Aquinas’ natural law theory contains a set of basic goods, such as survival, reproduction and the pursuit of truth. However, whether and how there is a hierarchical relationship among these goods remains disputed. Given the importance of Aquinas’ natural law theory for Christianity and the philosophy of law, this issue merits a closer investigation. By carefully examining various modern scholars’ theories and Aquinas’ texts, it is demonstrated that according to Aquinas, firstly, there are hierarchies of basic goods and sins; secondly, (...) these hierarchies are horizontal and vertical according to the order of participation and the dignity of substances, respectively.Contribution: This research reconsiders the modern debate over Aquinas’ hierarchical theory of basic goods and provides a more authentic understanding of Aquinas’ own view, which can be applied to his theory of sin. Aquinas’ natural law theory can hence be clarified in a more profound way. (shrink)

The ubiquity of top-down causal explanations within and across the sciences is prima facie evidence for the existence of top-down causation. Much debate has been focused on whether top-down causation is coherent or in conflict with reductionism. Less attention has been given to the question of whether these representations of hierarchical relations pick out a single, common hierarchy. A negative answer to this question undermines a commonplace view that the world is divided into stratified ‘levels’ of organization and suggests (...) that attributions of causal responsibility in different hierarchical representations may not have a meaningful basis for comparison. Representations used in top-down and bottom-up explanations are primarily ‘local’ and tied to distinct domains of science, illustrated here by protein structure and folding. This locality suggests that no single metaphysical account of hierarchy for causal relations to obtain within emerges from the epistemology of scientific explanation. Instead, a pluralist perspective is recommended—many different kinds of top-down causation (explanation) can exist alongside many different kinds of bottom-up causation (explanation). Pluralism makes plausible why different senses of top-down causation can be coherent and not in conflict with reductionism, thereby illustrating a productive interface between philosophical analysis and scientific inquiry. (shrink)

We establish some results on the Borel and difference hierarchies in φ-spaces. Such spaces are the topological counterpart of the algebraic directed-complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non-collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question (...) of characterizing the ω-ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (shrink)

Intersectional feminist scholars emphasize how overlapping systems of oppression structure gender inequality, but in focusing on the gendered, classed, and racialized bases of stratification, many often overlook disability as an important social category in determining economic outcomes. This is a significant omission given that disability severely limits opportunities and contributes to cumulative disadvantage. We draw from feminist disability and intersectional theories to account for how disability intersects with gender, race, and education to produce economic insecurity. The findings from our analyses (...) of 2015 American Community Survey data provide strong empirical support for hierarchies of disadvantage, where women and racial minority groups with disabilities and less education experience the highest poverty levels, report the lowest total income, and have a greater reliance on sources outside the labor market for economic security. By taking disability into account, our study demonstrates how these multiple characteristics lead to overlapping oppressions that become embedded and reproduced within the larger social structure. (shrink)

A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.

A previous work by Friedman et al. (Theory and Decision, 61:305–318, 2006) introduces the concept of a hierarchy of a simple voting game and characterizes which hierarchies, induced by the desirability relation, are achievable in linear games. In this paper, we consider the problem of determining all hierarchies, conserving the ordinal equivalence between the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices, achievable in simple games. It is proved that only four hierarchies are non-achievable in simple games. Moreover, it is also (...) proved that all achievable hierarchies are already obtainable in the class of weakly linear games. Our results prove that given an arbitrary complete pre-ordering defined on a finite set with more than five elements, it is possible to construct a simple game such that the pre-ordering induced by the Shapley–Shubik and the Penrose–Banzhaf–Coleman power indices coincides with the given pre-ordering. (shrink)

People have three cognitive representations of the self, namely, the individual, relational, and collective selves, which are indispensable components of selfhood but not necessarily given equal preference. Previous studies found that people displayed varied self-hierarchy in miscellaneous tasks involving different research materials that had pre-existing learned associations established over long periods of time. Therefore, this study tries to explore a purer self-hierarchy without the influence of research materials, using perceptual matching tasks. The behavioral and event-related potentials’ findings showed (...) that people recognized information association with their individual self faster compared with their relational and CS. Smaller N2, stronger P3 and late positive complex amplitudes were evoked during IS compared with RS and CS. However, the three selves evoked equal P2 amplitudes at the early processing stage. Moreover, CS showed a weaker advantage than RS, demonstrating a longer reaction time, lower d prime, and weaker P3 and LPC amplitudes in the parietal region. Overall, self-hierarchy during simple perceptual processing manifested as IS > RS > CS at the late processing stage but manifested as IS = RS = CS at the early processing stage. Self-hierarchy varies according to the processing stage, even without meaningful information and during the simple perception processing. This result provides direct evidence that all selves can be tagged with neutral actions, which would fit the idea of an organism attuned to self-survival at multiple processing levels. (shrink)

