This paper is a discussion note on Isaacs et al. (2022), who have claimed to offer a new motivation for imprecise probabilities, based on the mathematical phenomenon of non-measurability. In this note, I clarify some consequences of their proposal. In particular, I show that if their proposal is applied to a bounded 3-dimensional space, then they have to reject at least one of the following: (i) If A is at most as probable as B and B is at most as (...) probable as C, then A is at most as probable as C. (ii) Let A ∩ C = B ∩ C = ∅. A is at most as probable as B iff (A ∪ C) is at most as probable as (B ∪ C). But rejecting either statement seems unattractive. (shrink)

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, (...) whether a certain outcome is associated with a non-measurable region or a measurable one. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is (...) a natural way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability (...) has conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

How to measure performance in charitable organisations continues to excite interest among academics and practitioners. Despite the intellectual interest, little consensus has emerged as to what are the best measures of performance in charities. This is against the backdrop of an increased demand by donors and other stakeholders on charities to provide information on their performance. Building on prior studies, this paper examines the measures of performance in charities using a hybrid methodological approach which consists of 14 exploratory interviews and (...) a quantitative survey of 105 chief executive officers/board of trustees of large British charities. The results of factor analysis and internal reliability produced five broad measures of performance of charities: financial measures; client satisfaction; management effectiveness; stakeholder involvement; and benchmarking, indicating that the overall performance of charities is best measured by a set of factors that reflect the multiple and diverse stakeholders associated with charities. Further analysis using structural equation modelling corroborates the results that non-financial measures such as management effectiveness, stakeholder involvement and benchmarking are important to the performance of charities. (shrink)

This book provides an introduction to measurement theory for non-specialists and puts measurement in the social and behavioural sciences on a firm mathematical foundation. Results are applied to such topics as measurement of utility, psychophysical scaling and decision-making about pollution, energy, transportation and health. The results and questions presented should be of interest to both students and practising mathematicians since the author sets forth an area of mathematics unfamiliar to most mathematicians, but which has many potentially significant applications.

In this paper, non-additivity of a set function is interpreted as a method to express relations between sets which are not modeled in a set theoretic way. Drawing upon a concept called “quasi-analysis” of the philosopher Rudolf Carnap, we introduce a transform for sets, functions, and set functions to formalize this idea. Any image-set under this transform can be interpreted as a class of (quasi-)components or (quasi-)properties representing the original set. We show that non-additive set functions can be represented as (...) signed σ-additive measures defined on sets of quasi-components. We then use this interpretation to justify the use of non-additive set functions in various applications like for instance multi criteria decision making and cooperative game theory. Additionally, we show exemplarily by means of independence, conditioning, and products how concepts from classical measure and probability theory can be transfered to the non-additive theory via the transform. (shrink)

We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $, which we denote by $\mathcal {N}_J$. In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$. We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is equivalent to (...) $\mathcal {N}^*_J=\mathcal {E}$. Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$. We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$. We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals. (shrink)

IntroductionThe National Institute for Health and Care Excellence guidelines acknowledge the importance of the parent–infant relationship for child development but highlight the need for further research to establish reliable tools for assessment, particularly for parents of children under 1 year. This study explores the acceptability and psychometric properties of a co-developed tool, ‘Me and My Baby’.Study designA cross-sectional design was applied. The MaMB was administered universally with mothers during routine 6–8-week Health Visitor contacts. The sample comprised 467 mothers. Dimensionality of (...) instrument responses were evaluated via exploratory and confirmatory ordinal factor analyses. Item response modeling was conducted via a Rasch calibration to evaluate how the tool conformed to principles of ‘fundamental measurement’. Tool acceptability was evaluated via completion rates and comparing ‘completers’ and ‘non-completers’ demographic differences on age, parity, ethnicity, and English as an additional language. Free-text comments were summarized. Data sharing agreements and data management were compliant with the General Data Protection Regulation, and University of York data management policies.ResultsHigh completion rates suggested the MaMB was acceptable. Psychometric analyses showed the response data to be an excellent fit to a unidimensional confirmatory factor analytic model. All items loaded statistically significantly and substantially on a single underlying factor. The item response modeling showed that most MaMB items fitted the Rasch model. item reliability was high yet the test yielded little information on each respondent, as highlighted by the relatively low ‘person separation index’ of 0.1.Conclusion and next stepsMaMB reliably measures a single construct, likely to be infant bonding. However, further validation work is needed, preferably with ‘enriched population samples’ to include higher-need/risk families. The MaMB tool may benefit from reduced response categories and some modest item wording amendments. Following further validation and reliability appraisal the MaMB may ultimately be used with fathers/other primary caregivers and be potentially useful in research, universal health settings as part of a referral pathway, and clinical practice, to identify dyads in need of additional support/interventions. (shrink)

