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Plural quantification logic: A critical appraisal
Review of Symbolic Logic 2 (1):208232 (2009)
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The goal of this paper is to present a new reconstruction of Aristotle's assertoric logic as he develops it in Prior Analytics, A17. This reconstruction will be much closer to Aristotle's original text than other such reconstructions brought forward up to now. To accomplish this, we will not use classical logic, but a novel system developed by BenYami [2014. ‘The quantified argument calculus’, The Review of Symbolic Logic, 7, 120–46] called ‘QUARC’. This system is apt for a more adequate reconstruction (...) 

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on (...) 

In a series of publications I have claimed that by contrast to standard formal languages, quantifiers in natural language combine with a general term to form a quantified argument, in which the general term's role is to determine the domain or plurality over which the quantifier ranges. In a recent paper Zoltán Gendler Szabó tried to provide a counterexample to this analysis and derived from it various conclusions concerning quantification in natural language, claiming it is often ‘bare’. I show that (...) 