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MATRIX-BASED LOGIC FOR APPLICATION IN PHYSICS

Published online by Cambridge University Press:  01 March 2009

PAUL WEINGARTNER
PAUL WEINGARTNER*
Affiliation:
Department Of Philosophy, University Of Salzburg
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF SALZBURG AND INSTITUT FÜR WISSENSCHAFTSTHEORIE SALZBURG, AUSTRIA, A-5020, E-mail:paul.weingartner@sbg.ac.at
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Abstract

The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense “irrelevant” from those which are “relevant” or “nonredundant” in the sense of allowing only the most informative consequences in the derivations. The latter derivations are strictly valid in RMQ, whereas the former are only materially valid. RMQ is a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper how RMQ by its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 1 , March 2009 , pp. 132 - 163
Copyright
Copyright © Association for Symbolic Logic 2009

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