Ruth Barcan Marcus on the Deduction Theorem in Modal Logic

History and Philosophy of Logic:1-21 (forthcoming)
  Copy   BIBTEX

Abstract

In this paper, I examine Ruth Barcan Marcus's early formal work on modal systems and the deduction theorem, both for the material and the strict conditional. Marcus proved that the deduction theorem for the material conditional does not hold for system S2 but holds for S4. This last result is at odds with the recent claim that without proper restrictions the deduction theorem fails also for S4. I explain where the contrast stems from. For the strict conditional, Marcus proved the deduction theorem for S4 though restricted to arguments with necessary premises. I discuss Marcus's result and analyze her philosophical position on the significance of the deduction theorem for modal systems designed to express the notion of deducibility.

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 98,418

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2024-05-02

Downloads
13 (#1,229,100)

6 months
6 (#732,743)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Roberta Ballarin
University of British Columbia

Citations of this work

No citations found.

Add more citations

References found in this work

Symbolic Logic.C. I. Lewis & C. H. Langford - 1932 - Erkenntnis 4 (1):65-66.
On axiomatizability within a system.William Craig - 1953 - Journal of Symbolic Logic 18 (1):30-32.
Modalities and quantification.Rudolf Carnap - 1946 - Journal of Symbolic Logic 11 (2):33-64.

View all 29 references / Add more references