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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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The Rational Disciplines: Logic and Mathematics 1

The Rational Disciplines: Logic and Mathematics 1

Chapter:
(p.88) Chapter 12 The Rational Disciplines: Logic and Mathematics1
Source:
Sketch for a Systematic Metaphysics
Author(s):

David M. Armstrong

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199590612.003.0012

Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem is partly met by recognizing that the rational sciences are sciences of the possible. Only the mathematical structures that are instantiated in space‐time are existents. Furthermore, using the Entailment Principle, it is seen that only the logico‐mathematical axioms require truthmakers. We should recognize laws in these sciences, but laws that are necessary. Such laws will be truthmakers for truths about uninstantiated structures, for instance large infinite numbers. What is the source of these necessary laws? Perhaps it is a necessity in the nature of things.

Keywords:   logic, mathematics, W.V. Quine, entailment principle, mereology, laws, necessity

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