My argument owes much to two contemporary philosophical scholars of the development of modern physics beginning with Newton and extending through the late nineteenth and early twentieth centuries: George Smith and Howard Stein. From the former I take a conception of theory-mediated measurement, from the latter a conception of abstract structures in the phenomena. The relevant notion of phenomena, as we shall see, is closely related to Newtonian scientific methodology, a methodology that is clearly embraced by both philosophers. (...) The conception of abstract structures, however, is not so clear, and it is especially to be distinguished from the more recent conception of “structural realism.”. (shrink)

The last thirty years have seen a resurgence of interest in virtue among philosophers, psychologists, and educators. This co-authored book brings an interdisciplinary response to the study of virtue: it not only provides a framework for quantifying virtues, but also explores how we can understand virtue in a philosophically-informed way that is compatible with the best current thinking in personality psychology. The volume presents a major contribution to theemerging science of virtue and character measurement.

There is a consistent and simple interpretation of the quantum theory of isolated systems. The interpretation suffers no measurement problem and provides a quantum explanation of state reduction, which is usually postulated. Quantum entanglement plays an essential role in the construction of the interpretation.

The content of our propositional attitudes is often characterized by assigning them abstract entities, namely propositions. In decision theory the attitudes are also assigned numerical measures. It may thus be asked how assignments of these two types are related to each other — both metaphysically and structurally. In the first section of this paper I argue for the importance of this question and I review Davidson’s unified account of decision theory and radical interpretation as a failed attempt to (...) answer it. Then, in the main part of the paper, I present a unified measurement-theoretic account of linguistic meaning, propositional mental content, and action, an account that avoids the difficulties of Davidson’s picture. Thus in the second section I outline two theoretical preliminaries (the representational theory of measurement and Savage’s decision theory), in the third section I present the proposed novel account, and in the fourth section I defend it against various objections. (shrink)

Introducing the main theories of distributional justice the book covers utilitarianism and welfare economics, moving on to Rawls's social contract and the Sen/Nussbaum capability approach with a refreshingly readable style. There is a chapter covering the position of mothers and children in theories of justice. The book then studies empirical methods used in analysing the distribution of economic goods, covering Lorenz curves and inequality measures. The concepts of income, wealth and economic goods are comprehensively discussed, with a particular view to (...) their role in theories of justice. This book is an important read for economists and other social scientists, as well as philosophers who want to quantify social and economic justice. (shrink)

In the following article, we propose to show that following the general verificationist epistemic programme (its demand that the truth of our judgments be verifiable), the analysis of measurement on the one hand, and the classical positivist analysis of common-sense observation on the other, do not lead to same conclusions. This is especially important, because the differences in conclusions concern the positivist theory/observation distinction. In particular, the analysis of measurement does not fully support this distinction. This fact (...) might have important consequences for the problem of scientific realism and related ontological and epistemological problems in the philosophy of science. (shrink)

The need for quantitative measurement represents a unifying bond that links all the physical, biological, and social sciences. Measurements of such disparate phenomena as subatomic masses, uncertainty, information, and human values share common features whose explication is central to the achievement of foundational work in any particular mathematical science as well as for the development of a coherent philosophy of science. This book presents a theory of measurement, one that is "abstract" in that it is concerned with (...) highly general axiomatizations of empirical and qualitative settings and how these can be represented quantitatively. It was inspired by, and represents a generalization and extension of, the last major research work in this field, Foundations of Measurement Vol. I, by Krantz, Luce, Suppes, and Tversky published in 1971. (shrink)

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.

