Worlds and Propositions Set Free


Otávio Bueno, Christopher Menzel, and Edward N. Zalta


Erkenntnis, 79 (2014): 797–820.


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 the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory to define 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.

[Preprint available online in PDF]