In the aftermath of various corporate scandals, management research and practice have taken great interest in ethical leadership. Ethical leadership is referred to as “normatively appropriate conduct” (Brown et al. in Organ Behav Hum Decis Process 97(2):117–134, 2005), but the prescriptive norms that actually underlie this understanding constitute an open question. We address this research gap by turning to relational models theory (Fiske in Structures of social life: the four elementary forms of human relations, Free Press, New York, 1991), which (...) contextualizes four distinct moralities in four distinct interactional norms (i.e., the relational models). We expect that the norms inherent in each model dictate the type of leader relationship that followers deem ethical. Specifically, we hypothesize that, for each norm, followers will perceive leaders as less ethical the more discrepant, i.e., the more incongruent, followers’ ideal relational norm is with the perceived norm that they attribute to their actual leader–follower interaction. We tested the respective incongruence hypothesis in a cross-sectional survey of 101 Dutch employees. Polynomial regression and surface response analyses provide support for the hypothesized incongruence effects in each of the four relational models, suggesting that normatively appropriate conduct should not be limited to caring (i.e., community-oriented) behaviors. Indeed, all four relational models can predict ethical leadership perceptions. We discuss the implications in the context of ethical leadership research and managerial practice. (shrink)

Any account of “what is special about the human brain” (Passingham 2008) must specify the neural basis of our unique ability to produce speech and delineate how these remarkable motor capabilities could have emerged in our hominin ancestors. Clinical data suggest that the basal ganglia provide a platform for the integration of primate-general mechanisms of acoustic communication with the faculty of articulate speech in humans. Furthermore, neurobiological and paleoanthropological data point at a two-stage model of the phylogenetic evolution of this (...) crucial prerequisite of spoken language: (i) monosynaptic refinement of the projections of motor cortex to the brainstem nuclei that steer laryngeal muscles, presumably, as part of a “phylogenetic trend” associated with increasing brain size during hominin evolution; (ii) subsequent vocal-laryngeal elaboration of cortico-basal ganglia circuitries, driven by human-specificFOXP2mutations.;>This concept implies vocal continuity of spoken language evolution at the motor level, elucidating the deep entrenchment of articulate speech into a “nonverbal matrix” (Ingold 1994), which is not accounted for by gestural-origin theories. Moreover, it provides a solution to the question for the adaptive value of the “first word” (Bickerton 2009) since even the earliest and most simple verbal utterances must have increased the versatility of vocal displays afforded by the preceding elaboration of monosynaptic corticobulbar tracts, giving rise to enhanced social cooperation and prestige. At the ontogenetic level, the proposed model assumes age-dependent interactions between the basal ganglia and their cortical targets, similar to vocal learning in some songbirds. In this view, the emergence of articulate speech builds on the “renaissance” of an ancient organizational principle and, hence, may represent an example of “evolutionary tinkering” (Jacob 1977). (shrink)

To describe leadership as ethical is largely a perceptional phenomenon informed by beliefs about what is normatively appropriate. Yet there is a remarkable scarcity in the leadership literature regarding how to define what is "normatively appropriate." To shed light on this issue, we draw upon Relational Models Theory (Fiske, 1992, Psychol Rev, 99:689-723), which differentiates between four types of relationships: communal sharing, authority ranking, equality matching, and market pricing. We describe how each of these relationship models dictates a distinct set (...) of normatively appropriate behaviors. We argue that perceptions of unethical leadership behavior result from one of three situations: (a) a mismatch between leader's and follower's relational models, (b) a different understanding about the behavioral expression, or preos, of the same relational model, or (c) a violation of a previously agreed upon relational model. Further, we argue that the type of relational model mismatch impacts the perceived severity of a transgression. Finally, we discuss the implications of our model with regard to understanding, managing, and regulating ethical leadership failures. (shrink)

