Some measurement-theoretic concerns about Hale's ‘reals by abstraction';

Philosophia Mathematica 10 (3):286-303 (2002)
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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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Vadim Batitsky
St. John's University

Citations of this work

What is neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
On the Philosophical Significance of Frege’s Constraint.Andrea Sereni - 2019 - Philosophia Mathematica 27 (2):244–275.
The Epistemological Question of the Applicability of Mathematics.Paola Cantù - 2018 - Journal for the History of Analytical Philosophy 6 (3).

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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Intuitionism, an Introduction.A. Heyting - 1958 - Studia Logica 7:277-278.
Philosophy of Mathematics.Paul Benacerraf & Hilary Putnam - 1985 - Philosophy of Science 52 (3):488-489.

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