The formal methods of the representational theory of measurement (RTM) are applied to the extensive scales of physical science, with some modifications of interpretation and of formalism. The interpretative modification is in the direction of theoretical realism rather than the narrow empiricism which is characteristic of RTM. The formal issues concern the formal representational conditions which extensive scales should be assumed to satisfy; I argue in the physical case for conditions related to weak rather than strong (...) extensive measurement, in the sense of Holman 1969 and Colonius 1978. The problem of justifying representational conditions is addressed in more detail than is customary in the RTM literature; this continues the study of the foundations of RTM begun in an earlier paper. The most important formal consequence of the present interpretation of physical extensive scales is that the basic existence and uniqueness properties of scales (representation theorem) may be derived without appeal to an Archimedean axiom; this parallels a conclusion drawn by Narens for representations of qualitative probability. It is concluded that there is no physical basis for postulation of an Archimedean axiom. (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. (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)

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)

Axiomatic measurement theories are commonly interpreted as claiming that, in order to quantify an empirical domain, the qualitative structure of data about that domain must be mapped to a numerical structure. Such mapping is supposed to be established independently, i.e., without presupposing that the domain can be quantified. This interpretation is based on two myths: that it is possible to independently infer the qualitative structure of objects from empirical data, and that the adequacy of numerical representations can only be (...) justified by mapping such qualitative structures to numerical ones. I dispel the myths and show that axiomatic measurement theories provide an inadequate characterization of the kind of evidence required to detect quantities. (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)

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.

In Part I we saw that the works of Helmholtz, Holder, Campbell and Stevens contain the main ingredients for the analysis of the conditions which make measurement possible, but, so to speak, that what is lacking in the work of the first three is to be found in the work of the last, and vice versa. The first tradition focuses on the conditions that an empirical qualitative system must satisfy in order to be numerically representable, but pays no attention (...) to the relation between possible different representations. The second tradition focuses on the study of scale types and the mathematical properties of the transformations that characterize the scales, but says nothing about the empirical facts these scales represent and the nature of such representation. Then, these two lines of research need to be appropriately integrated. In this Part II, we shall see how this integration is brought about in the foundational work of Suppes, the extensions and modifications which are generated around this work and the mature theory which results from all of this. (shrink)

It has become customary to locate the origins of modern measurement theory in the works of Helmholtz and Hölder. If by ‘modern measurement theory’ is meant the representational theory, then this may not be an accurate assessment. Both Helmholtz and Hölder present theories of measurement which are closely related to the classical conception of measurement. Indeed, Hölder can be interpreted as bringing this conception to fulfilment in a synthesis of Euclid, Newton, and (...) Dedekind. The first explicitly representational theory appears to have been Russell's. He rejected the traditional concept of quantity and its connection to number, making the use of number in quantitative science problematical. He solved the problem via representationalism. (shrink)

Erik Angner has argued that simultaneous endorsement of the representational theory of measurement and psychometrics leads to inconsistency. His claim rests on an implicit assumption: RTM and psychometrics are full-fledged approaches to measurement. I argue that RTM and psychometrics are only partial approaches that deal with different aspects of measurement, and that therefore simultaneous endorsement of the two is not inconsistent. The argument has implications for the improvement of measurement practices.

In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources of mathematical analysis) are used as a unified mathematical framework for modeling (a) the time-dependent behavior of natural systems, (b) interactions between natural systems and measuring instruments, (c) error and uncertainty in measurement, and (d) the formal propositional language for describing and reasoning about measurement results. We also discuss how a celebrated theorem in (...) analysis, known as Gelfand representation, guarantees that autonomously specified algebras of quantities can be interpreted as algebras of observables on a suitable state space. Such an interpretation is then used to support (i) a realist conception of quantities as objective characteristics of natural systems, and (ii) a realist conception of measurement results (evaluations of quantities) as determined by and descriptive of the states of a target natural system. As a way of motivating the analytic approach to measurement, we begin with a discussion of some serious philosophical and theoretical problems facing the well-known representational theory of measurement. We then explain why we consider the analytic approach, which avoids all these problems, to be far more attractive on both philosophical and theoretical grounds. (shrink)

