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Deflationary Truth and Pathologies

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Abstract

By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It turns out in particular that a certain natural closure condition imposed on a satisfaction class—namely, closure of truth under sentential proofs—generates a nonconservative extension of a syntactic base theory (Peano arithmetic).

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References

  1. Buss, S. (1994). On Gödel’s theorems on lengths of proofs I: Number of lines and speedup for arithmetics. Journal of Symbolic Logic, 39, 737–756.

    Google Scholar 

  2. Engström, F. (2002). Satisfaction classes in nonstandard models of first order arithmetic. Chalmers University of Technology and Göteborg University.

  3. Field, H. (1999). Deflating the conservativeness argument. Journal of Philosophy, 96, 533–540.

    Article  Google Scholar 

  4. Hajek, P., & Pudlak, P. (1993). Metamathematics of first order arithmetic. Berlin: Springer.

    Google Scholar 

  5. Halbach, V. (1999). Disquotationalism and infinite conjunctions. Mind, 108, 1–22.

    Article  Google Scholar 

  6. Halbach, V. (2001). How innocent is deflationism? Synthese, 126, 167–194.

    Article  Google Scholar 

  7. Horwich, P. (1990). Truth. Oxford: Basil Blackwell.

    Google Scholar 

  8. Kaye, R. (1991). Models of Peano arithmetic. Oxford: Clarendon Press.

    Google Scholar 

  9. Ketland, J. (1999). Deflationism and Tarski’s paradise. Mind, 108, 69–94.

    Article  Google Scholar 

  10. Kotlarski, H., Krajewski, S., & Lachlan, A. H. (1981). Construction of satisfaction classes for nonstandard models. Canadian Mathematical Bulletin, 24, 283–293.

    Google Scholar 

  11. Kotlarski, H. (1986). Bounded induction and satisfaction classes. Zeitschrift für Mathematische Logik, 32, 531–544.

    Article  Google Scholar 

  12. Kotlarski, H. (1991). Full satisfaction classes: A survey. Notre Dame Journal of Formal Logic, 32, 573–579.

    Article  Google Scholar 

  13. Krajewski, S. (1976). Non-standard satisfaction classes. In Set theory and hierarchy theory (Proc. Second Conf. Bierutowice, 1975). Lecture notes in mathematics (Vol. 537, pp. 121–144).

  14. McGee, V. (2006). In praise of the free lunch: Why disquotationalists should embrace compositional semantics. In V. Hendricks, S. Pedersen, & T. Bollander (Eds.), Self-Reference (pp. 95–120). CSLI, Stanford.

  15. Robinson, A. (1963). On languages which are based on non-standard arithmetic. Nagoya Mathematical Journal, 22, 83–117.

    Google Scholar 

  16. Shapiro, S. (1998). Proof and truth—through thick and thin. Journal of Philosophy, 95, 493–552.

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Philosophy, University of Warsaw, Krakowskie Przedmiescie 3, 00-047, Warsaw, Poland

    Cezary Cieśliński

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  1. Cezary Cieśliński
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Correspondence to Cezary Cieśliński.

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Cieśliński, C. Deflationary Truth and Pathologies. J Philos Logic 39, 325–337 (2010). https://doi.org/10.1007/s10992-010-9128-4

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  • DOI: https://doi.org/10.1007/s10992-010-9128-4

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