Graduate studies at Western
Measurement Science Review 8 (6):129-146 (2008)
|Abstract||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.|
|Keywords||measuring process quantity algebra observables|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Aldo Frigerio, Alessandro Giordani & Luca Mari (2010). Outline of a General Model of Measurement. Synthese 175 (2):123-149.
Giovanni Rossi (2006). A Probabilistic Theory of Measurement. Measurement 39:34-50.
Luca Mari (2000). Beyond the Representational Viewpoint: A New Formalization of Measurement. Measurement 27 (2):71-84.
Luca Mari (2005). The Problem of Foundations of Measurement. Measurement 38 (4):259-266.
Giovanni Rossi (2007). Measurability. Measurement 40:545-562.
Reinhard Niederée (1992). What Do Numbers Measure? A New Approach to Fundamental Measurement. Mathematical Social Sciences 24:237-276.
Henry E. Kyburg (ed.) (1984). Theory and Measurement. Cambridge University Press.
Alessandro Giordani & Luca Mari (forthcoming). Modeling Measurement: Error and Uncertainty. In Marcel Boumans, Giora Hon & Arthur Petersen (eds.), Error and Uncertainty in Scientific Practice. Pickering & Chatto.
Luca Mari & Sergio Sartori (2007). A Relational Theory of Measurement: Traceability as a Solution to the Non-Transitivity of Measurement Results. Measurement 40 (2):233-242.
Brent Mundy (1988). Extensive Measurement and Ratio Functions. Synthese 75 (1):1 - 23.
Ludwik Finkelstein (1984). A Review of the Fundamental Concepts of Measurement. [REVIEW] Measurement 2 (1):25-34.
Luca Mari & Alessandro Giordani (2012). Quantity and Quantity Value. Metrologia 49 (6):756-764.
Ludwik Finkelstein (1994). Measurement and Instrumentation Science. An Analytical Review. Measurement 14 (1):3-14.
Alessandro Giordani & Luca Mari (2012). Measurement, Models, and Uncertainty. IEEE Transactions on Instrumentation and Measurement 61 (8):2144 - 2152.
Added to index2012-01-09
Total downloads18 ( #74,621 of 739,447 )
Recent downloads (6 months)1 ( #61,680 of 739,447 )
How can I increase my downloads?