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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References found in this work BETA
Hans Colonius (1978). On Weak Extensive Measurement. Philosophy of Science 45 (2):303-308.

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Citations of this work BETA
Theodore Sider (2008). Monism and Statespace Structure. Royal Institute of Philosophy Supplement 83 (62):129-150.
Bradford Skow (2007). Are Shapes Intrinsic? Philosophical Studies 133 (1):111 - 130.
Maya Eddon (2013). Quantitative Properties. Philosophy Compass 8 (7):633-645.

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