The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity type t there is a generalized quantifier of type t which is not definable in the extension of first order logic by all generalized quantifiers of type smaller than t. This was proved for unary similarity types by Per Lindström [17] with (...) a counting argument. We extend his method to arbitrary similarity types. (shrink)

This article describes how ethical issues in health are approached and resolved within the framework of Jewish bioethics. Its main purpose is to explore the range of sources and methodologies used to determine the appropriate hierarchy of values for various ethical scenarios. Its major thrust is to illustrate how a divinely based but humanly negotiated ethical code stands firm upon ‘red flag’ principles, while at the same time, allowing for ‘shades of gray’ flexibility informed by given contexts. It provides (...) significant insights and practical tools that can be instrumental in decision making for nurses and other health providers of all faiths. The following ethical domains are addressed: respect for patient autonomy, truth-telling and allocation of resources. (shrink)

The concept of a generalized quantifier of a given similarity type was defined in [12]. Our main result says that on finite structures different similarity types give rise to different classes of generalized quantifiers. More exactly, for every similarity typetthere is a generalized quantifier of typetwhich is not definable in the extension of first order logic by all generalized quantifiers of type smaller thant. This was proved for unary similarity types by Per Lindström [17] with a counting argument. We extend (...) his method to arbitrary similarity types. (shrink)

The question of whether the modern evolutionary synthesis requires an extension has recently become a topic of discussion, and a source of controversy. We suggest that this debate is, for the most part, not about the modern synthesis at all. Rather, it is about the extent to which genetic mechanisms can be regarded as the primary determinants of phenotypic characters. The modern synthesis has been associated with the idea that phenotypes are the result of gene products, while supporters of the (...) extended synthesis have suggested that environmental factors, along with processes such as epigenetic inheritance, and niche construction play an important role in character formation. We argue that the methodology of the modern evolutionary synthesis has been enormously successful, but does not provide an accurate characterization of the origin of phenotypes. For its part, the extended synthesis has yet to be transformed into a testable theory, and accordingly, has yielded few results. We conclude by suggesting that the origin of phenotypes can only be understood by integrating findings from all levels of the organismal hierarchy. In most cases, parts and processes from a single level fail to accurately explain the presence of a given phenotypic trait. The debate between the proponents of the modern and extended syntheses is somewhat reminiscent of the duck-rabbit illusion. The two sides are probably talking about the same thing, but from different perspectives. If not, then we argue that the challenge is to do an experiment that rules out the alternative view. (shrink)

At the turn of the last century, paleontologists wagered that they could find the missing link between lobe-finned fish and early terrestrial vertebrates. Given how these evolutionary relatives are distributed in the fossil record, Daeschler et al. predicted that some transitional form awaited discovery in late Devonian outcrops of the Canadian Arctic. It was there that they won their bet: the team soon found Tiktaalik roseae, a “fishopod” with a mix of aquatic and terrestrial traits. Tiktaalik’s discovery now stands as (...) paleontologists’ textbook case of scientific reasoning done right. (shrink)

Some philosophers of fiction – most famously Jerold Levinson1 - have tried to argue that fictional narrators can never be identified with real authors. This argument relies on the claim that narration involves genuine assertion (not just the pretense of assertion that lacks truthfulness) and that real authors are not in a position to assert anything about beings on the fictional plain - given that they don’t rationally believe in their existence. This debate on the status of narrators depends on (...) the idea that fictional beings and beings in the real worlds reside, as it were, at different levels. The assumption that there is a gap separating the levels of fiction and reality serves as a rationale for the claim that real authors could not possibly be en rapport with the fictional characters that they create (e.g. entertain beliefs about them, etc.). (shrink)

