An Alternative Propositional Calculus for Application to Empirical Sciences

Studia Logica 95 (1/2):233 - 257 (2010)
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
Keywords Quantum Logic  Applied Logic  Relevance  Basic Logic  Quantum Physics
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DOI 10.1007/s11225-010-9259-1
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References found in this work BETA
Logic, Semantics, Metamathematics.Alfred Tarski - 1956 - Oxford, Clarendon Press.
Many-Valued Logic.Nicholas Rescher - 1969 - New York: Mcgraw-Hill.
Relevant Deduction.Gerhard Schurz - 1991 - Erkenntnis 35 (1-3):391 - 437.
The Interpretation of Quantum Mechanics and the Measurement Process.Peter Mittelstaedt - 1998 - British Journal for the Philosophy of Science 49 (4):649-651.

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Prior’s OIC Nonconservativity Example Revisited.Lloyd Humberstone - 2014 - Journal of Applied Non-Classical Logics 24 (3):209-235.

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