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Basis Logic for Application in Physics and Its Intuitionistic Alternative

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Abstract

This article proposes a basic logic for application in physics dispensing with the Principle of Excluded Middle. It is based on the article “Matrix Based Logics for Application in Physics (RMQ) which appeared 2009. In his article with Stachow on the Principle of Excluded Middle in Quantum Logic (QL), Peter Mittelstaedt showed that for some suitable QLs, including their own, the Principle of Excluded Middle can be added without any harm for QL; where ‘without any harm for QL’ means that the basic desiderata and the basic results (theorems) of those QLs remain satised in the sense that they avoid the well known difficulties with commensurability and distributivity.

In the following article I want to show that the basic desiderata and results (theorems) of RMQ (of avoiding the well-known difficulties with commensurability, distributivity, fusion and Bell’s inequalities) remain satised if by introducing a strong negation (or strong negation and disjunction) the resulting weak intuitionist system RMQI dispenses with the Principle of Excluded Middle; it becomes either invalid or not strictly valid.

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  1. Department of Philosophy, University of Salzburg, Salzburg, 5020, Austria

    Paul Weingartner

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  1. Paul Weingartner
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Correspondence to Paul Weingartner.

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Weingartner, P. Basis Logic for Application in Physics and Its Intuitionistic Alternative. Found Phys 40, 1578–1596 (2010). https://doi.org/10.1007/s10701-009-9406-6

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