We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier $\sf Q$ in ${\rm FO}({\vec Q}_k)$ , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two ${\rm FO}({\vec Q}_1)$ -equivalent models with certain additional structure, yields a pair of ${\rm FO}({\vec Q}_k)$ -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity and (...) planarity. (shrink)

During the last few years, several sociological accounts of scientific consensus appeared in which a radically skeptical view of cognitive consensus in science was advocated. Challenging the traditional realist conception of scientific consensus as a sui generis social fact, the radical skeptics claim to have shown that the traditional historical sociologist's supposedly definitive account of scientific consensus is only a linguistic chimera that easily can be deconstructed by the application of different interpretive schema to the given data. I will argue (...) in this article that such an idealistic conception of scientific consensus results from the radical skeptics' failure to take into account the following three factors that are central to the historical sociologist's narrative account of consensus formation: the "judgmental" character of the reconstruction of scientists' beliefs, the hierarchical nature of the consensus change in science, and the importance of the "temporal dimension" in the explanation of scientific consensus formation. To substantiate these three points, I will draw extensively on two recent historical-sociological studies of scientific consensus formation. (shrink)

We show that there is a model of ZF in which the Borel hierarchy on the reals has length ω2. This implies that ω1 has countable cofinality, so the axiom of choice fails very badly in our model. A similar argument produces models of ZF in which the Borel hierarchy has exactly λ + 1 levels for any given limit ordinal λ less than ω2. We also show that assuming a large cardinal hypothesis there are models of ZF (...) in which the Borel hierarchy is arbitrarily long. (shrink)

It would seem that we in the West are suffering from an increasing glut of rights. To the sixty-odd human rights that the Universal Declaration and its Covenants have long given us, must now be added the particular rights claims of an increasing number of ‘oppressed’ minorities, claims to compensation rights for just about every conceivable harm done and claims to ever more trivial things. This tendency is harmful insofar as it trivialises rights and devalues the coverage of rights. Human (...) rights are fundamental and ought to be protected from these tendencies. Using an analysis of the foundations of human rights, and their function in maintaining autonomy in particular, this article analyses the content of rights – what must be fulfilled in order for a right to be protected – as a means of demonstrating the possibility of reducing the volume of rights without reducing rights coverage and of creating a defensible hierarchy. (shrink)

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e., sequent) isomorphisms corresponding to the high‐school identities, we show that one can obtain a more compact variant of a proof system, consisting of non‐invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalization procedure. Moreover, for (...) certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non‐invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first‐order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism. (shrink)

Cause and effect relationships play a central role in how we perceive and make sense of the world around us, how we act upon it, and ultimately, how we understand ourselves. Almost two decades ago, computer scientist Judea Pearl made a breakthrough in understanding causality by discovering and systematically studying the “Ladder of Causation” [Pearl and Mackenzie 2018], a framework that highlights the distinct roles of seeing, doing, and imagining. In honor of this landmark discovery, we name this the Pearl (...) Causal Hierarchy (PCH). In this chapter, we develop a novel and comprehensive treatment of the PCH through two complementary lenses, one logical-probabilistic and another inferential-graphical. Following Pearl’s own presentation of the hierarchy, we begin by showing how the PCH organically emerges from a well-specified collection of causal mechanisms (a structural causal model, or SCM). We then turn to the logical lens. Our first result, the Causal Hierarchy Theorem (CHT), demonstrates that the three layers of the hierarchy almost always separate in a measure theoretic sense. Roughly speaking, the CHT says that data at one layer virtually always underdetermines information at higher layers. Since in most practical settings the scientist does not have access to the precise form of the underlying causal mechanisms – only to data generated by them with respect to some of PCH’s layers – this motivates us to study inferences within the PCH through the graphical lens. Specifically, we explore a set of methods known as causal inference that enable inferences bridging PCH’s layers given a partial specification of the SCM. For instance, one may want to infer what would happen had an intervention been performed in the environment (second-layer statement) when only passive observations (first-layer data) are available. We introduce a family of graphical models that allows the scientist to represent such a partial specification of the SCM in a cognitively meaningful and parsimonious way. Finally, we investigate an inferential system known as docalculus, showing how it can be sufficient, and in many cases necessary, to allow inferences across PCH’s layers. We believe that connecting with the essential dimensions of human experience as delineated by the PCH is a critical step towards creating the next generation of AI systems that will be safe, robust, human-compatible, and aligned with the social good. (shrink)

