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The Quantified Argument Calculus, with Application to the Barcan Formulas and Necessary Existence (Hanoch Ben-Yami)

The Logic and Metaphysics Workshop will meet on September 24th from 4:15-6:15 in room 6494 of the CUNY Graduate Center for a talk by Hanoch Ben-Yami (CEU).

Title: The Quantified Argument Calculus, with Application to the Barcan Formulas and Necessary Existence

Abstract: I present a logic system I recently developed (RSL 2014), the Quantified Argument Calculus or Quarc. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, on any of its versions, and it is no less powerful than the first-order Predicate Calculus. This makes analysing the Barcan formulas and necessary existence by its means particularly interesting. As we shall see, the analogues in Quarc of the Barcan formulas and their converses are straightforwardly invalid. And, since quantification and existence in Quarc come apart, existence isn’t logically necessary. The issues with both the Barcan formulas and necessary existence were an artefact of a specific formal language, the Predicate Calculus, and they are eliminated once it is replaced by a formal language with a claim of providing an improved representation of the logic of Natural Language.

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