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)

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)

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)

Differential privacy (DP) aims to confer data processing systems with inherent privacy guarantees, offering strong protections for personal data. But DP’s approach to privacy carries with it certain assumptions about how mathematical abstractions will be translated into real-world systems, which—if left unexamined and unrealized in practice—could function to shield data collectors from liability and criticism, rather than substantively protect data subjects from privacy harms. This article investigates these assumptions and discusses their implications for using DP to govern data-driven systems. In (...) Parts 1 and 2, we introduce DP as, on one hand, a mathematical framework and, on the other hand, a kind of real-world sociotechnical system, using a hypothetical case study to illustrate how the two can diverge. In Parts 3 and 4, we discuss the way DP frames privacy loss, data processing interventions, and data subject participation, arguing it could exacerbate existing problems in privacy regulation. In part 5, we conclude with a discussion of DP’s potential interactions with the endogeneity of privacy law, and we propose principles for best governing DP systems. In making such assumptions and their consequences explicit, we hope to help DP succeed at realizing its promise for better substantive privacy protections. (shrink)

The University of Tehran English Proficiency Test (UTEPT) is a high-stakes entrance examination taken by more than 10,000 master’s degree holders annually. The examinees’ scores have a significant influence on the final decisions concerning admission to the University of Tehran Ph.D. programs. As a test validation investigation, the present study, which is a bias detection research in nature, utilized multistep logistic regression (LR) procedure to examine the presence of gender differential item functioning (DIF) in the UTEPT with a sample of (...) 6,555 examinees who took the test in November 2006. Specifically, the LR DIF two-degree of freedom Chi-squared test of significance was employed to test the significance of DIF. Following what has been recently suggested in the literature, the test of significance for DIF was accompanied by a measure of magnitude, namely the R-squared effect size for LR DIF, for the interpretation of which the two widely accepted classification schemes were used comparatively. The results reveal that 39 of the 100 items in the test display significant gender differences. However, these group differences are viewed as “negligible” based on both of the schemes. Accordingly, it could be argued that the UTEPT is a gender DIF-free test, though the Reading Comprehension section of the test remains in need of further analysis as it seems that the general trend of DIF indices at the item level may hint at an inclination towards males. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...) geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

'A Differential Play of Forces' is a study of transcendental empiricism in musical contexts. It presents a reading of Gilles Deleuze and Félix Guattari’s philosophical apparatus and explores how music can be thought of as functioning in the operation Deleuze terms transcendental empiricism. Central to transcendental empiricism is the idea of an encounter with intensive difference and the consequent experience of intensive and virtual forces. The thesis sets out to explore this idea in three interwoven steps. First, it develops transcendental (...) empiricism as a philosophical framework, expounding central notions related to time and aesthetic experience. In the context of this philosophical apparatus, music is then discussed as an encounter with intensity and what this may entail for our understanding of musical experience and its potential. The third part of the thesis explores the idea of experiencing intensive forces through music in the thinking and poietic of three composers of the twentieth century: Arnold Schönberg, Olivier Messiaen and Giacinto Scelsi. The thesis develops three ‘images of thought’ corresponding, respectively, to the composers’ expressed theoretical ideas, identifying central concepts from Deleuze and Guattari’s philosophy. A mutual illumination of ideas about music and transcendental empiricism is thus presented, pointing towards a possible convergence between theory and practice, thinking and aesthetic experience as a differential play of intensive forces. (shrink)

The study examined the differential item functioning (DIF) of 2018 Basic Education Certificate examination (BECE) in Mathematics tests of National Examination Council (NECO) and BECE of Akwa Ibom State government in Nigeria. The invariance in the tests with regards to sex was considered using Item Response Theory (IRT) approach. The study area was Akwa Ibom state of Nigeria having a student population of 58,281 for the examination. The sample was made of up 3810 students drawn through a multi-stage sampling approach. (...) The multidimensional IRT (MIRT) package implemented in R-programming language software was applied in analyzing the data. The findings reveal that BECE of NECO displayed 23(38.3%) DIF items while BECE of Akwa Ibom State had 37 (61.7%) DIF items in terms of sex. The findings also revealed that, in the two examinations, more items favoured the male candidates more than the female candidates in terms of performance. It was recommended that IRT model should be adopted by test developers to determine item parameters for selection of good items to ensure quality of items before administration. Test equating of students who write equivalent form examinations conducted by different examining bodies was also recommended for admission and placement of candidates to determine actual group differences in performance. The study posits that research on Differential Item Functioning is inconclusive, so should be encouraged. (shrink)