The Representational Theory of Measurement is the best known account of the kind of representation measurement requires. However, RTM has been challenged from various angles, with critics claiming e.g. that RTM fails to account for actual measurement practice and that it is ambiguous about the nature of measurable attributes. In this paper I use the critical literature on RTM to formulate Representation Minimalism – a characterization of what measurement-relevant representation requires at the minimum. I (...) argue that Representation Minimalism avoids the main problems with RTM while acknowledging its usefulness as the formal foundation of representation in measurement. (shrink)

The problem of measurement can be reformulated as the problem of measurability: What are the conditions under which measurement becomes possible at all? And what is the ontological status of concrete measurement outcomes? It will be shown in the course of this article that what Joel Michell deemed the ‘representational theory’ of measurement provides an adequate framework for answering these questions. However, contrary to Michell, I will point out that Hermann von Helmholtz should be (...) seen as an important forerunner of the representational view. Furthermore, it will be argued that the Finnish logical empiricist Eino Kaila carried on Helmholtz’s approach by combining it with a certain form of ontological invariantism. On the whole, a ‘structural realist’ account of measurement will be suggested. (shrink)

Part II: Suppes and the mature theory. Representation and uniqueness.

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical (...) representation is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably-based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (shrink)

The paper introduces and formally defines a functional concept of a measuring system, on this basis characterizing the measurement as an evaluation performed by means of a calibrated measuring system. The distinction between exact and uncertain measurement is formalized in terms of the properties of the traceability chain joining the measuring system to the primary standard. The consequence is drawn that uncertain measurements lose the property of relation-preservation, on which the very concept of measurement is founded according (...) to the representational viewpoint. Finally, from the analysis of the inter-relations between calibration and measurement the fundamental reasons of the claimed objectivity and intersubjectivity of measurement are highlighted, a valuable epistemological result to characterize measurement as a particular kind of evaluation. (shrink)

Psychometrics and the representational theory of measurement are widely used in social scientific measurement. They are currently pursued largely in isolation from one another. I argue that despite their separation in practice, RTM and psychometrics are complementary approaches, because they can contribute in complementary ways to the establishment of what I argue is a crucial measurement property, namely, representational interpretability. Because RTM and psychometrics are complementary in the establishment of representational interpretability, the current (...) separation of measurement approaches is unfounded. 1Introduction2Two Approaches to Measurement 2.1Representational theory of measurement2.2Psychometrics2.3Representational interpretability3Complementarity, Conceptually 3.1Representational theory of measurement: Conditions of representational interpretability3.2Psychometrics: Evidence of representational interpretability4Complementarity in Action 4.1What is the Rasch model?4.2Rasch and conjoint measurement5Conclusion: Critics and Fruits of Complementarity. (shrink)

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)

In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two metaphysical presuppositions —accepted in the present as dogmas that all interpretations must follow. (...) We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the paper, we revisit, from a representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence. (shrink)

The Representational Theory of Measurement (RTM), especially the canonical three volume Foundations of Measurement by Krantz et al., is a landmark accomplishment in our understanding of measurement. Despite this, it has been far from easy to pinpoint what exactly we can learn about measurement from RTM, and who the target audience for RTM’s formal results should be. In what sense does RTM provide foundations of measurement, and what is the philosophical significance of such (...) foundations? I argue that RTM provides semantic foundations of measurement, and that their philosophical significance lies in a shift towards structural representation. (shrink)

Ordinary measurement using a standard scale, such as a ruler or a standard set of weights, has two fundamental properties. First, the results are approximate, for example, within 0.1 g. Second, the resulting indistinguishability is transitive, rather than nontransitive, as in the standard psychological comparative judgments without a scale. Qualitative axioms are given for structures having the two properties mentioned. A representation theorem is then proved in terms of upper and lower measures.