The use of Extended Logics to replace ordinary second order definability in Kleene’s Ramified Analytical Hierarchy is investigated. This mirrors a similar investigation of Kennedy, Magidor and Väänänen [11] where Gödel’s universe L of constructible sets is subjected to similar variance. Enhancing second order definability allows models to be defined which may or may not coincide with the original Kleene hierarchy in domain. Extending the logic with game quantifiers, and assuming strong axioms of infinity, we obtain minimal correct (...) models of analysis. A wide spectrum of models can be so generated from abstract definability notions: one may take an abstract Spector Class and extract an extended logic for it. The resultant structure is then a minimal model of the given kind of definability. (shrink)

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using (...) analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning. (shrink)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different (...) inferential level. Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)

International human rights concepts and documents figure prominently within theories of global justice. Appeals to human rights often rely on theories and interpretations that rank human rights in relation to one another designating some as more important or more crucial than others such that they may or must be given priority. In this paper I argue that hierarchical ranking of human rights should be rejected by theorists of global justice because such ranking: (a) undermines the effectiveness with which human rights (...) operate as principled constraints on state actors; and (b) is inconsistent with the international legal framework and practice from which the human rights concepts and documents draw their rhetorical force. Instead theorists of global justice should accept the indivisibility principle, which states that all human rights are interrelated and interdependent and must be treated on the same footing and given the same emphasis. The attraction of hierarchical ordering rests on misguided concerns about the practicality of indivisibility that fail to properly distinguish between rights and claims and ignore important dimensions of human rights implementation and assessment. I argue that indivisibility is both pragmatically defensible, provides a better theoretical grounding for understanding complaints about violations, and offers a better framework for understanding the relationship between human rights and legitimacy than hierarchical ordering. (shrink)

We study large cardinal properties associated with Ramseyness in which homogeneous sets are demanded to satisfy various transfinite degrees of indescribability. Sharpe and Welch [25], and independently Bagaria [1], extended the notion of $\Pi ^1_n$ -indescribability where $n<\omega $ to that of $\Pi ^1_\xi $ -indescribability where $\xi \geq \omega $. By iterating Feng’s Ramsey operator [12] on the various $\Pi ^1_\xi $ -indescribability ideals, we obtain new large cardinal hierarchies and corresponding nonlinear increasing hierarchies of normal ideals. We provide (...) a complete account of the containment relationships between the resulting ideals and show that the corresponding large cardinal properties yield a strict linear refinement of Feng’s original Ramsey hierarchy. We isolate Ramsey properties which provide strictly increasing hierarchies between Feng’s $\Pi _\alpha $ -Ramsey and $\Pi _{\alpha +1}$ -Ramsey cardinals for all odd $\alpha <\omega $ and for all $\omega \leq \alpha <\kappa $. We also show that, given any ordinals $\beta _0,\beta _1<\kappa $ the increasing chains of ideals obtained by iterating the Ramsey operator on the $\Pi ^1_{\beta _0}$ -indescribability ideal and the $\Pi ^1_{\beta _1}$ -indescribability ideal respectively, are eventually equal; moreover, we identify the least degree of Ramseyness at which this equality occurs. As an application of our results we show that one can characterize our new large cardinal notions and the corresponding ideals in terms of generic elementary embeddings; as a special case this yields generic embedding characterizations of $\Pi ^1_\xi $ -indescribability and Ramseyness. (shrink)

Hierarchical views of nature have for centuries been used to justify the enslaving of peoples perceived as inferior, the often violent and coercive “reeducation” of indigenous peoples, the patriarchal subjugation of women, the cruel use of nonhuman animals for often trivial purposes, and the wanton destruction of the natural world. I join those who condemned the oppressive nature of these forms of hierarchical thinking. Yet, I fear that, in their effort to right past wrongs, too many thinkers are in danger (...) of throwing the axiological baby out with the ontological bathwater. Though the aim at a great ontological leveling is certainly understandable, I fear that, in embracing the opposite extreme and rejecting all hierarchical thinking, some may be in danger of doing violence to the many real and even morally significant differences between individuals. My claim in this paper is that Alfred North Whitehead’s philosophy of organism provides a model for how to appreciate the many grades and types of beings in the world, while avoiding an invidious normative hierarchy that inevitably places everything at the whim of human beings. That is, I will argue that it is possible to defend hierarchy without anthroparchy. To provide context, I will begin with a brief analysis of Aristotle’s “Great Chain of Being” and will then contrast it with Whitehead’s process philosophy. Given this context, using the subtle and perceptive work of the ecofeminist Karen J. Warren, I will then present a model for how to recognize a “descriptive hierarchy” while rejecting a simplistic “prescriptive hierarchy.” . (shrink)