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. (shrink)

We characterize access to empirical objects in biology from a theoretical perspective. Unlike objects in current physical theories, biological objects are the result of a history and their variations continue to generate a history. This property is the starting point of our concept of measurement. We argue that biological measurement is relative to a natural history which is shared by the different objects subjected to the measurement and is more or less constrained by biologists. We call symmetrization (...) the theoretical and often concrete operation which leads to considering biological objects as equivalent in a measurement. Last, we use our notion of measurement to analyze research strategies. Some strategies aim to bring biology closer to the epistemology of physical theories, by studying objects as similar as possible, while others build on biological diversity. (shrink)

We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of (...) discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. (shrink)

We investigate the implications of protective measurement for de Broglie-Bohm theory, mainly focusing on the interpretation of the wave function. It has been argued that the de Broglie-Bohm theory gives the same predictions as quantum mechanics by means of quantum equilibrium hypothesis. However, this equivalence is based on the premise that the wave function, regarded as a Ψ-field, has no mass and charge density distributions. But this premise turns out to be wrong according to protective measurement; (...) a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. Then in the de Broglie-Bohm theory both Ψ-field and Bohmian particle will have charge density distribution for a charged quantum system. This will result in the existence of an electrostatic self-interaction of the field and an electromagnetic interaction between the field and Bohmian particle, which not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Therefore, the de Broglie-Bohm theory as a realistic interpretation of quantum mechanics is problematic according to protective measurement. Lastly, we briefly discuss the possibility that the wave function is not a physical field but a description of some sort of ergodic motion (e.g. random discontinuous motion) of particles. (shrink)

Over the last few decades, virtue has become increasingly important in philosophy, psychology, cognitive science, and education. However, as each of these disciplines approaches virtue from a decidedly different perspective, it has proven difficult to come up with an understanding of virtue that satisfies the standards of all four disciplines. In their book, Jennifer Wright, Michael Warren, and Nancy Snow attempt to put forward such an understanding.

Our primary aim in this paper is to sketch the account of virtue that we think most amenable to virtue measurement. Our account integrates Whole Trait Theory from psychology with a broadly neo-Aristotelian approach to virtue. Our account is ‘ecumenical’ in that it has appeal for a wide range of virtue ethicists. According to WTT, a personality trait is composed of a set of situation-specific trait-appropriate responses, which are produced when certain “social-cognitive” mechanisms are triggered by the perception (...) of trait-relevant stimuli in a person’s external and/or internal environment. Moving from this starting point, we discuss our conception of a virtue and respects in which it both aligns with and diverges from Aristotle’s conception. We discuss roles for practical wisdom and motivation in our conception of virtue, and highlight respects in which WTT provides an amenable empirical framework into which key Aristotelian elements can be integrated. We conclude with brief remarks about our conception as an empirically adequate and measurable account. (shrink)

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably (...) additive on open sets. (shrink)

Measurement is said to be the basis of exact sciences as the process of assigning numbers to matter (things or their attributes), thus making it possible to apply the mathematically formulated laws of nature to the empirical world. Mathematics and empiria are best accorded to each other in laboratory experiments which function as what Nancy Cartwright calls nomological machine: an arrangement generating (mathematical) regularities. On the basis of accounts of measurement errors and uncertainties, I will argue for two (...) claims: 1) Both fundamental laws of physics, corresponding to ideal nomological machine, and phenomenological laws, corresponding to material nomological machine, lie, being highly idealised relative to the empirical reality; and also laboratory measurement data do not describe properties inherent to the world independently of human understanding of it. 2) Therefore the naive, representational view of measurement and experimentation should be replaced with a more pragmatic or practice-based view. (shrink)

I address the recent debate between Meehan and Vaidman concerning the claim made by the former for a new problem to quantum mechanics. I argue that while Meehan's incompatibility claim does hold in the situation he presents, it does not genuinely involve considerations that can limit quantum state preparation, nor does it introduce new constrains over possible interpretations of quantum theory.

Sometimes it is possible in quantum theory for a system to interact with another system in such a way that the information contained in the wave function becomes very scrambled and apparently incoherent. We produce an example which is exactly calculable, in which a macroscopic change is induced in the environment, and all phase information for the system is apparently lost, so that a measurement has seemingly been made. But actually, although the wave function has been badly scrambled, (...) all the original information is still present. We call this situation one of “latent order.”Subsequently, the system interacts again with the environment, wiping out the macroscopic change, and the wave function once again becomes manifestly coherent. Thus the apparent measurement has been undone, and leaves no aftereffect. Thus, our “measurement” has disappeared without a trace. We call such a measurement a “haunted measurement,” and we believe that until the measurement process is rigorously understood, the concept of measurement is ambiguous. It is just not good enough to say that an amplification stage occurs “somewhere” in the process.We also point out the connection between the haunted measurement and delayed-choice experiments and discuss a haunted version of the “Schrödinger's Cat” experiment and of the Einstein-Podolsky-Rosen experiment. (shrink)

