We work in set theory ZF without axiom of choice. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gateaux-differentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f: F → ℝ is a linear functional such that f ≤ p|F then there exists a linear functional g : E → ℝ such that g extends (...) f and g ≤ p. We also prove that the continuous Hahn-Banach property on a topological vector space E is equivalent to the classical geometrical forms of the Hahn-Banach theorem on E. We then prove that the axiom of Dependent choices DC is equivalent to Ekeland's variational principle, and that it implies the continuous Hahn-Banach property on Gateaux-differentiable Banach spaces. Finally, we prove that, though separable normed spaces satisfy the continuous Hahn-Banach property, they do not satisfy the whole Hahn-Banach property in ZF+DC. (shrink)

One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...) and Patashnik's claim that "there's no corresponding chain rule of finite calculus"). (shrink)

Two prominent relational egalitarians, Elizabeth Anderson and Niko Kolodny, object to giving people in a democratic community differential voting weights on the grounds that doing so would lead to unequal relations between them. Their claim is that deviating from a “one-person, one-vote” scheme is incompatible with realizing relational egalitarian justice. In this article, I argue that they are wrong. I do so by showing that people can relate as moral, epistemic, social, and empirical equals in a scheme with differential voting (...) weights. I end the article by showing that from the perspective of relational egalitarianism, it is sometimes true that differential voting weights are more just than equal voting weights. (shrink)

If the traditional problem of demandingness is that a theory demands too much of all agents, for example by asking them to maximize utility in every decision, then we should ask whether there is a related problem of “differential demandingness”, when a theory places vastly different demands on different agents. I argue that even according to common-sense morality, the demands faced by particular agents depend on a variety of contingent factors. These include the general circumstances, the compliance of others, the (...) available resources, the agent’s relevant relationships, the agent’s psychological constitution, and the agent’s knowledge. Some agents, for instance, find themselves in a “sacrifice hazard”: a situation where morality calls for a huge unforeseen sacrifice. I argue that if moral demands are differential, it is harder than one might think to assess a theory’s general level of demandingness in the abstract. (shrink)

Recognising that offers of payment to research participants can serve various purposes—reimbursement, compensation and incentive—helps uncover differences between participants, which can justify differential payment of participants within the same study. Participants with different study-related expenses will need different amounts of reimbursement to be restored to their preparticipation financial baseline. Differential compensation can be acceptable when some research participants commit more time or assume greater burdens than others, or if inter-site differences affect the value of compensation. Finally, it may be permissible (...) to offer differential incentive payments if necessary to advance the goals of a study. We encourage investigators and Institutional Review Boards to think about whether to offer payment, in what amounts and for what purpose, and also to consider whether differential payment can help promote the scientific and ethical goals of clinical research. (shrink)

It is often argued that human emotions, and the cognitions that accompany them, involve refinements of, and extensions to, more basic functionality shared with other species. Such refinements may rely on common or on distinct processes and representations. Multi-level theories of cognition and affect make distinctions between qualitatively different types of representations often dealing with bodily, affective and cognitive attributes of self-related meanings. This paper will adopt a particular multi-level perspective on mental architecture and show how a mechanism of subsystem (...) differentiation could have allowed an evolutionarily “old” role for emotion in the control of action to have altered into one more closely coupled to meaning systems. We conclude by outlining some illustrative consequences of our analysis that might usefully be addressed in research in comparative psychology, cognitive archaeology, and in laboratory research on memory for emotional material. (shrink)

Even the simplest cell exhibits a high degree of functional differentiation (FD) realized through several mechanisms and devices contributing differently to its maintenance. Searching for the origin of FD, we briefly argue that the emergence of the respective organizational complexity cannot be the result of either natural selection (NS) or solely of the dynamics of simple self-maintaining (SM) systems. Accordingly, a highly gradual and cumulative process should have been necessary for the transition from either simple self-assembled or self-maintaining systems of (...) functionless structural components to systems with FD. We follow results of recent in vitro experiments with respect to competition among protocells, where a primitive type of selection begins to operate among them accompanied by a parallel evolution of their functional domain. We argue that minimal forms of FD should be established within the evolution of SM processes in protocells as they undergo a simpler selection process for stability and persistence in a prebiotic environment. We then suggest the concept of closure of constraints (CoC) as a way to identify and describe minimal FD in a far-from-equilibrium SM organization. We show in detail how the concept of CoC together with the conditions for its fulfillment can be applied in the case of a simple protocellular system that begins to couple internal chemical reactions with the formation of its membrane components. Finally, we discuss how such SM systems can evolve towards significantly higher levels of FD, suggesting this is mainly the result of functional recombination (formation of mechanisms) in the context of a modular SM organization. (shrink)

