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)

The philosophy of measurement studies the conceptual, ontological, epistemic, and technological conditions that make measurement possible and reliable. A new wave of philosophical scholarship has emerged in the last decade that emphasizes the material and historical dimensions of measurement and the relationships between measurement and theoretical modeling. This essay surveys these developments and contrasts them with earlier work on the semantics of quantity terms and the representational character of measurement. The conclusions highlight four characteristics of the emerging research program in (...) philosophy of measurement: it is epistemological, coherentist, practice oriented, and model based. (shrink)

Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we draw some limitations for measurement procedures: procedures that verify if a quantity is measured cannot work in every case.

John Locke’s treatment of quantity in the Essay Concerning Human Understanding is not nearly as extensive or as well-known as his treatment of quality and his distinction between primary and secondary qualities. Yet I contend that a close examination of Locke’s comments on quantity in the Essay reveals that he endorses a general theory of quantity that not only distinguishes quantities from qualities, but also plays several other important roles in his overall philosophy—particularly in his treatments of infinity and demonstrative (...) knowledge. Moreover, I argue that this theory does not appear out of thin air, but is in certain respects one and the same as the approach to quantity found in Aristotle and developed by medieval Aristotelian thinkers. Identifying the core tenets of this approach in the texts of Aristotle and medieval Aristotelians, and formulating them clearly enough to shed light on Locke’s theory of quantity in the Essay, is the principal task of this paper. (shrink)

The attribution of beliefs and other propositional attitudes is best understood as a form of measurement, however counter-intuitive this may seem. Measurement theory does not require that the thing measured should be a magnitude, or that the calibration of the measuring instrument should be numerical. It only requires a homomorphism between the represented domain and the representing domain. On this basis, maps measure parts of the world, usually geographical locations, and 'belief' statements measure other parts of the world, namely people's (...) aptitudes. Having outlined an argument for this view, I deal with an obvious objection to it: that self-attribution of belief cannot be an exercise in measurement, because we are all aware, from introspection, that our beliefs have an intrinsically semantic form. Subsequently, I turn to the philosophical and methodological ramifications of the measurement theoretic view. I argue, first, that it undermines at least one version of constructivism and, second, that it provides an effective alternative to the residually Cartesian philosophy that underpins much qualitative research. Like other anti-Cartesian strategies, belief-attribution-as-measurement implies that the objective world is far more knowable than the subjective one, and that reality is ontologically prior to meaning. I regard this result as both plausible and welcome. (shrink)

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structured and yet leave this presupposition unexplained. We propose to fill this gap with an account that attributes structures to targets through structure generating descriptions. These descriptions are physical descriptions (...) and so there is no such thing as a solely mathematical account of a target system. (shrink)

Hermann von Helmholtz has been widely acknowledged as one of the forerunners of contemporary theories of measurement. However, his conception of measurement differs from later, representational conceptions in two main respects. Firstly, Helmholtz advocated an empiricist philosophy of arithmetic as grounded in some psychological facts concerning quantification. Secondly, his theory implies that mathematical structures are common to both subjective experiences and objective ones. My suggestion is that both of these differences depend on a classical approach to measurement, according to which (...) the arithmetic laws of addition define what is measurable as a particular domain for their application, and, at the same time, the extensibility of these laws to all known physical processes works as a heuristic principle for empirical research. Such an approach is worth reconsidering, not only because it lends plausibility to some of the controversial aspects of Helmholtz’s theory, but also because it offers a philosophical perspective on quantification problems that originated in the nineteenth-century.This paper draws insights on Helmholtz’s philosophical views from his engagement with the measurability of sensations via Fechner’s psychophysical law. This seems to be in contrast with the fact that the reception of Helmholtz’s theory culminated with the formulation of the theory of extensive measurement. I will contend that Helmholtz reached a no less important standpoint in the nineteenth-century debate on whether sensations are different (i.e., intensive) kinds of magnitudes and on how, if at all, they can be measured. (shrink)

Putnam and Searle famously argue against computational theories of mind on the skeptical ground that there is no fact of the matter as to what mathematical function a physical system is computing: both conclude (albeit for somewhat different reasons) that virtually any physical object computes every computable function, implements every program or automaton. There has been considerable discussion of Putnam's and Searle's arguments, though as yet there is little consensus as to what, if anything, is wrong with these arguments. In (...) the present paper we show that an analogous line of reasoning can be raised against the numerical measurement (i.e., numerical representation) of physical magnitudes, and we argue that this result is a reductio ad absurdum of the challenge to computational skepticism. We then use this reductio to get clearer about both (i) what's wrong with Putnam's and Searle's arguments against computationalism, and (ii) what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument. (shrink)

In the late 1970s and early 1980s a number of philosophers, notably Churchland, Field, Stalnaker, Dennett, and Davidson, began to argue that propositional attitude predicates (such as believes that it’s sunny outside) are a species of measure predicate, analogous in important ways to numerical predicates by which we attribute physical magnitudes (such as mass, length, and temperature). Other philosophers, including myself, have subsequently developed the idea in greater detail. In this paper I sketch the general outlines of measurement‐theoretic accounts of (...) propositional attitudes, explaining in the briefest terms the basic idea of such accounts, why some have thought such accounts plausible, how these accounts might go, what their implications might be both for our conception of propositional attitudes and for their role in cognitive scientific theorizing, and where the potential problems with such accounts might lie. (shrink)

