Two concepts of validity and completeness
Graduate studies at Western
|Abstract||A formula is (materially) valid iff all its instances are true sentences; and an axiomatic system is called (materially) sound and complete iff it proves all and only valid formulas. These are 'natural' concepts of validity and completeness, which were, however, in the course of the history of modern logic, stealthily replaced by their formal descendants: formal validity and completeness. A formula is formally valid iff it is true under all interpretations in all universes; and an axiomatic system is called formally sound and complete iff it proves all and only formulas valid in this sense. Though the step from material to formal validity and completeness may seem to be merely an unproblematic case of explication, I argue that it is not; and that mistaking the latter concepts for the former ones may lead to serious conceptual confusions.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|External links||This entry has no external links. Add one.|
|Through your library||Only published papers are available at libraries|
Similar books and articles
T. Achourioti & M. van Lambalgen (forthcoming). A Formalisation of Kant's Transcendental Logic. Review of Symbolic Logic.
William H. Hanson & James Hawthorne (1985). Validity in Intensional Languages: A New Approach. Notre Dame Journal of Formal Logic 26 (1):9-35.
Yannis Stephanou (2000). Model Theory and Validity. Synthese 123 (2):165-193.
Susanne Bobzien (1996). Stoic Syllogistic. Oxford Studies in Ancient Philosophy 14:133-92.
Gerard Allwein & Wendy MacCaull (2001). A Kripke Semantics for the Logic of Gelfand Quantales. Studia Logica 68 (2):173-228.
Peter Schroeder-Heister (2006). Validity Concepts in Proof-Theoretic Semantics. Synthese 148 (3):525 - 571.
Max A. Freund (2000). A Complete and Consistent Formal System for Sortals. Studia Logica 65 (3):367-381.
Wolfgang Stegmüller (1964). Remarks on the Completeness of Logical Systems Relative to the Validity-Concepts of P. Lorenzen and K. Lorenz. Notre Dame Journal of Formal Logic 5 (2):81-112.
H. C. M. Swart & C. J. Posy (1981). Validity and Quantification in Intuitionism. Journal of Philosophical Logic 10 (1):117 - 126.
Max A. Freund (2001). A Temporal Logic for Sortals. Studia Logica 69 (3):351-380.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Total downloads1 ( #292,081 of 739,303 )
Recent downloads (6 months)0
How can I increase my downloads?