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Basic modal logic

Published online by Cambridge University Press:  12 March 2014

John L. Pollock
John L. Pollock*
Affiliation:
State University of New York at Buffalo
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Extract

As anyone who is familiar with the literature knows, there is a great deal of controversy concerning which, if any, of the extant theories of propositional modal logic correctly formalizes the logic of certain logical concepts such as analyticity and logical necessity. Most of the controversy concerns certain principles that involve iterated modalities (where one modal operator occurs within the scope of another). For example, there is considerable disagreement about whether the principle (□p⊃□□p) should be considered valid. However, when philosophers and logicians apply modal logic to concrete problems, they rarely need principles which involve iterated modalities. For most practical purposes, principles involving only one layer of modalities are all that are needed. This suggests that if we try to construct a theory of modal logic in which there are no iterated modalities, we can avoid most of the controversy and still have a theory that is strong enough for all of the normal uses to which modal logic is put.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 3 , 09 October 1967 , pp. 355 - 365
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Kripke, Saul, A completeness theorem in modal logic, this Journal, vol. 24 (1959), pp. 1–15.Google Scholar
[2]Kripke, Saul, Semantical analysis of modal logic. I, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 9 (1963), pp. 67–96.CrossRefGoogle Scholar
[3]Hintikka, Jaakko, Modality and quantification, Theoria (Lund), vol. 27 (1961), pp. 119–128.CrossRefGoogle Scholar
[4]Hintikka, Jaakko, The modes of modality, Ada Philosophica Fennica, Fasc. XVI (1963), pp. 65–81.Google Scholar
[5]Carnap, Rudolph, Quantification and modalities, this Journal, vol. 11 (1946), pp. 33–64.Google Scholar
[6]Montague, Richard, Logical necessity, physical necessity, ethics, and quantifiers, Inquiry, vol. 3 (1960), pp. 259–269.CrossRefGoogle Scholar
[7]Kanger, Stig, The morning star paradox, Theoria (Lund), vol. 23 (1957), pp. 1–11.CrossRefGoogle Scholar
[8]Lemmon, E. J., New foundations for Lewis modal systems, this Journal, vol. 22 (1957), pp. 176–186.Google Scholar
[9]Lewis, C. I. and Lanoford, C. H., Symbolic logic, New York, 1932.Google Scholar
[10]von Wright, G. H., An essay in modal logic, North-Holland, Amsterdam, 1951.Google Scholar
[11]Pollock, John L., Logical validity in modal logic, The monist, vol. 51 (1967), No. 1.CrossRefGoogle Scholar