The book is addressed to all readers interested in cognitive science, and especially in research combining a logical analysis with psychological, linguistic and neurobiological approaches. The publication is the result of a collaboration between the Department of Cognitive Science at University of Lodz and the Department of Cognitive Science at Lund University. It is intended to provide a comprehensive presentation of the key research issues undertaken in both Departments, including considerations on meaning, natural language and reasoning, linguistic as well as (...) numerical competence, the theory of decision making, modelling of conceptual representations, cognitive and game theoretic approach to social interactions. (shrink)

Les contributions de Carnap au Congrès de 1935 marquent un triple changement dans sa philosophie: son tournant sémantique; ce qui sera appelé plus tard « la libéralisation de l’empirisme»; et son adoption du « langage des choses» comme base du langage de la science. C’est ce troisième changement qui est examiné ici. On s’interroge en particulier sur les motifs qui ont poussé Carnap à adopter le langage des choses comme langage protocolaire de la science unifiée et sur les vertus de (...) ce langage, comparé aux autres types de langage protocolaire. (shrink)

The representational theory of measurement has long been the central paradigm in the philosophy of measurement. Such is not the case anymore, partly under the influence of the critique according to which RTM offers too poor descriptions of the measurement procedures actually followed in science. This can be called the metrological critique of RTM. I claim that the critique is partly irrelevant. This is because, in general, RTM is not in the business of describing measurement procedures, be it in idealized (...) form. To support this claim, I present various cases where RTM can be said to investigate measurement without providing any measurement procedure. Such limit cases lead to a better understanding of the RTM project. They also illustrate some of the questions which the philosophy of measurement can explore, when it is ready to go beyond the metrological viewpoint. (shrink)

In his recent book The Measure of Mind Robert Matthews presents the most elaborate and convincing attempt to date to account for the propositional attitudes in measurement theoretic terms. In the first section of this paper I review earlier applications of measurement-theoretic conceptualization to the discussion of the mind, I outline Matthews' own account, and I raise two questions concerning it. Then, in the second section of the paper, I present a unified measurement-theoretic account of both linguistic meaning and the (...) propositional attitudes, in which a variant of Matthews' position is embedded. Such a unified account, I argue, yields satisfactory answers to the questions raised with respect to Matthews' original view, and demonstrates other advantages. (shrink)

Proponents of meaning holism often invoke notions of meaning similarity and semantic spatiality in order to counter accusations that holism renders language unstable and chaotic. However, talk of such notions often falls short of being explicit and formal. In this paper I present an algebraically couched theory of inferential similarity and spatiality, motivated by measurement theory, and I apply it to the discussion of meaning holism. I argue that the proposed theory offers new and improved conceptual resources for facing the (...) challenges raised against the thesis. (shrink)

L’article a pour but d’analyser la conception de la géométrie et de la mesure présentée dans Intuition et Raisonnement [Hölder 1900], « Les axiomes de la grandeur et la théorie de la mensuration » [Hölder 1901] et La Méthode mathématique [Hölder 1924]. L’article examine les relations entre a) la démarcation introduite par Hölder entre géométrie et arithmétique à partir de la notion de ‘concept donné’, b) sa position philosophique par rapport à l’apriorisme kantien et à l’empirisme et c) le choix (...) du postulat de la continuité de Dedekind parmi les axiomes de la théorie des grandeurs. L’article montre que les choix faits au niveau axiomatique sont reliés au cadre épistémologique et que l’originalité de Hölder consiste surtout dans son analyse au cas par cas des procédures déductives en mathématiques. (shrink)

ArgumentIn this comparative historical analysis, we will analyze the intellectual tendency that emerged between 1946 and 1956 to take advantage of the popularity of communication theory to develop a kind of informational epistemology of statistical mechanics. We will argue that this tendency results from a historical confluence in the early 1950s of certain theoretical claims of the so-called English School of Information Theory, championed by authors such as Gabor (1956) or MacKay (1969), and from the attempt to extend the profound (...) success of Shannon’s ([1948] 1993) technical theory of sign transmission to the field of statistical thermal physics. As a paradigmatic example of this tendency, we will evaluate the intellectual work of Léon Brillouin (1956), who, in the mid-fifties, developed an information theoretical approach to statistical mechanical physics based on a concept of information linked to the knowledge of the observer. (shrink)

The concept of measurement is fundamental to a whole range of different disciplines, including not only the natural and engineering sciences, but also laboratory medicine and certain branches of the social sciences. This being the case, the concept of measurement has a particular relevance to the development of top-level ontologies in the area of knowledge engineering. For this reason, the present paper is concerned with ontological aspects of measurement. We are searching for a list of concepts that are apt to (...) characterize measurement methods in a general manner. To establish such means of characterization, we will primarily deal with the semantics of measurement values. (shrink)

El recurso cognitivo por el cual la ciencia ha obtenido información del mundo empírico ha sido, desde su origen, la medición. Ésta está sujeta a un proceso continuo de regeneración y transformación histórica. Los principales análisis metateóricos que se han realizado sobre la medición son en su mayoría sobre sus aspectos formales. En este artículo desarrollo un bosquejo de un enfoque histórico y cognitivo de la medición científica con el fin de mostrar sus diversos aspectos cognitivos, metodológicos y epistemológicos, mismos (...) que han sido sistemáticamente descuidados por la gran mayoría de los análisis en filosofía de la ciencia. Measurement has been the main cognitive resource through which science has obtained empirical information about the world. Scientific measurement is not a fixed process but an historical and dynamical one; nevertheless, almost all philosophical analysis have studied it from a formal point of view. My aim in this paper is to outline a cognitive and historical notion of scientific measurement that allows us to appreciate its diverse epistemic, methodological, and cognitive features. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.