ABSTRACTEmotion differentiation, the ability to describe and label our own emotions in a differentiated and specific manner, has been repeatedly associated with well-being. However, it is unclear exactly what type of differentiation is most strongly related to well-being: the ability to make fine-grained distinctions between emotions that are relatively closely related, the ability to make larger distinctions between very distinct emotions, or the combination of both. To determine which type of differentiation is most predictive of well-being, we performed a comprehensive (...) meta-analysis across six datasets. We examined the correlations between these three types of differentiation and several indicators of well-being. Results showed that individuals differentiated most between very distinct emotions and least between more related emotions, and that an index computed across emotions from both the same and di... (shrink)

The differentiation of trait anxiety and depression in nonclinical and clinical populations is addressed. Following the tripartite model, it is assumed that anxiety and depression share a large portion of negative affectivity, but differ with respect to bodily hyperarousal and anhedonia. In contrast to the tripartite model, NA is subdivided into worry and dysthymia, which leads to a four-variable model of anxiety and depression encompassing emotionality, worry, dysthymia, and anhedonia. Item-level confirmatory factor analyses and latent class cluster analysis based on (...) a large nation-wide representative German sample substantiate the construct validity of the model. Further evidence concerning convergent and discriminant validity with respect to related constructs is obtained in two smaller nonclinical and clinical samples. Factors influencing the association between components of anxiety and depression are discussed. (shrink)

In this study, we analyse the notion of “differential heterogenesis” proposed by Deleuze and Guattari on a morphogenetic perspective. We propose a mathematical framework to envisage the emergence of singular forms from the assemblages of heterogeneous operators. In opposition to the kind of differential calculus that is usually adopted in mathematical-physical modelling, which tends to assume a homogeneous differential equation applied to an entire homogeneous region, heterogenesis allows differential constraints of qualitatively different kinds in different points of space and time. (...) These constraints can then change in time, opening the possibility for new kinds of differential dynamics and the emergence of distinct entities and forms. Formally, we show that operators with different phase spaces can be assembled on the basis of a result of Rothschild & Stein (1976. Hypoelliptic differential operators and nilpotent groups. Acta Mathematica 137. 247–320). Furthermore, operators with different dynamics can be assembled by means of a partition of the unit.After stating the concept of differential heterogenesis in terms of contemporary mathematics, we show that this construction sheds light on the constitution of the semiotic function. In fact, both the Merleau-Pontian and the Deleuzian approaches share a common conceptualisation of the semiotic function and its emergence in terms of amorphodynamics of heterogeneous assemblages with a divergent actualisation. This divergent actualisation allows the co-constitution of various expression and content planes. Finally, we show that the divergent actualisation can be interpreted as the directions of principal eigenvectors of the actualized flow. (shrink)

An argument evaluation inventory distinguishing between different levels of theory-evidence differentiation was designed corresponding to the levels of argument observed in argument generation tasks. Five scenarios containing everyday theories about a social problem, and arguments to support those theories were presented to 170 participants from two age groups (15 and 22 years) and different educational tracks. Participants had to rate the validity of arguments proposed by a story figure, to support the theory, to choose the best argument, and to justify (...) their choice. The rating task proved to be very difficult for all age groups, with only 49% of the university students consistently rating valid evidence-based arguments higher than flawed arguments. Competence improved with age and educational level. In the choice task more than 80% of the adults preferred an argument that reflected theory-evidence differentiation over mere theory elaboration or flawed reasoning. However, only adults with a university education were able to also explicitly justify their choice. Overall, these findings imply that laypersons have similar conceptual problems in differentiating theory from evidence as it has been reported for evidence generation tasks (Kuhn, 1991). Performance on the choice task suggests that some implicit awareness of differences between theory and evidence may precede a full, explicit understanding. Implications for education are discussed. (shrink)

