The Quantified Argument Calculus

Graduate Program (& Advanced Certificate) Status

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Course Description: 

The Quantified Argument Calculus (QUARC) is a new logic system, developed by Hanoch Ben-Yami, collaborating with a growing number of other philosophers and logicians. Its basic departure from Frege’s logic is in its treatment of quantification: quantifiers are not sentential operators but connect to one‑place predicates to form arguments – quantified arguments – of other predicates. QUARC is closer to natural language in its syntax and the inferences it validates than the Predicate Calculus, while being at least as strong as the latter. By now, QUARC comprises a family of closely related systems.

We introduce the basic QUARC system and prove it is sound and complete. In the process we develop an alternative to model-theoretic semantics: the truth-valuational, substitutional approach. We also show that QUARC contains Aristotle’s assertoric logic. QUARC also separates quantification from existence, shedding light on logic’s lack of ontological commitments. We then extend QUARC to modality, invalidating its analogues of the Barcan formulas. We also develop three-valued versions of it. Additional quantifiers shall be incorporated, such as ‘most’ and ‘more’. We also compare it to the Predicate Calculus, showing in what sense quantification in the latter is restricted relative to QUARC’s. Further research into QUARC is currently being conducted, and we describe some of this work-in-progress and open questions.

Learning Outcomes: 

Familiarity with the truth-valuational substitutional approach, an important alternative, logically and philosophically, to model-theoretic semantics. Familiarity with Quarc, an alternative to Predicate Logic which is closer to the logic of Natural Language and contributes to the clarification of several logic concepts.

In addition, 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 contemporary philosophy.


Term Paper.


The course will assume good knowledge of logic on the level of advanced undergraduate courses, which includes familiarity with soundness and completeness proofs and some knowledge of modal logic.

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