David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 64 (3):377-410 (1997)
Quantities are naturally viewed as functions, whose arguments may be construed as situations, events, objects, etc. We explore the question of the range of these functions: should it be construed as the real numbers (or some subset thereof)? This is Carnap's view. It has attractive features, specifically, what Carnap views as ontological economy. Or should the range of a quantity be a set of magnitudes? This may have been Helmholtz's view, and it, too, has attractive features. It reveals the close connection between measurement and natural law, it makes dimensional analysis intelligible, and explains the concern of scientists and engineers with units in equations. It leaves the philosophical problem of the relation between the structure of magnitudes and the structure of the reals. What explains it? And is it always the same? We will argue that on the whole, construing the values of quantities as magnitudes has some advantages, and that (as Helmholtz seems to suggest in "Numbering and Measuring from an Epistemological Viewpoint") the relation between magnitudes and real numbers can be based on foundational similarities of structure
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Chris Pincock (2007). A Role for Mathematics in the Physical Sciences. Noûs 41 (2):253-275.
Christopher Pincock (2007). A Role for Mathematics in the Physical Sciences. Noûs 41 (2):253 - 275.
Similar books and articles
Vadim Batitsky (2002). Some Measurement-Theoretic Concerns About Hale's ‘Reals by Abstraction';. Philosophia Mathematica 10 (3):286-303.
Paola Cantù (2010). Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities. Synthese 174 (2):225 - 235.
Bradley J. Morris & Amy M. Masnick (2008). Making Numbers Out of Magnitudes. Behavioral and Brain Sciences 31 (6):662-663.
Peter Ospald (2010). Michael Friedmans Behandlung Des unterschieDes Zwischen Arithmetik Und Algebra Bei Kant in Kant and the Exact Sciences. Kant-Studien 101 (1):75-88.
Michael Dummett (2000). Is Time a Continuum of Instants? Philosophy 75 (4):497-515.
Joel Michell (1997). Bertrand Russell's 1897 Critique of the Traditional Theory of Measurement. Synthese 110 (2):257-276.
Richard Healey (2004). Change Without Change, and How to Observe It in General Relativity. Synthese 141 (3):1-35..
Richard Healey (2004). Change Without Change, and How to Observe It in General Relativity. Synthese 141 (3):381 - 415.
Joel Michell (1994). Numbers as Quantitative Relations and the Traditional Theory of Measurement. British Journal for the Philosophy of Science 45 (2):389-406.
Bob Hale (2002). Real Numbers, Quantities, and Measurement. Philosophia Mathematica 10 (3):304-323.
Added to index2009-01-28
Total downloads35 ( #71,879 of 1,696,808 )
Recent downloads (6 months)1 ( #346,744 of 1,696,808 )
How can I increase my downloads?