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

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.

The Logic and Metaphysics Workshop will be meeting on Mondays from 4:15 to 6:15 in room 6494 of the Graduate Center, CUNY (365 5th Avenue). The (provisional) schedule is as follows:

Sep 17. Sander Breckers, Utrecht

Sep 24. Hanoch Ben-Yami, CEU

Oct 1. Otavio Bueno, Miami

Oct 8. GC CLOSED. NO MEETING

Oct 15. Alfredo Freire, Campinas

Oct 22. Yale Weiss, GC

Oct 29. Boris Kment, Princeton

Nov 5. Melissa Fusco, Columbia

Nov 12. Amy Seymour, Fordham

Nov 19. Andrew Tedder, UConn

Nov 26. Justin Bledin, Johns Hopkins

Dec 3. Suki Finn, Southampton

Dec 10. Byong Yi, Toronto