A contingent Russell’s paradox. (English) Zbl 0860.03010

Orilia, Francesco

Notre Dame J. Formal Logic 37, No. 1, 105-111 (1996).

Two Cocchiarella type-free systems of nonstandard second-order logic are shown to produce a contingent Russell paradox, i.e., derivability of a contradiction from contingent premisses.

Reviewer: P.Materna (Praha)

MSC:

03B15	Higher-order logic; type theory (MSC2010)
03A05	Philosophical and critical aspects of logic and foundations

Keywords:

nominalized predicates; type-free systems of nonstandard second-order logic; contingent Russell paradox

References:

[1]	Chierchia, G., Topics in the Syntax and Semantics of Infinitives and Gerunds , Ph.D. dissertation, University of Massachusetts, Amherst, 1984.
[2]	Cocchiarella, N., “The theory of homogeneous simple types as a second order logic,” Notre Dame Journal of Formal Logic , vol. 20 (1979), pp. 505–524. · Zbl 0314.02027 · doi:10.1305/ndjfl/1093882656
[3]	Cocchiarella, N., “Two \(\lambda\)-extensions of the theory of homogeneous simple types,” Notre Dame Journal of Formal Logic , vol. 26 (1985), pp. 377–407. · Zbl 0588.03006 · doi:10.1305/ndjfl/1093870930
[4]	Cocchiarella, N., “Frege, Russell and logicism: a logical reconstruction,” pp. 197–252 in Frege Synthesized , edited by L. Haaparanta and J. Hintikka, Reidel, Dordrecht, 1986.
[5]	Cocchiarella, N., Logical Investigations of Predication Theory and the Problem of Universals , Bibliopolis Press, Naples, 1986. · Zbl 0614.03003
[6]	Cocchiarella, N., “Conceptualism, realism, and intensional logic,” Topoi , vol. 5 (1989), pp. 75–87. · doi:10.1007/BF00138676
[7]	Gupta, A., “Truth and paradox,” Journal of Philosophical Logic , vol. 11 (1982), pp. 1–60. · Zbl 0512.03002 · doi:10.1007/BF00302338
[8]	Kripke, S., “Outline of a theory of truth,” Journal of Philosophy , vol. 72 (1975), pp. 690–716. · Zbl 0952.03513
[9]	Landini, G., Meinong Reconstructed Versus Early Russell Reconstructed: A Study in the Formal Ontology of Fiction , Ph.D. dissertation, Indiana University, Bloomington, 1986.
[10]	Landini G., “How to Russell another Meinongian: a Russellian theory of fictional objects versus Zalta’s theory of abstract objects,” Grazer Philosophische Studien , vol. 37 (1990), pp. 93–122.
[11]	Orilia, F., “Belief representation in a deductivist type-free doxastic logic,” Minds and Machines , vol. 4 (1994), pp. 163–203. · doi:10.1111/j.1467-8640.1995.tb00049.x
[12]	Quine, W., Set Theory and Its Logic , Harvard University Press, Cambridge, 1963. · Zbl 0122.24601
[13]	Tarski, A., “The concept of truth in formalized languages,” pp. 152–278 in Logic, Semantics, Metamathematics , Clarendon, Oxford, 1956.