David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophical Studies 51 (1):29 - 54 (1987)
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
W. V. Quine (1960). Word and Object. The MIT Press.
Clark Glymour (1980). Theory and Evidence. Princeton University Press.
D. M. Armstrong (1983). What is a Law of Nature? Cambridge University Press.
Hartry Field (1980). Science Without Numbers. Princeton University Press.
D. M. Armstrong (1978). Universals and Scientific Realism. Cambridge University Press.
Citations of this work BETA
Bradford Skow (2007). Are Shapes Intrinsic? Philosophical Studies 133 (1):111 - 130.
Theodore Sider (2013). Replies to Dorr, Fine, and Hirsch. Philosophy and Phenomenological Research 87 (3):733-754.
Zee R. Perry (2015). Properly Extensive Quantities. Philosophy of Science 82 (5):833-844.
Theodore Sider (2004). Replies to Gallois, Hirsch and Markosian. [REVIEW] Philosophy and Phenomenological Research 68 (3):674–687.
Joongol Kim (forthcoming). What Are Quantities? Australasian Journal of Philosophy:1-16.
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