On the received view, the Representational Theory of Measurement reduces measurement to the numerical representation of empirical relations. This account of measurement has been widely criticized. In this article, I provide a new interpretation of the Representational Theory of Measurement that sidesteps these debates. I propose to view the Representational Theory of Measurement as a library of theorems that investigate the numerical representability of qualitative relations. Such theorems are useful (...) tools for concept formation that, in turn, is one crucial aspect of measurement for a broad range of cases in linguistics, rational choice, metaphysics, and the social sciences. (shrink)

Measurement theory in (Hand in The world through quantification. Oxford University Press, 2004; Suppes and Zinnes in Basic measurement theory. Psychology Series, 1962) is concerned with the assignment of number to objects of phenomena. Representational aspect of measurement is the extent to which the assigned numbers and arithmetics truthfully represent the underlying objects and their relations, and is characteristic to natural sciences; pragmatic aspect is the extent to which the assigned numbers serve purposes other (...) than representing the underlying phenomena, and is characteristic to social sciences (Hand in The world through quantification. Oxford University Press, 2004). Here I criticise this distinction of representational and pragmatic measurements on the basis of the earlier history of the periodic system of chemical elements, viewed in terms of a practice based philosophy of science by Rein Vihalemm. I argue that the periodic system, although a natural scientific system interpretable as a measurement system, has considerable, in Hand’s terms pragmatic, aspects in it. Those aspects include: tampering with the material measurement results for the theoretical ideal of systematicity; adopting metaphysical assumptions that cannot be experimentally proven, like individuality of elements and atomicity; theoretical construction of the abstract entity—element—as the reference of the measurement system amenable to mathematically elegant ordering. Contrary to Suppes and Zinnes (Basic measurement theory. Psychology Series, 1962) I also argue for the dependence of the assigned numerical system on the material-procedural base of the measurement. (shrink)

Narrative Representation Theory, an evolved framework of Verse Analysis, has come into existence with the mission of explaining the operation of macro-systemic structure that could be hardwired in the brain. Based on the analyses of creoles or archetypal human languages, the theory puts forward the premise stating that the fundamental design of the human language faculty possesses the computational system for internalized discourse. The theory preserves the principles of Quint-patterning, Idea-formatting, N-ary-branching and X-numbering, complying respectively with the (...) hierarchical orderings of constituency, the atomic elements of componentiality, the linear sequences of precedence and the specific measurement of terminal nodes. NRT tells that the macro-system of narrative superstructure must have emerged autonomously, yet links closely with the micro-system of phonology, morphology and syntax. This article explores for the first time scientific insights into the nature of human language, referring to recent research on the right cerebrum as well as on the prefrontal lobes of the brain, the relationship between mental disorders and their genetic deficiencies, and the investigations of human evolution during the period 200,000–40,000 years BP. All the converging evidence in biological sciences reinforces the hypothesis that the narrative superstructure of language faculty manifests as an inherent linguistic capacity in our mind. (shrink)

We introduce and study several nonstandard representations of Banach-valued operators defined on the space of Bochner integrable functions. They will be less restrictive than the usual standard representation. In particular, without any hypothesis, we shall find a representation whose kernel belongs to a space of “extended Bochner integrable functions”, introduced by Zimmer by using Loeb measures.

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of (...) events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems. (shrink)

Algebraic theories for extensive measurement are traditionally framed in terms of a binary relation $\lesssim $ and a concatenation (x,y)→ xy. For situations in which the data is "noisy," it is proposed here to consider each expression $y\lesssim x$ as symbolizing an event in a probability space. Denoting P(x,y) the probability of such an event, two theories are discussed corresponding to the two representing relations: p(x,y)=F[m(x)-m(y)], p(x,y)=F[m(x)/m(y)] with m(xy)=m(x)+m(y). Axiomatic analyses are given, and representation theorems are proven in detail.