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical (...) situations involving more than one maximal value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A, where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U- uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U = 1/h 0 h log [1+]d, where h is the largest membership value obtained by any element of A and is the measure of the -cut of A defined by the Lebesge integral of its characteristic function. (shrink)

Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements have coherent ancilla density matrices that encode the memory of the entire set of quantum measurements (...) that came before, and that the chain of this entire set is therefore non-Markovian. In contrast, sequences of amplified measurements are equivalent to a quantum Markov chain. We argue that the non-Markovian nature of quantum measurement has empirical consequences that are incompatible with the assumption of wave function collapse, thus elevating the collapse assumption into a testable hypothesis. Finally, we find that all of the information necessary to reconstruct an arbitrary non-Markovian quantum chain of measurements is encoded on the boundary of that chain, reminiscent of the holographic principle. (shrink)

Reality is hierarchically structured, or so proponents of the metaphysical posit of grounding argue. The less fundamental facts obtain in virtue of, or are grounded in, the more fundamental facts. But what exactly is it for one fact to be more fundamental than another? The aim of this paper is to provide a measure of relative fundamentality. I develop and defend an account of the metaphysical hierarchy that assigns to each fact a set of ordinals representing the levels on which (...) it occurs. The account allows one to compare any two facts with respect to their fundamentality and it uses immediate grounding as its sole primitive. In the first section, I will set the stage and point to some shortcomings of a rival account proposed by Karen Bennett. The second section will present my own proposal and the third section will discuss how it can be extended to non-foundationalist settings. The fourth section discusses potential objections. (shrink)

For non-additive set functions, the independent product, in general, is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of Gilboa and Schmeidler (Math Oper Res 20:197–212, 1995) to extend the Möbius product for non-additive set functions to non-finite spaces. We extend the uniqueness result of Ghirardato (J Econ Theory 73:261–291, 1997) for products of two belief functions and weaken the requirements on the marginals necessary to obtain the Fubini property (...) in the product. More importantly, we show that for the Möbius product one side of the Fubini theorem holds for all integrable functions if one of the marginals either is a probability or a convex combination of a chain of unanimity games, i.e., we relax the requirement of slice-comonotonicity and enrich the set of possible applications. (shrink)

This paper makes two central claims. The first is that there is an intimate and non-trivial relation between the mass/count distinction on the one hand and the measure/individuation distinction on the other: a defining property of mass nouns is that they denote sets of entities which can be measured, while count nouns denote sets of entities which can be counted. Crucially, this is a difference in grammatical perspective and not in ontological status. The second claim is that the mass/count distinction (...) between two types of nominals has its direct correlate at the level of classifier phrases: classifier phrases like two bottles of wine are ambiguous between a counting, or individuating, reading and a measure reading. On the counting reading, this phrase has count semantics, on the measure reading it has mass semantics. (shrink)

