Basis Logic for Application in Physics and Its Intuitionistic Alternative

Weingartner, Paul

doi:10.1007/s10701-009-9406-6

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…For a comparison of some systems of QL with RMQ see section 5. below. For a detailed discussion of those principles of CPC which make too strong classical assumptions and cause difficulties especially when applied to Quantum Physics see Weingartner [36] ch.2. 20 Cf.…”

Section: The Problem With Distributivity and Commensurabilitymentioning

confidence: 99%

An Alternative Propositional Calculus for Application to Empirical Sciences

Weingartner

2010

Stud Logica

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The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities.

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Section: The Problem With Distributivity and Commensurabilitymentioning

confidence: 99%

An Alternative Propositional Calculus for Application to Empirical Sciences

Weingartner

2010

Stud Logica

Self Cite

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show abstract

“…In a number of papers [8][9][10], Weingartner introduces the matrix-based logics RM Q − and RM Q * . He presents only their semantics though, and leaves the question of its axiomatizability open (see [9, p. 241] for details).…”

Section: Introductionmentioning

confidence: 99%

“…He claims that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. [9, p. 233] In [9,10] and [8] such a concept of relevant consequence is defined and studied in more detail. Weingartner further claims that his logic approximates this notion of relevant consequence.…”

Section: Introductionmentioning

confidence: 99%