Feferman on Foundations pp 449-467 | Cite as
Sameness
Chapter
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Abstract
I attempt an explication of what it means for an operation across domains to be the same on all domains, an issue that (Feferman, S.: Logic, logics and logicism. Notre Dame J. Form. Log. 40, 31–54 (1999)) took to be central for a successful delimitation of the logical operations. Some properties that seem strongly related to sameness are examined, notably isomorphism invariance, and sameness under extensions of the domain. The conclusion is that although no precise criterion can satisfy all intuitions about sameness, combining the two properties just mentioned yields a reasonably robust and useful explication of sameness across domains.
Keywords
Logical constants Isomorphism invariance Extension Generalized quantifiers2010 Mathematics Subject Classification
03B65 03C80 91F20References
- 1.Barwise, J., Cooper, R.: Generalized quantifiers and natural language. Linguist. Philos. 4, 159–219 (1981)CrossRefMATHGoogle Scholar
- 2.Bonnay, D.: Logicality and invariance. Bull. Symb. Log. 14(1), 29–68 (2008)MathSciNetCrossRefMATHGoogle Scholar
- 3.Bonnay, D., Engström, F.: Invariance and definability, with and without equality. Notre Dame J. Form. Log. 58 (2016)Google Scholar
- 4.Feferman, S.: Logic, logics and logicism. Notre Dame J. Form. Log. 40, 31–54 (1999)MathSciNetCrossRefMATHGoogle Scholar
- 5.Feferman, S.: Set-theoretical invariance criteria for logicality. Notre Dame J. Form. Log. 51, 3–20 (2010)MathSciNetCrossRefMATHGoogle Scholar
- 6.Feferman, S.: Which quantifiers are logical? a combined semantical and inferential criterion. In: Torza, A. (ed.) Quantifiers, Quantifiers and Quantifiers, pp. 19–30. Springer, Berlin (2015)CrossRefGoogle Scholar
- 7.Kolaitis, P., Väänänen, J.: Generalized quantifiers and pebble games on finite structures. Ann. Pure Appl. Log. 74, 23–75 (1995)MathSciNetCrossRefMATHGoogle Scholar
- 8.Lindström, P.: First order predicate logic with generalized quantifiers. Theoria 32, 175–71 (1966)MathSciNetMATHGoogle Scholar
- 9.McGee, V.: Logical operations. J. Philos. Log. 25, 567–80 (1996)MathSciNetCrossRefMATHGoogle Scholar
- 10.Mundici, D.: Other quantifiers: An overview. In: Barwise, J., Feferman, S. (eds.) Model-Theoretic Logics, pp. 211–233. Springer-Verlag, Berlin (1985)Google Scholar
- 11.Peters, S., Westerståhl, D.: Quantifiers in Language and Logic. Oxford University Press, Oxford (2006)Google Scholar
- 12.Peters, S., Westerståhl, D.: The semantics of possessives. Language 89(4), 713–759 (2013)CrossRefGoogle Scholar
- 13.Rescher, N.: Plurality-quantification (abstract). J. Symb. Log. 27, 373–374 (1962)CrossRefGoogle Scholar
- 14.Shelah, S.: Generalized quantifiers and compact logic. Trans. Am. Math. Soc. 204, 342–364 (1975)MathSciNetCrossRefMATHGoogle Scholar
- 15.Sher, G.: The Bounds of Logic. The MIT Press, Cambridge (1991)MATHGoogle Scholar
- 16.Tarski, A.: What are logical notions? Hist. Philos. Log. 7, 145–154 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 17.Väänänen, J.: Models and Games. Cambridge University Press, Cambridge (2011)CrossRefMATHGoogle Scholar
- 18.Väänänen, J., Westerståhl, D.: On the expressive power of monotone natural language quantifiers over finite models. J. Philos. Log. 31, 327–358 (2002)MathSciNetCrossRefMATHGoogle Scholar
- 19.van Benthem, J.: Questions about quantifiers. J. Symb. Log. 49, 443–466 (1984)MathSciNetCrossRefMATHGoogle Scholar
- 20.van Benthem, J.: Essays in Logical Semantics. Kluwer, Dordrecht (1986)CrossRefMATHGoogle Scholar
- 21.van Benthem, J.: Logical constants across varying types. Notre Dame J. Form. Log. 315–342 (1989)Google Scholar
- 22.Westerståhl, D.: Logical constants in quantifier languages. Linguist. Philos. 8, 387–413 (1985)CrossRefGoogle Scholar
- 23.Westerståhl, D.: Relativization of quantifiers in finite models. In: van der Does, J., van Eijck, J. (eds.) Generalized Quantifier Theory and Applications, pages 187–205. ILLC, Amsterdam. (1991) Also in Quantifiers: Logic, Models and Computation (same editors), pp. 375–383, CSLI Publications, Stanford (1996)Google Scholar
- 24.Westerståhl, D.: Constant operators: Partial quantifiers. In: Larsson, S., Borin, L. (eds.) From Quantification to Conversation, pp. 11–35. College Publications, London (2012)Google Scholar
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