This chapter contains sections titled: Sorting without Gaps Sharp Semantic Cutoffs and Higher‐Order Vagueness Judgment Situations References.

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)

This paper considers Kamp and Partee's account of graded membership within a conceptual spaces framework and puts the account to the test in the domain of colors. Three experiments are reported that are meant to determine, on the one hand, the regions in color space where the typical instances of blue and green are located and, on the other hand, the degrees of blueness/greenness of various shades in the blue–green region as judged by human observers. From the locations of the (...) typical blue and typical green regions in conjunction with Kamp and Partee's account follow degrees of blueness/greenness for the color shades we are interested in. These predicted degrees are compared with the judged degrees, as obtained in the experiments. The results of the comparison support the account of graded membership at issue. (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)

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)

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)

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability (...) of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand. (shrink)

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)

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)

An action is unratifiable when, on the assumption that one performs it, another option has higher expected utility. Unratifiable actions are often claimed to be somehow rationally defective. But in some cases where multiple options are unratifiable, one unratifiable option can still seem preferable to another. We should respond, I argue, by invoking a graded notion of ratifiability.

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)

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)

This chapter contains sections titled: The Climbing Grade Question Relationalism About Climbing Grades Climbing Grades as Emerging Real Dispositions Standard Climbers in Standard Climbing Conditions Relationalism: The Better Theory Notes.

This paper is concerned with a version of Kamp and Partee's account of graded membership that relies on the conceptual spaces framework. Three studies are reported, one to construct a particular shape space, one to detect which shapes representable in that space are typical for certain sorts of objects, and one to elicit degrees of category membership for the various shapes from which the shape space was constructed. Taking Kamp and Partee's proposal as given, the first two studies allowed us (...) to predict the degrees to which people would judge shapes representable in the space to be members of certain categories. These predictions were compared with the degrees that were measured in the third study. The comparison yielded a test of the account of graded membership at issue. The outcome of this test was found to support the conceptual spaces version of Kamp and Partee's account of graded membership. (shrink)

This paper investigates the relationship between two evaluative claims about agents’ de- grees of belief: (i) that it is better to have more, rather than less accurate degrees of belief, and (ii) that it is better to have less, rather than more probabilistically incoherent degrees of belief. We show that, for suitable combinations of inaccuracy measures and incoherence measures, both claims are compatible, although not equivalent; moreover, certain ways of becoming less incoherent always guarantee improvements in accuracy. Incompatibilities between particular (...) incoherence and inaccuracy measures can be exploited to argue against particular ways of measuring either inaccuracy or incoherence. (shrink)

Drawing on the work of Linda Farmer, this article describes a detailed grading grid coupled with a rubric designed for the purpose of assessing argumentative papers. The rubric consists of two main parts: Content and Style. Relying upon Bloom’s taxonomy of learning, the “Content” part of the rubric assesses a student’s understanding of the material, the argument of their paper, and various abilities concerning analysis, synthesis, evaluation, and creation. The “Style” part of the rubric is split into two parts: Clarity (...) and Organization. Coupling this rubric with a grading grid, the author provides an example of a method for the effective grading of argumentative essays. (shrink)

The inclusion of attendance and participation in course grade calculations is ubiquitous in postsecondary syllabi, but can penalize the silent or anxious student unfairly. I outline the obstacles posed by social anxiety, then describe an assignment developed with the twin goals of assisting students with obstacles to participating in spoken class discussions, and rewarding methods of participation other than oral interaction. When homework assignments habituating practices of writing well-justified questions regarding well-documented passages in reading assignments are the explicit project of (...) weekly class meetings, participation increases on the part of all students. My focus shifted away from concern that I must get students to talk more, and turned instead to ensuring their marks reflected their learning rather than their speaking. Students’ improved engagement as a result of the assignment bears out evidence in the literature for active learning and for alternatives to taking attendance and quantifying participation. (shrink)

