Chapter

The Rational Disciplines: Logic and Mathematics<sup>1</sup>

David M. Armstrong

in Sketch for a Systematic Metaphysics

Published in print July 2010 | ISBN: 9780199590612
Published online September 2010 | e-ISBN: 9780191723391 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199590612.003.0012
The Rational Disciplines: Logic and Mathematics1

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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

Chapter.  1509 words. 

Subjects: Philosophy of Mind

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