In standard logical systems, quantifiers and variables are essential to express complex relations among objects. Natural language has expressions that have an analogous function: some noun phrases play the role of quantifiers (e.g. every man), and some pronouns play the role of variables (e.g. him, as in Every man likes people who admire him). Since the 1980’s, there has been a vibrant debate in linguistics about the way in which pronouns come to depend on their antecedents. According to one view, natural language is governed by a ‘dynamic’ logic which allows for dependencies that are far more flexible than those of standard (classical) logic. According to a competing view, the treatment of variables in classical logic does not have to be fundamentally revised to be applied to natural language. While the debate centers around the nature of the formal links that connect pronouns to their antecedents, these links are not overtly expressed in spoken language, and the debate has remained open. In sign language, by contrast, the connection between pronouns and their antecedents is often made explicit by pointing. We argue that data from French and American Sign Language provide crucial evidence for the dynamic approach over one of its main classical competitors; and we explore further sign language data that can help choose among competing dynamic analyses.

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