Ratajczyk, Z., Subsystems of true arithmetic and hierarchies of functions, Annals of Pure and Applied Logic 64 95–152. The combinatorial method coming from the study of combinatorial sentences independent of PA is developed. Basing on this method we present the detailed analysis of provably recursive functions associated with higher levels of transfinite induction, I, and analyze combinatorial sentences independent of I. Our treatment of combinatorial sentences differs from the one given by McAloon [18] and gives more natural sentences. The same (...) method give also a combinatorial technique with no use of the cut-elimination theorem which is appropriate to study proof-theoretic strength of subsystems of first order arithmetic and some of their expansions. It was used to analyze iterated reflection principle and system of transfinite induction with a satisfaction class. (shrink)

We construct a class of relations on computable structures whose degree spectra form natural classes of degrees. Given any computable ordinal and reducibility r stronger than or equal to m-reducibility, we show how to construct a structure with an intrinsically invariant relation whose degree spectrum consists of all nontrivial r-degrees. We extend this construction to show that can be replaced by either or.

We propose a novel model to explain the mechanisms underlying dominance hierarchical structures. Guided by a predetermined social convention, agents with limited cognitive abilities optimize their strategies in a Hawk-Dove game. We find that several commonly observed hierarchical structures in nature such as linear hierarchy and despotism, emerge as the total fitness-maximizing social structures given different levels of cognitive abilities.

In this paper we apply the idea of Revision Rules, originally developed within the framework of the theory of truth and later extended to a general mode of definition, to the analysis of the arithmetical hierarchy. This is also intended as an example of how ideas and tools from philosophical logic can provide a different perspective on mathematically more “respectable” entities. Revision Rules were first introduced by A. Gupta and N. Belnap as tools in the theory of truth, and (...) they have been further developed to provide the foundations for a general theory of (possibly circular) definitions. Revision Rules are non-monotonic inductive operators that are iterated into the transfinite beginning with some given “bootstrapper” or “initial guess.” Since their iteration need not give rise to an increasing sequence, Revision Rules require a particular kind of operation of “passage to the limit,” which is a variation on the idea of the inferior limit of a sequence. We then define a sequence of sets of strictly increasing arithmetical complexity, and provide a representation of these sets by means of an operator G(x, φ) whose “revision” is carried out over ω2 beginning with any total function satisfying certain relatively simple conditions. Even this relatively simple constraint is later lifted, in a theorem whose proof is due to Anil Gupta. (shrink)

A project conceiving of political assemblages as anything larger than just an object of intellectual history will have to face a question—what is the potential scope and entailments of the idea of political assemblages outside of the very specific late twentieth-century milieu that it was conceived in? And given the present moment, there is also is much more specific question that should well be taken up: what place any project organized as a political assemblage could have in an era of (...) global capitalist accelerated economic inequalities and anthropocentric warming? Drawing on debates in contemporary social and cultural anthropology about Dumont, hierarchy, actor-network theory, and ontology, this essay... (shrink)

Using a sample of over 700 business people and students, this study tested the premise of promise-keeping as a core ethical value in the work place.The exercise consisted of in-basket planning for layoffs within an organization. Only one of the five employees within the group had been given an express commitment/promise of continued employment for a two year period. The layoffs were being considered six months after the two year promise had been made. All five employees were performing their jobs (...) adequately, and each had either personal or work attributes representing competing values that would have made it difficult to choose among them.Clearly, promise-keeping does not matter most in the workplace: subjects overwhelmingly ignored their promises even when legally bound to keep them. Further, promise-keeping consistently was found to rank last in a hierarchy of workplace values. The legal system was suggested as a viable mechanism for encouraging promise-keeping in the workplace. Although the possibility of legal sanctions increased the frequency with which promises were kept, overall fewer than one-third (30%) of the subjects kept their word. Of those respondents who expressly were told that the promise was legally enforceable, the number who stated that they would keep their promise increased to 57%. (shrink)

