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Property theory and the revision theory of definitions

Published online by Cambridge University Press:  12 March 2014

Francesco Orilia
Francesco Orilia*
Affiliation:
Dipartimento di Filosofia e Scienze Umane, Università di Macerata, 62100 Macerata, Italy, E-mail: orilia@unimc.it
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§1. Introduction. Russell's type-theory can be seen as a theory of properties, relations, and propositions (PRPs) (in short, a property theory). It relies on rigid type distinctions at the grammatical level to circumvent the property theorist's major problem, namely Russell's paradox, or, more generally, the paradoxes of predication. Type theory has arguably been the standard property theory for years, often taken for granted, and used in many applications. In particular, Montague [27] has shown how to use a type-theoretical property-theory as a foundation for natural language semantics.

In recent years, it has been persuasively argued that many linguistic and ontological data are best accounted for by using a type-free property theory. Several type-free property theories, typically with fine-grained identity conditions for PRPs, have therefore been proposed as potential candidates to play a foundational role in natural language semantics, or for related applications in formal ontology and the foundations of mathematics (Bealer [6], Cocchiarella [18], Turner [35], etc.).

Attempts have then been made to combine some such property theory with a Montague-style approach in natural language semantics. Most notably, Chierchia and Turner [15] propose a Montague-style semantic analysis of a fragment of English, by basically relying on the type-free system of Turner [35]. For a similar purpose Chierchia [14] relies on one of the systems based on homogeneous stratification due to Cocchiarella. Cocchiarella's systems have also been used for applications in formal ontology, inspired by Montague's account of quantifier phrases as, roughly, properties of properties (see, e.g., Cocchiarella [17], [19], Landini [25], Orilia [29]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 212 - 246
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[1]Aczel, P., Frege structures and the notions of propositions, truth and set, The Kleene symposium (Barwise, J., Keisler, H. J., and Kunen, K., editors), North-Holland, Amsterdam, 1980, pp. 31–39.CrossRefGoogle Scholar
[2]Antonelli, G. A., The complexity of revision, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 67–72.CrossRefGoogle Scholar
[3]Antonelli, G. A., The complexity of revision, revised, unpublished manuscript, 1998.Google Scholar
[4]Asher, N. and Kamp, H., The knower paradox and representational theories of attitudes, Theoretical aspects of reasoning about knowledge: Proceedings of the 1986 conference (Halpern, J. Y., editor), Morgan Kaufmann, 1986, pp. 131–144.CrossRefGoogle Scholar
[5]Asher, N., Self-reference, attitudes, and paradox, Properties, types, and meaning (Chierchia, G., Partee, B., and Turner, R., editors), vol. 1, Kluwer, Dordrecht, 1989, pp. 85–158.CrossRefGoogle Scholar
[6]Bealer, G., Quality and concept, Oxford University Press, London, 1982.CrossRefGoogle Scholar
[7]Bealer, G., Fine-grained type-free intensionality, Properties, types, and meaning (Chierchia, G., Partee, B., and Turner, R., editors), vol. 1, Kluwer, Dordrecht, 1989, pp. 177–230.CrossRefGoogle Scholar
[8]Bealer, G. and Mönnich, U., Property theories, Handbook of philosophical logic (Gabbay, D. and Guenthner, F., editors), vol. IV, Reidel, Dordrecht, 1989, pp. 133–251.CrossRefGoogle Scholar
[9]Belnap, N., Gupta's rule of revision theory of truth, Journal of Philosophical Logic, vol. 11 (1982), pp. 103–116.CrossRefGoogle Scholar