In the human cognitive economy there are four grades of epistemic involvement. Knowledge partitions into distinct sorts, each in turn subject to gradations. This gives a fourwise partition on ignorance, which exhibits somewhat different coinstantiation possibilities. The elements of these partitions interact with one another in complex and sometimes cognitively fruitful ways. The first grade of knowledge I call “anselmian” to echo the famous declaration credo ut intelligam, that is, “I believe in order that I may come to know”. (...) As construed here, one knows in this anselmian way that E = mc2 just in case one knows that sentence expresses a true statement, but without having to understand the proposition it expresses. Most epistemologists ignore the significance of this grade of epistemic involvement. In a second grade of epistemic involvement, knowing that E = mc2 is knowing what that sentence means and understanding the proposition it express. This is knowledge in the propositional or semantic sense, and is the dominant target of epistemological investigation. Tacit and implicit knowledge occupies another tier. A typical example would be something that someone has “known all along” but, until now, hasn’t had occasion to put her mind to it or formulate in words. TI-knowledge remains a minority interest in today’s epistemology. Operating at a fourth grade of epistemic involvement is what I call “impact”-knowledge, which is the knowledge of a matter at its deepest and most widespread. An example, to be discussed below, is the knowledge that was generated by the Wiles proof of Fermat’s last theorem. Its true importance lies not only, or even mainly, in its verification of a commonly accepted fact about numbers, but rather in its enrichment of the mathematics of elliptical curves and the promise it holds for greater advancement into the mathematical unknown. Knowledge of this fourth grade has yet to find a seat in the parliaments of epistemology. Knowledge of the anselmian sort is independent of the other three. Tacit and implicit knowledge is incompatible with anselmian and semantic knowledge but coinstantiable with impact-knowledge. Semantic knowledge is incompatible with tacit and implicit knowledge but coinstantiable with the others. Impact-knowledge is pairwise coinstantiable with the others. Below I will bring the ignorance partitions into such alignment as they have with these ones. In doing so, I’ll propose a naturalized causal response epistemology designed to give these interactive distinctions the theoretical air they need to breathe. (shrink)

In this paper, I explore how to accommodate non-consequentialist constraints with a broadly value-based conception of reasons for action. It turns out that there are two grades of non-consequentialist constraints. The first grade involves attaching ethical importance to such distinctions as the doing/allowing distinction, and the distinction between intended and unintended consequences that is central to the Doctrine of Double Effect. However, at least within the value-based framework, this first grade is insufficient to explain rights, which ground weighty reasons (...) against infringing those rights that need not be outweighed even when infringing those rights is necessary for preventing a larger number of people from having their rights infringed in the same way. Such rights form a second grade of non-consequentialist constraints: within the value-based framework, this second grade is best explained in terms of the intrinsically relational values and disvalues of interpersonal interactions and relationships. (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)

This work intends to be a generalization and a simplification of the techniques employed in [2], by the proposal of a general strategy to prove satisfiability theorems for NLGM-s (= normal logics with graded modalities), analogously to the well known technique of the canonical models by Lemmon and Scott for classical modal logics.

Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics.

It is argued herein that there are two distinct ways in which all observation vocabularies are prejudiced with respect to theory. An argument based on the demands of adequate translation is invoked to show that even the simplest of our observation predicates must display the first and more obvious grade of bias--intensional bias. It is also argued that any observation vocabulary whose predicates are corrigibly applicable must manifest a second and equally serious grade of bias--extensional bias--independently of whatever intensional bias (...) its predicates may or may not have. (shrink)

Whether visual perceptual consciousness is gradable or dichotomous has been the subject of fierce debate in recent years. If perceptual consciousness is gradable, perceivers may have less than full access to—and thus be less than fully phenomenally aware of—perceptual information that is represented in working memory. This raises the question: In virtue of what can a subject be less than fully perceptually conscious? In this chapter, we provide an answer to this question, according to which inexact categorizations of visual input (...) may result in a representation of the visual information in working memory that is less than fully available to the perceiver, and of which the perceiver is therefore less than fully phenomenally aware. The latter proposal is a natural extension of a theory of perception we have proposed in previous works, namely, the template tuning theory (TTT). We argue that although TTT is compatible with both gradable and dichotomous conceptions of perceptual consciousness, the available empirical evidence favours a gradable conception of perceptual consciousness. (shrink)

The adjective ‘is justified’ has all the hallmarks of a gradable adjective. But the relationship between gradable uses and straightforward predications of the form ‘x is justified’ has been underexplored by epistemologists. In this paper we undertake to do some ground clearing as a prelude to better understanding this relationship.

Psychophysics and neuroscience demonstrate that different sensory systems interact and influence each other. Perceiving involves extensive cooperation and coordination among systems associated with sight, hearing, touch, smell, and taste. Nonetheless, it remains unclear in what respects conscious perceptual awareness is multisensory. This paper distinguishes six differing varieties of multisensory awareness, explicates their consequences, and thereby elucidates the multisensory nature of perception. It argues on these grounds that perceptual awareness need not be exhausted by that which is associated with each of (...) the respective sensory modalities along with whatever accrues thanks to simple co-consciousness. (shrink)

The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not (...) only from a semantical or model-theoretic viewpoint but from a prooftheoretical and axiomatic stance as well. A paramount feature of the approach is its use of so-called systematic frame constants as labels of diverse grades of probability. Apart from this novel feature our approach can be seen to go back to pioneering work by Lou Goble in 1970. (shrink)