In this paper, the notions of Fα-categorical and Gα-categorical structures are introduced by choosing the isomorphism such that the function itself or its graph sits on the α-th level of the Ershov hierarchy, respectively. Separations obtained by natural graphs which are the disjoint unions of countably many finite graphs. Furthermore, for size-bounded graphs, an easy criterion is given to say when it is computable-categorical and when it is only G2-categorical; in the latter case it is not Fα-categorical for any (...) recursive ordinal α. (shrink)

Lachlan observed that any nonzero d.c.e. degree bounds a nonzero c.e. degree. In this paper, we study the c.e. predecessors of d.c.e. degrees, and prove that given a nonzero d.c.e. degree , there is a c.e. degree below and a high d.c.e. degree such that bounds all the c.e. degrees below . This result gives a unified approach to some seemingly unrelated results. In particular, it has the following two known theorems as corollaries: there is a low c.e. degree isolating (...) a high d.c.e. degree [S. Ishmukhametov, G. Wu, Isolation and the high/low hierarchy, Arch. Math. Logic 41 259–266]; there is a high d.c.e. degree bounding no minimal pairs [C.T. Chong, A. Li, Y. Yang, The existence of high nonbounding degrees in the difference hierarchy, Ann. Pure Appl. Logic 138 31–51]. (shrink)

In this essay, I consider Sally Haslanger’s social constructivist account of race and propose a modification to the nature of hierarchy specified. According to Haslanger, race will cease to exist post-hierarchy, given that she builds in a requirement of synchronic hierarchy for the existence of race. While Haslanger maintains that racial identity would linger beyond hierarchical treatment in the form of ethnicity, I will suggest this fails to provide adequate conceptual justice for the cultures and aesthetics which (...) emerged out of past oppression. In response, I propose a modification which would allow us to recognize the possibility of post-hierarchical races. (shrink)

The levels that compose biological hierarchies each have their own energetic, spatial and temporal structure. Indeed, it is the discontinuity in energy relationships between levels, as well as the similarity of sub-systems that support them, that permits levels to be defined. In this paper, the temporal structure of living hierarchies, in particular that pertaining to Human society, is examined. Consideration is given to the period defining the lifespan of entities at each level and to a periodic event considered fundamental to (...) the maintenance of that level. The ratio between the duration of these two periods is found to be approximately 2.5 × 104. A similar relationship is found when lower, non-living levels of molecules and atoms are considered. This suggests that there is a constant factor of amplification between analogous periodic events at successive levels of the Human hierarchy. (shrink)

