Journal of Philosophical Logic

, Volume 31, Issue 6, pp 591–612

Diamonds are a Philosopher's Best Friends

  • Heinrich Wansing

DOI: 10.1023/A:1021256513220

Cite this article as:
Wansing, H. Journal of Philosophical Logic (2002) 31: 591. doi:10.1023/A:1021256513220


The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.

constructive negationepistemic logicknowability paradoxmodal logicparaconsistent logicrelevance logic

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Heinrich Wansing
    • 1
  1. 1.Dresden University of TechnologyInstitute of PhilosophyDresdenGermany