There is no way literally to measure health, because health is multi-dimensional, and there is no metric whereby one person who is healthier than a second with respect to one dimension but less healthy with respect to another counts as healthier, less healthy or equally healthy overall. Health analysts instead measure how good or bad health states are in some regard. If these values are measures of health states, then identical health states must have identical values. But in different circumstances, (...) the same health state may have different values. It may be better or worse. Uniform values can nevertheless be assigned to kinds of health states, either as a weighted average of the values of their tokens or as the value of the performance in a standard environment of the capacity the health state constitutes. These uniform values are not well suited for some of the purposes for which summary measures of population health have been intended, and a set of non-evaluative indicators may be an attractive alternative. (shrink)

This paper introduces considerations about constraints in the construction of measures of an agent's freedom. It starts with motivating the exercise from both the philosophical and the informational point of view. Then it presents two rankings of opportunity sets based on information about the extent of options and the constraints that a decision maker faces. The first ranking measures freedom as variety of choice; the second as non-restrictedness in choice.

We show that in contrast with the Cohen version of Solovay's model, it is consistent for the continuum to be Cohen-measurable and for every function to be continuous on a non-meagre set.

A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric informationally complete positive-operator-valued measure, is, remarkably, also analogous to an affine plane, but with the roles of points and lines interchanged. In this paper I present these analogies and ask whether they shed any light on the existence or non-existence of such symmetric (...) quantum measurements for a general quantum system with a finite-dimensional state space. (shrink)

Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper is the (...) search for such examples of the structure mentioned above that do not stem from Jordan operator algebras; first natural candidates are matrix algebras over the octonions and other nonassociative rings. Therefore, the case when a nonassociative commutative multiplication exists is studied without assuming that it satisfies the Jordan condition. The characteristics of the resulting algebra are analyzed. This includes the uniqueness of the spectral resolution as well as a criterion for its existence, subalgebras that are Jordan algebras, associative subalgebras, and more different levels of compatibility than occurring in standard quantum mechanics. However, the paper cannot provide the desired example, but contribute to the search by the identification of some typical differences between the potential examples and the Jordan operator algebras and by negative results concerning some first natural candidates. The possibility that no such example exists cannot be ruled out. However, this would result in an unexpected new characterization of Jordan operator algebras, which would have a significant impact on quantum axiomatics since some customary axioms (e.g., power-associativity or the sum postulate for observables) might turn out to be redundant then. (shrink)

An empirically based view of size and distance perceptual content and phenomenology is introduced, in which perceivers measure worldly size and distance against their bodies. Central principles of the formal, representational theory of the measurement of extensive magnitudes are then applied in framing the account in a precise way. The question of whether spatial-perceptual experience is “unit-free” is clarified. The framework is used to assess Dennis Proffitt's proposal that spatial setting is perceived in various “units,” “scales,” or “rulers”, some of (...) them non-spatial—distance in terms of calories burned to traverse and the like. The debate between Proffitt and Firestone about the commensurability of differing measurement scales held by Proffitt to be relied on by perceivers is then clarified and resolved. Finally, the measurement theory framed account of size and distance perception is used to illuminate Gibson’s famous but elusive contrasts between “geometrical optics” and “ecological optics” and between the “physical world” and the “animal environment”. (shrink)

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions. The principle of “local equity” assumes the transaction completed (...) (regardless of the result) of the states of transaction partners are not changed in connection with the reception of new information on proposed offers or adopted decisions (consent or refusal of the transaction). However it has no relation to the paradoxes of quantum theory connected with non-local interaction of entangled states. In the economic systems the mechanism of entangling has a classical interpretation, while the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness. (shrink)

This paper brings together Dana Scottʼs measure-based semantics for the propositional modal logic S4, and recent work in Dynamic Topological Logic. In a series of recent talks, Scott showed that the language of S4 can be interpreted in the Lebesgue measure algebra, M, or algebra of Borel subsets of the real interval, [0,1], modulo sets of measure zero. Conjunctions, disjunctions and negations are interpreted via the Boolean structure of the algebra, and we add an interior operator on M that interprets (...) the □-modality. In this paper we show how to extend this measure-based semantics to the bimodal logic S4C. S4C is interpreted in ‘dynamic topological systems,’ or topological spaces together with a continuous function acting on the space. We extend Scottʼs measure based semantics to this bimodal logic by defining a class of operators on the algebra M, which we call O-operators and which take the place of continuous functions in the topological semantics for S4C. The main result of the paper is that S4C is complete for the Lebesgue measure algebra. A strengthening of this result, also proved here, is that there is a single measure-based model in which all non-theorems of S4C are refuted. (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)

