Some measurement-theoretic concerns about Hale's ‘reals by abstraction';
Philosophia Mathematica 10 (3):286-303 (2002)
| Abstract | 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 | |||||||||
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Eli Dresner (2006). A Measurement Theoretic Account of Propositions. Synthese 153 (1):1 - 22.
Peter Sullivan & Michael Potter (1997). Hale on Caesar. Philosophia Mathematica 5 (2):135--52.
Bob Hale & Crispin Wright (2008). Abstraction and Additional Nature. Philosophia Mathematica 16 (2):182-208.
Joel Michell (1994). Numbers as Quantitative Relations and the Traditional Theory of Measurement. British Journal for the Philosophy of Science 45 (2):389-406.
Michael Potter & Timothy Smiley (2001). Abstraction by Recarving. Proceedings of the Aristotelian Society 101 (3):327–338.
Henry E. Kyburg Jr (1997). Quantities, Magnitudes, and Numbers. Philosophy of Science 64 (3):377-410.
Michael Potter & Peter Sullivan (2005). What Is Wrong with Abstraction? Philosophia Mathematica 13 (2):187-193.
Bob Hale (2000). Reals by Abstractiont. Philosophia Mathematica 8 (2):100--123.
Roy T. Cook (2002). The State of the Economy: Neo-Logicism and Inflationt. Philosophia Mathematica 10 (1):43-66.
Bob Hale (2002). Real Numbers, Quantities, and Measurement. Philosophia Mathematica 10 (3):304-323.
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