It is shown that the physics and semantics of quantum measurement provide a natural interpretation of the weak neighborhoods of the states on observable algebras without invoking any idea of “a reading error” or “a measured range.” Then the state preparation process in quantum measurement theory is shown to give the normal (or locally normal) states on the observable algebra. Some remarks are made concerning the physical implications of normal states for systems with an infinite number of (...) degrees of freedom, including questions on open and closed algebraic theories. (shrink)

Useful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups. From the reviews: "Will serve the interested student to find his way to active and creative work in the field of Hilbert space theory." --MATHEMATICAL REVIEWS.

Recently, a number of scholars have warned against the risk of a new form of deliberately deceptive communication companies use to assure stakeholders of their good intentions in the adoption and development of digital technologies and advanced information systems based on artificial intelligence. This corporate behaviour, defined as machinewashing, in an attempt to empower engagement processes in the stakeholders’ network and satisfy stakeholder expectations with regard to the ethical implications of the use of artificial intelligence, has, in the final instance, (...) the prevailing purpose of achieving better levels of corporate performance and reputation. However, thus far, scholars have not provided any empirical studies on the existence of corporate machinewashing strategies, and there is a significant lack of clarity as to how to measure machinewashing. Utilising the corporate digital responsibility theory, this paper offers an original methodological contribution to the nascent research field dedicated to machinewashing behaviour. Particularly, this paper provides considerations for detecting machinewashing through an analysis based on the comparison between the information capacity of the reporting and the information reliability level as a proxy for machinewashing strategies and, thus, for the real impact of digitalisation strategies on stakeholders. To this end, we conducted an exploratory content analysis of the reports of 10 Italian-listed companies from 10 different industries. Overall, looking at the gap between what companies say about the impact of digitalisation from an ethical perspective, and what really happens, our results define a possible path for identifying machinewashing, the fields where it happens and the practices that companies use in order to realise these strategies. (shrink)

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)

It is shown that the application of the Lax-Phillips scattering theory to quantum mechanics provides a natural framework for the realization of the ideas of the “Many-Hilbert-Space” theory of Machida and Namiki to describe the development of decoherence in the process of measurement. We show that if the quantum mechanical evolution is pointwise in time, then decoherence occurs only if the Hamiltonian is time-dependent. If the evolution is not pointwise in time (as in Liouville space), then the (...) decoherence may occur even for closed systems. These conclusions apply as well to the general problem of mixing of states. (shrink)

A highly abstracted theory of measurement is synthesized from classical measurement theory, fuzzy set theory, generalized information theory, and predicate calculus. The theory does not require specific truth value concepts, nor does it specify what subsets of the reals can be observed, thus avoiding the usual fundamental difficulties. Problems such as the definition of systems, the significance of observations, numerical scales and observables, etc. are examined. The general logico-algebraic approach to quantum/classical physics is (...) justified as a special case of measurement theory. (shrink)

The Bohm-Bub hidden-variable theory is able to predict the results of measuring a quantum system only in the special case where the set of commuting observables being measured is complete. To handle the much more common case where the set is incomplete, Tutsch has proposed a generalization of the Bohm-Bub model. Unfortunately, as we show here, Tutsch's original method does not yield the correct quantum mechanical transition probabilities. On the other hand, Belinfante's modification of Tutsch's method does yield the (...) correct probabilities, and it gives a satisfactory hidden-variable theory of partial measurement for the case where one or more commuting variable(s) are measured at a single space-time point. In the case where the variables are measured at different space-time points, the theory is inadequate, due to the fact that it is not relativistically covariant, and does not take relaxation of the hidden variables into account. (shrink)

The paper reconstructs the connections between the evolution of Patrick Suppes’ measurement theory from 1951 to 1958 and the research in utility analysis he conducted between 1953 and 1957 within the Stanford Value Theory Project. In particular, the paper shows that Suppes’ superseding of the classical understanding of measurement, his endorsement of the representational view of measurement, and his conceiving of an axiomatic version of the latter were prompted by his research in utility analysis.