In Hegel ou Spinoza,1 Pierre Macherey challenges the influence of Hegel’s reading of Spinoza by stressing the degree to which Spinoza eludes the grasp of the Hegelian dialectical progression of the history of philosophy. He argues that Hegel provides a defensive misreading of Spinoza, and that he had to “misread him” in order to maintain his subjective idealism. The suggestion being that Spinoza’s philosophy represents, not a moment that can simply be sublated and subsumed within the dialectical progression of the (...) history of philosophy, but rather an alternative point of view for the development of a philosophy that overcomes Hegelian idealism. Gilles Deleuze also considers Spinoza’s philosophy to resist the totalising effects of the dialectic. Indeed, Deleuze demonstrates, by means of Spinoza, that a more complex philosophy antedates Hegel’s, which cannot be supplanted by it. Spinoza therefore becomes a significant figure in Deleuze’s project of tracing an alternative lineage in the history of philosophy, which, by distancing itself from Hegelian idealism, culminates in the construction of a philosophy of difference. It is Spinoza’s role in this project that will be demonstrated in this paper by differentiating Deleuze’s interpretation of the geometrical example of Spinoza’s Letter XII (on the problem of the infinite) in Expressionism in Philosophy, Spinoza,2 from that which Hegel presents in the Science of Logic.3. (shrink)

Plato’s Sophist and Statesman stand out from many other Platonic dialogues by at least two features. First, they do not raise a ti esti question about a single virtue or feature of something, but raise the questions what sophist, statesman, and philosopher are, how they differ from each other, and what worth each should be accorded. Second, a visitor from Elea, rather than Socrates, seeks to addressed these questions and does so by employing what is commonly referred to as the (...) method of collection and division. Some scholars have argued that this so-called method is value neutral and therefore unable to address the question how philosophy differs from sophistry and statesmanship according to worth. This article contends that the procedures of collection and division does not preclude the visitor from taking considerations of worth into account, but rather helps establish an objective basis for settling the main questions of the dialogue. (shrink)

In a (2016) paper in this journal, I defuse allegations that theoretical ecological research is problematic because it relies on teleological metaphysical assumptions. Mark Sagoff offers a formal reply. In it, he concedes that I succeeded in establishing that ecologists abandoned robust teleological views long ago and that they use teleological characterizations as metaphors that aid in developing mechanistic explanations of ecological phenomena. Yet, he contends that I did not give enduring criticisms of theoretical ecology a fair shake in my (...) paper. He says this is because enduring criticisms center on concerns about the nature of ecological networks and forces, the instrumentality of ecological laws and theoretical models, and the relation between theoretical and empirical methods in ecology that that paper does not broach. Below I set apart the distinct criticisms Sagoff presents in his commentary and respond to each in turn. (shrink)

Maimon’s theory of the differential has proved to be a rather enigmatic aspect of his philosophy. By drawing upon mathematical developments that had occurred earlier in the century and that, by virtue of the arguments presented in the Essay and comments elsewhere in his writing, I suggest Maimon would have been aware of, what I propose to offer in this paper is a study of the differential and the role that it plays in the Essay on Transcendental Philosophy (1790). In (...) order to do so, this paper focuses upon Maimon’s criticism of the role played by mathematics in Kant’s philosophy, to which Maimon offers a Leibnizian solution based on the infinitesimal calculus. The main difficulties that Maimon has with Kant’s system, the second of which will be the focus of this paper, include the presumption of the existence of synthetic a priori judgments, i.e. the question quid facti, and the question of whether the fact of our use of a priori concepts in experience is justified, i.e. the question quid juris. Maimon deploys mathematics, specifically arithmetic, against Kant to show how it is possible to understand objects as having been constituted by the very relations between them, and he proposes an alternative solution to the question quid juris, which relies on the concept of the differential. However, despite these arguments, Maimon remains sceptical with respect to the question quid facti. (shrink)

At the heart of Rik Peels’s Responsible Belief: A Theory in Ethics and Epistemology is the idea that responsibility for belief ought to be understood on the model of responsibility for states of affairs that are subject to our influence but not under our intentional control, or what he calls derivative responsibility. In this article, I argue that reflection on the nature and scope of derivative responsibility reveals important lacunae in Peels’s account of responsible belief and his account of responsibility (...) for belief. (shrink)