This paper argues that the dominant mainstream neo‐classical economic theory propounds a world‐view which is based not simply on half‐truths, but on straight lies. This is particularly significant since the influence of the economic world‐view reaches into every realm of social thought. Although overtly grounded in utilitarianism, the basis of neo‐classical thought has undergone two shifts of meaning which have converted the original self‐evident utilitarian presuppositions into an ideology. The first of these alters the utilitarian proposition that ‘we seek (...) satisfaction’ into the statement that ‘we only seek satisfaction’. It follows that human action is motivated by nothing other than selfishness and greed, and that altruism therefore cannot exist: anything that looks like altruism is therefore nothing other than egoism in disguise, and there is no place for ethical reasoning in individual choice. The second shift alters the premise that our goal is ‘maximum satisfaction’ to the assertion that what we seek is ‘maximum monetary gain’. This shift is already present in the writings of Jeremy Bentham, and forms the basis of much subsequent work in economics. In particular, it has facilitated the emergence of what one might term ‘economic imperialism’, i.e. the use of economic theory to analyse social issues – family size, racial discrimination, marriage, education choices, among others. In all of these cases monetary gain is the paramount criterion. For business ethics the most obvious example here is the absolutisation of profit as the sole criterion of business achievements, and of salary as the sole criterion of work choice and worker satisfaction. Both of these premises are then used to demonstrate that it is free competition which will ensure maximum social welfare. This conclusion is both relativistic and reductionistic. In the first place, the necessary conditions for perfect competition can never exist. Nor can ‘optimum social welfare’ be translated into ‘optimum welfare for all’ in an economic world‐view which sees wealth and poverty as the ‘just deserts’ of hard work and laziness respectively. The dominant economic theory is thus explicitly immoral in that it enshrines the absolute sovereignity of the individual and the law of the jungle as social norms. The qualitative measure of human happiness is desire, the quantitative measure is money. From an ethical perspective we must reject the falsity of this world‐view. (shrink)

The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have (...) received adequate justification: the assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. (...) The metrological structure of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

Extensive measurement theory is developed in terms of theratio of two elements of an arbitrary (not necessarily Archimedean) extensive structure; thisextensive ratio space is a special case of a more general structure called aratio space. Ratio spaces possess a natural family of numerical scales (r-scales) which are definable in non-representational terms; ther-scales for an extensive ratio space thus constitute a family of numerical scales (extensive r-scales) for extensive structures which are defined in a non-representational manner. This (...) is interpreted as involving arelational theory of quantity which contrasts in certain respects with thequalitative theory of quantity implicit in standard representational extensive measurement theory. The representational properties of extensiver-scales are investigated, and found to coincide withweak extensive measurement in the sense of Holman. This provides support for the thesis (developed in a separate paper) that weak extensive measurement is a more natural model of actual physical extensive scales than is the standard model using strong extensive measurement. Finally, the present apparatus is applied to slightly simplify the existing necessary and sufficient conditions for strong extensive measurement. (shrink)

This paper argues that the dominant mainstream neo‐classical economic theory propounds a world‐view which is based not simply on half‐truths, but on straight lies. This is particularly significant since the influence of the economic world‐view reaches into every realm of social thought. Although overtly grounded in utilitarianism, the basis of neo‐classical thought has undergone two shifts of meaning which have converted the original self‐evident utilitarian presuppositions into an ideology.The first of these alters the utilitarian proposition that ‘we seek satisfaction’ (...) into the statement that ‘we only seek satisfaction’. It follows that human action is motivated by nothing other than selfishness and greed, and that altruism therefore cannot exist: anything that looks like altruism is therefore nothing other than egoism in disguise, and there is no place for ethical reasoning in individual choice.The second shift alters the premise that our goal is ‘maximum satisfaction’ to the assertion that what we seek is ‘maximum monetary gain’. This shift is already present in the writings of Jeremy Bentham, and forms the basis of much subsequent work in economics. In particular, it has facilitated the emergence of what one might term ‘economic imperialism’, i.e. the use of economic theory to analyse social issues – family size, racial discrimination, marriage, education choices, among others. In all of these cases monetary gain is the paramount criterion. For business ethics the most obvious example here is the absolutisation of profit as the sole criterion of business achievements, and of salary as the sole criterion of work choice and worker satisfaction.Both of these premises are then used to demonstrate that it is free competition which will ensure maximum social welfare. This conclusion is both relativistic and reductionistic. In the first place, the necessary conditions for perfect competition can never exist. Nor can ‘optimum social welfare’ be translated into ‘optimum welfare for all’ in an economic world‐view which sees wealth and poverty as the ‘just deserts’ of hard work and laziness respectively.The dominant economic theory is thus explicitly immoral in that it enshrines the absolute sovereignity of the individual and the law of the jungle as social norms. The qualitative measure of human happiness is desire, the quantitative measure is money. From an ethical perspective we must reject the falsity of this world‐view. (shrink)