We extend the languages of both basic and graded modal logic with the infinity diamond, a modality that expresses the existence of infinitely many successors having a certain property. In both cases we define a natural notion of bisimilarity for the resulting formalisms, that we dub $\mathtt {ML}^{\infty }$ and $\mathtt {GML}^{\infty }$, respectively. We then characterise these logics as the bisimulation-invariant fragments of the naturally corresponding predicate logic, viz., the extension of first-order logic with the infinity quantifier. Furthermore, for (...) both $\mathtt {ML}^{\infty }$ and $\mathtt {GML}^{\infty }$ we provide a sound and complete axiomatisation for the set of formulas that are valid in every Kripke frame, we prove a small model property with respect to a widened class of weighted models, and we establish decidability of the satisfiability problem. (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)

: While Augustine distinguishes free choice from true liberty, his account of human freedom implies further distinctions which Augustine himself does not make explicit. More importantly, Augustine regards these distinct types of freedom as qualitatively different; some are clearly superior to others. Descartes also distinguishes qualitatively different types of freedom, and does so in a way that parallels Augustine's view. I here argue that Augustine divides freedom into four qualitatively distinct grades, and then demonstrate that Descartes’ account of freedom (...) is a rationalist adaptation of the theory of free choice found in Augustine. (shrink)

-/- Professor Hick's recent contribution to Religious Studies, ‘On Grading Religions’, is, like all his work, lucidly written and full of philosophical meat. A complete discussion of his paper in the light of his earlier work would require a lengthy study for which there is no space here; the intention of this short reply to Professor Hick is different. We feel that the view expressed in this and other works of Professor Hick's is in danger of becoming the conventional wisdom (...) about the functions of reason in assessing religious truth-claims among philosophers of religion on both sides of the Atlantic, and that this should not be permitted to happen without some wider ventilation of the extremely important philosophical issues at stake. This reply is thus an attempt to stimulate controversy and to explore alternatives. (shrink)

We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.

ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be obtained by a chain of (...) classical closure operators. (shrink)

Functionally graded materials (FGMs) have been used in many different kinds of applications in recent years and have attracted significant research attention. However, we do not yet have a commonly accepted way of representing the various aspects of FGMs. Lack of standardised vocabulary creates obstacles to the extraction of useful information relating to pertinent aspects of different applications. A standard resource is needed for describing various elements of FGMs, including existing applications, manufacturing techniques, and material characteristics. This motivated the creation (...) of the FGM Ontology (FGMO) in 2016. Here, we present a revised and expanded version of the FGM Ontology, which includes enrichments along four dimensions: (1) documenting recent FGMs applications; (2) reorganising the framework to incorporate an updated representation of types of manufacturing processes; (3) enriching the axioms of the ontology; and (4) importing mid-level ontologies from the Common Core Ontologies (CCO) and Product Life Cycle (PLC) Ontologies. The work is being carried out within the framework of the Industry Ontology Foundry (IOF), and the ontology is conformant to Basic Formal Ontology (BFO). (shrink)

Though it has become a commonplace that probabilistic contexts are intentional, the precise sense in which this is true has never, to my knowledge, been stated. By making use of a relatively non-controversial set of distinctions regarding the grades of modal involvement, I am able to state more exactly than has been done previously the grade of intensionality which probability statements have prima facie. The distinctions I employ are, with certain qualifications, those introduced by Quine in his wellknown paper, (...) Three Grades of Modal Involvement. By means of paraphrases, I am able to show that probability statements exemplify what Quine calls the third grade of modal involvement. Consequently, they are intensional in a way not acceptable to the majority of extensionalists. (shrink)

While Augustine distinguishes free choice from true liberty, his account of human freedom implies further distinctions which Augustine himself does not make explicit. More importantly, Augustine regards these distinct types of freedom as qualitatively different; some are clearly superior to others. Descartes also distinguishes qualitatively different types of freedom, and does so in a way that parallels Augustine's view. I here argue that Augustine divides freedom into four qualitatively distinct grades, and then demonstrate that Descartes’ account of freedom is (...) a rationalist adaptation of the theory of free choice found in Augustine. (shrink)

In a much-discussed article on fair grading, Daryl Close said that impartial and consistent grading of students forbids practices like grading on a curve and dropping the lowest grade. I show—negatively—that impartiality and consistency don’t forbid these practices. I also show—positively—that some other conditions on fair and reasonable grading do rule out grading on a curve and dropping the lowest grade.

1. Introduction. Like other direct realists, Thomas Reid offered an alternative to indirect realist and idealist accounts of perception. Reids alternative aimed to preserve the indirect realists commitment to realism about the objects of perception, and the idealists commitment to the immediacy of the minds relation to the objects of perception. Reid holds that what you perceive is mind independent or external; and your relation to such objects in perception is direct or immediate. In his own words, something which is (...) extended and solid, which may be measured and weighed, is the immediate object of my touch and sight. And this object I take to be matter, and not an idea (IP II xi, 154). (shrink)