This paper defends a realist interpretation of theories and a modest realism concerning the existence of quantities as providing the best account both of the logic of quantity concepts and of scientific measurement practices. Various operationist analyses of measurement are shown to be inadequate accounts of measurement practices used by scientists. We argue, furthermore, that appeals to implicit definitions to provide meaning for theoretical terms over and above operational definitions fail because implicit definitions cannot generate the requisite (...) descriptive content. The special case of establishing a temperature scale is examined to show that nonrealist accounts fail to provide insight into the theoretical connections that scientific laws postulate to hold among quantities. (shrink)

Given the common assumption that measurement plays an important role in the foundation of science, the paper analyzes the possibility that Measurement Science, and therefore measurement itself, can be properly founded. The realist and the representational positions are analyzed at this regards: the conclusion, that such positions unavoidably lead to paradoxical situations, opens the discussion for a new epistemology of measurement, whose characteristics and interpretation are sketched here but are still largely matter of investigation.

Psychologists debate whether mental attributes can be quantified or whether they admit only qualitative comparisons of more and less. Their disagreement is not merely terminological, for it bears upon the permissibility of various statistical techniques. This article contributes to the discussion in two stages. First it explains how temperature, which was originally a qualitative concept, came to occupy its position as an unquestionably quantitative concept (§§1–4). Specifically, it lays out the circumstances in which thermometers, which register quantitative (or cardinal) differences, (...) became distinguishable from thermoscopes, which register merely qualitative (or ordinal) differences. I argue that this distinction became possible thanks to the work of Joseph Black, ca. 1760. Second, the article contends that the model implicit in temperature’s quantitative status offers a better way for thinking about the quantitative status of mental attributes than models from measurement theory (§§5–6). (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)

The logic of inexactness, presented in this paper, is a version of the Łukasiewicz logic with predicates valued in [0, ∞). We axiomatize multi-valued models of equality and ordering in this logic guaranteeing their imbeddibility in the real line. Our axioms of equality and ordering, when interpreted as axioms of proximity and dominance, can be applied to the foundations of measurement (especially in the social sciences). In two-valued logic they provide theories of ratio scale measurement. In multivalued (...) logic they enable us to treat formally errors arising in nominal and ordinal measurements. (shrink)

In this paper, first, the question of what a measurement is in General Relativity is tackled; then, some foundational problems it involves are analysed. In particular, by recalling what a measurement is in general, we will try to precisely define what it is in General Relativity. Then, we will analyse, by means of a suitable example, some foundational problems it involves. It will be stressed that such foundational problems do not arise owing to the gauge invariance or the (...) correlation among the measuring observers but owing to the principle of equivalence. (shrink)

It is well known that Hermann Cohen was one of the first philosophers who engaged in the debate about non-Euclidean geometries and the concept of space. His relation to Hermann von Helmholtz, who played a major role in the same debate, is an illuminating example of how some of the leading ideas of Marburg neo-Kantianism, although motivated independently of scientific debates, naturally led to the examination of scientific works and scientists’ epistemological views. This paper deals with Cohen’s view of magnitudes (...) and measurement and with his – less known – review of Helmholtz’s paper “Zählen und Messen, erkenntnistheoretisch betrachtet”, which contains one of the first attempts to formulate a theory of measurement in the modern sense. The first part provides a brief introduction to this debate in its connection with the earlier discussion on geometrical axioms and the concept of space. The main sections deal with Helmholtz’s and Cohen’s approaches to the foundations of measurement. Cohen’s criticism of some of Helmholtz’s assumptions notwithstanding, my emphasis is on some unexpected affinities between these two approaches. In the concluding section, I rely on the constructive side of Cohen’s criticisms to reconsider the philosophical aspects of Helmholtz’s theory and draw a few comparisons with contemporary measurement theory. (shrink)

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that (...) are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

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)

In economics, the concept of time discounting introduces weights on future goods to make these less valuable. Yet, both the conceptual motivation for time discounting and its specic functional form remain contested. To address these problems, this paper provides a measurement-theoretic framework of representation for time discounting. The representation theorem characterises time discounting factors by representations of time dierences. This general result can be interpreted with existing theories of time discounting to clarify their formal and conceptual assumptions. It also (...) provides a conceptually neutral framework for comparing the descriptive and normative merits of those theories. (shrink)