Al final del cap. 1 de Foundations of Measurement. Vol.I los autores anuncian un segundo volumen y presentan un esbozo de los capítulos que han de componerlo. Aunque su publicación estaba prevista inicialmente para 1975, pasaban los años y a la comunidad científica llegaban tan sólo las versiones mecanuscritas parciales de algunos capítulos. Por fin, casi dos décadas después de FM I aparece el, por entonces ya mítico, segundo volumen desdoblado a su vez y convertido en FM II y (...) FM III. No es difícil adivinar los motivos de tanto retraso: a la cantidad y diversidad de material que quedó ya inicialmente para el segundo volumen, debía sumarse la ingente producción sobre measurement theory que, especialmente a partir de los setenta y por influencia en parte de FM I, la investigación producía año tras año. Como era de esperar, el resultado final de la obra no se ajusta exactamente a los planes originales, se eliminan algunos temas anunciados y se introducen otros nuevos. En primer lugar, se recoge la investigación sobre MT durante esos años: tanto la relacionada con cuestiones ya tratadas en FM I sobre las que se han obtenido resultados nuevos o más generales, como la derivada de un enfoque parcialmente nuevo desarrollado principalmente en torno a la obra de Narens y sus colaboradores. En segundo lugar, se suprime del plan original el capítulo dedicado al tratamiento estadístico del error y el último previsto en el que se resumiría el enfoque adoptado y se compararía con otros. (shrink)

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce (...) novel domain restrictions, independence conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all (...) those convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and its inseparable thermal bath, formally “entangled” like (...) an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions. (shrink)

Voting Advice Applications (VAAs) are interactive online tools designed to assist voters by improving the basis on which they decide how to vote. In recent years, they have been widely adopted, but their design is the subject of ongoing and often heated criticism. Most of these debates focus on whether VAAs accurately measure the standpoints of political parties and the preferences of users and on whether they report valid results while avoiding political bias. It is generally assumed that if their (...) methodology is sound, then VAAs can be seen as strengthening the democratic process. But as we argue in this chapter, the setup of VAAs raises basic questions of normative democratic theory as well. Insofar as VAAs are supposed to improve the functioning of the democratic process, it must be clarified in what sense they aim to make a contribution, before it even makes sense to discuss their effectiveness at doing so. -/- VAAs are often intended to enhance the democratic process by one or all of the following: (I) informing voters about the policy standpoints of political parties (or individual candidates), (2) increasing voter turnout, and (3) ensuring that the composition of parliaments more accurately reflects the political attitudes of the electorate. In the next three sections, we discuss three central bones of contention in current democratic theory that are crucial to these ways in which VAAs typically take themselves to contribute to strengthening the democratic process: -/- 1. Questions about citizen competence: What forms of competence do citizens need to have, and to what extent, for a democracy to function properly? -/- 2. Questions about political participation: What forms and extent of participation are vital to democracy? -/- 3. Questions about democratic representation: How should the relation between the elected and the electorate be understood? -/- For each issue we aim to show, first, how the design and setup of mainstream VAAs are tacitly structured by a specific conception of the democratic aim at issue and, second, what some alternative positions on these questions are within contemporary political theory. In the final section, we will discuss some of the implications of this analysis for the responsibilities of VAA developers, and particularly for the procedural neutrality to which they are typically committed. Our conclusion will be that once these issues are identified, developers of VAAs should either argue in favour of their views on democratic competence, participation and representation, or they should rethink the design of VA As in ways that move beyond their current assumptions, or both. (shrink)

The social welfare functional approach to social choice theory fails to distinguish a genuine change in individual well-beings from a merely representational change due to the use of different measurement scales. A generalization of the concept of a social welfare functional is introduced that explicitly takes account of the scales that are used to measure well-beings so as to distinguish between these two kinds of changes. This generalization of the standard theoretical framework results in a more satisfactory (...) formulation of welfarism, the doctrine that social alternatives are evaluated and socially ranked solely in terms of the well-beings of the relevant individuals. This scale-dependent form of welfarism is axiomatized using this framework. The implications of this approach for characterizing classes of social welfare orderings are also considered. (shrink)