Objectives To increase postmortem organ donation rates, several countries are adopting an opt-out (presumed consent) policy, meaning that individuals are deemed donors unless they expressly refused so. Although opt-out countries tend to have higher donation rates, there is no conclusive evidence that this is caused by the policy itself. The main objective of this study is to better assess the direct impact of consent policy defaults per se on deceased organ recovery rates when considering the role of the family in (...) the decision-making process. This study does not take into account any indirect effects of defaults, such as potential psychological and behavioural effects on individuals and their relatives. -/- Design Based on previous work regarding consent policies, we created a conceptual model of the decision-making process for deceased organ recovery that included any scenario that could be directly influenced by opt-in or opt-out policies. We then applied this model to internationally published data of the consent process to determine how frequently policy defaults could apply. -/- Main outcome measures We measure the direct impact that opt-in and opt-out policies have per se on deceased organ recovery. -/- Results Our analysis shows that opt-in and opt-out have strictly identical outcomes in eight out of nine situations. They only differ when neither the deceased nor the family have expressed a preference and defaults therefore apply. The direct impact of consent policy defaults is typically circumscribed to a range of 0%–5% of all opportunities for organ recovery. Our study also shows that the intervention of the family improves organ retrieval under opt-in but hinders it under opt-out. -/- Conclusions This study may warn policy makers that, by emphasising the need to introduce presumed consent to increase organ recovery rates, they might be overestimating the influence of the default and underestimating the power granted to families. (shrink)

In this essay I take issue with the ease which the work of Sade has been, since Roland Barthes, integrated into academic discourse and try to reawaken a sense for what is unacceptable in Sade, but without lapsing into moralism. I try to give a reinvigorated account of the materialism of Sade's writing (as opposed to formalist appropriations of Sade like Barthes') which I then apply to the two characteristic Sadian devices: first, the encyclopedic enumeration and the (quite separate) philosophical (...) discourse. The encyclopedic enumeration is not only a kind of anti-literature but also comprises an irreducibly counter-conceptual geometry of affect whose structure I explore. I evaluate Bataille's claim that at the philosophical and discursive level Sade is primarily a thinker of transgression and defend, using the special case of blasphemy, the notion against critics who view it is puerile or self-defeating. In so doing, I unearth a profound pragmatism in Sade aimed at 'deprogramming' him from Western, Christian values, a move that anticipates Nietzsche in crucial and interesting ways. (shrink)

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...) able to work numerically with finite, infinite, and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and, in particular, to take advantage of infinitesimal values of h. To show the potential of the new framework a number of results is established. It is proved that the Infinity Computer is able to calculate derivatives of the solution y(x) and to reconstruct its Taylor expansion of a desired order numerically without finding the respective derivatives analytically (or symbolically) by the successive derivation of the ODE as it is usually done when the Taylor method is applied. Methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced. Numerical examples are given. (shrink)

In the article "What Sin Is: A Differential Analysis," Jesse Couenhoven delves into the definitions and categorizations of sin according to various Christian doctrines. The author critically examines traditional definitions, such as those provided by the Westminster Confession and catechisms, and argues that they fail to adequately distinguish between sin and evil, often conflating natural evils with sinful acts. Couenhoven also considers gray areas of ethical behavior, such as the actions of a schizophrenic who curses against God or the mistakes (...) made by medical residents that result in harm to patients, and questions whether these actions should be classified as sin. The primary question driving the article is how sin is differentiated from that which is "merely" evil. To address this, Couenhoven analyzes and evaluates three views of sin, testing their coherence with Christian beliefs and practices. The article aims to provide a more nuanced and sufficient understanding of sin within the Christian tradition, going beyond the necessary elements of the doctrine of sin to better identify and differentiate sin from evil. (shrink)

Saturated free fatty acids-induced hepatocyte lipoapoptosis plays a pivotal role in non-alcoholic steatohepatitis. Theactivation of endoplasmic reticulum (ER) stress isinvolved in hepatocyte lipoapoptosis induced by thesaturated free fatty acidpalmitate (PA). However, the underlying mechanismsof the role of ER stress in hepatocyte lipoapoptosis remain largely unclear.In this study, we showed that PA and tunicamycin (Tun), a classic ER stress inducer, resulted in differential activation of ERstress pathways. Our data revealed that PA inducedchronic and persistent ER stress response, but Tuninduced acute and (...) transientER stress response. Compared with Tun treatment, PAinduced much lower glucose-regulated protein 78 (GRP78), a centralregulator of ER homeostasis, accumulation. It is noteworthy that GRP78 over-expression not only inhibited PA-induced ERstress but also decreased PA-induced apoptosis. Taken together, our data suggest that the differentialactivation of ER stresssignal plays an important role in PA-induced hepatocyte lipoapoptosis. More detailed studies on the mechanisms of PA inrepressing the accumulation of GRP78 will contribute to the understanding of molecular mechanisms of lipoapoptosis. (shrink)