Conceptual Foundations of Quantum Mechanics provides a detailed view of the conceptual foundations and problems of quantum physics, and a clear and comprehensive account of the fundamental physical implications of the quantum formalism. This book deals with nonseparability, hidden variable theories, measurement theories and several related problems. Mathematical arguments are presented with an emphasis on simple but adequately representative cases. The conclusion incorporates a description of a set of relationships and concepts that could compose a legitimate view (...) of the world. (shrink)

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The (...) discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem. (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)

The London and Bauer monograph occupies a central place in the debate concerning the quantum measurement problem. Gavroglu has previously noted the influence of Husserlian phenomenology on London's scientific work. However, he has not explored the full extent of this influence in the monograph itself. I begin this paper by outlining the important role played by the monograph in the debate. In effect, it acted as a kind of 'lens' through which the standard, or Copenhagen, 'solution' to the (...) class='Hi'>measurement problem came to be perceived and, as such, it was robustly criticized, most notably by Putnam and Shimony. I then spell out the Husserlian understanding of consciousness in order to illuminate the traces of this understanding within the London and Bauer text. This, in turn, yields a new perspective on this 'solution' to the measurement problem, one that I believe has not been articulated before and, furthermore, which is immune to the criticisms of Putnam and Shimony. (shrink)

We present a novel kind of “socio-functional” foundationalism rooted in the division of scientific labor. Our foundationalism is social in that it involves a socio-epistemic phenomenon we dub epistemic outsourcing, whereby claims from one group of scientists provide epistemological foundations for another group of scientists. We argue that: (1) epistemic outsourcing results in a legitimate form of epistemic foundationalism, (2) this sort of foundationalism can be used to shed light on the epistemology of measurement; and (3) epistemic outsourcing (...) is a distinctively collective epistemic phenomenon. (shrink)

Statistical mechanics is the name of the ongoing attempt to explain and predict certain phenomena, above all those described by thermodynamics on the basis of the fundamental theories of physics, in particular mechanics, together with certain auxiliary assumptions. In another paper in this journal, Foundations of statistical mechanics: Mechanics by itself, I have shown that some of the thermodynamic regularities, including the probabilistic ones, can be described in terms of mechanics by itself. But in order to prove those regularities, (...) in particular the time asymmetric ones, it is necessary to add to mechanics assumptions of three kinds, all of which are under debate in contemporary literature. One kind of assumptions concerns measure and probability, and here, a major debate is around the notion of “typicality.” A second assumption concerns initial conditions, and here, the debate is about the nature and status of the so-called past hypothesis. The third kind of assumptions concerns the dynamics, and here, the possibility and significance of “Maxwell's Demon” is the main topic of discussions. This article describes these assumptions and examines the justification for introducing them, emphasizing the contemporary debates around them. (shrink)

Measures of algorithmic bias can be roughly classified into four categories, distinguished by the conditional probabilistic dependencies to which they are sensitive. First, measures of "procedural bias" diagnose bias when the score returned by an algorithm is probabilistically dependent on a sensitive class variable (e.g. race or sex). Second, measures of "outcome bias" capture probabilistic dependence between class variables and the outcome for each subject (e.g. parole granted or loan denied). Third, measures of "behavior-relative error bias" capture probabilistic dependence between (...) class variables and the algorithmic score, conditional on target behaviors (e.g. recidivism or loan default). Fourth, measures of "score-relative error bias" capture probabilistic dependence between class variables and behavior, conditional on score. Several recent discussions have demonstrated a tradeoff between these different measures of algorithmic bias, and at least one recent paper has suggested conditions under which tradeoffs may be minimized. -/- In this paper we use the machinery of causal graphical models to show that, under standard assumptions, the underlying causal relations among variables forces some tradeoffs. We delineate a number of normative considerations that are encoded in different measures of bias, with reference to the philosophical literature on the wrongfulness of disparate treatment and disparate impact. While both kinds of error bias are nominally motivated by concern to avoid disparate impact, we argue that consideration of causal structures shows that these measures are better understood as complicated and unreliable measures of procedural biases (i.e. disparate treatment). Moreover, while procedural bias is indicative of disparate treatment, we show that the measure of procedural bias one ought to adopt is dependent on the account of the wrongfulness of disparate treatment one endorses. Finally, given that neither score-relative nor behavior-relative measures of error bias capture the relevant normative considerations, we suggest that error bias proper is best measured by score-based measures of accuracy, such as the Brier score. (shrink)

