What is it to know more? By what metric should the quantity of one's knowledge be measured? I start by examining and arguing against a very natural approach to the measure of knowledge, one on which how much is a matter of how many. I then turn to the quasi-spatial notion of counterfactual distance and show how a model that appeals to distance avoids the problems that plague appeals to cardinality. But such a model faces fatal problems of its (...) own. Reflection on what the distance model gets right and where it goes wrong motivates a third approach, which appeals not to cardinality, nor to counterfactual distance, but to similarity. I close the paper by advocating this model and briefly discussing some of its significance for epistemic normativity. In particular, I argue that the 'trivial truths' objection to the view that truth is the goal of inquiry rests on an unstated, but false, assumption about the measure of knowledge, and suggest that a similarity model preserves truth as the aim of belief in an intuitively satisfying way. (shrink)

Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks. Here we study how the multilayer structure affects the antifragility of the whole system. By comparing single-layer and multilayer Boolean networks based on our recently proposed antifragility (...) measure, we found that the multilayer structure facilitated the production of antifragile systems. Our measure and findings will be useful for various applications such as exploring properties of biological systems with multilayer structures and creating more antifragile engineered systems. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem (...) of measure sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

The deflationary aim of this book, which occupies Part I, is to show that a widely held view has little to be said for it. The constructive aim, pursued in Part II, is to make plausible a measure-theoretic account of propositional attitudes. The discussion is throughout instructive, illuminating and sensitive to the many intricacies surrounding attitude ascriptions and how they can carry information about a subject's psychology. There is close engagement with cognitive science. The book should be read by (...) anyone seriously engaged with issues about propositional attitudes.According to the widely held view, which Matthews calls the Received View, the attitude of Φing that p is a matter of standing in a computational/functional relation to an explicit Representation that expresses the proposition that p, and thinking is ‘an inferential computational process defined over one or more of these Representations that eventuates in the production of either another Representation or a behavior’. The representations are understood to be sentences in a language of thought and thus to have a compositional syntax and semantics. The theory that Matthews aims to make plausible has it that ascriptions of propositional attitudes in the form ‘X Φs that p’, ascribe a state to a person by relating that person to an abstract object that is the representative of the state in roughly the way that numbers on a scale are the measure-theoretic representations of certain physical magnitudes. We are to think of the role of ‘Jones believes that interest rates will fall’ by analogy with that of ‘Jones weighs 150lbs’. The latter depends on there being arithmetical relations defined over numbers that enable its particular assignment of a number to Jones's weight to represent physical properties that Jones has in virtue …. (shrink)

I argue that prioritarianism cannot be assessed in abstraction from an account of the measure of utility. Rather, the soundness of this view crucially depends on what counts as a greater, lesser, or equal increase in a person’s utility. In particular, prioritarianism cannot accommodate a normatively compelling measure of utility that is captured by the axioms of John von Neumann and Oskar Morgenstern’s expected utility theory. Nor can it accommodate a plausible and elegant generalization of this theory that (...) has been offered in response to challenges to von Neumann and Morgenstern. This is, I think, a theoretically interesting and unexpected source of difficulty for prioritarianism, which I explore in this article. (shrink)

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to (...) investigate Carnap’s measure regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

We identify several ongoing debates related to implicit measures, surveying prominent views and considerations in each debate. First, we summarize the debate regarding whether performance on implicit measures is explained by conscious or unconscious representations. Second, we discuss the cognitive structure of the operative constructs: are they associatively or propositionally structured? Third, we review debates whether performance on implicit measures reflects traits or states. Fourth, we discuss the question of whether a person’s performance on an implicit measure reflects characteristics (...) of the person who is taking the test or characteristics of the situation in which the person is taking the test. Finally, we survey the debate about the relationship between implicit measures and (other kinds of) behavior. (shrink)

Drawing on the latest work in cognitive neuroscience, a philosopher proposes that delusions are narrative models that accommodate anomalous experiences.

If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.

This article describes the development of a computerized version of a measure of ethical sensitivity to racial and gender intolerance, the Racial Ethical Sensitivity Test. The REST was based on James Rest's 4-component model of moral development and the professional codes of ethics from school-based professions. The new version, Racial and Ethical Sensitivity Test-Compact Disk, consists of 5 videotaped scenarios followed by an interactive "interview" presented on compact discs. Data from a study with 58 students provides initial validation of (...) the REST-CD. Ethical sensitivity to racial and gender intolerance in schools, as measured by the REST-CD, was moderately related to attitudes toward racial and gender equity issues in society as measured by the Quick Discrimination Index. The results provide evidence for both interrater and internal reliability of the REST-CD scores. This study also tests the hypothesized relationship between REST-CD scores and previous multicultural and ethics course work. Students with multicultural and ethics course experience have scored significantly higher on the REST-CD than students without course work. The paper-and-pencil tests are not significantly related to previous ethics/multicultural course work. In this article, we discuss the implications of the results and directions for future research. (shrink)

How do we know when one person or society is 'freer' than another? Can freedom be measured? Is more freedom better than less? This book provides the first full-length treatment of these fundamental yet neglected issues, throwing new light both on the notion of freedom and on contemporary liberalism.

