The metaphysics of quantity

Philosophical Studies 51 (1):29 - 54 (1987)
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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DOI 10.1007/BF00353961
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References found in this work BETA
Word and Object.W. V. Quine - 1960 - MIT Press.
Theory and Evidence.Clark Glymour - 1980 - Princeton University Press.
What is a Law of Nature?D. M. Armstrong - 1983 - Cambridge University Press.
Science Without Numbers.Hartry Field - 1980 - Princeton University Press.
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Citations of this work BETA
Are Shapes Intrinsic?Bradford Skow - 2007 - Philosophical Studies 133 (1):111 - 130.
Replies to Gallois, Hirsch and Markosian. [REVIEW]Theodore Sider - 2004 - Philosophy and Phenomenological Research 68 (3):674–687.
Replies to Dorr, Fine, and Hirsch.Theodore Sider - 2013 - Philosophy and Phenomenological Research 87 (3):733-754.
Quantitative Properties.Maya Eddon - 2013 - Philosophy Compass 8 (7):633-645.

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