This paper develops axiomatic foundations for a probabilistic-interventionist theory of causal strength. Transferring methods from Bayesian confirmation theory, I proceed in three steps: I develop a framework for defining and comparing measures of causal strength; I argue that no single measure can satisfy all natural constraints; I prove two representation theorems for popular measures of causal strength: Pearl's causal effect measure and Eells' difference measure. In other words, I demonstrate these two measures can be derived from a set of (...) plausible adequacy conditions. The paper concludes by sketching future research avenues. (shrink)

Deliberative democracy is now an influential approach to the study of democracy and political behaviour. Its key proposition is that, in politics, it is not only power that counts, but good discussions and arguments too. This book examines the interplay between the normative and empirical aspects of the deliberative model of democracy. Jürg Steiner presents the main normative controversies in the literature on deliberation, including self-interest, civility and truthfulness. He then summarizes the empirical literature on deliberation and proposes methods by (...) which the level of deliberation can be measured rather than just assumed. Steiner's empirical research is based in the work of various research groups, including experiments with ordinary citizens in the deeply divided societies of Colombia, Bosnia-Herzegovina and Belgium, as well as Finland and the European Union. Steiner draws normative implications from a combination of both normative controversies and empirical findings. (shrink)

We prove that if $$\mathcal {A}$$ A is an infinite Boolean algebra in the ground model V and $$\mathbb {P}$$ P is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any $$\mathbb {P}$$ P -generic extension V[G], $$\mathcal {A}$$ A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account of the nature of quantum (...) information. Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

The revolution brought about by quantum mechanics in the early 20th century was nothing short of remarkable. It shattered the foundational principles of classical physics, giving rise to a plethora of controversial and intriguing conceptual questions. Questions that still perplex and confound the scientific community today. Is the quantum mechanical description of physical reality complete? Are the objects of nature truly inseparable? And most importantly, do objects not have a specific position before measurement, and are there non-causal quantum jumps? (...) These vital problems continue to garner more attention as time passes, particularly with the fading of positivism. If you're a student seeking to explore the fascinating philosophical foundations of quantum mechanics, this book might be just what you need. Written in Persian, brings you closer to the heart of quantum controversies and the fascinating world of quantum mechanics. (shrink)

It is demonstrated that neither the arguments leading to inconsistencies in the description of quantum-mechanical measurement nor those “explaining” the process of measurement by means of thermodynamical statistics are valid. Instead, it is argued that the probability interpretation is compatible with an objective interpretation of the wave function.

This article considers the development of the idea of universal moral principles in the work of Thomas Aquinas and his predecessors in the thirteenth century. Like other medieval authors who sought to place the principles of moral practice on a foundation more secure than on the choices of the good person, as described by Aristotle, Thomas chooses to introduce a measure of ethical certitude through the concept of the innate habit of synderesis. This idea, introduced by Jerome in his commentary (...) on Ezekiel, locates an inextinguishable spark of conscience in all humans. Thomas, influenced by Philip the Chancellor and Albert the Great, locates the principles of natural law in this innate habit of synderesis. By so doing he can claim that all human beings have the ability to recognize universally binding moral imperatives, regardless of their background and societal influences. Through this natural ability the human basis for moral action found in Aristotle's Ethics yields to one based upon the eternal immutable laws of a divine being. (shrink)

The foundations of systematics lie in ontology, not in subjective epistemology. Systems and their elements should be distinguished from classes; only the latter are constructed from similarities. The term classification should be restricted to ordering into classes; ordering according to systematic relations may be called systematization.The theory of organization levels portrays the real world as a hierarchy of open systems, from energy quanta to ecosystems; followingHartmann these systems as extended in time are considered the primary units of reality. Organization (...) levels should be distinguished from levels of differentiation within each organization level.Certain biological systems, such as species, continue to be misinterpreted as classes, particularly by logicians unfamiliar with modern biological theory. Replacement of Aristotelian definitions of species by “polytypic” definitions achieves nothing, because species are individual systems which can be defined from an ontological viewpoint only as wholes. The dispute whether classes are real per se or only in individuals is of no scientific importance; irrespective of which view is taken, any ordering of physical objects into classes constitutes an hypothesis about the structure of the real world.The distinction between essential and contingent characters is relevant only to classification. There are no universal rules for evaluating characters for purposes of systematization. Character statements do not form separate linear sequences. The search for “unit characters” in an absolute sense is futile. All real characters are reducible to relations and are in principle measurable, although there are limitations on the extent to which this can be presently achieved.The concept of the sexual species is fundamental to theories of biosystematics. Sexual species may be defined as lineages consisting at any given time of series of populations between which genetic exchange can occur and delimited in time by two successive processes of speciation. Linnaean nomenclature needs modification; in its traditional form it is appropriate only to non-truncated hierarchies, whereas real phylogenies form truncated hierarchies. In consequence of the distinction between systematization and classification it is concluded that, while taxa may be classified into age classes or evolutionary grades, their limits as taxa can be no different in either case. Classification into evolutionary grades remains an imprecise endeavour, since no general measure of evolutionary differentiation has been devised.The spatial and temporal extent of ecosystems, the postulated basic units of ecosystematics, remains unclarified. Nevertheless there are grounds for expecting progress in this field as the energetic relations between organisms become better understood. Biotic communities are not “abstract” classes, but systematic units. Physiognomic classification should not be confused with systematization of plant communities; both approaches contribute to an understanding of vegetational structure. (shrink)