A physical mechanical sequence is proposed representing measurement interactions ‘hidden' within QM's proverbial ‘black box'. Our ‘beam splitter' pairs share a polar angle, but head in opposite directions, so ‘led' by opposite hemisphere rotations. For orbital ‘ellipticity', we use the inverse value momentum ‘pairs' of Maxwell's ‘linear' and ‘curl' momenta, seen as vectors on the Poincare spherical surface. Values change inversely from 0 to 1 over 90 degrees, then ± inverts.. Detector polarising screens consist of electrons with the same vector (...) distributions, but polar angles set independently by A & B. The absorption/re-emission interaction process is modelled as surface vector additions at the angle of polar latitude of each interaction. This ‘collapse' of characteristic ‘wave values' is really then simply ‘re-polarisation', with new ellipticity. We then obtain the relation Cosθ at polarisers. We may simplify this to new ellipses with major/minor axis values. Considering as spherical orbital angular momentum rotation we invoke the unique quality of spheres to rotate concurrently on three axes! Rotating on y or z axes concurrent with x axis spin can return surface points to starting positions with non-integer x axis rotations, from half to infinity!. Second interactions at photomultiplier/ analysers are identical but at two orthogonal ‘channels'. Vector addition interactions at BOTH channel orientations normally produce a vector value of adequate amplitude to give a *click* from the MAJOR axis direction. At the ‘crossover' points at near circular polarity the orthogonal ‘certainty' is ~ 50:50, so both or neither channels may produce a ‘click'. The apparently unphysical but proved ‘Malus' law' relation; Cos2θ emerges physically from the 2nd set of interactions. The main departure from QM's assumptions are; That the original pair members each actually possessed two inverse momenta sets; ‘curl' and ‘linear'. Also that complex ‘vector additions' of those pairs occurs. Vector quantities allow A & B to reverse their OWN finding by reversing dial setting, reproducing experimental outputs without problematic ‘non-locality'. (shrink)

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.

BackgroundHuman female orgasm is a vexed question in the field while there is credible evidence of cryptic female choice that has many hallmarks of orgasm in other species. Our initial goal was to produce a proof of concept for allowing females to study an aspect of infertility in a home setting, specifically by aligning the study of human infertility and increased fertility with the study of other mammalian fertility. In the latter case - the realm of oxytocin-mediated sperm retention mechanisms (...) seems to be at work in terms of ultimate function while the proximate function remains unresolved.MethodA repeated measures design using an easily taught technique in a natural setting was used. Participants were a small, non-representative sample of females. The introduction of a sperm-simulant combined with an orgasm-producing technique using a vibrator/home massager and other easily supplied materials.ResultsThe sperm flowback (simulate... (shrink)

I briefly sketch Bohm's causal interpretation (BCI) and its solution to the measurement problem. Crucial to BCI's no-collapse account of both ideal and non-ideal measurement is the existence of particles in addition to wavefunctions. The particles in their role as the producers of the observable experimental outcomes render practical considerations, such as what observables can be reasonably measured or how to get rid of interference terms in non-ideal measurements, secondary to BCI's account of measurement. I then explain why it is (...) not easy for BCI to justify its statistical postulate. To successfully justify the postulate would be to solve the distribution problem. Two proposed deterministic solutions to this problem are only briefly set out and not discussed in detail. BCI can solve the measurement problem whether or not the distribution problem is solved. However, if the distribution problem is not solved, BCI cannot be shown to be empirically adequate. (shrink)