In this article, I argue that Merleau-Ponty underpins an idea of differentiation without ultimate unification through intertwining. I trace this idea of intertwining to Phenomenology of Perception. I argue that what perception marks is already differentiation prior to any identification. For this purpose, firstly, I will introduce Merleau-Ponty’s depiction of intertwining; secondly, I will elaborate perception in Phenomenology of Perception; finally, I will discuss flesh as intertwining in The Visible and The Invisible.

In this paper I present an interpretation of Deleuze's concept of the virtual. I argue that this concept is best understood in relation to the problematic of individuation or differentiation, which Deleuze inherits from Duns Scotus. After analysing Scotus' critique of Aristotelian or hylomorphic approaches to the problem of individuation, I turn to Deleuze's account of differentiation and his interpretation of the calculus in chapter 4 of Difference and Repetition. The paper seeks thereby to explicate Deleuze's dialectics or theory of (...) Ideas, his approach to the principle of sufficient reason, and the concept of the virtual itself. (shrink)

The aim of this research was to determine the degree to which undergraduate students’ learning approach, academic achievement and satisfaction were determined by the combination of an intrapersonal factor (self-regulation) and a interpersonal factor (contextual or regulatory teaching). The hypothesis proposed that greater combined regulation (internal and external) would be accompanied by more of a deep approach to learning, more satisfaction and higher achievement, while a lower level of combined regulation would determine a surface approach, less satisfaction and lower achievement. (...) Within an ex post facto design by selection, 1036 university students completed validated questionnaires using an online tool. Several multivariate analyses were conducted. Results showed that the combination of self-regulation and external regulation can be ordered as levels along a five-point scale or heuristic. These levels linearly determine type of learning approach, academic achievement and satisfaction. Implications are established for quality and improvement of the teaching and learning process at university. (shrink)

In this musing we consider how social distancing, the primary public health measure introduced to mitigate the spread of the COVID-19 virus, is creating social encounters characterized by a self-and-other-consciousness and an atmosphere of suspicion, leading to what we call “alienated embodied communication.” Whilst interaction rituals dominated by avoidance, fear and distrust are novel for many individuals who occupy positions of social privilege, Black and ethnic minority writers have demonstrated that the alienated bodily communication of COVID-19 social distancing is “nothing (...) new” for people who routinely experience marginalization as a result of racism. Our aim in this musing, then, is to reflect on how on-going experiences of stigma, shame, and marginalization can shape how social distancing is registered on an embodied and existential level, and therefore how social distancing may differentially impact individuals with lived experiences of racism. (shrink)

How does shame differ from guilt? Empirical psychology has recently offered distinct and seemingly incompatible answers to this question. This article brings together four prominent answers into a cohesive whole. These are that (a) shame differs from guilt in being a social emotion; (b) shame, in contrast to guilt, affects the whole self; (c) shame is linked with ideals, whereas guilt concerns prohibitions and (d) shame is oriented towards the self, guilt towards others. After presenting the relevant empirical evidence, we (...) defend specific interpretations of each of these answers and argue that they are related to four different dimensions of the emotions. This not only allows us to overcome the conclusion that the above criteria are either unrelated or conflicting with one another, it also allows us to tell apart what is constitutive from what is typical of them. -/- . (shrink)

We revisit the characterization of the Shapley value by van den Brink (Int J Game Theory, 2001, 30:309–319) via efficiency, the Null player axiom, and some fairness axiom. In particular, we show that this characterization also works within certain classes of TU games, including the classes of superadditive and of convex games. Further, we advocate some differential version of the marginality axiom (Young, Int J Game Theory, 1985, 14: 65–72), which turns out to be equivalent to the van den Brink (...) fairness axiom on large classes of games. (shrink)

This paper uses an environmental justice framework to examine government response to weather-related disasters dating back some eight decades. It places the 2005 Hurricane Katrina disaster in socio-historical context of past emergencies with an emphasis on race and class dynamics and social vulnerability. Key questions explored include: What went wrong? Can it happen again? Is government equipped to plan for, mitigate against, respond to, and recover from natural and manmade disasters? Can the public trust government response to be fair? Why (...) are so many African Americans Alocked out@ of New Orleans= post-Katrina rebuilding, reconstruction, and recovery? (shrink)

Conscientious disobedients often face the demand to differentiate themselves from criminals whose law-breaking actions are not undergirded by conscientious convictions. In public and philosophical discourse, conscientious disobedients are often criticised on the basis that their actions render them no different from criminals. I provide a qualified defence of disobedients in this essay. I argue that the differentiation demand can be satisfied even by disobedients who engage in what are typically regarded as radical acts of disobedience. In practical terms, this means (...) that even disobedients who engage in actions such as arson, looting, rioting, vandalism or vigilantism can also successfully differentiate themselves from criminals. (shrink)

Ineffability, the degree to which percepts or concepts resist linguistic coding, is a fairly unexplored nook of cognitive science. Although philosophical preoccupations with qualia or nonconceptual content certainly touch upon the area, there has been little systematic thought and hardly any empirical work in recent years on the subject. We argue that ineffability is an important domain for the cognitive sciences. For examining differential ineffability across the senses may be able to tell us important things about how the mind works, (...) how different modalities talk to one another, and how language does, or does not, interact with other mental faculties. (shrink)

In The Face of Emotions, which was Carroll Izard’s first major attempt at elaborating his differential emotions theory, he stated that the book “presents a theoretical framework for the study of emotions and their role in personality and interpersonal processes.” Yet, over the years, his contribution to personality theory has generally been overshadowed by the attention focused on his views on facial expressions and the structure of emotions. This article will begin with a brief overview of the DET perspective on (...) personality development. Then, it will examine how the DET framework can be used to organize recent findings from three lines of research on adult personality. It will conclude with suggestions for future research as well as some personal recollections. (shrink)

ABSTRACTEmotion differentiation refers to the precision with which people can identify and distinguish their emotions and has been associated with well-being in adults. This study investigated ED and its relation with emotional well-being in adolescents. We used an experience sampling method with 72 participants to assess adolescents’ positive and negative emotions at different time points over the course of two weekends and a baseline questionnaire to assess emotional well-being. Differentiating negative emotions was related to less negativity intensity and propensity, and (...) to the belief that emotions are malleable. Differentiating positive emotions was not related to any of the assessed well-being variables. Together, these results suggest that a detailed awareness of one’s negative emotional states is an important dimension of well-being, also in adolescence. (shrink)

In _Differentiating the Pearl from the Fish-Eye_, Eyal Aviv offers an account of Ouyang Jingwu, a revolutionary Buddhist thinker and educator. The book surveys the life and career of Ouyang and his influence on modern Chinese intellectual history.

Endothelial cells line the inside of all blood vessels, forming a structurally and functionally heterogenous population of cells. Their complexity and diversity has long been recognized, yet very little is known about the molecules and regulatory mechanisms that mediate the heterogeneity of different endothelial cell populations. The constitutive organ‐ and microenvironment‐specific phenotype of endothelial cells controls internal body compartmentation, regulating the trafficking of circulating cells to distinct vascular beds. In contrast, surface molecules associated with the activated cytokine‐inducible endothelial phenotype play (...) a critical role in pathological conditions including inflammation, tumor angiogenesis, and wound healing. Differentiation of the endothelial cell phenotypes appears to follow similar mechanisms to the differentiation of hematopoietic cells, with the exception that endothelial cells maintain transdifferentiating competence. The present review offers a scheme of endothelial cell differentially expressed endothelial cell molecules as targets for directed therapeutic intervention. (shrink)