Saturated free fatty acids-induced hepatocyte lipoapoptosis plays a pivotal role in non-alcoholic steatohepatitis. Theactivation of endoplasmic reticulum (ER) stress isinvolved in hepatocyte lipoapoptosis induced by thesaturated free fatty acidpalmitate (PA). However, the underlying mechanismsof the role of ER stress in hepatocyte lipoapoptosis remain largely unclear.In this study, we showed that PA and tunicamycin (Tun), a classic ER stress inducer, resulted in differential activation of ERstress pathways. Our data revealed that PA inducedchronic and persistent ER stress response, but Tuninduced acute and (...) transientER stress response. (shrink)

The purpose of this study was to evaluate the differentiated learning training program at the mathematics subject teachers' meeting (MGMP). A descriptive quantitative approach was used to identify the successes of the program and areas that require improvement. The sample included 21 mathematics teachers in Sub Rayon 2 of Lebak District. The instruments used were questionnaires in which data on participants' responses to resource persons, materials, and suggestions for future activities were collected, and the results of direct observations. Data analysis (...) was carried out using descriptive statistical methods to describe the overall evaluation results. Based on the findings, it is expected to provide an in-depth view of the differentiated learning program, contribute to the development of the program in the future, and become a guideline for improving the quality of mathematics learning in the Lebak district. The results of this training program evaluation show that the differentiated learning training activities have been well implemented in MGMP Mathematics Sub Rayon 2 Lebak District. This is evidenced by the level of teacher satisfaction in participating in the training, the majority of which were at scores 4 and 5, namely agreeing and strongly agreeing. This was also the case with the resource persons, materials, and training facilities, and organization. It is hoped that in the future continue to carry out ongoing training related to differentiated learning by current needs and to improve the competence of mathematics teachers in particular, as well as teachers of other subjects in general. (shrink)

The goal of this chapter is to provide an interpretation of experiential learning that fully detaches itself from the epistemological presuppositions of empiricist and intellectualist accounts of learning. I first introduce the concept of schema as understood by Kant and I explain how it is related to the problems implied by the empiricist and intellectualist frameworks. I then interpret David Kolb’s theory of learning that is based on the concept of learning cycle and represents an attempt to overcome the corresponding (...) drawbacks of these frameworks. I show that Kolb’s theory fails to achieve its goal because it is rooted in some of the fundamental epistemological presuppositions of these frameworks. Subsequently, I present a group of works from phenomenology, in particular Merleau-Ponty’s, in order to show that Kolb’s attempt is insufficient due to a lack of understanding of the problem expressed by Kant via the concept of schema. Finally, I outline an interpretation of experiential learning as differentiation of experiential schemas and explain how it meets the epistemological challenges outlined above. (shrink)

As a philosophical paradigm, differential heterogenesis offers us a novel descriptive vantage with which to inscribe Deleuze’s virtuality within the terrain of “differential becoming,” conjugating “pure saliences” so as to parse economies, microhistories, insurgencies, and epistemological evolutionary processes that can be conceived of independently from their representational form. Unlike Gestalt theory’s oppositional constructions, the advantage of this aperture is that it posits a dynamic context to both media and its analysis, rendering them functionally tractable and set in relation to other (...) objects, rather than as sedentary identities. Surveying the genealogy of differential heterogenesis with particular interest in the legacy of Lautman’s dialectic, I make the case for a reading of the Deleuzean virtual that departs from an event-oriented approach, galvanizing Sarti and Citti’s dynamic a priori vis-à-vis Deleuze’s philosophy of difference. Specifically, I posit differential heterogenesis as frame with which to examine our contemporaneous epistemic shift as it relates to multi-scalar computational modeling while paying particular attention to neuro-inferential modes of inductive learning and homologous cognitive architecture. Carving a bricolage between Mark Wilson’s work on the “greediness of scales” and Deleuze’s “scales of reality”, this project threads between static ecologies and active externalism vis-à-vis endocentric frames of reference and syntactical scaffolding. (shrink)

The problem discussed in this paper arises from the observation that in the course of inter-subjective communication "understanding" seems to be entrusted to the implementation of a real process, not only affective but also cognitive, of processing information contained in the perceived behavior. In a previous study (Greco, 1979) we proposed to consider this process of "reconstruction" of meaning as analogous to the process of "construction" used for oneself. Here we will deal with this process of construction or awareness using (...) theoretical models offered by experimental research. (shrink)

We discuss central aspects of history of the concept of an affine differentiable manifold, as a proposal confirming the need for using some quantitative methods (drawn from elementary Model Theory) in Mathematical Historiography. In particular, we prove that this geometric structure is a syntactic rigid designator in the sense of Kripke-Putnam.

