The Quantified Argument Calculus

Graduate Program (& Advanced Certificate) Status

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Course Description: 

The Quantified Argument Calculus – Quarc – is a recent formal logic system invented by Ben-Yami and further expended and applied by other researchers. It was first published in 2014 but is based on work published in the preceding decade. It incorporates quantification in a way different than the one used in Fregean logic, closer to quantification in Natural Language. This deviation leads Quarc to be closer to Natural Language in other respects as well, and consequently it gives, arguably, a better representation of the logic of Natural Language than does the Predicate Calculus.

Following the 2014 publication of the formal system, Ben-Yami and others have published on Quarc, extending and applying it in various ways. A modal system has been developed, a sequent calculus, the relation of Quarc to the Predicate Calculus investigated, Quarc was employed to provide a representation of Aristotle’s logic (which it incorporates), issues of modality and quantification and of existence discussed, and more. There’s also much work in progress being done, on completeness, so-called existential sentences, definite descriptions, axiomatic systems, properties of modal systems and natural deduction for modal systems, and more.

The seminar will start with an introduction to Quarc, which will take around four meetings, and continue with presentations of mostly work in progress, by various researchers working on Quarc.

Learning Outcomes: 

The students will acquire improved competence in formal logic, knowledge of the history of logic, and a deeper understanding of some of the logic issues that have occupied recent philosophy.


Term paper of up to 2500 words. When one writes formulas, fewer words can contain much more information, so the acceptability of shorter papers will be decided according to their subject matter.


Knowledge of logic on the level of an advanced undergraduate course in Philosophy is required. This includes familiarity with the Propositional- and Predicate Calculi, including proof systems and for the latter model theoretic semantics; familiarity with the ideas of soundness and completeness, if not with proofs thereof; and at least basic knowledge of modal logic, preferably including possible worlds semantics.