The metaphysics of quantity

Philosophical Studies 51 (1):29 - 54 (1987)
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Abstract

A formal theory of quantity T Q is presented which is realist, Platonist, and syntactically second-order (while logically elementary), in contrast with the existing formal theories of quantity developed within the theory of measurement, which are empiricist, nominalist, and syntactically first-order (while logically non-elementary). T Q is shown to be formally and empirically adequate as a theory of quantity, and is argued to be scientifically superior to the existing first-order theories of quantity in that it does not depend upon empirically unsupported assumptions concerning existence of physical objects (e.g. that any two actual objects have an actual sum). The theory T Q supports and illustrates a form of naturalistic Platonism, for which claims concerning the existence and properties of universals form part of natural science, and the distinction between accidental generalizations and laws of nature has a basis in the second-order structure of the world.

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Citations of this work

Degrees of Consciousness.Andrew Y. Lee - 2023 - Noûs 57 (3):553-575.
Naturalness.Cian Dorr & John Hawthorne - 2013 - In Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics, Volume 8. Oxford, GB: Oxford University Press. pp. 1.
Properties.Francesco Orilia & Michele Paolini Paoletti - 2020 - Stanford Encyclopedia of Philosophy.

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References found in this work

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
What is a Law of Nature?D. M. Armstrong - 1983 - New York: Cambridge University Press. Edited by Sydney Shoemaker.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.

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