The original book chapter does not have an abstract. However, I have written an abstract for this repository: Religious life encompasses a wide diversity of situations for which the emotional tone is on a continuum from extreme euphoria to extreme dysphoria. In this book chapter, we propose the novel hypothesis that euphoria and dysphoria have distinctly separate functional consequences for religious evolution and survivability. This is due to the differential cognitive states that are created in euphoric and dysphoric situations. Based (...) on readings from religious studies and cognitive psychology, we propose that euphoria in religion is conducive to social bonding and situations needing lateral thinking and creativity; whereas dysphoria in religion is conducive to situations where precision and analogical reasoning are necessary. (shrink)

In a number of articles, Hans-Johann Glock has argued against the »lingualist« view that higher mental capacities are a prerogative of language-users. He has defended the »assimilationist« claim that the mental capacities of humans and of non-human animals differ only in degree. In the paper under discussion, Glock argues that animals are capable of acting for reasons, provided that reasons are construed along the lines of the new »objectivist« theory of practical reasons. The paper critizices these views.

Background: Individuals with psychopathic traits demonstrate an attenuated emotional response to aversive stimuli. However, recent evidence suggests heterogeneity in emotional reactivity among individuals with psychopathic or callous-unemotional (CU) traits, the emotional detachment dimension of psychopathy. We hypothesize that primary variants of psychopathy will respond with blunted affect to negatively valenced stimuli, whereas individuals marked with histories of childhood trauma/maltreatment exposure, known as secondary variants, will display heightened emotional reactivity. To test this hypothesis, the present study examined fear-potentiated startle between psychopathy (...) variants while viewing aversive, pleasant, and neutral scenes. Method: 238 incarcerated adolescent (M age = 16.8, SD = 1.11 years) boys completed a picture-startle paradigm and self-report questionnaires assessing CU traits, antisocial-aggressive behavior, and maltreatment. Results: Latent profile analyses identified four classes; primary variants (high CU traits, high aggression, low maltreatment; n = 46), secondary variants (high CU traits, high aggression, high maltreatment; n = 42), and two nonpsychopathic groups differentiated on maltreatment experience (n = 148). Findings from an ANOVA comparing identified groups on startle amplitude difference scores (i.e., aversive-neutral) suggested a main effect for group, F(3,196)=8.91, p<.001, η2 = .12. Primary variants of juvenile psychopathy displayed reduced startle potentiation to aversive images (threat and victim scenes), whereas secondary variants distinguished by high levels of childhood maltreatment did not. Conclusions: Findings add to a rapidly growing body of literature supporting the possibility of multiple developmental pathways to psychopathy (i.e., equifinality), and extend it by finding support for divergent potential biomarkers between primary and secondary psychopathy variants. (shrink)

The purpose of the article is to consider the socio-cultural aspect of the processes of integration and differentiation in the development of the system of education in Russia that undergoes changes in a globalized society.

The study aimed to determine if differentiated instruction effectively addresses learning gaps in mathematics. In particular, it explored how it can improve the student’s learning gaps concerning mathematical performance and confidence. The study employed a quasi-experimental design with 30 purposively-selected Grade 10 participants divided into differentiated (n = 15) and control groups (n = 15), ensuring the utmost ethical measures. The mean and standard deviation were used to describe the participants’ performance and confidence. Independent samples t-tests were used to determine (...) the significant differences in the performance and confidence between the two groups. In contrast, dependent samples t-tests were used to determine the significant differences in each group’s pre and posttest performance and confidence. Findings bared that the differentiated instruction successfully addressed students’ performance in mathematics even in a short period. It also increased the participants’ confidence when answering fundamental problems. Continuing differentiated instruction activities are recommended since it benefits students who struggle in mathematics, particularly in answering fundamental operations. Differentiated teaching activities in mathematics can boost academic achievement and engagement and prepare students for future success while fostering a positive and inclusive classroom culture that values individual learning needs and preferences. (shrink)

