Necessity, meaning, and rationality: The notion of logical consequence

A Companion to Philosophical Logic

Volumn , Issue , 2007, Pages 226-240

  Shapiro, Stewart ^a,b  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

Author keywords

Epistemic matters; Logical consequence; Modality; Recapitulation; Semantics

Indexed keywords

EID: 84955407706     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470996751.ch15     Document Type: Chapter

References (20)

1. Coffa, A. (1991) The Semantic Tradition from Kant to Carnap. Cambridge: Cambridge University Press.
2. Corcoran, J. (1974) Aristotle's natural deduction system. In J. Corcoran (ed.), Ancient Logic and its Modern Interpretations (pp. 85-131). Dordrecht: Reidel, 85-131.
3. Gödel, K. (1930) Die Vollständigkeit der Axiome des logischen Funktionenkalkuls. Montatshefte für Mathematik und Physik, 37, 349-60; translated as "The completeness of the axioms of the functional calculus of logic," in Jean van Heijenoort (ed.), From Frege to Gödel, Cambridge, MA: Harvard University Press, 1967, 582-91.
4. Hacking, I. (1979) What is logic? Journal of Philosophy, 76, 285-319.
5. McCarthy, T. (1981) The idea of a logical constant. Journal of Philosophy, 78, 499-523.
6. Peacocke, C. (1976) What is a logical constant? Journal of Philosophy, 78, 221-40.
7. Shapiro, S. (1991) Foundations without Foundationalism: A Case for Second-order Logic. Oxford: Oxford University Press.
8. Sher, G. (1991) The Bounds of Logic. Cambridge, MA: MIT Press.
9. Tarski, A. (1986) What are logical notions. In John Corcoran (ed.), History and Philosophy of Logic, 7, 143-54.
10. Tennant, N. (1987) Anti-Realism and Logic. Oxford: Oxford University Press.
11. Anderson, A. and Belnap, N. (1975) Entailment: The Logic of Relevance and Necessity I. Princeton, NJ: Princeton University Press. (An extensive study of logical consequence, arguing that the premises of a logical consequence must be relevant to its conclusion.)
12. Anderson, A., Belnap, N. and Dunn, M. (1992) Entailment: The Logic of Relevance and Necessity II. Princeton, NJ: Princeton University Press. (A sequel to the above.)
13. Bolzano, B. (1837) Theory of Science, trans. R. George. Berkeley, University of California Press, 1972. (A presentation of a substitutional account of consequence, along the lines of (Sub).)
14. Corcoran, J. (1973) Meanings of implication. Dialogos, 25, 59-76. (Presents a lucid account of several different notions of consequence, focusing on the role of formal deductive systems and a relation like (Ded).)
15. Etchemendy, J. (1990) The Concept of Logical Consequence. Cambridge, MA: Harvard University Press. (A critical study of the influential account in Tarski (1935) and of contemporary modeltheoretic consequence. This book generated many responses, including Sánchez-Miguel (1993), Sher (1996), and Shapiro (1998).
16. Quine, W. V. O. (1986) Philosophy of Logic, 2nd edn., Englewood Cliffs, NJ: Prentice-Hall. (An influential substitutional account, along the lines of (Sub), relating that conception to the formal notions of model-theoretic consequence and deducibility in a standard deductive system.)
17. Sánchez-Miguel, M. (1993) The grounds of the model-theoretic account of the logical properties. Notre Dame Journal of Formal Logic, 34, 107-31. (A nice study of the role of modeltheoretic consequence, responding to Etchemendy (1990).)
18. Shapiro, S. (1998) Logical consequence: models and modality. In M. Schirn (ed.), The Philosophy of Mathematics Today. Oxford: Oxford University Press, 131-56. (A defense of model-theoretic consequence, relating it to the various intuitive notions.)
19. Sher, G. (1996) Did Tarski commit "Tarski's fallacy"? Journal of Symbolic Logic, 61, 653-86. (A reaction to Etchemendy (1990), relating Tarski's account to the model-theoretic one.)
20. Tarski, A. (1935) On the concept of logical consequence. In A. Tarski, Logic, Semantics and Metamathematics. Oxford: Clarendon Press, 1956; 2nd edn., edited and introduced by John Corcoran (Indianapolis: Hackett, 1983), 417-29. (A very influential article, developing a notion of consequence evolving from (Sub) but avoiding the tie to the expressive resources of the base language. The notion of satisfaction is introduced. The connection between this Tarskian notion and the contemporary model-theoretic one is a matter of controversy.)