[10]Burgess, J. P., The truth is never simple, this Journal, vol. 51 (1986), pp. 663–681.Google Scholar
[11]Castañeda, H.-N., Ontology and grammar: I. Russell's paradox and the general theory of properties in natural language, Theoria, vol. 42 (1976), pp. 44–92.CrossRefGoogle Scholar
[12]Castañeda, H.-N., The semantics and causal roles of proper names in our thinking of particulars: the restricted-variable/retrieval view of proper names, Thinking and the structure of the world (Jacobi, K. and Pape, H., editors), de Gruyter, Berlin, 1990, pp. 11–56.Google Scholar
[13]Chapuis, A., Alternative revision theories of truth, Journal of Philosophical Logic, vol. 25 (1996), pp. 399–423.CrossRefGoogle Scholar
[14]Chffirchia, G., Topics in the syntax and semantics of infinitives and gerunds, Ph.D. thesis, University of Massachusetts, Amherst, 1984.Google Scholar
[15]Chierchia, G. and Turner, R., Semantics andproperty theory, Linguistics and Philosophy, vol. 11 (1988), pp. 261–302.CrossRefGoogle Scholar
[16]Church, A., Introduction to mathematical logic, vol. I, Princeton University Press, Princeton, NJ, 1956.Google Scholar
[17]Cocchiarella, N., Meinong reconstructed versus early Russell reconstructed, Journal of Philosophical Logic, vol. 11 (1982), pp. 183–215.CrossRefGoogle Scholar
[18]Cocchiarella, N., Logical investigations of predication theory and the problem of universals, Bibliopolis Press, Naples, 1986.Google Scholar
[19]Cocchiarella, N., Conceptualism, realism, and intensional logic, Topoi, vol. 8 (1989), pp. 15–34.CrossRefGoogle Scholar
[20]Creswell, M., Structured meanings, MIT Press, Cambridge, 1985.Google Scholar
[21]Gupta, A., Truth and paradox, Journal of Philosophical Logic, vol. 11 (1982), pp. 1–60.CrossRefGoogle Scholar
[22]Gupta, A. and Belnap, N., The revision theory of truth, The MIT Press, Cambridge, MA, 1993.CrossRefGoogle Scholar
[23]Herzberger, H. G., Notes on naive semantics, Journal of Philosophical Logic, vol. 11 (1982), pp. 61–102.CrossRefGoogle Scholar
[24]Kremer, P., The Gupta-Belnap systems S# and S* are not axiomatisable, Notre Dame Journal of Formal Logic, vol. 34 (1993), pp. 583–596.CrossRefGoogle Scholar
[25]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.Google Scholar
[26]McGee, V., Truth and paradox, Hackett, Indianapolis, 1991.Google Scholar
[27]Montague, R., The proper treatment of quantification in ordinary English, Formal philosophy: Selected papers of Richard Montague (Thomason, R., editor), Yale University Press, New Haven, CN, 1974, pp. 247–270.Google Scholar
[28]Montague, R., Syntactical treatment of modality, with corollaries on reflection principles and finite axiomatizability, Formal philosophy: Selected papers of Richard Montague (Thomason, R., editor), Yale University Press, New Haven, CN, 1974, pp. 286–302.Google Scholar
[29]Orilia, F., Belief representation in a type-free doxastic logic, Minds and Machines, vol. 4 (1994), pp. 163–203.CrossRefGoogle Scholar
[30]Orilia, F., A contingent Russell's paradox, Notre Dame Journal of Formal Logic, vol. 37 (1996), pp. 105–111.CrossRefGoogle Scholar
[31]Parsons, T., Type theory and ordinary language, Linguistics, philosophy and Montague grammar (Mithun, M. and Davis, S., editors), University of Texas Press, Austin, TX, 1979.Google Scholar
[32]Quine, W. V. O., From a logical point of view, Harper and Row, New York, 1953.Google Scholar
[33]Smullyan, R., First-order logic, Springer-Verlag, Berlin, 1968.CrossRefGoogle Scholar
[34]Thomason, R., A note on syntactical treatments of modality, Synthese, vol. 44 (1980), pp. 391–395.CrossRefGoogle Scholar
[35]Turner, R., A theory of properties, this Journal, vol. 52 (1987), pp. 455–472.Google Scholar
[36]Turner, R., Truth and modality for knowledge representation, Pitman, London, 1990.Google Scholar