Practitioners of science treat evidence as a separate and objective body of materials that is independent of, and possibly also prior to, all of theorizing. Philosophers of science, by contrast, are increasingly wary of the role of theory in testing and measurement contexts, and hence have problematized the notion of evidence as prior or independent, even in the context of measurement. This paper argues that there is an important sense in which empirical certification of a quantity, via (...) class='Hi'>measurement, is indeed prior to theorizing, albeit not necessarily in order of time. The case for this priority distinguishes between the certification of the measurability of a given quantity, as a quantity appropriately measured on a specified scale, and the epistemic warrant due to an assignment of a specific magnitude to that quantity on a given occasion. The result is an account of the certification of a measurable quantity, independent of any theory in which that quantity features. The effect is to render certification of quantities theory-neutral. The aim of the essay is thus to bolster and re-establish a more nuanced empiricist view, via building a case for quantity certification as the epistemic basis (i.e., foundation) of the scientific enterprise. (shrink)

Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of (...) awareness internalism. The article draws three main concluding lessons. First, epistemological probability is not to be identified with the sort of objective, experience-independent probability that is familiar from statistical and propensity interpretations of probability. Second, it is doubtful that epistemological probability is measurable, in any useful way, by real numbers, even if it admits of comparative assessments. Third, contrary to the familiar claim of C. I. Lewis, epistemological probability should not be viewed as requiring a basis of certainty. (shrink)

ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of (...) space could be construed. Yet, due to the problem of illusion inherent in the subject’s self-assessment of muscular activity, this solution yielded new difficulties, in that if the manifold is abstracted from rigid bodies which serve as empirical justification of the geometrical notion of space, then illusionary bodies will produce fictive manifolds. The present article is meant to disentangle these difficulties. (shrink)

In the age of digitization, the world seems to be reducible to a digital computer. However, mathematically, modern quantum field theories do not only depend on discrete, but also continuous concepts. Ancient debates in natural philosophy on atomism versus the continuum are deeply involved in modern research on digital and computational physics. This example underlines that modern physics, in the tradition of Newton’s Principia Mathematica Philosophiae Naturalis, is a further development of natural philosophy with the rigorous methods of mathematics, measuring, (...) and computing. We consider fundamental concepts of natural philosophy with mathematical and computational methods and ask for their ontological and epistemic status. The following article refers to the author’s book, “The Digital and the Real World. Computational Foundations of Mathematics, Science, Technology, and Philosophy.”. (shrink)

The propensity interpretation of fitness (PIF) holds that evolutionary fitness is an objectively probabilistic causal disposition (i.e., a propensity) toward reproductive success. I characterize this as the conceptual foundation of the PIF. Reproductive propensities are meant to explain trends in actual reproductive outcomes. In this paper, I analyze the minimal theoretical and ontological commitments that must accompany the explanatory power afforded by the PIF’s foundation. I discuss three senses in which these commitments are less burdensome than has typically been recognized: (...) the PIF’s foundation is (i) compatible with a principled pluralism regarding the mathematical relationship between measures of individual and trait reproductive success; (ii) independent of the propensity interpretation of probability; and (iii) independent of microphysical indeterminism. The most substantive ontological commitment of the PIF’s foundation is to objective modal structures wherein macrophysical probabilities and causation can be found, but I hedge against metaphysically inflationary readings of this modality. (shrink)