The first thing to realize about grading as a psychological process is that it precedes measurement and counting. Judgments of the type “A is larger than B” or “This can contains less milk than that” are made long before it is possible to say, e.g., “A is twice as large as B” or “A has a volume of 25 cubic feet, B a volume of 20 cubic feet, therefore A is larger than B by 5 cubic feet,” or “This can (...) contains a quart of milk, that one 3 quarts of milk, therefore the former has less milk in it.” In other words, judgments of quantity in terms of units of measure or in terms of number always presuppose, explicitly or implicitly, preliminary judgments of grading. The term four means something only when it is known to refer to a number which is “less than” certain others, say five, six, seven, arranged in an ordered series of relative mores and lesses, and “more than” certain others, say one, two, three, arranged in an ordered series of relative mores and lesses. Similarly, a foot as a unit of linear measure has no meaning whatever unless it is known to be more than some other stretch, say an inch, and less than a third stretch, say a yard. (shrink)

This paper begins with a description of common grading practices at universities in the U.S., and analyzes the unfairness, injustice, and harm they produce. It then proposes a solution to these problems in the form of an alternative grading system: institutions should adopt a grading system that assesses students’ performance relative to the performance of their peers. That is, institutions should abolish the practice of attempting to assign grades that correspond to an absolute standard of intrinsic merit. Instead, our (...) evaluation should simply communicate how the quality of a student’s work compares to the work submitted by other students in the class. (shrink)

Any adequate semantics of generic sentences (e.g., “Philosophers evaluate arguments”) must accommodate both what we call the positive data and the negative data. The positive data consists of observations about what felicitous interpretations of generic sentences are available. Conversely, the negative data consists of observations about which interpretations of generic sentences are unavailable. Nguyen argues that only his pragmatic neo-Gricean account and Sterken’s indexical account can accommodate the positive data. Lee and Nguyen have advanced the debate by arguing that the (...) negative data is a problem for both Nguyen’s and Sterken’s accounts; these two accounts seem to incorrectly predict that generics have felicitous interpretations that they, in fact, fail to have. In this paper, we advance this debate—and, more generally, the task of developing an adequate formal semantics of generics—by arguing that a neglected class of theories are compatible with both the positive data and the negative data. Specifically, we argue that treating the generic operator GEN as a relative gradable expression with a positive, upper- and lower- bounded scale helps accommodate the positive data and the negative data. While developing this view, we show how several previously developed semantics of generics may systematically accommodate both sets of data. One broad contribution of this paper is to show that, while they generate important desiderata, the positive and negative data cannot determine a unique semantics for generics. A further contribution of this paper is to highlight previously unnoted ways in which degree semantics may inform semantic theories of generic meaning. (shrink)

A child’s age in comparison to the age of her or his classmates (relative age) has been found to be an influential factor on academic achievement, particularly but not exclusively at the beginning of formal schooling. However, few studies have focused on the generalizability of relative age effects. To close this gap, the present study analyzes the generalizability across students with and without immigrant backgrounds, across three student cohorts that entered school under a changing law of school enrollment, and across (...) classes. To this end, we capitalized on representative large-scale data sets from three student cohorts attending public schools in Berlin, the capital of Germany. We analyzed the data using a multilevel framework. Our results for the overall student sample indicate relative age effects for reading and mathematics in favor of the relatively older students in Grade 2 that become somewhat smaller in size in Grade 3. By Grade 8, relative age effects had vanished in reading and had even reversed in favor of the relatively young in mathematics. Furthermore, relative age effects were not found to be systematically different among students with and without immigrant backgrounds, student cohorts, or across classes. Taken together, these results empirically underscore the broad generalizability of the findings as found for the overall student population and replicate the pattern of findings on relative effects as identified by the majority of previous studies. (shrink)

In this work we extend results from [4], [3] and [2] about propositional calculi with graded modalities to the predicative level. Our semantic is based on Kripke models with a single domain of interpretation for all the worlds. Therefore the axiomatic system will need a suitable generalization of the Barcan formula. We haven't considered semantics with world-relative domains because they don't present any new difficulties with respect to classical case. Our language will have, as in [1], constant and function symbols, (...) but they will have a rigid interpretation. In this instance the terms will be considered rigid designators, that is, their interpretations will be the same in all possible worlds (cfr. [5]). Nevertheless we will not consider languages with identity: in this way we avoid the problems of identity in modal contexts. On the other hand, we think that in that context would arise essentially the same problems which occur in classical predicative modal logic. Finally we will consider only denumerable languages because the extension to non denumerable ones isn't conceptually problematic. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been (...) studied in some detail. However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (shrink)

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...) spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: that a conditional is logically independent from its antecedent; that a sequence of antecedents behaves like a single conjunctive antecedent ; and that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. (shrink)

