The Quantified Argument Calculus: Introduction and Research Directions

ABSTRACT

The talk will present the Quantified Argument Calculus (Quarc) [1]: a logic system developed by Ben-Yami over the last decade, 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. This departure is accompanied by others, and together they make Quarc 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 comprises a family of closely related systems. On all or some of its versions, it has been shown to be sound and complete; to contain and validate Aristotle’s assertoric 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; decidability of Quarc fragments is being researched; 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. The purpose of the talk is both to introduce the audience to this burgeoning area of research, which has already produced more than a dozen publications, most in leading journals, by several researchers; and to indicate additional areas of promising research. [1] https://philosophy.ceu.edu/quantified-argument-calculus

SHORT BIO (from JKU):

Hanoch Ben-Yami is Professor of Philosophy at the Central European University in Vienna. He received his Ph.D. from Tel Aviv University, and his most recent work is on logic and language. He works on various issues in the philosophy of mind; on questions of space and time, especially in relation to special relativity and quantum mechanics; on Descartes; and on Wittgenstein.