David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 10 (3):304-323 (2002)
Defining the real numbers by abstraction as ratios of quantities gives prominence to then- applications in just the way that Frege thought we should. But if all the reals are to be obtained in this way, it is necessary to presuppose a rich domain of quantities of a land we cannot reasonably assume to be exemplified by any physical or other empirically measurable quantities. In consequence, an explanation of the applications of the reals, defined in this way, must proceed indirectly. This paper explains the main complications involved and answers the main objections advanced in Batitsky's paper in this issue.
|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
No citations found.
Similar books and articles
John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
Henry E. Kyburg Jr (1997). Quantities, Magnitudes, and Numbers. Philosophy of Science 64 (3):377-410.
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 (2000). Reals by Abstractiont. Philosophia Mathematica 8 (2):100--123.
Michael Dummett (2000). Is Time a Continuum of Instants? Philosophy 75 (4):497-515.
Rosanna Keefe (1998). Vagueness by Numbers. Mind 107 (427):565-579.
Zoltan Domotor & Vadim Batitsky (2008). The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective. Measurement Science Review 8 (6):129-146.
Louis Narens (1974). Measurement Without Archimedean Axioms. Philosophy of Science 41 (4):374-393.
Yaroslav D. Sergeyev (2008). A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities. Informatica 19 (4):567-596.
Vadim Batitsky (2002). Some Measurement-Theoretic Concerns About Hale's ‘Reals by Abstraction';. Philosophia Mathematica 10 (3):286-303.
Added to index2009-01-28
Total downloads35 ( #56,276 of 1,413,298 )
Recent downloads (6 months)5 ( #42,184 of 1,413,298 )
How can I increase my downloads?