IntroductionApproaches to improve heart rate variability and reduce stress such as breathing retraining are more frequently being integrated into psychotherapy but little research on their effectiveness has been done to date. Specifically, no studies to date have directly compared using a breathing pacer at 6 breaths per minute with compassion focused soothing rhythm breathing.Current StudyIn this randomized controlled experiment, 6 breaths per minute breathing using a pacer was compared with compassion focused soothing rhythm breathing, with a nature video being used (...) as a control group condition.MethodsHeart rate variability measures were assessed via electrocardiogram and respiration belt, and an automated blood pressure machine was used to measure systolic diastolic blood pressure, and heart rate. A total of 96 participants were randomized into the three conditions. Following a 5-min baseline, participants engaged in either 6 breath per minute breathing, soothing rhythm breathing, or watched a nature video for 10 min. To induce a stressful state, participants then wrote for 5 min about a time they felt intensely self-critical. Participants then wrote for 5 min about a time they felt self-compassionate, and the experiment ended with a 10-min recovery period.ResultsConditions did not significantly differ at baseline. Overall, HRV, as measured by standard deviation of NN intervals, low frequency HRV, and LF/HF ratio, increased during the intervention period, decreased during self-critical writing, and then returned to baseline levels during the recovery period. High frequency HRV was not impacted by any of the interventions. The participants in the 6 breath per minute pacer condition were unable to consistently breathe at that rate and averaged about 12 breaths per minute. Time by Condition analyses revealed that both the 6 breaths per minute pacer and soothing breathing rhythm conditions lead to significantly higher SDNN than the nature video condition during breathing practice but there were no significant differences between conditions in response to the self-critical and self-compassionate writing or recovery periods. The 6 breath per minute pacer condition demonstrated a higher LF HRV and LF/HF ratio than the soothing rhythm breathing condition, and both intervention conditions had a higher LF HRV and LF/HF ratio than the nature video.ConclusionsAlthough the 6 breath per minute pacer condition participants were not able to breath consistently at the low pace, both the participants attempting to breathe at 6 breaths per minute as well as those in the soothing rhythm breathing condition effectively increased HR variability as measured by SDNN, and attempting to breathe at 6 breaths per minute led to the highest LF HRV and LF/HF ratio. Both breathing approaches impacted HRV more than watching a relaxing nature video and can potentially be used as key adjuncts in psychotherapy to aid in regulating physiological functioning, although it appears that consistent breathing practice would be needed. (shrink)

We construct the set of the title, answering a question of Cholak, Jockusch, and Slaman [1], and discuss its connections with the study of the proof-theoretic strength and effective content of versions of Ramsey's Theorem. In particular, our result implies that every ω-model of RCA 0 + SRT 2 2 must contain a nonlow set.

Understanding terrestrial carbon metabolism is critical because terrestrial ecosystems play a major role in the global carbon cycle. Furthermore, humans have severely disrupted the carbon cycle in ways that will alter the climate system and directly affect terrestrial metabolism. Changes in terrestrial metabolism may well be as important an indicator of global change as the changing temperature signal. Improving our understanding of the carbon cycle at various spatial and temporal scales will require the integration of multiple, complementary and independent methods (...) that are used by different research communities. Tools such as air sampling networks, inverse numerical methods, and satellite data allow us to study the strength and location of the global- and continental-scale carbon sources and sinks. Bottom-up studies provide estimates of carbon fluxes at finer spatial scales and examine the mechanisms that control fluxes at the ecosystem, landscape, and regional scales. Bottom-up approaches include comparative and process studies that provide the necessary mechanistic information to develop and validate terrestrial biospheric models. An iteration and reiteration of top-down and bottom-up approaches will be necessary to help constrain measurements at various scales. We propose a major international effort to coordinate and lead research programs of global scope of the carbon cycle. (shrink)

Successful surgical treatment of patients with focal drug-resistant epilepsy remains challenging, especially in cases for which it is difficult to define the area of cortex from which seizures originate, the seizure onset zone. Various diagnostic methods are needed to select surgical candidates and determine the extent of resection. Interictal magnetoencephalography with source imaging has proven to be useful for presurgical evaluation, but the use of ictal MEG data remains limited. The purpose of the present study was to determine whether pre-ictal (...) variations of spectral properties of neural activity from ictal MEG recordings are predictive of SOZ location.We performed a 4 h overnight MEG recording in an 8-year-old child with drug-resistant focal epilepsy of suspected right fronto-temporal origin and captured one ~45-s seizure. The patient underwent a right temporal resection from the anterior temporal neocortex and amygdala to the mid-posterior temporal neocortex, sparing the hippocampus proper. She remains seizure-free 21 months postoperatively. The histopathological assessment confirmed frank focal cortical dysplasia type IIa in the MEG-defined SOZ, which was based on source imaging of averaged ictal spikes at seizure onset. We investigated temporal changes together with spatial differences in spectral parameters of background brain activity, namely the aperiodic broadband offset and slope, and assessed how they confounded the interpretation of apparent variations of signal power in typical electrophysiological bands. Our data show that the SOZ was associated with a higher aperiodic offset and exponent during the seizure compared to control regions. Both parameters increased in all regions from 2 min before the seizure onwards. Regions anatomically closer to the SOZ also expressed higher values compared to contralateral regions, potentially indicating ictal spread. We also show that narrow-band power changes were caused by these fluctuations in the aperiodic component of ongoing brain activity. Our results indicate that the broadband aperiodic component of ongoing brain activity cannot be reduced to background noise of no physiological interest, and rather may be indicative of the neuropathophysiology of the SOZ. We believe these findings will inspire future studies of ictal MEG cases and confirm their significance. (shrink)

