David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 39 (3):315-321 (1972)
What has been learned about logic by means of "uninterpreted" logistic systems can be supplemented by comparing the latter with systems which are more uninterpreted, as well as with others which are less uninterpreted than the well-known logistic systems. By somewhat extending the meaning of 'uninterpreted', I hope to establish certain claims about the nature of logistic systems and also to cast some light on the nature of "logic itself." My procedure involves looking at three major "degrees" of interpretation: first, systems uninterpreted both semantically and syntactically, second, systems uninterpreted semantically but not syntactically, and third, systems uninterpreted neither semantically nor syntactically. We shall be forced to limit ourselves to the truth-functional part of logic in this brief study. What are usually called uninterpreted systems can be seen on a continuum of "degrees" of interpretation, from ordinary reasoning at one extreme to a "thoroughly uninterpreted system" at the other. "Logic itself" apparently lies nearer to the interpreted, deformalized end of the spectrum than to the uninterpreted, formalized end. Logic is not identical with any particular logistic system, but is that which the particular logistic systems aim to formalize or model or capture. I propose that it is that minimum set of logical, rather than syntactical, primitive terms, definitions, and rules which is needed to generate logically, rather than syntactically, the principles of ordinary reasoning as it is used by logicians in their metalinguistic discussions and informal proofs of metatheorems. This minimum set is somewhat larger than the primitive bases of most logistic systems; its truth-functional part is presented in the "Deformalized Logic" at degree twelve
|Keywords||No keywords specified (fix it)|
|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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Henk Barendregt, Martin Bunder & Wil Dekkers (1993). Systems of Illative Combinatory Logic Complete for First-Order Propositional and Predicate Calculus. Journal of Symbolic Logic 58 (3):769-788.
Ioannis Votsis (2007). Uninterrupted Equations and the Structure-Nature Distinction. Philosophical Inquiry 29 (1):57-71.
David Fernández-Duque (2011). Dynamic Topological Logic Interpreted Over Minimal Systems. Journal of Philosophical Logic 40 (6):767-804.
Michael Moortgat (1996). Multimodal Linguistic Inference. Journal of Logic, Language and Information 5 (3-4):349-385.
Torben Braüner (2004). Two Natural Deduction Systems for Hybrid Logic: A Comparison. [REVIEW] Journal of Logic, Language and Information 13 (1):1-23.
Norman M. Martin (1989). Systems of Logic. Cambridge University Press.
Leon Horsten (2005). Canonical Naming Systems. Minds and Machines 15 (2):229-257.
Kosta Došen (1992). Modal Logic as Metalogic. Journal of Logic, Language and Information 1 (3):173-201.
Hannes Leitgeb (2005). Interpreted Dynamical Systems and Qualitative Laws: From Neural Networks to Evolutionary Systems. Synthese 146 (1-2):189 - 202.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #515,279 of 1,692,616 )
Recent downloads (6 months)1 ( #181,402 of 1,692,616 )
How can I increase my downloads?