In the reported, experiment participants hit a ball to aim at the vertex of a Müller–Lyer configuration. This configuration either remained stable, changed its shaft length or the orientation of the tails during movement execution. A significant illusion bias was observed in all perturbation conditions, but not in the stationary condition. The illusion bias emerged for perturbations shortly after movement onset and for perturbations during execution, the latter of which allowed only a minimum of time for making adjustments . These (...) findings indicate that allocentric information is exploited for online control when people make rapid adjustments in response to a sudden change in the environment and not when people guide their limb movements to interact with a stable environment. (shrink)

The “DNA is a program” metaphor is still widely used in Molecular Biology and its popularization. There are good historical reasons for the use of such a metaphor or theoretical model. Yet we argue that both the metaphor and the model are essentially inadequate also from the point of view of Physics and Computer Science. Relevant work has already been done, in Biology, criticizing the programming paradigm. We will refer to empirical evidence and theoretical writings in Biology, although our arguments (...) will be mostly based on a comparison with the use of differential methods (in Molecular Biology: a mutation or alike is observed or induced and its phenotypic consequences are observed) as applied in Computer Science and in Physics, where this fundamental tool for empirical investigation originated and acquired a well-justified status. In particular, as we will argue, the programming paradigm is not theoretically sound as a causal(as in Physics) or deductive(as in Programming) framework for relating the genome to the phenotype, in contrast to the physicalist and computational grounds that this paradigm claims to propose. (shrink)

One way in which the practice of inclusion can be actualised in classrooms is through the use of consistent, appropriate differentiated instruction. What remains elusive, however, is insight into what teachers in different contexts think and believe about differentiation, how consistently they differentiate instruction and what challenges they experience in doing so. In the study reported on here high school classrooms in a private and a government school in Lesotho were compared in order to determine teachers’ thoughts and beliefs about (...) differentiation, the frequency of differentiated instruction, and the challenges faced by teachers who implement this inclusive practice. Sampled teachers offered their views on what they understood differentiated instruction to be, the frequency of differentiated instruction, and identified challenges via an administered questionnaire. Data analysis was based on frequency counts and bar charts for comparative purposes. Findings indicate that private school teachers have a higher frequency of differentiated teaching practice, with time constraints indicated as the main challenge. Government school teachers had a lower frequency of differentiation, and identified a lack of resources, and the learner-teacher ratio as challenges, among others. In the study we highlighted the critical role that private schools can play in the national call for the implementation of inclusive teaching in Lesotho, in terms of active collaboration with surrounding government schools. Private schools, with their resources and access to professional development opportunities, can become catalysts in the implementation of inclusive teaching practices. (shrink)

The aim of this research was to establish linear relations (association and prediction) and inferential relations between three constructs at different levels of psychological research –executive dysfunction(microanalysis),self-regulation(molecular level), andself-vs.external regulation(molar level), in the prediction of emotion regulation difficulties. We hypothesized that personal and contextual regulatory factors would be negatively related to levels of executive dysfunction and emotion regulation difficulties; by way of complement, non-regulatory and dysregulatory personal, and contextual factors would be positively related to these same difficulties. To establish relationships, (...) we used a retrospective,ex postfacto design, where 298 university students voluntarily participated by completing standardized self-reports. Linear and structural correlational, predictive analyses were performed, as well as inferential analyses. Results were consistent and validated the proposed hypotheses, for both association and prediction. The most important result refers to the discriminant value of the five-level combination heuristic for predicting Executive Function and External (contextual) Dys-Regulation. In conclusion: (1) both personal and contextual regulation factors must be analyzed in order to better understand the variation in executive functions and emotion regulation difficulties; (2) it is important to continue connecting the different levels of the constructs referring to self-regulation, given their complementary role in the behavioral analysis of regulation difficulties. (shrink)

Teachers' approaches to differentiation are described as a relationship between their planning, daily practice and thinking. Differences between the practice and thinking of teachers and implications for improving practice in differentiation are considered.

