## Worlds and Propositions Set Free

### Authors

Otávio Bueno, Christopher Menzel, and Edward N. Zalta
### Reference

*Erkenntnis*, 79 (2014): 797–820.
### 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
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.

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