Purpose: Performance measurement systems (PMS) in Nonprofit Organizations (NPOs) are more complex than in for-profit organizations. NPOs have an orientation towards social mission and values, and they consider not only organizational efficiency and viability, but also the social impact of the organization. This research provides a comprehensive synthesis of PMSs in NPOs. Design/methodology/approach: Using a literature review, supported by bibliometric and network analyses. A paper set of 240 articles related to this research field is examined. Topics that are the most (...) prevalent in this research area and their interrelationships are identified, presenting an outline of current efforts. Findings: Despite the descriptive analyses for the paper set, a framework is proposed for organizing the design-implementation factors of PMSs in nonprofit organizations, identifying the main requirements for their successful development. Originality/value: Investigation on performance measurement in nonprofit organizations is still in its early stages of development with many opportunities to further develop the field. Conceptual frameworks and models, as well as specific theories, are being generated for this field of research, and the process of adapting models from the general field of performance measurement is taking place. The meta-framework that organizes the main research topics of PMS in nonprofit organizations and the framework that consolidates factors that influence the design-implementation of PMSs in nonprofit organizations developed represents this paper contribution. (shrink)

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values (...) to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure. (shrink)

Management scholars have paid close attention to the construct of organizational or corporate reputation, particularly in the applied business ethics and corporate social responsibility fields. Extant research demonstrates that CR is one of the key mediators between CSR and important organizational outcomes, which ultimately improve organizational performance. Yet, hitherto the research focused on CR construct has been plagued by multiple definitions, conflicting conceptualizations, and unclear operationalizations. The purpose of this article is to provide theoretical ground for positioning of CR as (...) an assessment construct that is modeled as a second-order factor affecting individual first-order dimensions, and to provide methodological and empirical support toward such conceptualization. We assert that intangible, socially complex, and causally ambiguous CR can be accurately estimated through its individual measurable dimensions. Using survey data from Peru, we empirically test the hypothesized second-order reflective model within a hierarchy of nested and non-nested models, and compare its model fit and predictive power with alternative conceptualizations. Modeling CR as a second-order reflective construct relies on a set of theoretical propositions and yields several methodological advantages, including strong conceptual interpretability and parsimony when tested within a nomological context. We explicitly demonstrate positive organizational outcomes of CR: customer trust, corporate identification, in-role behavior, and extra-role behavior. Then, we demonstrate that the shorter scales of CR can be used as a good proxy for the full construct measure. The paper concludes by highlighting theoretical insights, and methodological and managerial implications of the findings. (shrink)

We prove completeness of the propositional modal logic S 4 for the measure algebra based on the Lebesgue-measurable subsets of the unit interval, [0, 1]. In recent talks, Dana Scott introduced a new measure-based semantics for the standard propositional modal language with Boolean connectives and necessity and possibility operators, and . Propositional modal formulae are assigned to Lebesgue-measurable subsets of the real interval [0, 1], modulo sets of measure zero. Equivalence classes of Lebesgue-measurable subsets form a measure (...) algebra, , and we add to this a non-trivial interior operator constructed from the frame of ‘open’ elements—elements in with an open representative. We prove completeness of the modal logic S 4 for the algebra . A corollary to the main result is that non-theorems of S 4 can be falsified at each point in a subset of the real interval [0, 1] of measure arbitrarily close to 1. A second corollary is that Intuitionistic propositional logic (IPC) is complete for the frame of open elements in. (shrink)