People judge positive information to be more alike than negative information. This good-bad asymmetry in similarity was argued to constitute a true property of the information ecology (Alves, H., Koch, A., & Unkelbach, C. (2017). Why good is more alike than bad: Processing implications. Trends in Cognitive Sciences, 21, 69–79). Alternatively, the asymmetry may constitute a processing outcome itself, namely an influence of phasic affect on information processing. Because no research has yet tested whether phasic affect influences perceived similarity among (...) stimuli, we conducted 5 Experiments that also tested whether phasic affect can account for the higher judged similarity among positive compared to negative stimuli. In three experiments, we affectively charged pictures of different Pokemon by pairing them with monetary gains and losses (Exp. 1a, 1b) as well as positive and negative trait words (Exp. 2); yet, the evaluative charge did not differentially influence perceived similarity among the Pokemon. Experiment 3 replicated the basic similarity asymmetry among positive and negative words, and found that it was unaffected by externally induced phasic affect. Experiment 4 showed that phasic affect had no influence on perceived similarity of non-evaluative words either. We conclude that albeit a weak influence of phasic affect on perceived similarity of stimuli cannot be ruled out entirely, it can most likely not account for the typically medium to large sized asymmetry in similarity among positive and negative stimuli. (shrink)

In this paper I argue that ethics and evidence are intricately intertwined within the clinical practice of differential diagnosis. Too often, when a disease is difficult to diagnose, a physician will dismiss it as being “not real” or “all in the patient’s head.” This is both an ethical and an evidential problem. In the paper my aim is two-fold. First, via the examination of two case studies (late-stage Lyme disease and Addison’s disease), I try to elucidate why this kind of (...) dismissal takes place. Then, I propose a potential solution to the problem. I argue that instead of dismissing a patient’s illness as “not real,” physicians ought to exercise a compassionate suspension of judgment when a diagnosis cannot be immediately made. I argue that suspending judgment has methodological, epistemic, and ethical virtues and therefore should always be preferred to patient dismissal in the clinical setting. (shrink)

Recognizing that offers of payment to research participants can serve various purposes—reimbursement, compensation, and incentive—helps uncover differences between participants that can justify differential payment of participants within the same study. Participants with different study-related expenses will need different amounts of reimbursement to be restored to their pre-participation financial baseline. Differential compensation can be acceptable when some research participants commit more time or assume greater burdens than others, or if inter-site differences affect the value of compensation. Finally, it may be permissible (...) to offer differential incentive payments if necessary to advance a study’s goals. We encourage investigators and Institutional Review Boards to think not only about whether to offer payment, in what amounts, and for what purpose, but also to consider whether differential payment can help promote the scientific and ethical goals of clinical research. (shrink)

In recent decades, considerable progress has been made in our understanding of emotional development. Yet no single current theory can fully encompass all of the empirical findings. Herein I propose that aspects of several theoretical approaches can be incorporated into a novel view that is informed by the dynamical systems perspective.

We consider first-order theories of topological fields admitting a model-completion and their expansion to differential fields . We give a criterion under which the expansion still admits a model-completion which we axiomatize. It generalizes previous results due to M. Singer for ordered differential fields and of C. Michaux for valued differential fields. As a corollary, we show a transfer result for the NIP property. We also give a geometrical axiomatization of that model-completion. Then, for certain differential valued fields, we extend (...) the positive answer of Hilbert’s seventeenth problem and we prove an Ax–Kochen–Ershov theorem. Similarly, we consider first-order theories of topological fields admitting a model-companion and their expansion to differential fields, and under a similar criterion as before, we show that the expansion still admits a model-companion. This last result can be compared with those of M. Tressl: on one hand we are only dealing with a single derivation whereas he is dealing with several, on the other hand we are not restricting ourselves to definable expansions of the ring language, taking advantage of our topological context. We apply our results to fields endowed with several valuations. (shrink)

Common‐sense morality seems to dictate that newborn babies strictly outrank non‐human animals on an ordered list of subjects of moral consideration. This is best described as the view that newborn babies have a higher moral status than any non‐human animal. In this article, I will argue that this common‐sense claim about the special moral status of newborn babies makes it hard to avoid the conclusion that fetuses, including pre‐conscious fetuses, also have a higher moral status than any non‐human animal—indeed, as (...) high as newborn babies. While this conclusion does not quite entail that abortion is generally seriously immoral, it does seem to follow that it would be no less difficult to justify (even relatively early) abortion than it would be to justify killing a newborn. (shrink)