Journal of Philosophical Logic

, Volume 30, Issue 3, pp 259–265

No Future

  • Leon Horsten
  • Hannes Leitgeb
Article

Abstract

The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore arises whether the notions that are investigated in tense logic can be consistently formalized as predicates. In this paper it is shown that the answer to this question is negative. The logical treatment of the notions of future and past as predicates gives rise to paradoxes due the specific interplay between both notions. For this reason, the tense paradoxes that will be presented are not identical to the paradoxes referred to above.

tense logic tense predicates diagonalization paradox 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Boolos, G. and Jeffrey, R.: Computability and Logic, 3rd edn, Cambridge University Press, Cambridge, 1989.Google Scholar
  2. 2.
    Burgess, J.: Basic tense logic, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. II, Reidel, Dordrecht, 1984, pp. 89–133.Google Scholar
  3. 3.
    Friedman, H. and Sheard, M.: An axiomatic approach to self-referential truth, Ann. Pure Appl. Logic 33 (1987), 1–21.Google Scholar
  4. 4.
    Kaplan, D. and Montague, R.: A paradox regained, Notre Dame J. Formal Logic 1 (1960), 79–90.Google Scholar
  5. 5.
    McGee, V.: How truthlike can a predicate be? A negative result, J. Philos. Logic 14 (1985), 399–410.Google Scholar
  6. 6.
    Montague, R.: Syntactic treatments of modality with corollaries on reflexion principles and finite axiomatizability, Acta Philos. Fennica 16 (1963), 153–167.Google Scholar
  7. 7.
    Prior, A.: Past, Present and Future, Oxford University Press, London, 1967.Google Scholar
  8. 8.
    Sheard, M.: A guide to truth predicates in the modern era, J. Symbolic Logic 59 (1994), 1032–1054.Google Scholar
  9. 9.
    Tarski, A.: DerWahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica 1 (1935), 261–405.Google Scholar
  10. 10.
    Thomason, R.: A note on syntactical treatments of modality, Synthese 44 (1980), 391–395.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Leon Horsten
    • 1
  • Hannes Leitgeb
    • 2
  1. 1.Centrum LogicaLeuvenBelgium
  2. 2.Dept. of PhilosophyUniversity of Salzburg FranziskanergasseSalzburgAustria

Personalised recommendations