Half of the drug offenders incarcerated in the United States are black, even though whites and blacks use and sell drugs at the same rate, and blacks make up only 13 percent of the population. Noncomparativists about retributive justice see nothing wrong with this picture; for them, an offender’s desert is insensitive to facts about other offenders. By contrast, comparativists about retributive justice assert that facts about others can partially determine an offender’s desert. Not surprisingly, comparativists, especially comparative egalitarians, contend (...) that differential punishment is retributively unjust. I agree with this assessment, but take issue with the reasons egalitarians cite in its favor. In this paper, I argue that differential punishment violates retributive justice because it contributes to structural racial oppression. Over the course of developing and defending this claim, I identify the shortcomings of both comparative egalitarianism and respectarianism, which is the most popular and plausible brand of noncomparativism. (shrink)

In a number of articles, Hans-Johann Glock has argued against the »lingualist« view that higher mental capacities are a prerogative of language-users. He has defended the »assimilationist« claim that the mental capacities of humans and of non-human animals differ only in degree. In the paper under discussion, Glock argues that animals are capable of acting for reasons, provided that reasons are construed along the lines of the new »objectivist« theory of practical reasons.

Review of Daoist Identity. History, Lineage, and Ritual, by Livia Kohn and Harold D. Roth.

This chapter presents four arguments supporting an age-differentiated tax on bequests, that is, a tax rate on bequests that is varying with the age of the deceased. Whereas those arguments are based on various ethical foundations, and lead to an inheritance tax that can be either increasing or decreasing with the age of the deceased, our comparative analysis leads us to regard one of these arguments as more convincing than the three others: the argument supporting a bequest tax increasing with (...) the age of the deceased, on the grounds of the compensation of unlucky prematurely dead persons in a world of imperfect information. (shrink)

We evaluated the reliability, validity, and differential item functioning (DIF) of a shorter version of the Defining Issues Test-1 (DIT-1), the behavioral DIT (bDIT), measuring the development of moral reasoning. 353 college students (81 males, 271 females, 1 not reported; age M = 18.64 years, SD = 1.20 years) who were taking introductory psychology classes at a public University in a suburb area in the Southern United States participated in the present study. First, we examined the reliability of the bDIT (...) using Cronbach’s α and its concurrent validity with the original DIT-1 using disattenuated correlation. Second, we compared the test duration between the two measures. Third, we tested the DIF of each question between males and females. Findings reported that first, the bDIT showed acceptable reliability and good concurrent validity. Second, the test duration could be significantly shortened by employing the bDIT. Third, DIF results indicated that the bDIT items did not favour any gender. Practical implications of the present study based on the reported findings are discussed. (shrink)

According to the No Alternate Possibilities argument, if time passes then the rate at which it passes could be different but time cannot pass at different rates, and hence time cannot pass. Typically, defenders of the NAP argument have focussed on defending premise, and have taken the truth of for granted: they accept the orthodox view of rate necessitarianism. In this paper we argue that the defender of the NAP argument needs to turn her attention to. We describe a series (...) of worlds that appear to contain differential passage: worlds where time passes at different rates in different subregions. If the NAP argument is to succeed, rate necessitarians must show that each of these worlds is either metaphysically impossible, or does not contain differential passage. (shrink)

There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer - the Infinity Computer - able to work numerically with finite, infinite, and infinitesimal number. It is proved that the Infinity Computer is able (...) to calculate values of derivatives of a higher order for a wide class of functions represented by computer procedures. It is shown that the ability to compute derivatives of arbitrary order automatically and accurate to working precision is an intrinsic property of the Infinity Computer related to its way of functioning. Numerical examples illustrating the new concepts and numerical tools are given. (shrink)

We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...) to the compound formulas of PA over N---I_PA(N; SV ) and I_PA(N; SC). We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both I_PA(N; SV ) and I_PA(N; SC). We then show: (a) that if we assume the satisfaction and truth of the compound formulas of PA are always non-finitarily decidable under I_PA(N; SV ), then this assignment corresponds to the classical non-finitary putative standard interpretation I_PA(N; S) of PA over the domain N; and (b) that the satisfaction and truth of the compound formulas of PA are always finitarily decidable under the assignment I_PA(N; SC), from which we may finitarily conclude that PA is consistent. We further conclude that the appropriate inference to be drawn from Goedel's 1931 paper on undecidable arithmetical propositions is that we can define PA formulas which---under interpretation---are algorithmically verifiable as always true over N, but not algorithmically computable as always true over N. We conclude from this that Lucas' Goedelian argument is validated if the assignment I_PA(N; SV ) can be treated as circumscribing the ambit of human reasoning about `true' arithmetical propositions, and the assignment I_PA(N; SC) as circumscribing the ambit of mechanistic reasoning about `true' arithmetical propositions. (shrink)