I flesh out the sense in which the informational approach to interpreting quantum mechanics, as defended by Pitowsky and Bub and lately by a number of other authors, is (neo-)Bohrian. I argue that on this approach, quantum mechanics represents what Bohr called a “natural generalisation of the ordinary causal description” in the sense that the idea (which philosophers of science like Stein have argued for on the grounds of practical and epistemic necessity) that understanding a theory as a (...) class='Hi'>theory of physics requires that one be able to “schematise the observer” within it is elevated in quantum mechanics to the level of a postulate in the sense that interpreting the outcome of a measurement interaction, as providing us with information about the world, requires as a matter of principle, the specification of a schematic representation of an observer in the form of a ‘Boolean frame’—the Boolean algebra representing the yes-or-no questions associated with a given observable representative of a given experimental context. I argue that the approach’s central concern is with the methodological question of how to assign physical properties to what one takes to be a system in a given experimental context, rather than the metaphysical question of what a given state vector represents independently of any context, and I show how the quantum generalisation of the concept of an open system may be used to assuage Einstein’s complaint that the orthodox approach to quantum mechanics runs afoul of the supposedly fundamental methodological requirement to the effect that one must always be able, according to Einstein, to treat spatially separated systems as isolated from one another. (shrink)

This discussion centers on two desiderata: the role of measurement in information-gathering and physical interaction in scientific practice. By taking inspiration from van Fraassen’s view, we present a methodological account of perspectival measurement that addresses empirical practice where there is complex intervention, disagreeing results, and limited theory. The specific aim of our account is to provide a methodological prescription for developing measurement processes in the context of limited theory. The account should be useful to philosophers (...) of science, who are interested in the intersection between representation and intervention; scientists, who are interested in methodological suggestions for theory-development and reliability; and interdisciplinary researchers, who are interested in the intersections between the pandemic, built environments, and social processes. We apply the process-view of measurement to COVID-19, specifically, measuring replication in the SARS-CoV-2 virus. The aim is to show that our account tracks key elements—manipulation/intervention, independence, invariance, and theory-development—by organizing unfolding measurement processes. Additionally, we use our account to make prescriptive suggestions for measurement practice in the COVID-19 context by discussing the need to broaden measurement perspective on interaction, manipulation, and production. (shrink)

My thesis is that there are good reasons for a philosophical account of measurement to deal primarily with the properties or magnitudes of objects measured, rather than with the objects themselves. The account I present here embodies both a realism about measurement and a realism about the existence of the properties involved in measurement. It thus provides an alternative to most current treatments of measurement, many of which are operationalistic or conventionalistic, and nearly all of which (...) are nominalistic.1 This enables the present account to give better explanations of a number of features of measurement and other aspects of science than competing accounts of measurement can, and to be more readily integrated into a realist account of natural laws and causation. It also illustrates a general strategy for combining a familiar and powerful approach to representation with intensional entities like properties, which I think can be useful for dealing with a number of philosophical problems. (shrink)

The metrology literature neglects a strong empirical measurement tradition in economics, which is different from the traditions as accounted for by the formalist representational theory of measurement. This empirical tradition comes closest to Mari's characterization of measurement in which he describes measurement results as informationally adequate to given goals. In economics, one has to deal with soft systems, which induces problems of invariance and of self-awareness. It will be shown that in the empirical economic (...) measurement tradition both problems have been on the agenda for a long while, and that the proposed solutions to these problems provide clues for the directions in which one could develop a measurement theory that takes account of soft systems. (shrink)

The transition from the traditional to the representational theory of measurement around the turn of the century was accompanied by little sustained criticism of the former. The most forceful critique was Bertrand Russell''s 1897 Mind paper, On the relations of number and quantity. The traditional theory has it that real numbers unfold from the concept of continuous quantity. Russell''s critique identified two serious problems for this theory: (1) can magnitudes of a continuous quantity be defined (...) without infinite regress; and (2) can additive relations between such magnitudes exist if magnitudes are not divisible? The present paper shows how the traditional theory answers these questions and compares the traditional and representational theories as contributions to our understanding of the logic of application. (shrink)

