<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>Gelfand representation</italic>, 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.</p></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.

The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

Department of Philosophy, Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, PA 19104, USA

Department of Philosophy, St. John's University, Queens, NY 11439, USA

Measurement Science Review

In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources...

The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

Published Online: Dec 29, 2008

Page range: 129 - 146

DOI: https://doi.org/10.2478/v10048-008-0031-x

Keywords
Gelfand representation, quantity algebra, state space, observables, measuring process, quantity conversion, quantity restoration

This content is open access.

The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

Published Online: Dec 29, 2008

Page range: 129 - 146

DOI: https://doi.org/10.2478/v10048-008-0031-x

KeywordsGelfand representation, quantity algebra, state space, observables, measuring process, quantity conversion, quantity restoration

This content is open access.

Keywords
Gelfand representation, quantity algebra, state space, observables, measuring process, quantity conversion, quantity restoration