Nineteenth-century scientist Hermann von Helmholtz’s peculiar wavering between empiricism and transcendentalism in his philosophy of science in general, and in his theory of perception in particular, is a much debated and well-documented topic in the history and philosophy of science. This contribution aims at providing a fresh angle on this classical issue, by considering Helmholtz’s account of differential consciousness against the background of a centuries-old philosophical debate between the empiricist tradition and the tradition of transcendental idealism. By placing Helmholtz’s psychology (...) against the background of a historical narrative stretching from Hume to Fichte, one can gain insight into the possible merits of his empirico-transcendentalism with regard to the problem of differentiation. More particularly, it is argued that Helmholtz’s psychology tilted towards transcendentalism when met with the classical theoretical problems of strict empiricism in dealing with the foundation of consciousness, most notably circularity and infinite regress. Without claiming that Helmholtz’s theorizing presented a self-conscious attempt to overcome the latter issues, his well-known wavering between perspectives in general, and his appropriation of the a priori in particular, might have served him well in avoiding the deadlocks of empiricism. As noted at the end, however, Helmholtz’s account produced complex philosophical problems of its own. (shrink)

In this paper we study the connection between the use of evaluative language and the building of both personal and social identities, from the perspective of Dynamical System Theory. We primarily discuss two issues: 1) The use of evaluation ) as a means to the construction of both individual and group identities, thus exploring how the connection between linguistic choices and social identities is shaped by interactional needs for stancetaking. In order to illustrate this connection, we examine examples of the (...) use of evaluative language in a web social network, and we analyze some of the discourse elements showing ways of positioning that act as catalysts for the emergence of a multifactorial dynamic system of identities. 2) The consideration of Dynamical System Theory as a theoretical framework for the modeling of language and identity. Although originally a mathematical theory, DST has been adopted by cognitive science as a valid framework for the study of cognitive phenomena, on the grounds that natural cognition is a dynamical phenomenon. Within the realm of linguistics and pragmatics, this study is to a certain degree in line with some recent studies such as Gibbs, Geeraerts, Kristiansen and Peirsman, or Moreno Fernández. Thus, we herein focus on how linguistic evaluation intervenes in the intricate dynamical system of identity, and even though we do not engage in complex mathematical disquisition, we argue that the idea and philosophical foundation underlying DST can lead us towards the ‘integration’ of the complex equation of identity construction, and that consequently the field has great potential for further research. (shrink)

Some have argued that advances in the science of human decision-making, particularly research on automaticity and unconscious priming, would ultimately thwart our commonsense understanding of free will and moral responsibility. Do people interpret this research as a threat to their self-understanding as free and responsible agents? We approached this question by seeing how feelings of surprise mediate the relationship between personal sense of control and third-personal attributions of free will and responsibility. Across three studies (N = 1,516) we found that (...) people with a greater sense of personal control were more surprised at the results of experiments showing effects of unconscious priming on moral behavior. Surprise differentially mediated the relationship between personal control and attributions of free will and responsibility: people attributed less free will and more responsibility as they were more surprised. This suggests that people exhibit defensive thinking with respect to responsibility, but not free will. (shrink)

In this perspective paper, I tried to explain that what will be the possible prospect of multiple functions in one and another through the chain rule of differentiation? The chain rule is a formula to compute the derivative of the functional composition of two or more functions. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. The (...) chain rule in that what changes I noted, how it can be modified to reduce the differentiation process of multiple functions in one and another and implementing that process in the inverse of multiple functions in one and another, further proceedings them through the chain rule of differentiation with all prospects. Here I claim that the differentiation’s chain rule is not changed but the sequences of finding the derivative of multiple functions are changed. (shrink)

The influential apoha theory of concept formation of the seventh-century Buddhist Dharmakīrti stands as a philosophically powerful articulation of how language could work in the absence of real universals. In brief, Dharmakīrti argues that concepts are constructed through a goaloriented process that delimits the content of an experience by ignoring whatever does not conform to one's conditioned expectations. There are no real similarities that ground this process. Rather, a concept is merely what's left over once one has glossed over enough (...) of the differences between elements of one's awareness that one can judge the remainder to have the same effects as what one... (shrink)

