Worlds and Propositions Set Free

Otávio Bueno, Christopher Menzel, Edward N. Zalta

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence can be rejected on the strongest possible grounds—not only in object theory but for the very framework of propositional modal logic in which Kaplan frames his argument. The authors close by fending off a possible objection that object theory avoids the Russell paradox only by refusing to incorporate set theory and, hence, that the object-theoretic solution is only a consequence of the theory’s weakness.

Original languageEnglish (US)
Pages (from-to)797-820
Number of pages24
JournalErkenntnis
Volume79
Issue number4
DOIs
StatePublished - Aug 1 2014

ASJC Scopus subject areas

  • Philosophy
  • Logic

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