David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
J. S. Bell (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press.
Alfred Tarski (1956). Logic, Semantics, Metamathematics. Oxford, Clarendon Press.
Nicholas Rescher (1969). Many-Valued Logic. New York, Mcgraw-Hill.
Peter Mittelstaedt (1998). The Interpretation of Quantum Mechanics and the Measurement Process. British Journal for the Philosophy of Science 49 (4):649-651.
Gerhard Schurz (1991). Relevant Deduction. Erkenntnis 35 (1-3):391 - 437.
Citations of this work BETA
Albert J. J. Anglberger & Jonathan Lukic (2015). Hilbert-Style Axiom Systems for the Matrix-Based Logics RMQ − and RMQ. Studia Logica 103 (5):985-1003.
Similar books and articles
Othman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.
Branislav R. Boričić (1986). A Cut-Free Gentzen-Type System for the Logic of the Weak Law of Excluded Middle. Studia Logica 45 (1):39 - 53.
Michael J. Carroll (1976). On Interpreting the S5 Propositional Calculus: An Essay in Philosophical Logic. Dissertation, University of Iowa
Lloyd Humberstone (2000). Contra-Classical Logics. Australasian Journal of Philosophy 78 (4):438 – 474.
Mojtaba Aghaei & Mohammad Ardeshir (2001). Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic. Studia Logica 68 (2):263-285.
Leon Horsten & Philip Welch (2007). The Undecidability of Propositional Adaptive Logic. Synthese 158 (1):41 - 60.
Carlo Dalla Pozza & Claudio Garola (1995). A Pragmatic Interpretation of Intuitionistic Propositional Logic. Erkenntnis 43 (1):81 - 109.
Andrew Bacon (2013). Non-Classical Metatheory for Non-Classical Logics. Journal of Philosophical Logic 42 (2):335-355.
D. A. Bochvar & Merrie Bergmann (1981). On a Three-Valued Logical Calculus and its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus. History and Philosophy of Logic 2 (1-2):87-112.
Added to index2010-06-09
Total downloads16 ( #167,478 of 1,726,249 )
Recent downloads (6 months)3 ( #231,316 of 1,726,249 )
How can I increase my downloads?