Bioscientists generate far more data than their minds can handle, and this trend is likely to continue. With the aid of a small set of versatile tools for mathematical modeling and statistical assessment, bioscientists can explore their real-world systems without experiencing data overflow. This article outlines an approach for combining modern high-throughput, low-cost, but non-selective biospectroscopy measurements with soft, multivariate biochemometrics data modeling to overview complex systems, test hypotheses, and making new discoveries. From preliminary, broad hypotheses and goals, many relevant (...) samples are selected and measured with respect to many informative variables. The resulting tables represent a “cacophony” of data. From these, the most relevant and reliable “underlying harmonies and rhythms” are extracted and tested statistically, displayed for interpretation, and used for prediction. Outliers are detected automatically. Interesting subsets of samples can then be chosen for in-depth analyses in subsequent research cycles. This pragmatic, top-down approach takes advantage of developments in both “soft,” data-driven modeling and “hard,” knowledge-driven cultures. Data analytical examples show how information-rich biospectroscopy can be used for characterizing and quantifying known and unknown chemical constituents and physical phenomena in intact biosamples. This is based on a combination of deductive “hard” and inductive “soft” modeling. The examples represent NIR spectra of biochemical mixtures, FTIR spectra of a microbiological fermentation process, and FTIR analysis of fatty acids in milk for functional genomics. (shrink)

It is illegitimate to read any ontology about "race" off of biological theory or data. Indeed, the technical meaning of "genetic variation" is fluid, and there is no single theoretical agreed-upon criterion for defining and distinguishing populations (or groups or clusters) given a particular set of genetic variation data. Thus, by analyzing three formal senses of "genetic variation"—diversity, differentiation, and heterozygosity—we argue that the use of biological theory for making epistemic claims about "race" can only seem plausible when it relies (...) on the user’s own assumptions about race; the move from biological measures to claims about “race” inevitably amounts to a pernicious reification. We also excavate assumptions in the history of the technical discourse over the concept of "race" (e.g., Livingstone's and Dobzhansky's 1962 exchange, Edwards' 2003 response to Lewontin 1972, as well as contemporary discussions of cladistic "race", and "races" as clusters). We show that claims about the existence (or non-existence) of "race" are underdetermined by biological facts, methods, and theories. Biological theory does not force the concept of "race" upon us; our social discourse, social ontology, and social expectations do. We become prisoners of our abstractions at our own hands, and at our own expense. (shrink)

We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in (...) favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define “the same incoming state” and “the same detector” when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time. (shrink)

We study closure properties of measurable ultrapowers with respect to Hamkin's notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. (...) In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties. (shrink)

Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external system that switches (...) on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures. That is, for example, rather than using a complete set of orthogonal (...) projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, ] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors. We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical. (shrink)

In common with much of the Western world, agrarianism—valuing farmers and agricultural activity as intrinsically worthwhile, noble, and contributing to the strength of the national character—runs through Australian culture and politics. Agrarian sentiments and attitudes have been identified through empirical research and by inference from analysis of political debate, policy content, and studies of media and popular culture. Empirical studies have, however, been largely confined to the US, with little in the way of recent re-evaluations of, or developments from, early (...) work. This paper reports on research that seeks quantitative empirical evidence for the existence of agrarianism in the Australian community and seeks to identify its core characteristics. Using a purpose-designed sub-set of items within a large, omnibus-style survey of regional and rural Australia, we demonstrate that agrarianism exists as a scientifically quantifiable concept identifiable through responses to four key propositions: that Australians should support policies aimed at improving the position of the agricultural industries; that working in agriculture and associated industries brings out the best in people; that agricultural producers make a major contribution to environmental protection and biodiversity conservation; and that the development of agriculture in Australia contributed to the development of the national character. We found very little variation in the degree to which different demographic groupings agree with agrarianism. Older people, farmers, and non-Indigenous Australian-born respondents were among those who were statistically significantly more likely to agree with the defining propositions of agrarianism, but their scores were only very slightly higher than those of other sub-populations in the sample. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...) it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

We present a set of experiments investigating how English- and Japanese-speaking children interpret Measure Phrase comparatives. We show that despite overt cues to the comparative interpretation, children representing both languages diverge from their adult counterparts in that they access a non-adult-like ‘absolute measurement’ interpretation. We propose to account for their response pattern by appealing to proposals by Svenonius and Kennedy and Sawada and Grano that Meas in the head of the DegP, which houses the differential, selects for an absolute minimal (...) value: zero. We argue that young children appeal to this absolute zero minimum in lieu of the correct derived standard, and must learn to override this value by appealing to the context to set the standard of comparison when interpretation requires them to do so. (shrink)

