17,015 research outputs found
An axiomatic version of Fitch’s paradox
A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the parado
Montague's Paradox without Necessitation
Some such as Dean (2014) suggest that Montague's paradox requires the
necessitation rule, and that the use of the rule in such a context is
contentious. But here, I show that the paradox arises independently of the
necessitation rule. A derivation of the paradox is given in modal system T
without deploying necessitation; a necessitation-free derivation is also
formulated in a significantly weaker system
Paradoxes of rational agency and formal systems that verify their own soundness
We consider extensions of Peano arithmetic which include an assertibility
predicate. Any such system which is arithmetically sound effectively verifies
its own soundness. This leads to the resolution of a range of paradoxes
involving rational agents who are licensed to act under precisely defined
conditions.Comment: 10 page
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