A New Modal Liar

T. Parent
Virginia Tech
Montague's modal liar is thought to show that 'necessarily' cannot be treated as a predicate of sentences. However, if 'necessarily' is treated as an operator on propositions (as is standard), we can also generate paradox (and without Montague's contentious use of the necessitation rule). The reasoning of the new modal liar is not immediately obvious--however, assuming that accessibility is reflexive, one can derive a contradiction from the proposition: This very proposition is not necessary. Thus the key advantage of the operator view is shown to be illusory
Keywords modal logic  possible worlds semantics  paradox  soundness proof  truth
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References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1966 - Journal of Symbolic Logic 31 (2):276-277.
Montague’s Paradox, Informal Provability, and Explicit Modal Logic.Walter Dean - 2014 - Notre Dame Journal of Formal Logic 55 (2):157-196.
On the Benefits of a Reduction of Modal Predicates to Modal Operators.Volker Halbach - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 323--333.
The Possible Liar.John F. Post - 1970 - Noûs 4 (4):405-409.

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