Beliefs come in degrees, and we often represent those degrees with numbers. We might say, for example, that we are 90% confident in the truth of some scientific hypothesis, or only 30% confident in the success of some risky endeavour. But what do these numbers mean? What, in other words, is the underlying psychological reality to which the numbers correspond? And what constitutes a meaningful difference between numerically distinct representations of belief? In this Element, we discuss the main approaches to (...) the measurement of belief. These fall into two broad categories—epistemic and decision-theoretic—with divergent foundations in the theory of measurement. Epistemic approaches explain the measurement of belief by appeal to relations between belief states themselves, whereas decision-theoretic approaches appeal to relations between beliefs and desires in the production of choice and preferences. -/- (This book is part of the Cambridge Elements in Decision Theory and Philosophy series.). (shrink)

In the context of theistic religions, God representations are an important factor in explaining associations between religion/spirituality and well-being/mental health. Although the limitations of self-report measures of God representations are widely acknowledged, well-validated implicit measures are still unavailable. Therefore, we developed an implicit Attachment to God measure, the Apperception Test God Representations. In this study, we examined reliability and validity of an experimental scale based on attachment theory. Seventy-one nonclinical and 74 clinical respondents told stories about 15 cards with (...) images of people. The composite Attachment to God scale is based on scores on two scales that measure dimensions of Attachment to God: God as Safe Haven and God as Secure Base. God as Safe Haven scores are based on two subscales: Asking Support and Receiving Support from God. Several combinations of scores on these latter subscales are used to assess Anxious and Avoidant attachment to God. A final scale, Percentage Secure Base, measures primary appraisal of situations as nonthreatening. Intraclass correlation coefficients showed that the composite Attachment to God scale could be scored reliably. Associations of scores on the ATGR scales and on the explicit Attachment to God Inventory with scores on implicitly and explicitly measured distress partly confirmed the validity of the ATGR scales by demonstrating expected patterns of associations. Avoidant attachment to God seemed to be assessed more validly with the implicit than with the explicit scale. Patients scored more insecure on the composite Attachment to God scale and three subscales than nonpatients. (shrink)

Intelligent systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing both the needs of superordinate and basic-level categorization and of identification of specific instances of familiar categories. According to the proposed theory, a shape is represented by its similarity to a number of reference shapes, measured in a high-dimensional space of elementary features. This amounts to embedding the stimulus in (...) a low-dimensional proximal shape space. That space turns out to support representation of distal shape similarities which is veridical in the sense of Shepard's (1968) notion of second-order isomorphism (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical, as in the multidimensional scaling models (Shepard, 1980), to discrete and non-hierarchical, as in the general contrast models (Tversky, 1977; Shepard and Arabie, 1979). (shrink)

This paper addresses the doubts voiced by Wigner about the physical relevance of the concept of geometrical points by exploiting some facts known to all but honored by none: Almost all real numbers are transcendental; the explicit representation of any one will require an infinite amount of physical resources. An instrument devised to measure a continuous real variable will need a continuum of internal states to achieve perfect resolution. Consequently, a laboratory instrument for measuring a continuous variable in a finite (...) time can report only a finite number of values, each of which is constrained to be a rational number. It does not matter whether the variable is classical or quantum-mechanical. Now, in von Neumann’s measurement theory (von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, [1955]), an operator A with a continuous spectrum—which has no eigenvectors—cannot be measured, but it can be approximated by operators with discrete spectra which are measurable. The measurable approximant F(A) is not canonically determined; it has to be chosen by the experimentalist. It is argued that this operator can always be chosen in such a way that Sewell’s results (Sewell in Rep. Math. Phys. 56: 271, [2005]; Sewell, Lecture given at the J.T. Lewis Memorial Conference, Dublin, [2005]) on the measurement of a hermitian operator on a finite-dimensional vector space (described in Sect. 3.2) constitute an adequate resolution of the measurement problem in this theory. From this follows our major conclusion, which is that the notion of a geometrical point is as meaningful in nonrelativistic quantum mechanics as it is in classical physics. It is necessary to be sensitive to the fact that there is a gap between theoretical and experimental physics, which reveals itself tellingly as an error inherent in the measurement of a continuous variable. (shrink)