A note on formality and logical consequence

Citation
M. Gomez-torrente, A note on formality and logical consequence, J PHILOS LO, 29(5), 2000, pp. 529-539
Citations number
20
Categorie Soggetti
Philosiphy
Journal title
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN journal
00223611 → ACNP
Volume
29
Issue
5
Year of publication
2000
Pages
529 - 539
Database
ISI
SICI code
0022-3611(200010)29:5<529:ANOFAL>2.0.ZU;2-X
Abstract
Logic is formal in the sense that all arguments of the same form as logical ly valid arguments are also logically valid and hence truth-preserving. How ever, it is not known whether all arguments that are valid in the usual mod el-theoretic sense are truth-preserving. Tarski claimed that it could be pr oved that all arguments that are valid (in the sense of validity he contemp lated in his 1936 paper on logical consequence) are truth-preserving. But h e did not offer the proof. The question arises whether the usual model-theo retic sense of validity and Tarskis 1936 sense are the same. I argue in thi s paper that they probably are not, and that the proof Tarski had in mind, although unusable to prove that model-theoretically valid arguments are tru th-preserving, can be used to prove that arguments valid in Tarskis 1936 se nse are truth-preserving.