There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...) Then S3 proves to be the smallest Lewis modal system where PI can be defined as SE. We extend S3 to a non-Fregean logic with propositional quantifiers such that necessity and PI are integrated as non-interdefinable concepts. CA is not valid and PI refines SE. Models are expansions of SCI-models. We show that SCI-models are Boolean prealgebras, and vice-versa. This associates non-Fregean logic with research on Hyperintensional Semantics. PI equals SE iff models are Boolean algebras and CA holds. A representation result establishes a connection to Fine’s approach to propositional quantifiers and shows that our theories are conservative extensions of S3–S5, respectively. If we exclude the Barcan formula and a related axiom, then the resulting systems are still complete w.r.t. a simpler denotational semantics. (shrink)

We show that the Π 4 -theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.

We show that the $\Pi_4$-theory of the partial order of recursively enumerable weak truth-table degrees is undecidable, and give a new proof of the similar fact for r.e. T-degrees. This is accomplished by introducing a new coding scheme which consists in defining the class of finite bipartite graphs with parameters.

We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).

We show the decidability of the existential theory of the recursively enumerable degrees in the language of Turing reducibility, Turing reducibility of the Turing jumps, and least and greatest element.

R. Suszko’s Sentential Calculus with Identity \( SCI \) results from classical propositional calculus \( CPC \) by adding a new connective \(\equiv \) and axioms for identity \(\varphi \equiv \psi \) (which we interpret here as ‘propositional identity’). We reformulate the original semantics of \( SCI \) using Boolean prealgebras which, introduced in different ways, are known in the literature as structures for the modeling of (hyper-) intensional semantics. We regard intensionality here as a measure for the discernibility of (...) propositions (and hyperintensionality as a high degree of intensionality). As concrete examples of \( SCI \) -based intensional modeling, we review and study algebraic semantics of some Lewis-style modal logics in the vicinity of \( S3 \) and present conditions under which those modal systems can be restored, in a precise sense, as certain axiomatic extensions of \( SCI \). This generalizes work of Suszko which is focused on the modal systems \( S4 \) and \( S5 \). Our approach is particularly intended as a proposal to consider and to further study \( SCI \) (and its extensions) as a general framework for the modeling of (hyper-) intensional semantics. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

An r.e. degree a ≠ 0, 0' is called strongly noncappable if it has no inf with any incomparable r.e. degree. We show the existence of a high strongly noncappable degree.

We show that the top of any diamond with bottom 0 in the r.e. degrees is also the top of a stack of n diamonds with bottom 0.

It has been argued that philosophers that base their theories of meaning on communicative intentions and language conventions cannot accommodate the fact that natural languages are compositional. In this paper I show that if we pay careful attention to Grice’s notion of “resultant procedures” we see that this is not the case. The argument, if we leave out all the technicalities, is fairly simple. Resultant procedures tell you how to combine utterance parts, like words, into larger units, like sentences. You (...) cannot have that unless you have R-correlations (reference) and Dcorrelations (denotation). These in turn, the argument goes, depend on communicative intentions, since without communicative intentions any attempt to R-correlate or D-correlate a word with an object or sets of objects would inevitably result in correlation-relations between that word and everything that exists. In other words, without communicative intentions in the equation it would turn out that every time we speak, we inevitably speak about everything, but clearly we do not. So communicative intentions, instead of being nebulous things that are in possible conflict with the Principle of Compositionality, are in fact a prerequisite for that very principle. (shrink)

It has been argued that philosophers that base their theories of meaning on communicative intentions and language conventions cannot accommodate the fact that natural languages are compositional. In this paper I show that if we pay careful attention to Grice's notion of “resultant procedures” we see that this is not the case. The argument, if we leave out all the technicalities, is fairly simple. Resultant procedures tell you how to combine utterance parts, like words, into larger units, like sentences. You (...) cannot have that unless you have R-correlations (reference) and D-correlations (denotation). These in turn, the argument goes, depend on communicative intentions, since without communicative intentions any attempt to R-correlate or D-correlate a word with an object or sets of objects would inevitably result in correlation-relations between that word and everything that exists. In other words, without communicative intentions in the equation it would turn out that every time we speak, we inevitably speak about everything, but clearly we do not. So communicative intentions, instead of being nebulous things that are in possible conflict with the Principle of Compositionality, are in fact a prerequisite for that very principle. (shrink)

According to Paul Grice, when we address someone, we intend to make ourselves understood, partly by the addressee’s recognition of that intention. Call this set of nested audience-directed intentions an M-intention. The standard Gricean analysis of speaker’s meaning goes as follows: “U meant something by uttering x” is true iff, for some audience A, U uttered x intending: (1) A to produce a particular response r (2) A to think (recognize) that U intends (1) (3) A to fulfill (1) on (...) the basis of his fulfillment of (2). (Grice 1969, p. 92) Call this analysis the M-schema, and to fulfill it, to M-intend. In the Gricean tradition there has been a debate as to the exact form of Mintentions (especially whether clause (3) is needed or should be left out of the analysis), but these are details that I will not address here. The phenomenon of talking to infants challenges the Gricean analysis of addressing others. We talk to infants, but such cases cannot be described as M-intending anything, since the speaker must realize that he will not be able to make himself understood in the required manner. The Gricean mechanism lacks an appropriate addressee. Some Griceans have argued that in cases of no appropriate addressee, the speaker is actually addressing himself (Schiffer 1972, p. 80; Avramides 1989, p. 66). This response might be tempting for soliloquy, but I will show that it is unsuited for the phenomenon of talking to infants. (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)

By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.

Poniższa praca odnosi się głównie do tezy Huberta Orłowskiego, według której „niemiecka dyskusja o Polsce miała legitymujące, nic do pominięcia znaczenie dla wynalezienia niemieckiego narodu”. Wobec rozmiarów i rozdrobnienia społeczno-wyznaniowego Rzeszy Niemieckiej ok. 1700 r. temat ten ograniczony jest do Prus Zachodnich i głównego problemu debaty o przyczynach funkcjonowania powstałego obrazu Polski. Koncentracja na Prusach Zachodnich wynika z modalnego charakteru, jaki musiał mieć „problem Polski” jako odzwierciedlenie procesów tworzenia się granic na danym obszarze, którego niemiecki rejon kulturalny miał polską przynależność (...) państwową. Przedstawia się tu sposób, w jaki nowa, w dyskusyjnych ramach europejskiego wczesnego Oświecenia powstająca świadomość wnosiła stopniowy odwrót od rozpadającej się polskiej Republiki Szlacheckiej, a tym samym konieczność poszukiwania nowej władzy ochronnej. Wynikała z tego pewna opcja narodowa, która następnie zmieniła regionalnie obraz Polski. Ta trafnie podkreślana przez Orłowskiego konccplualizacja obrazu Polski służyła do przekształcenia stanowo uformowanej boruskiej świadomości regionalnej w nowożytną skupioną na Prusach świadomość państwową. Punktem wyjścia poniższych rozważań jest spór o to, czy forma państwa polskiej Republiki Szlacheckiej w drugiej połowie XVII w. mogła jeszcze być wystarczającą dla ekonomicznych i politycznych potrzeb mieszczaństwa. Rozważania te wskazują zarówno z obcej jak też z własnej perspektywy na ten w tamtym okresie z mieszczańskiego punktu widzenia mało atrakcyjny obraz Polski. Obcy znaczy tu jednak nie tyle trochę specyficzny „polski”, ile nie do zaakceptowania jako patriotyczny i nierozsądny ekonomicznie dla mieszczanina sposób postępowania polskiego szlachcica. W tymże sensie informuje zrekonstruowana tu debata o wczesnym mieszczańskim obrazie Polski. Przedstawia ona jednocześnie, w jak wielkim stopniu konstruowany był portret własny mieszczaństwa w kulturalnie niemiecko ukształtowanych miastach Polski, według etosu protestanckiego w przeciwieństwie do katolickiej szlachty polskiej. Rozwijający się z tego późny pruski obraz Polski jest następnie podejmowany jako kompleks dalej działających i umacniających się uprzedzeń, które powstają na początku XVIII w. i oddzielają się stopniowo od ich prawdziwych kulis. Jako stereotyp ma to więc swoje korzenie w przeciwieństwie mieszczańsko-boruskich i polskich, skierowanych na konstelacje władzy w Republice Szlacheckiej interesów i poczynań. Teza ta uwidacznia też, że nie chodziło tylko o opis stereotypowej struktury dziś rozprzestrzenionych opinii o Polsce. Dużo większe zainteresowanie skierowane zostało na „ziarenko prawdy”, które, z historycznego punktu widzenia, zawarte jest w każdym stereotypie. (shrink)

