Journal of Philosophical Logic

, Volume 30, Issue 3, pp 259–265

No Future

  • Leon Horsten
  • Hannes Leitgeb
Article

DOI: 10.1023/A:1017569601150

Cite this article as:
Horsten, L. & Leitgeb, H. Journal of Philosophical Logic (2001) 30: 259. doi:10.1023/A:1017569601150

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 logictense predicatesdiagonalizationparadox

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