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non- (...) class='Hi'>measurable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 539 ls There a Measure on Earth? Foundations for a Nonmetaphysical Ethics. By WERNER MARX. Trans. Thomas J. Nenon and Reginald Lilly. Chicago: University of Chicago Press, 1987. Pp. 172. (Hardcover.) (Originally published as Gibt es au/ Erden ein Mass? Grundbestimmungen einer nichtmetaphysischen Ethik. Hamburg: Felix Meiner, 1983.) Is there a non-metaphysical earthly measure for responsible action? Marx takes his question from Holderlin and directs it at (...) Heidegger, in whom Marx finds no explicit answer. It is not the case that Heidegger simply fails to ask or answer this question, but rather that the corpus of Heidegger's later work itself motivates the question and leaves us searching for the path to an answer which must, on Heideggerian principles, differ from the one embraced by Holderlin, Schelling, and the metaphysical tradition in general. Marx explores.the various possibilities offered in Heidegger's texts but fails to. find a definite answer with respect to a measure for responsible action. In his concise interpretation Marx is led in one inevitable direction--4:owards the concept of death. How does death qualify as a measure for action? Before he addresses this question Marx attempts to understand 1the concept of measure, which, he contends, can be viewed as either a metaphysical or a nonmetaphysical concept. He sets out the metaphysical concept of measure on the basis of his reading of Schelling. Schelling's onto-theological concept of measure is characterized as normative, transcendent, immanently powerful, obligatory, self-same, manifest and univocal (20). This conception is then taken to represent the traditional metaphysical position. Here a number of questions could be raised regarding what Marx himself calls the "not completely satisfactory route" of his own analysis (17). One could certainly agree with his beginning assumption, "ithat our contemporary understanding of measure still contains certain residual traditional meanings" (17). But the stronger and genuinely operative assumption in Marx's analysis is more questionable. Why does Schelling's conception stand as.the representative of an entire metaphysical tradition? Although Schelling's conception of measure nicely facilitates Marx's projecl: vis-a-vis Heidegger, the reader might remain unconvinced that the full metaphysical conception of measure is reflected therein. Consider, for example, Marx's contention ithat 1the traditional measure is univocal and therefore leaves no room for ambiguity (42). On this basis he asserts that we cannot take Heidegger's notion of "the fourfold," which involves an "inner mobility " of play, as a.traditional measure. The ambiguity and "basic 540 BOOK REVIEWS instability inherent in playing and mirroring is irreconcilable with the traditional meaning of a measure" (42). By avoiding the more extensive analysis to which he makes reference, Marx neatly steps around an extremely important problematic involved in the concepts of ambi· guity and univocity. The following question indicates this problem in the simplest way: Does univocity belong to the measure itself or to our perception or predication of the measure? We might say, for example,,that there is no ambiguity in God, but that there is a high degree of ambiguity involved in our perception or predication of God. Certainly in the tradition, whether we take Arisotle's spoudaios, or God's eternal law, or Christian love in the model of Christ as our measure, we do not escape the ambiguity of our own finite interpretations. Thus Aristotle's caution about.the nature of ethics (N. Ethics 1094bl2-15), Aquinas's qualification about knowing the natural law with respect to details (ST 94,, 4), or Kierkegaard's acknowledgment of the paradox of Christ. This problematic is also to be found in Heidegger's writings where he indicates a play of concealedness-unconcealedness involved in Being or "the fourfold," and thus an ambiguity in the measure itself. But would Heidegger say that this concealing-unconcealing play of Being is something that happens in itself, outside of language, or independent· ly of the one who is looking after Being? (See Marx's discussion, 9192, 123). The difference between Heidegger and the tradition on this point is.this: in the tradition the " location " of ambiguity is unambiguous ; it is found in human perception, language, and reason, hut not in the measure itself. In Heidegger, ·the location... (shrink)

