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On formalizing the distinction between logical and factual truth

Published online by Cambridge University Press:  12 March 2014

William H. Hanson
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Extract

Semantical systems that distinguish between logically true and factually true formulas are well-known from the work of Carnap. The present paper is concerned with extending the formalization of this distinction in two ways. First, we show how to construct syntactical (i.e., logistic) systems that correspond to semantical systems of the type just mentioned. Such a syntactical system for propositional logic is developed in section 3. Similar systems for first-order logic are sketched in section 5. Second, we show how to extend semantical systems that make the logical-factual distinction to languages containing modal connectives. Carnap's work on modal logic conspicuously lacks this feature. Section 4 contains such semantical systems for four well-known modal logics. It also contains a syntactical equivalent of one of these modal semantical systems.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 460 - 477
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Carnap, Rudolf, Modalities and quantification, this Journal, XI (1946), 33–64.Google Scholar
[2]Carnap, Rudolf, Meaning and Necessity, Enlarged, ed., Chicago, 1956.Google Scholar
[3]Church, Alonzo, A formulation of the logic of sense and denotation, Structure, Method and Meaning; Essays in Honor of Henry M. Sheffer, Henle, Paul, et al, eds., New York, 1951.Google Scholar
[4]Church, Alonzo, Introduction to Mathematical Logic, vol. 1, Princeton, 1956.Google Scholar
[5]Hanson, William H., Syntactical systems that reflect the logical-factual distinction, (abstract), this Journal, XXXI (1966), 148.Google Scholar
[6]Kripke, Saul A., A completeness theorem in modal logic, this Journal, XXIV (1959), 1–14.Google Scholar
[7]Kripke, Saul A., Semantical analysis of modal logic I, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, IX (1963), 67–96.CrossRefGoogle Scholar