Hume discusses the distinction of reason to explain how we distinguish things inseparable, and so identical, e.g., the color and figure of a white globe. He says we note the respect in which the globe is similar to a white cube and dissimilar to a black sphere, and the respect in which it is dissimilar to the first and similar to the second. Unfortunately, Hume takes these differing respects of resemblance to be identical with the white globe itself. Contradiction results, (...) undermining his theory of abstraction. The way out is apparently to admit an intrinsic complexity in even simple things. (shrink)

Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to be indefensible (...) for mathematical reasons. This implies that the relation between to-pology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as logical empiricists used to say. (shrink)

Bioethicists often present ‘saving lives’ as a goal distinct from, and competing with, that of extending lives by as much as possible. I argue that this usage of the term is misleading, and provides unwarranted rhetorical support for neglecting the magnitudes of the harms and benefits at stake in medical allocation decisions, often to the detriment of the young. Equal concern for all persons requires weighting equal interests equally, but not all individuals have an equal interest in ‘life-saving’ treatment.

In recent years, a growing discussion about how we should design our cities has emerged, particularly for the more controversial modes of design such as “defensive,” “hostile,” or “disciplinary” architecture (i.e., benches on which one cannot sleep, or metal studs on which one cannot skate). Although this debate is relatively mature, many studies have argued that these design notions are undertheorized and are, thus, challenging to study from an empirical and normative perspective. In this paper, I will defne the most (...) common terms used in the literature and show how they are interconnected by utilizing a set of “conditions of adequacy” from philosophy to facilitate a more transparent and well-grounded discussion of them. Terms such as “hostile” and “defensive” design are underlined by several diferent phenomena, not just one as is sometimes commonly assumed. I will also show that these phenomena and their conceptualizations require—and sometimes force us to use—diferent moral reasons when justifying the utilization of diferent designs. (shrink)

There is a conflict between a strictly political approach to LGBT rights, in which the battle must never cease. and the less encountered notion that individuals can let the battle settle into the background and simply get on with unpolitical life. at least unpolitical at home. The article takes the example of India as a salient place to view this conflict. As a democratic nation, India has had some limited progress in protecting LGBT rights. How its massively differentiated and traditional (...) society has adopted and tolerated this moral enjoinder is another matter. Certainly, acceptance is as important as legal recognition. But how are the politics faring at the individual level? One of the best media for feeling a nation’s political pulse is not internet or television but literature. Two current Indian authors exemplify how, at the personal level, some sexual politicking has already succeeded, in some social realms, by almost disappearing from the narrative. (shrink)

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation .

In this paper, I attempt to look at the differential (as in interventionist) readings undertaken by speculative realists (A school of contemporary thought reacting against post-Kantian 'Correlationism') Iain Hamilton Grant and Ray Brassier, with the former concentrating on reading Schelling's naturalism relating to reason, while the latter claiming the constancy of thought's connection to thought. For Brassier, thought must be transcendentally separate from nature, or what he calls 'exteriority', and Grant insists on nature's thinking as plain nature. This doesn't mean (...) 'interiority' is given weight in Grant's thought, but, on the contrary isn't a concern, as for him, the limiting factor of thinking (dichotomy in subject-object relationality) is the regionality of a particular identity attempting to grasp nature's infintude. Brassier maintains scientific statements as capable of supplying reasons for believing in the possibilities of determining thought's tracking and missing nature. He accomplishes this by clarifying notions of concept and distinguishing objects from concepts. This alien-ness of thought generates the possibilities of questioning the human production as against nature. This cardinal issue tries to answer the repercussions probably generated in the wake of either apathetic aspects of mind or the deepest powers of speculation. Not only that, a simultaneous questioning of the legitimacy of ontology and epistemology in the natural world is encountered. Grant advocates the objectifying of the self to grasp the productivity of self's thinking, but at the same time considering objectifying as an ongoing process, a kind of 'becoming'. In other words, it is the questioning of the limits of 'being' in the creation of episteme that takes precedence in Grant. Brassier on the other hand is concerned with the doing away of the dichotomy of being and thinking of meaning. This tension raises the issue of nature philosophy in a duel of 'eliminativism' and 'materialism', between the extent that calls for grounding nature without reliance on a structure undermining the discovery of contemporary science or supporting an anthropic view. (shrink)