Traditional portfolio selection models mainly obtain the optimized portfolio ratio by focusing on the prices of financial products. However, investors’ multiple preferences and risk appetites are also significant factors that should be taken into account. In consideration of these two factors simultaneously, we propose a double-hierarchy model in this paper. Specifically, the first hierarchy quantifies investors’ risk appetite based on a historical simulation method and probabilistic preference theory. This hierarchy can be utilized to describe investors’ variable risk (...) appetites and ensure the obtained investment ratios meet investors’ immediate risk requirements. Then, using the cross-efficiency evaluation principle, the optimal investment ratios can be derived by fusing investors’ multiple preferences and risk appetites in the second hierarchy. Lastly, an illustrative example about evaluating the 10 largest capitalized stocks on the Shenzhen Stock Exchange is given to verify the feasibility and effectiveness of our newly proposed model. We make the theoretical contribution to improve the traditional portfolio selection model, especially considering investors’ subjective preferences and risk appetite. Moreover, the proposed model can be practical for assisting investors with their investment strategies in real life. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Beauty, Transcendence, and the Inclusive Hierarchy of Creation1Thomas Joseph White, O.P.Interpreters of Thomas Aquinas have long argued about whether he holds that beauty is a “transcendental,” a feature of reality coextensive with all that exists, like unity, goodness, and truthfulness.2 In the first part of this article, I will argue that Aquinas can [End Page 1215] be read to affirm in an implicit way that beauty is a (...) transcendental. In the second part, I will consider what it might mean from a Thomistic point of view to speak of a transcendent divine beauty, given Aquinas’s metaphysical commitments, particularly with respect to his doctrine of divine simplicity. In the final part, I will treat the question of how the beauty of the creation both manifests and conceals divine beauty.Beauty as a Transcendental Feature of RealityAquinas does not list beauty as a transcendental term in texts on transcendental notions. Perhaps, then, one should simply exclude it from a responsible account of his teaching on this subject. However, at least two well-known texts should give us reason to pause before reaching such a conclusion. One is found in his Commentary on Dionysius’ Divine Names, chapter 4, lectio 5. The other is in his discussion of the beauty of the eternal Son of God in a discussion of the Holy Trinity in the Summa theologiae I, q. 39, a. 8.In the first of these texts, Aquinas is commenting on Dionysius. The extended text is analytically dense. Aquinas is discussing ways in which one might say that God is beautiful and in what ways one might not say so. I will return to his topic below. Here, however, it is pertinent to consider Aquinas’s discussion of the presence of beauty in all that exists. He makes six main points.3 First, all beauty comes [End Page 1216] from God insofar as God is the cause of all that exists. Second, he gives a first definition of beauty: beauty can be defined ontologically as the splendor (claritas) that results from form; everything has a formal determination of some kind insofar as it has existence (esse); therefore, insofar as anything exists (and has some formal ontological content) it has some degree of beauty. Third, the splendor of the form in created things is a participation in the divine splendor from which it originates. The divine nature is the transcendent exemplar of beauty in diverse finite created realities. Fourth, then (and perhaps most importantly), “ex divina pulchritudine esse omnium derivatur”: literally, the existence of everything originates from divine beauty. Fifth, a second definition of beauty is considered: beauty can be defined ontologically as a property of being that emerges from proportion or harmony (consonantia). For example, authentic relationships of personal friendship imply spiritual harmony or concord and are beautiful and noble in this respect. Sixth, then, the concord or beautiful harmonies we find in the created order are expressive of the wisdom of God, who is the author of creation.Evidently, if the existence of everything derives from divine beauty, and if everything that has existence is in some way beautiful by virtue of its intrinsic form, then it would seem to follow logically that beauty, for Aquinas, is a characteristic of being that is coextensive with all that exists. We see a similar idea expressed in the aforementioned passage of ST. Here, however, Aquinas gives a more synthetic definition of beauty in things that combines both the definitions found in our previous discussion, claritas and proportio, but it also adds a third, integritas: ontological integrity or wholeness.Species or beauty has a likeness to the property of the Son. For beauty includes three conditions, “integrity” or “perfection,” [End Page 1217] since those things which are impaired are by the very fact ugly; due “proportion” or “harmony”; and lastly, “brightness” or “clarity,” whence things are called beautiful which have a bright color.4The implication of this point of view is readily apparent. God is essentially beautiful, and God has created all that exists in light of the eternal Word and Wisdom of God, who is the Son. Consequently, all that exists and that... (shrink)

In analyzing European institutional structures, the multi-level governance literature speaks of mutual interdependence, of cooperative and coordinated processes between different levels of authority. The emergence of these processes is sometimes associated with the disappearance of hierarchical relationships organized across vertical channels of communication. The type of hierarchy, which is declared 'eroded', is not further specified. In the first part of the article a definition of hierarchy is given and an attempt is then made to develop a diversified concept (...) of hierarchy consisting of two types : unilateral and asymmetrically interdependent. The second part applies this modified concept of hierarchy to relationship structures in those federations which are part of European multi-level polity, and examines the types of hierarchy that exist between federal and federated levels when the latter act within the European framework. The external policies of German and Belgian federated units are analyzed in a comparative perspective. (shrink)

Using a sample of over 700 business people and students, this study tested the premise of promise-keeping as a core ethical value in the work place.The exercise consisted of in-basket planning for layoffs within an organization. Only one of the five employees within the group had been given an express commitment/promise of continued employment for a two year period. The layoffs were being considered six months after the two year promise had been made. All five employees were performing their jobs (...) adequately, and each had either personal or work attributes representing competing values that would have made it difficult to choose among them. (shrink)

I prove that there is a recursive function T that does the following: Let X be transitive and rudimentarily closed, and let X ′ be the closure of X ∪ {X } under rudimentary functions. Given a Σ0-formula φ and a code c for a rudimentary function f, T is a Σω-formula such that for any equation image ∈ X, X ′ ⊧ φ [f ] iff X ⊧ T [equation image]. I make this precise and show relativized versions of (...) this. As an application, I prove that under certain conditions, if Y is the Σω extender ultrapower of X with respect to some extender F that also is an extender on X ′, then the closure of Y ∪ {Y } under rudimentary functions is the Σ0 extender ultrapower of X′ with respect to F, and the ultrapower embeddings agree on X. (shrink)