Uncertainty about the actual orientation of the measurement device has been claimed to open a loophole for hidden variable models of quantum mechanics. In this paper I describe the statistics of inaccurate spin measurements by unsharp spin observables. A no‐go theorem for hidden variable models of the inaccurate measurement statistics follows: There is a finite set of directions for which not all results of inaccurate spin measurements can be predetermined in a non‐contextual way. In contrast to an earlier theorem (Breuer (...) 2002) this result does not rely on the assigment of approximate truth values, and it holds under weaker assumptions on the measurement inaccuracy. (shrink)

We construct models containing exactly one supercompact cardinal in which level by level inequivalence between strong compactness and supercompactness holds. In each model, above the supercompact cardinal, there are finitely many strongly compact cardinals, and the strongly compact and measurable cardinals precisely coincide.

A conjectural inference is proposed, aimed at producing conjectural theorems from formal conjectures assumed as axioms, as well as admitting contradictory statements as conjectural theorems. To this end, we employ Paraconsistent Informational Logic, which provides a formal setting where the notion of conjecture formulated by an epistemic agent can be defined. The paraconsistent systems on which conjectural deduction is based are sequent formulations of the C-systems presented in Carnielli-Marcos [CAR 02b]. Thus, conjectural deduction may also be considered to be a (...) tool for investigating the properties of paraconsistency in general. (shrink)

Personality traits describe dispositions influencing individuals' behavior and performance at work. However, in the context of personnel selection, the use of personality measures has continuously been questioned. To date, research in selection settings has focused uniquely on predicting task performance, missing the opportunity to exploit the potential of personality traits to predict non-task performance. Further, personality is often measured with self-report inventories, which are susceptible to self-distortion. Addressing these gaps, the planned study seeks to design new personality measures to be (...) used in the selection context to predict a wide range of performance criteria. Specifically, we will develop a situational judgment test and a behavior description interview, both assessing Big Five personality traits and Honesty-Humility to systematically compare these new measures with traditional self-report inventories regarding their criterion-related validity to predict four performance criteria: task performance, adaptive performance, organizational citizenship behavior, and counterproductive work behavior. Data will be collected in a simulated selection procedure. Based on power analyses, we aim for 200 employed study participants, who will allow us to contact their supervisors to gather criterion data. The results of this study will shed light on the suitability of different personality measures to predict an expanded range of performance criteria. (shrink)

Propositional dynamic logic (PDL) provides a natural setting for semantics of means-end relations involving non-determinism, but such models do not include probabilistic features common to much practical reasoning involving means and ends. We alter the semantics for PDL by adding probabilities to the transition systems and interpreting dynamic formulas 〈α〉 ϕ as fuzzy predicates about the reliability of α as a means to ϕ. This gives our semantics a measure of efficacy for means-end relations.

We recall one Tarski's result about the existence of a non-zero additive measure defined on power set of an infinite set vanishing on finite subsets. This rather surprising result goes back to 1930 and it allows to introduce a non-trivial linear functional invariant under changes of finitely many inputs.

Many individual difference variables predict Bayesian reasoning performance, including cognitive reflection (thoughtful engagement with a problem rather than intuitive responding). The cognitive reflection test (CRT), though, is interdependent with numerical literacy. Two non-mathematics versions of this test (CRTverbal) are integrated and evaluated here, concurrent with other individual difference measures, as predictors of Bayesian reasoning performance. Two studies found CRTverbal appears to measure a fairly unitary underlying construct that is correlated with Bayesian reasoning performance. However, all other measures were also correlated (...) with Bayesian reasoning, as well as generally with each other (including numerical literacy correlating with CRTverbal). Stepwise regressions found that Bayesian reasoning was best predicted by visuospatial ability and sets reasoning ability, excluding numeracy, working memory (Experiment 1), and pattern extrapolation abilities (Experiment 2). Although cognitive reflection remains a predictor of some utility, these positive manifold patterns of results suggest a broader cognitive ability may be generating these results. (shrink)