The problem of measurement in theories based on geometry with nonmetricity and contorsion is analyzed. In order to enable the use of atoms as measuring standards, one has to remove the nonintegrability of length in the interior of atoms. Geometrical descriptions appropriate fo this purpose are found in the general case and in the case of two-covariant theories.

This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971). Based on measurement theory’s four-way typology of measures, I claim that different adjectives are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution (...) of measure phrases, as well as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement theory. (shrink)

The interpretations of measurements in Bohm's and Everett's quantum theories are compared. Since both theories are based on the assumption of a universally valid Schrödinger equation, they face the common problem of how to explain that arrow of time, which in conventional quantum theory is represented by the collapse of the wave function. Its solution requires, in a statistical sense, a very improbable initial condition for thetotal wave function of the universe. The historical importance of Bohm's quantum theory (...) is pointed out. (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)

This paper examines how people assess inequality of income distribution and how inequality could be measured. We start from the philosophical analysis of Temkin, who distinguishes nine plausible aspects of inequality. His approach is based on the concept of ‘complaints’ or distances between incomes. We examine the Temkin approach by means of the questionnaire-experimental method pioneered by Amiel and Cowell to find out whether the aspects of equality have any plausibility for student respondents and, if so, whether there are aspects (...) which are more appealing than others. Both the numerical and verbal responses show that a considerable majority of the respondents might be influenced by the intuitions included in the combination of the Weighted Additive Principle and the Average view of complaints. The questionnaire results also shed some empirical light on the acceptance of the Transfer Principle and the attitudes towards the Sequence. Footnotes I would like to thank Erik Schokkaert, Frank Cowell, and Liema Davidovitz for various suggestions which have led to improvements in this paper. I am very grateful for helpful comments from seminar participants and an anonymous referee. I remain responsible for any remaining error. This paper was written while the author enjoyed the hospitality of Sticerd, LSE, London and he acknowledges the financial support provided by the Training and Mobility of Researchers Program of the European Communities, grant #ERBFMRXCT980248. (shrink)

The central thesis of this article is that measurement units are theoretical concepts because measurement presumes theoretical definition. New theoretical constructs can be defined in terms of algebraic combinations of previously defined measurement units. Physics has developed an impressive hierarchical knowledge structure on this basis. The unitless measures favored by psychology preclude the generation of such a knowledge hierarchy. It also leads to definitions of reliability and validity in correlational terms which can result in inaccurate measurement. (...) Psychology has long used time as a fundamental unit. Adoption of a second measurement unit would enable construction of a psychological knowledge hierarchy to begin. (shrink)

A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term ‘common prearranged context’. A formalised treatment requires a quantitative definition of the (...) similarity or dissimilarity between two complex structures which takes their internal structures into account. After some specific remarks on distance, metrics, and semi-metrics in mathematics, a procedure is described for setting up a similarity function with the required properties. This procedure is in analogy with the two-step character of measurement and with the well-known properties of perspective notions. A general methodology can be derived for handling perspective notions. Finally, these concepts supply heuristic clues towards a formalised treatment of the notions of ‘meaning’ and ‘interpretation’. (shrink)

In Chapter 6, Johanna E. Wolff uses models of measurements as a case for exploring two forms of scientific realism that are meant to address the problem of plurality of models in science: structural realism and perspectival realism. She distinguishes their motivations in the following way: structural realists address the plurality of models by looking for similarities, namely structural commonalities, between the models, whereas perspectival realists emphasize how differences among a plurality of models can be complementary. In comparing these realist (...) alternatives, Wolff chooses to focus on measurement theory. Wolff urges the idea that perspectival realism and structural realism are not competing realist accounts but complementary ones. (shrink)