Examining a range of sixth-century literary sources, this paper explores the authors' attitudes toward the marital relationship of the Late Roman emperor Justinian I and his empress, Theodora. It emerges that the sources characteristically appeal to the agency of Theodora or to an underlying level of mutual understanding between the imperial couple in order to reconcile inconsistencies or apparent contradictions between the regime's rhetoric and its actions. Recourse to such an interior dynamic gave scope to the recognition and expression of (...) contradiction without thereby entailing an admission of disorder: it enabled the imperial couple, and thus in an overarching sense the instrumental function of the imperial "role" in the state, to work if necessary at cross purposes while preserving an unbroken unity of purpose. Special attention is paid to the particular interests and expectations of two distinct groups: the classically-educated mandarinate of the Roman civil service, and the schismatic hierarchy of the nascent Monophysite church. (shrink)

The following three points are made. One must consider not only the levels of circulating hormone but the target tissue upon which the hormone acts. Increased testosterone levels alone do not account for differences in displayed intermale aggression, because testosterone and social environment interact in complex ways to influence behavior. A given behavior can be triggered by multiple motivational systems.

Feminism is going to ruin your life--in the best way possible--because society screams numerous messages every moment about how women must look, act, and speak in order to earn their right to be seen and heard. The only thing any human needs to do in order to earn their right to exist, however, is to exist. Break free of the insidious narratives that hold you back from being your most authentic self.

A dictionary is a set of finite words over some finite alphabet X. The omega-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [Omega-powers and descriptive set theory, JSL 2005] the complexity of the set of dictionaries whose associated omega-powers have a given complexity. In particular, he considered the sets $W({bfSi}^0_{k})$ (respectively, $W({bfPi}^0_{k})$, $W({bfDelta}_1^1)$) of dictionaries $V subseteq 2^star$ whose omega-powers are ${bfSi}^0_{k}$-sets (respectively, ${bfPi}^0_{k}$-sets, Borel sets). In (...) this paper we first establish a new relation between the sets $W({bfSigma}^0_{2})$ and $W({bfDelta}_1^1)$, showing that the set $W({bfDelta}_1^1)$ is ``more complex' than the set $W({bfSigma}^0_{2})$. As an application we improve the lower bound on the complexity of $W({bfDelta}_1^1)$ given by Lecomte. Then we prove that, for every integer $kgeq 2$, (respectively, $kgeq 3$) the set of dictionaries $W({bfPi}^0_{k+1})$ (respectively, $W({bfSi}^0_{k+1})$) is ``more complex' than the set of dictionaries $W({bfPi}^0_{k})$ (respectively, $W({bfSi}^0_{k})$). (shrink)

This will be an admittedly opinionated review that gives with one hand and takes with the other. Let me be clear though from the outset that there is much to admire and agree with here. Perhaps, the biggest complaint is the failure of the author to engage with other highly relevant literature in philosophy of science and metaphysics that would yield her natural allies or would provide natural foils that ought to be named and engaged. On the allies side, there (...) are many people now writing in the vein of emergence that have made many of the same claims and used many of the same case studies to bolster their claims as Thalos. Surely, this requires a response on her part given that “emergence” is one of her primary foils. Rather than discussing those people’s work, she chooses to focus on a particular brand of emergence as a foil and thereby throws out the baby with the bathwater. Thalos also fails to engage the huge and highly relevant literature on the causal (or d .. (shrink)

Within the Givenness Hierarchy framework of Gundel, Hedberg, and Zacharski (1993), lexical items included in referring forms are assumed to conventionally encode two kinds of information: conceptual information about the speaker’s intended referent and procedural information about the assumed cognitive status of that referent in the mind of the addressee, the latter encoded by various determiners and pronouns. This article focuses on effects of underspecification of cognitive status, establishing that, although salience and accessibility play an important role in (...) reference processing, the Givenness Hierarchy itself is not a hierarchy of degrees of salience/accessibility, contrary to what has often been assumed. We thus show that the framework is able to account for a number of experimental results in the literature without making additional assumptions about form-specific constraints associated with different referring forms. (shrink)