In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to use elements of a non-classical logic. Specifically, we focus here on causality, as a concept tightly related with the assumption of there being distinct, separate events, proposing a model according to which it can be considered (...) to be spatio-temporally graded. It is outlined how this can be described using the formalism of fuzzy sets theory, with the degree of causality varying between 1, that is no separation between causes and effects, and 0, that is perfect separation between causes and their effects as in classical ’billiard balls’ models of physical systems, namely such based on the notion of ideal mathematical point. Our model posits that subjective moments of time are like fuzzy sets, with their extension determined by local degrees of causality, resulting from information integration processes extended gradually in space and time. This, we argue, is how a notion of causality could be, to a certain degree, spared and reconciled with a variant of Bergsonian duration theory as formulated in the theory of continuous change. Relation of the proposed viewpoint to other theories, as well as possible solutions it suggests to various problems, in particular the measurement problem, are also discussed. (shrink)

As a branch of statistical latent variable modeling, multidimensional item response theory plays an important role in psychometrics. Multidimensional graded response model is a key model for the development of multidimensional computerized adaptive testing with graded-response data and multiple traits. This paper explores how to automatically identify the item-trait patterns of replenished items based on the MGRM in MCAT. The problem is solved by developing an exploratory pattern recognition method for graded-response items based on the least absolute shrinkage and selection (...) operator, which is named LPRM-GR and facilitates the subsequent parameter estimation of replenished items and helps maintaining the effectiveness of item replenishment in MCAT. In conjunction with the proposed approach, the regular BIC and weighted BIC are applied, respectively, to select the optimal item-trait patterns. Simulation for evaluating the LPRM-GR in pattern recognition accuracy of replenished items and the corresponding item estimation accuracy is conducted under multiple conditions across different numbers with respect to dimensionality, response-category numbers, latent trait correlation, stopping rules, and item selection criteria. Results show that the proposed method with the two types of BIC both have good performance in pattern recognition for item replenishment in the two- to four-dimensional MCAT with the MGRM, for which the weighted BIC is generally superior to the regular BIC. The proposed method has relatively high accuracy and efficiency in identifying the patterns of graded-response items, and has the advantages of easy implementation and practical feasibility. (shrink)

Selected elementary (Grades 4 through 6) and secondary (Grades 7 through 12) science textbooks were examined for their treatment of engineering and technology relative to the national science and mathematics standards in the areas of connections to technology and society.Elementary textbooks were found to have significant connections between science concepts and technology and society; however, the treatment was often superficial and/or indirect.Activities were mostly teacher-directed with little opportunity for designing, making, and testing things.Connections to mathematics concepts were rare.Secondary (...) textbooks made use of extensive technology in lab work and provided students with many connections between science concepts, technology, and society.They did a better job of presenting mathematics concepts in word problems, and some engineering and design projects were fostered.The major concern found with both elementary and secondary texts was the glaring lack of solid connections to mathematics. (shrink)

Parmi les travailleurs handicapés, plusieurs ont des emplois à temps partiel. Cependant, la recherche sur la relation entre handicap et travail à temps partiel n’a que partiellement éclaircit la façon dont les personnes handicapées qui reçoivent une pension d’invalidité complète ou partielle perçoivent et gèrent l’articulation entre travail à temps partiel et leur pension. Cet article s’intéresse aux stratégies employées par les personnes handicapées, tel qu’elles le racontent, pour gérer cette articulation. Le travail à temps partiel, utilisant les données d’entretiens (...) avec 10 citoyens norvégiens sont mobilisées. Les résultats montrent que la flexibilité et la visibilité sont des stratégies spécifiques que nos informateurs mettent en place quand les problèmes de santé et les heures de travail réduites ont comme résultat une connexion affaiblie avec le lieu de travail. L’article montre la façon dont le discours autour de l’emploi payé facilite ces stratégies. L’article se conclue sur des recommandations relatives aux conditions à mettre en place pour accompagner l’articulation entre travail à temps partiel et pension d’invalidité partielle. (shrink)

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by (...) adapting the Arrow–Sen framework for social choice to study grading in groups. (shrink)

This paper proposes a new model of graded modal judgment. It begins by problematizing the phenomenon: given plausible constraints on the logic of epistemic modality, it is impossible to model graded attitudes toward modal claims as judgments of probability targeting epistemically modal propositions. This paper considers two alternative models, on which modal operators are non-proposition-forming: (1) Moss (2015), in which graded attitudes toward modal claims are represented as judgments of probability targeting a “proxy” proposition, belief in which would underwrite belief (...) in the modal claim. (2) A model on which graded attitudes toward modal claims are represented as judgments of credence taking as their objects (non-propositional) modal representations (rather than proxy propositions). The second model, like Moss’ model, is shown to be semantically and mathematically tractable. The second model, however, can be straightforwardly integrated into a plausible model of the role of graded attitudes toward modal claims in cognition and normative epistemology. (shrink)

Theories of graded causation attract growing attention in the philosophical debate on causation. An important field of application is the controversial relationship between causation and moral responsibility. However, it is still unclear how exactly the notion of graded causation should be understood in the context of moral responsibility. One question is whether we should endorse a proportionality principle, according to which the degree of an agent’s moral responsibility is proportionate to their degree of causal contribution. A second question is whether (...) a theory of graded causation should measure closeness to necessity or closeness to sufficiency. In this paper, we argue that we should indeed endorse a proportionality principle and that this principle supports a notion of graded causation relying on closeness to sufficiency rather than closeness to necessity. Furthermore, we argue that this insight helps to provide a plausible analysis of the so-called ‘Moral Difference Puzzle’ recently described by Bernstein. (shrink)

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address (...) arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory—the Threshold Model—is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use. (shrink)

Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This article develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resulting account takes actual causation to be both graded and (...) comparative. We then show how our account would handle a number of standard cases. 1 Introduction2 Causal Models3 The HP Definition of Actual Causation4 The Problem of Isomorphism5 Defaults, Typicality, and Normality6 Extended Causal Models7 Examples7.1 Omissions7.2 Knobe effects7.3 Causes versus background conditions7.4 Bogus prevention7.5 Causal chains7.6 Legal doctrines of intervening causes7.7 Pre-emption and short circuits8 Conclusion. (shrink)

Fair grading is modeled on two fundamental principles. The first principle is that grading should be impartial and consistent. The second principle is that a fair grade should be based on the student’s competence in the academic content of the course. I derive corollary principles of fair grading from these two basic principles and use them to evaluate common grading practices. I argue that exempting students from completing certain grade components is unfair, as is grading on attendance, class rank, deportment,tardiness, (...) effort, institutional values, moral virtues such as cheerfulness and helpfulness, and other non-course-content criteria. (shrink)

This study investigated grade level differences in teacher feedback, students’ self-regulated learning (SRL), and their relationship. Secondary students participated (N = 1,260; 430 tenth-, 460 eleventh-, and 370 twelfth-graders). Latent factor mean difference analyses suggested that teacher feedback and students’ SRL level varied across grades. Comparatively, tenth-grade teachers were perceived to provide verification feedback, scaffolding feedback, and praise most frequently; twelfth-grade teachers were perceived to provide directive feedback and criticism most frequently; and eleventh-grade teachers were perceived to provide all (...) types of feedback least frequently. Students’ SRL generally declined as they aged. Results from three-group structural equation modelling indicated that praise generally had the strongest correlations with SRL regardless of grade level; directive feedback was negatively correlated with tenth-graders’ SRL but positively correlated with eleventh- and twelfth-graders’ SRL; scaffolding and verification feedback were positively correlated with eleventh-graders’ SRL; and criticism had small correlations with SRL, regardless of grade level. (shrink)

The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of metaphysical accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, another (...) based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multi-dimensional properties. Our second aim is to demonstrate that the choice between these accounts can make a substantial metaphysical difference. To make this point, we rely on two case studies (involving quantum observables and values) in which we apply the accounts in order to model apparent cases of metaphysical gradedness. (shrink)

This essay develops standards for grading religions including various forms of spiritualism. First, I examine the standards proposed by William James, John Hick, Paul Knitter, Dan Cohn-Sherbok, and Harold Netland. Most of them are useful in grading religions with or without conditions. However, those standards are not enough for refined and piercing evaluation. Thus, I introduce standards used in spiritualism. Although those standards are for grading spirits and their teachings, they are useful in refined and piercing evaluation of religious phenomena. (...) The spiritual standards complement James's, Hick's, Knitter's, and Netland's standards. Although most of the spiritual standards are rationally unjustifiable, they have practical value. (shrink)

Wilfred Sieg. Relative Consistency and Accesible Domains.

Excerpt from Relativity: The Electron Theory and Gravitation The first edition of this book was published while the General Principle of Relativity was being worked out, before it seemed possible to arrive at any confirmation from observation. Shortly after, however, it was shown that the new theory explained the motion of the perihelion of Mercury, and now the result of the Solar Eclipse expedition has clinched matters. It seemed best to leave practically untouched the account of the special (...) principle as the natural avenue of approach to the broader view, which is described at length in Part II. Acknowledgment is due to the authors friends, Prof. H. F. Baker and Mr. E. V. Appleton, who kindly read through the proofs of the new matter. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)