The Quantified Argument Calculus (Quarc) is a new logic system, developed by Hanoch Ben-Yami and 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 is the first-order Predicate Calculus, while being at least as strong as the latter.
By now, Quarc has been shown to be sound and complete; to contain and validate Aristotle’s logic; it separates quantification from existence, shedding new light on logic’s ontological commitments, and lack thereof; it has been extended to modality, invalidating its analogues of the Barcan formulas; three-valued versions of it have been developed, capturing presupposition failure; additional quantifiers have been incorporated in it, such as ‘most’ and ‘more’; several Quarc proof systems have been developed, including sequent calculi, and its metalogical properties have been researched in depth; the image of the Predicate Calculus it contains shows in what sense quantification in the latter is restricted relative to Quarc’s; and more. Further research is currently being conducted, and there’s much potential in additional directions.
In this meeting, the first of a postgraduate seminar on Quarc, Ben-Yami will introduce Quarc, with a discussion to follow. Although this is the first class in a course, it is self-contained. Knowledge of logic on at least the level of an advanced philosophy introductory course will be assumed.
The meeting took place on World Logic Day, Thursday, January 14, 15:30–17:10 CET.
A recording of the talk can be found here.