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)

ABSTRACT The current debate on scientific realism is an entire universe. A general thesis can be put like follows: scientific activity attains a world that is independent of science itself. This “reaching out” can be thought of in terms of theoretical practices, such as the formulation of true theories, and/or experimental practices, such as the construction of suficiently accurate methods to (re)formulate and test what is said by the theories. By this latter route, the debate about scientific realism in the (...) philosophy of science meets the discussions in the philosophy of measurement, an autonomous research area that investigates measurement practices, their concepts, applications and assumptions. As the “realism” in the philosophy of science in general, there are multiple postures that can be characterized as “realistic” through their theorizations about scientific measurements. Stating which are the criteria and reasons why these positions claim to be realistic and in what they are distinct is a complex task. This article is an attempt to do that, without exhausting the discussion or the field. (shrink)

This article explores some of the roles of computer simulation in measurement. A model-based view of measurement is adopted and three types of measurement—direct, derived, and complex—are distinguished. It is argued that while computer simulations on their own are not measurement processes, in principle they can be embedded in direct, derived, and complex measurement practices in such a way that simulation results constitute measurement outcomes. Atmospheric data assimilation is then considered as a case study. This practice, which involves combining information (...) from conventional observations and simulation-based forecasts, is characterized as a complex measuring practice that is still under development. The case study reveals challenges that are likely to resurface in other measuring practices that embed computer simulation. It is also noted that some practices that embed simulation are difficult to classify; they suggest a fuzzy boundary between measurement and non-measurement. 1 Introduction2 A Contemporary View of Measurement3 Three Types of Measurement4 Can Computer Simulations Measure Real-World Target Systems?5 Case Study: Atmospheric Data Assimilation5.1 Why data assimilation?5.2 A complex measuring practice under development5.3 Epistemic iteration6 The Boundaries of Measurement7 Epistemology, Not Terminology. (shrink)

The paper presents an argument for treating certain types of computer simulation as having the same epistemic status as experimental measurement. While this may seem a rather counterintuitive view it becomes less so when one looks carefully at the role that models play in experimental activity, particularly measurement. I begin by discussing how models function as “measuring instruments” and go on to examine the ways in which simulation can be said to constitute an experimental activity. By focussing on the connections (...) between models and their various functions, simulation and experiment one can begin to see similarities in the practices associated with each type of activity. Establishing the connections between simulation and particular types of modelling strategies and highlighting the ways in which those strategies are essential features of experimentation allows us to clarify the contexts in which we can legitimately call computer simulation a form of experimental measurement. (shrink)

In an attempt to determine the epistemic status of computer simulation results, philosophers of science have recently explored the similarities and differences between computer simulations and experiments. One question that arises is whether and, if so, when, simulation results constitute novel empirical data. It is often supposed that computer simulation results could never be empirical or novel because simulations never interact with their targets, and cannot go beyond their programming. This paper argues against this position by examining whether, and under (...) what conditions, the features of empiricality and novelty could be displayed by computer simulation data. I show that, to the extent that certain familiar measurement results have these features, so can some computer simulation results. (shrink)

Hale proposes a neo-logicist definition of real numbers by abstraction as ratios defined on a complete ordered domain of quantities (magnitudes). I argue that Hale's definition faces insuperable epistemological and ontological difficulties. On the epistemological side, Hale is committed to an explanation of measurement applications of reals which conflicts with several theorems in measurement theory. On the ontological side, Hale commits himself to the necessary and a priori existence of at least one complete ordered domain of quantities, which is extremely (...) implausible because science treats the logical structure of quantities as subject to experimentally and theoretically motivated refinements and revisions. (shrink)

Putnam's ``model-theoretic'' argument against metaphysical realism presupposes that an ideal scientific theory is expressible in a first order language. The central aim of this paper is to show that Putnam's ``first orderization'' of science, although unchallenged by numerous critics, makes his argument unsound even for adequate theories, never mind an ideal one. To this end, I will argue that quantitative theories, which dominate the natural sciences, can be adequately interpreted and evaluated only with the help of so-called theories of measurement (...) whose epistemological and methodological purpose is to justify systematic assignments of quantitative values to objects in the world. And, in order to fulfill this purpose, theories of measurement must have an essentially higher order logical structure. As a result, Putnam's argument fails because much of science turns out to rest on essentially higher order theoretical assumptions about the world. (shrink)

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)

We do indeed “live and work in a time when the issues facing education, many of which have been with us for a considerable period, are being approached primarilythrough measurement – classroom assessment, research methods, standardized testing, international comparisons”. It is also true that “we do not often stop to consider what counts – and alternatively, what doesn’t count – in a climate where measuring up to a standard is the name of the game. At a deeper level, we rarely (...) raise questions about measurement itself.” Heidegger argued that what is “most thought provoking [in this ‘thought provoking age’] is that we are still not thinking,” in What is called thinking? . This somewhat startling assertion deserves careful attention especially in relation to the quote above . Heidegger’s assertion is pertinent for a number of reasons: he associated this “not thinking” with a “critical moment in history”, with a “call”, and with a “miscalculation”. I will argue that it is important to reflect on a number of questions: what is thinking, especially in relation to measurement? Was Heidegger correct in arguing that we have “miscalculated” in so far as we have sought “the safety of the mere drive for calculation” ? And how does the desire for a higher form of “representational thinking” in these contexts serve and promote a number of aims in higher education, such as learning and even “flourishing”? I will attempt to provide answers to a number of these questions by reflecting on the broad but fundamentally important question of measurement and its limits. (shrink)