Informed choice is increasingly recognised as important in supporting patient autonomy and ensuring that people are neither deceived nor coerced. In cancer screening the emphasis has shifted away from just promoting the benefits of screening to providing comprehensive information to enable people to make an informed choice. Cancer screening programmes in the UK now have policies in place which state that it is their responsibility to ensure that individuals are making an individual informed choice. There is a need to evaluate (...) whether such policies mean that those people invited for screening are making informed choices, and how comprehensive information affects other variables such as uptake, cost effectiveness, and satisfaction. At the present time, there is no validated measure of informed choice in cancer screening. Such a measure could be used to evaluate the effectiveness of interventions to increase informed choice and levels of informed choice in a population invited for screening. It could encourage health professionals to be accountable. Factors important when measuring informed choice in cancer screening include an individual’s understanding of the limitations of screening, the ability to make an autonomous choice, and the difference between choice and behaviour. (shrink)

What does it mean to wonder in awe or terror about the world? How do you philosophically understand Judaism? In How to Measure a World?: A Philosophy of Judaism, Martin Shuster provides answers to these questions and more. Emmanuel Levinas suggested that Judaism is best understood as an anachronism. Shuster attempts to make sense of this claim by alternatively considering questions of the inscrutability of ultimate reality, of the pain and commonness of human suffering, and of the ways in (...) which Judaism is entangled with the world. Drawing on phenomenology and Jewish thought, Shuster offers novel readings of some of the classic figures of Jewish philosophy while inserting other voices into the tradition, from Moses Maimonides to Theodor W. Adorno to Walter Benjamin to Stanley Cavell. How to Measure a World? examines elements of the Jewish philosophical record to get at the full intellectual scope and range of Levinas's proposal. Shuster's view of anachronism thereby provokes an assessment of the world and our place in it. A particular understanding of Jewish philosophy emerges, not only through the traditions it encompasses, but also through an understanding of the relationship between humans and their world. In the end, Levinas's suggestion is examined theoretically as much as practically, revealing what's at stake for Judaism as much as for the world. (shrink)

The author constructs a philosophy of nature dealing with being, identity, value, space, time, motion, and causality, and uses that as a basis for a theory of hermeneutics to address contemporary problems of interpretation.

It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics (...) are given. (shrink)

A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.

The salience of social risks and the incidence of various crises in China have induced widespread concerns among urban residents. Encountering frequent risks places higher demands on the cognition of urban residents. The concept of safety cognition capability is defined within the context of urban residents' daily life, and measurement instruments are developed and tested to lay the foundation for grasping the current safety cognition capability of urban residents and conducting further research. In this study, the five-dimensional structure of urban (...) residents' safety cognition capability was proposed by using the grounded theory method to sort out the interview transcript of interviews with 30 urban residents, and a 38-item URSCC scale was designed and used for surveys conducted in China. The results show that the scale can be used as a valid tool to measure the URSCC, and it can help city managers to better understand the safety needs of residents, as well as monitor the effectiveness of policy implementation. (shrink)

As a neonatal neurologist, I serve families facing tragic decisions in which they must balance trade-offs between death and life with profound disability. I often find myself in complex discussions about future outcome, in which families sort through in real-time what information they value most in making such a choice. Will he laugh? Will he be in pain? Will he know how much he’s loved? In this month’s feature article, Brick et al share the results of an online survey aimed (...) at assessing public views on when a life is not worth living, in an effort to inform ongoing legal and clinical debates about withdrawal of life-sustaining treatment for children. These findings raise important questions about how we define and measure outcomes that matter to parents as they make these tragic decisions. It is challenging to interpret these findings in the absence of context of how decision-making for infants occurs in real-time. The nature of this study and its objective required that cases be substantially simplified. As the authors acknowledge, the prognoses and function of the children involved in these cases were often deeply contested. Prognostic uncertainty is common for children with significant …. (shrink)

Disability, mad and d/Deaf arts are motivated to transform the arts sector and beyond in ways that foreground differing embodiments. But how do we know if such arts-based interventions are actually disrupting conventional ways of experiencing and consuming art? This article presents three themes from a critical literature review relevant to curating and creating artwork meant to spur social change related to non-normative bodies. We highlight examples that push beyond standard survey measurement techniques, such as talk-back walls and guided tours (...) by people with lived experiences. We also explore the myriad affective outcomes of art and how we might measure emotional reactions, recognizing that disability itself is imbricated in structures of feeling. We argue that such efforts must integrate concepts of access from the field of critical disability studies. Ultimately, tools for measuring audience response to politicized art must contribute to challenging and transforming these structures. (shrink)

The point of formalisation is to model various aspects of natural language. Perhaps the main use to which formalisation is put is to model and explain inferential relations between different sentences. Judged solely by this objective, a formalisation is successful in modelling the inferential network of natural language sentences to the extent that it mirrors this network. There is surprisingly little literature on the criteria of good formalisation, and even less on the question of what it is for a formalisation (...) to mirror the inferential network of a natural language or some fragment of it. This paper takes some exploratory steps towards a quantitative account of the main ingredient in the goodness of a formalisation. We introduce and critically examine a mathematical model of how well a formalisation mirrors natural-language inferential relations. (shrink)

Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract Principal Principle is both weakly and strongly consistent. The Abstract Principal Principle is strengthened by adding a stability requirement to it. Weak and strong consistency of the resulting Stable Abstract Principal Principle are defined. It is shown that the Stable Abstract Principal Principle is weakly consistent. Strong consistency of the Stable Abstract Principal principle remains an (...) open question. (shrink)

Sorkin’s recent proposal for a realist interpretation of quantum theory, the anhomomorphic logic or coevent approach, is based on the idea of a “quantum measure” on the space of histories. This is a generalisation of the classical measure to one which admits pair-wise interference and satisfies a modified version of the Kolmogorov probability sum rule. In standard measure theory the measure on the base set Ω is normalised to one, which encodes the statement that “Ω happens”. (...) Moreover, the Kolmogorov sum rule implies that the measure of any subset A is strictly positive if and only if A cannot be covered by a countable collection of subsets of zero measure. In quantum measure theory on the other hand, simple examples suffice to demonstrate that this is no longer true. We propose an appropriate generalisation, the quantum cover, which in addition to being a cover of A, satisfies the property that if the quantum measure of A is non-zero then this is also the case for at least one of the elements in the cover. Our work implies a non-triviality result for the coevent interpretation for Ω of finite cardinality, and allows us to cast the Peres-Kochen-Specker theorem in terms of quantum covers. (shrink)

Wisdom, long a topic of interest to moral philosophers, is increasingly the focus of social science research. Philosophers have historically been concerned to develop a rationally defensible account of the nature of wisdom and its role in the moral life, often inspired in various ways by virtue theoretical accounts of practical wisdom (phronesis). Wisdom scientists seek to, among other things, define wisdom and its components so that we can measure them. Are the measures used by wisdom scientists actually measuring (...) what philosophers have in mind when they discuss practical wisdom? I argue that they are not. Contemporary measures of wisdom and its components may pick out some necessary prerequisites of practical wisdom, but they do not measure a philosophically plausible practical wisdom or its components. After explaining the argument and defending it against objections, I consider its implications. Should wisdom scientists ignore the philosophical conception of practical wisdom in favor of other conceptions, revise their methods to try to measure it, or continue the interdisciplinary study of practical wisdom without expecting to measure it? I make a preliminary argument for the third option. (shrink)

This paper offers a critical analysis of program evaluation in contemporary urban agriculture. Drawing on data from an exploratory study designed at the request of and in collaboration with urban agriculture practitioners in Massachusetts, it describes both their critiques of extant practices of program evaluation and their visions for alternative ways of telling the story of their work. Related, it explores practitioners’ interest in building capacity for policy advocacy, working collectively to create transformative social change, and, related, establishing new kinds (...) of relationships with state and philanthropic funders. Building on scholarship that has observed that urban agriculture is characterized by an internal contradiction—i.e., its simultaneous orientation to “neoliberal” and “radical” agendas —this analysis calls attention, especially, to the complex role of metrics, which may not only entrench neoliberalism in UA organizations, but also provide a mechanism for challenging its assumptions and advancing the radical project of food justice. (shrink)

The current literature standardly conceives of voting power in terms of decisiveness: the ability to change the voting outcome by unilaterally changing one’s vote. I argue that this classic conception of voting power, which fails to account for partial decisiveness or efficacy, produces erroneous results because it saddles the concept of voting power with implausible microfoundations. This failure in the measure of voting power in turn reflects a philosophical mistake about the concept of social power in general: a failure (...) to recognize that an agent can exercise individual social power with others’ assistance, in virtue of the group’s collective power, sometimes even when she could not unilaterally scuttle the group’s collective power. I therefore develop a conception of efficacy that admits of degrees and defend a Recursive Measure of voting power that takes partial efficacy into account. (shrink)

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya’s distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better and more robust. An illustrative example of the pattern recognition shows that the proposed method is simple and effective.

This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the literature.

Empathy plays a fundamental role in successful social interactions. However, most tasks currently available for measuring empathy have limited ecological validity and therefore may not elicit true emotional responses in observers. To address this gap, we developed the Empathic Measure of True Emotion (EMOTE), the first emotion stimuli set to include footage of genuine positive and negative emotions unfolding in naturalistic contexts. We validated the EMOTE in a sample of 216 participants. The EMOTE demonstrated acceptable internal consistency, construct validity, (...) and alternate forms reliability for both cognitive and affective empathy. We also found that, relative to conventional empathy measures, the EMOTE elicited stronger affective empathy ratings in observers, and the stimuli were rated higher in both genuineness and emotional intensity. Together, these findings demonstrate that the EMOTE is a reliable and valid measure of cognitive and affective empathy with enhanced ecological validity, providing a valuable new tool for measuring empathy in both clinical and research settings. (shrink)