An Alternative Propositional Calculus for Application to Empirical Sciences

Studia Logica 95 (1/2):233 - 257 (2010)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,817
External links
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
M. L. Dalla Chiara (1977). Quantum Logic and Physical Modalities. Journal of Philosophical Logic 6 (1):391-404.
R. I. Goldblatt (1974). Semantic Analysis of Orthologic. Journal of Philosophical Logic 3 (1/2):19 - 35.
Peter Mittelstaedt (1974). Quantum Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974:501 - 514.

View all 12 references

Citations of this work BETA

No citations found.

Similar books and articles
Analytics

Monthly downloads

Added to index

2010-06-09

Total downloads

12 ( #133,368 of 1,099,863 )

Recent downloads (6 months)

1 ( #303,846 of 1,099,863 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.