Abstract
In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain–outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails.
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References
Carnap, R.: 1942, Introduction to Semantics, Cambridge (US).
Church, A.: 1943, Carnap's Introduction to Semantics, Philos. Rev. 52, 298–304.
Frege, G.: 1892, Über Sinn und Bedeutung, Z. Philos. Philos. Kritik 100, 25–50.
Gödel, K.: 1944, Russell's Mathematical Logic, in P. Benacerraf and H. Putnam (eds.), (1983): Philosophy of Mathematics, Cambridge, pp. 447–469.
Kalish, D., Montague, R. and Mar, G.: 1980, Logic. Techniques of Formal Reasoning, New York.
Kaplan, D.: 1970, What is Russell's Theory of Descriptions, in W. Yourgrau and A. D. Breck (eds.), Physics, Logic, and History, New York, pp. 277–295.
Lambert, K.: 1991, Philosophical Applications of Free Logic, Oxford University Press.
Lambert, K.: 1997, Free Logics: Their Foundations, Character, and Some Applications Thereof, Sankt Augustin.
Lambert, K.: 2001, Free logics, in L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Oxford University Press, pp. 258–279.
Lambert, K.: 2003, Free Logic. Selected Essays, Cambridge (UK).
Leblanc, H. and Thomason, R. H.: 1968, Completeness Theorems for Some Presupposition-Free Logics, Fundam. Math. 62, 125–164.
Leeb, H.-P.: 1997, Formalisierung von Gödels ‘Slingshot’-Argument und die Referenzrelation, in P. Weingartner, G. Schurz and G. Dorn, (eds.), The Role of Pragmatics in Contemporary Philosophy, vol. 2, Kirchberg am Wechsel, pp. 532–538.
Leeb, H.-P.: 2001a, Essay Review: K. Lambert's Free Logics: Their Foundations, Character, and Some Applications Thereof (1997), Hist. Philos. Logic 22, 233–236.
Leeb, H.-P.: 2001b, Was sind extensionale Sprachen? in R. Born and O. Neumaier (eds.), Philosophie, Wissenschaft – Wirtschaft. Miteinander denken – voneinander lernen, Wien, pp. 185–190.
Leeb, H.-P.: 2004, Das Kompositionalitätsprinzip in seinen Anwendungen auf die “Slingshot-Argumente”, Sankt Augustin.
Morscher, E. and Hieke, A. (eds.): 2001, New Essays in Free Logic. In Honour of Karel Lambert, Dordrecht.
Quine, W. V. O.: 1960, Word and Object, Cambridge (US).
van Fraassen, B. C.: 1969, Facts and Tautological Entailments, J. Philos. 66, 477–487.
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Leeb, HP. State-of-affairs Semantics for Positive Free Logic. J Philos Logic 35, 183–208 (2006). https://doi.org/10.1007/s10992-005-9010-y
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DOI: https://doi.org/10.1007/s10992-005-9010-y