Musik ist eine Herausforderung für die Philosophie - die von dieser oft nicht angenommen wurde. In den letzten Jahrzehnten hat sich jedoch die Musikphilosophie im deutschsprachigen Raum als ein zunehmend dynamisches interdisziplinäres Feld zwischen Philosophie, Ästhetik und Kunsttheorie, Musikwissenschaft, Musiktheorie und musikalischer Praxis entwickelt. Die Beiträge dieses Bandes, u. a. von Daniel Martin Feige, Gunnar Hindrichs, Richard Klein, Cosima Linke und Matthias Vogel, ziehen erstmals ein Fazit und beleuchten die Perspektiven des mittlerweile ausdifferenzierten Diskurses über diese scheinbar unmittelbarste und zugleich (...) begrifflich am schwersten fassbare künstlerische Ausdrucksform. (shrink)

By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.

Diese unter der Leitung der Proff. Dres. Theophanopúlu-Kontú, Magulás und Charalampákés angefertigte, fleißige und umsichtige Diss. einer Gymnasiallehrerin, die sich dafür vier Jahre unbezahlten Urlaub genommen hatte, ist – nach zwei alten Arbeiten Maidhofs (1920 und 1931) – die erste systematische Behandlung der Rückwanderer im neugriechischen Wortschatz (im Folg.: RW). Die Verfasserin (Verf.) hat sich bestens in die internationale Literatur zu den aus einer Sprache A stammenden, in eine oder mehrere andere Sprachen (B, evtl. C usw.) entlehnten und schließlich in (...) ein jüngeres Stadium von A zurückentlehnten Wörter eingearbeitet: Ihre Literaturliste (S. 265–273) umfasst nicht weniger als 146 griech., engl., französ., italien., deutsche und türk. Titel. Das Thema ist für das Gesamtgriechische von besonderem Interesse, da während seiner so besonders langen und gut dokumentierten Existenz naturgemäß eine erkleckliche Zahl von Lexemen zurückgewandert sind, offensichtlich mehr als in jede andere Sprache Europas. So hat denn die Verf. nach eigener Angabe 170, realiter ca. 200 solche RW zusammengestellt und deren Geschichte meist ausführlich und überzeugend dokumentiert und damit ein Kapitel neugriechischer Etymologie geschrieben. Sinnvollerweise hat sie dabei auf eine Behandlung der immer uferloser werdenden gräkogenen Internationalismen in Technik und Wissenschaften verzichtet und sich auf das Alltagsvokabular beschränkt. Dass jedoch auch eine erste derartige Sammlung nicht annähernd vollständig sein wird, liegt auf der Hand; so ergänzt der Rezensent (im Folg.: R.) ohne langes Suchen folgende Fälle neuzeitlicher RW (nach Sprachen, aus denen sie zurückgekommen sind; vermittelnde Sprachen, etwa Latein, werden hierbei gewöhnlich weggelassen). (shrink)

Answering a question of Per Lindström, we show that there is no “plus-capping” degree, i.e. that for any incomplete r.e. degreew, there is an incomplete r.e. degreea>w such that there is no r.e. degreev>w witha∩v=w.

We give a decision procedure for the ∀∃-theory of the weak truth-table (wtt) degrees of the recursively enumerable sets. The key to this decision procedure is a characterization of the finite lattices which can be embedded into the r.e. wtt-degrees by a map which preserves the least and greatest elements: a finite lattice has such an embedding if and only if it is distributive and the ideal generated by its cappable elements and the filter generated by its cuppable elements are (...) disjoint. We formulate general criteria that allow one to conclude that a distributive upper semi-lattice has a decidable two-quantifier theory. These criteria are applied not only to the weak truth-table degrees of the recursively enumerable sets but also to various substructures of the polynomial many-one (pm) degrees of the recursive sets. These applications to the pm degrees require no new complexity-theoretic results. The fact that the pm-degrees of the recursive sets have a decidable two-quantifier theory answers a question raised by Shore and Slaman in [21]. (shrink)

Combinatorial operations on sets are almost never well defined on Turing degrees, a fact so obvious that counterexamples are worth exhibiting. The case we focus on is the symmetric-difference operator; there are pairs of degrees for which the symmetric-difference operation is well defined. Some examples can be extracted from the literature, e.g. from the existence of nonzero degrees with strong minimal covers. We focus on the case of incomparable r.e. degrees for which the symmetric-difference operation is well defined.

We show that for every nontrivial r.e. wtt-degree a, there are r.e. wtt-degrees b and c incomparable to a such that the infimum of a and b exists but the infimum of a and c fails to exist. This shows in particular that there are no strongly noncappable r.e. wtt-degrees, in contrast to the situation in the r.e. Turing degrees.

This paper considers reductions between types of numberings; these reductions preserve the Rogers Semilattice of the numberings reduced and also preserve the number of minimal and positive degrees in their semilattice. It is shown how to use these reductions to simplify some constructions of specific semilattices. Furthermore, it is shown that for the basic types of numberings, one can reduce the left-r.e. numberings to the r.e. numberings and the k-r.e. numberings to the k+1-r.e. numberings; all further reductions are obtained by (...) concatenating these reductions. (shrink)

Apologists for Christianity and Judaism have argued that their religions do not support an exploitative attitude towards the environment. L.H. Steffen, in particular, argues that it is the Hellenic rather than the (Judaeo-Christian tradition which promotes the instrumentalist view of nature. In contrast, I argue that Christianity is and has been an amalgam of the Hellenic and Hebrew traditions. In the course of this paper I indicate certain salient Hellenic influences which were prominent in medieval Christianity. I subsequently point (...) out that, contrary to Steffen's allegations, these influences originally contributed to a non-exploitative attitude to the natural world by the very nature of their anti-materialist prescriptions. However, with the Renaissance and the Reformation, religious attitudes shifted and a new religious morality was generated, one which associated morality and spiritual achievement with intense engagement in the material world and the exploitation of this world in the end of personal prosperity. In part I demonstrate this alteration in perspective by reference to the shifting religious attitudes towards ownership and property. (shrink)

Bayesian approaches for estimating multilevel latent variable models can be beneficial in small samples. Prior distributions can be used to overcome small sample problems, for example, when priors that increase the accuracy of estimation are chosen. This article discusses two different but not mutually exclusive approaches for specifying priors. Both approaches aim at stabilizing estimators in such a way that the Mean Squared Error of the estimator of the between-group slope will be small. In the first approach, the MSE is (...) decreased by specifying a slightly informative prior for the group-level variance of the predictor variable, whereas in the second approach, the decrease is achieved directly by using a slightly informative prior for the slope. Mathematical and graphical inspections suggest that both approaches can be effective for reducing the MSE in small samples, thus rendering them attractive in these situations. The article also discusses how these approaches can be implemented in Mplus. (shrink)

For the living, death has a moral dimension. When we confront death and dying in our own lives and in the lives of others, we ask questions about the good, right, and fitting as they relate to our experiences of human mortality. When others die, the living are left with moral questions--questions that often generate personal inquiry as to whether a particular death was "good" or whether it was tragic, terrifying, or peaceful. In The Ethics of Death, the authors, one (...) a philosopher and one a religious studies scholar, undertake an examination of the deaths that we experience as members of a larger moral community. Their respectful and engaging dialogue highlights the complex and challenging issues that surround many deaths in our modern world and helps readers frame thoughtful responses. Unafraid of difficult topics, Steffen and Cooley fully engage suicide, physician-assisted suicide, euthanasia, capital punishment, abortion, and war as areas of life where death poses moral challenges." -- Publisher's description. (shrink)