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Sketch for a Systematic Metaphysics$
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D. M. Armstrong

Print publication date: 2010

Print ISBN-13: 9780199590612

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199590612.001.0001

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(p.93) Chapter 13 Numbers
Sketch for a Systematic Metaphysics

David M. Armstrong

Oxford University Press

An account is given of the Forrest‐Armstrong theory of number (Peter Forrest). Natural numbers are argued to be relations holding between a certain property and a certain mereological whole (black swan on the lake now, and the whole that these swans make). With the rational numbers and the real numbers the relation becomes one of proportion, they are the units that measure the proportion. It is pointed out, however, that this view is largely to be found in Isaac Newton, and is even anticipated in Aristotle. What it is for a mathematical entity such as a number to be ‘instantiated’ is considered.

Keywords:   Peter Forrest, mereology, Isaac Newton, Aristotle, naturals, rationals, reals

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