prozac?Another Consideration of Causal Classifications Jennifer Hansen Keywords causal classification, descriptivism, melancholia, neurasthenia, depression, cultural relativism. The shape and detail of depression have gone through a thousand cartwheels, and the treatment of depression has alternated between the ridiculous and the sublime, but the excessive sleeping, inadequate eating, suicidiality, withdrawal from social (...) interaction, and relentless despair are all as old as the hill tribes, if not as old as the hills. In the years since man achieved the capacity for self-reference, shame has come and gone; treatments for bodily complaints have alternated and crossed with treatments for spiritual ones; pleas to external gods have echoed pleas to internal demons. To understand the history of depression is to understand the invention of human being as we now know and are him. Our Prozac-popping, cognitively focused, semi-alienated postmodernity is only a stage in the ongoing understanding and control of mood and character. (Solomon 2001, 286) ALTHOUGH ANDREW SOLOMON clearly believes that "the shape and detail of depression have gone through a thousand cartwheels," Jennifer Radden gives us pause before assuming that depression is just another name for Dame Melancholy. Solomon's claim depends on a deeper metaphysical claim about the nature of depression and its causes. The current method of psychiatric nosology, descriptivism, does not necessarily support equating melancholia and depression. Furthermore, it appears that adopting descriptivism as the sole method of classifying mental disorders commits us to cultural relativist psychiatry. Below I reconsider whether we want to rule out causal classifications and suggest that embracing both descriptivism and causal classifications offer us greater possibilities in understanding human illness and culture.Although the occasion for Jennifer Radden's essay is to investigate whether or not melancholia and depression refer to the same thing, her essay detours into a consideration of extra-descriptivist models of psychiatric illness versus the descriptivism of current psychiatric nosology. This detour turns out to be warranted; her purely academic question yields to a timelier question concerning the proper methodology for classifying mental disorders. Whereas debates about psychiatric nosology are perennial, the recent success of the new generation of antidepressants [End Page 57] is reviving biological psychiatry and its search for the neurochemical origins of depression. Hence, embedded in Radden's question concerning whether or not melancholia is the same thing as clinical depression, is another important question concerning the causes of mental illness, particularly depression.Currently, with its descriptivist approach, the Diagnostic and Statistical Manual of Mental Disorders (DSM) does not classify mental illness, such as clinical depression, based on underlying causes. The cluster of symptoms and behavioral signs that lead a clinician to diagnose one as depressed that are contained in either the DSM or the International Classification of Diseases (ICD) may be too fuzzy or elusive to give any clear distinction between major depression, mild depression, and the blues. For example, one group of epidemiologists points out that [t]he DSM-III, DSM-III-R, and DSM-IV acknowledge that depression, like many mental disorders, has no currently obvious natural classes... If natural classes of depression exist, then their nosology awaits the discovery of distinct and reliable genetic, biological, clinical, or other predictors of risk, severity, or clinical course. Clinicians have a tradition of separating depressions into subtypes; however, this subtyping has not yet led to clear-cut delineations of syndromes in populations. (Kaelber 1995, 4) The evidence is still insufficient to establish the biological or psychological origins of depression. Although many theories exist that explain why people become depressed, scientifically we are not yet in a position to determine which is the right theory. From a pragmatic perspective, however, whether or not we know what causes depression, we can nonetheless attempt to alleviate suffering from depression. And it is with this goal in mind that the DSM-IV and ICD-10 classify mental disorders.Now, given that our current methodology for psychiatric nosology does not establish causes, it is also insufficient for determining what... (shrink)