Model theory and validity

Synthese 123 (2):165-193 (2000)
Abstract
Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English expressions. Is the argument resulting from the replacement valid in the sense that the premisses could not have been true without the conclusion also being true? Can we reason from the model-theoretic concept of logical consequence to the modal concept of validity? Yes, if the model theory is the standard one for sentential logic; no, if it is the standard one for the predicate calculus; and yes, if it is a certain model theory for free logic. These conclusions rely inter alia on some assumptions about possible worlds, which are mapped into the models of model theory. Plural quantification is used in the last section, while part of the reasoning is relegated to an appendix that includes a proof of completeness for a version of free logic.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1005217809302
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
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 27,208
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Kripke Models.John P. Burgess - 2011 - In Alan Berger (ed.), Saul Kripke. Cambridge University Press.
Validity in Intensional Languages: A New Approach.William H. Hanson & James Hawthorne - 1985 - Notre Dame Journal of Formal Logic 26 (1):9-35.
On the Concept of Material Consequence.Tomis Kapitan - 1982 - History and Philosophy of Logic 3 (2):193-211.
A Note on Formality and Logical Consequence.Mario Gómez-Torrente - 2000 - Journal of Philosophical Logic 29 (5):529-539.
Ranked Partial Structures.Timothy J. Carlson - 2003 - Journal of Symbolic Logic 68 (4):1109-1144.

Monthly downloads

Added to index

2009-01-28

Total downloads

51 ( #101,831 of 2,164,535 )

Recent downloads (6 months)

1 ( #347,995 of 2,164,535 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums