Additive presuppositions are derived through activating focus alternatives

The additive presupposition of particles like "too"/"even" is uncontested, but usually stipulated. This paper proposes to derive it based on two properties. (i) "too"/"even" is cross-linguistically focus-sensitive, and (ii) in many languages, "too"/"even" builds negative polarity items and free-choice items as well, often in concert with other particles. (i) is the source of its existential presupposition, and (ii) offers clues regarding how additivity comes about. (i)-(ii) together demand a sparse semantics for "too/even," one that can work with different kinds of alternatives (focus, subdomain, scalar) and invoke suitably different further operators

The Good Samaritan and the Hygienic Cook: A Cautionary Tale About Linguistic Data

When developing formal theories of the meaning of language, it is appropriate to consider how apparent paradoxes and conundrums of language are best resolved. But if we base our analysis on a small sample of data then we may fail to take into account the influence of other aspects of meaning on our intuitions. Here we consider the so-called Good Samaritan Paradox (Prior, 1958), where we wish to avoid any implication that there is an obligation to rob someone from "You must help a robbed man". We argue that before settling on a formal analysis of such sentences, we should consider examples of the same form, but with intuitively ?different entailments ? such as "You must use a clean knife" ? and also actively seek other examples that exhibit similar contrasts in meaning, even if they do not exemplify the phenomena that is under investigation. This can refine our intuitions and help us to attribute aspects of interpretation to the various facets of meaning

Derived rules for predicative set theory: an application of sheaves

We show how one may establish proof-theoretic results for constructive Zermelo-Fraenkel set theory, such as the compactness rule for Cantor space and the Bar Induction rule for Baire space, by constructing sheaf models and using their preservation properties

Ethics and economics in Karl Menger: how did social sciences cope with Hilbertism

This paper deals with the contributions made to the social sciences by the mathematician Karl Menger (1902-1985), the son of the more famous economist, Carl Menger. Mathematician and a logician, he focused on whether it was possible to explain the social order in formal terms.1 He stressed the need to find the appropriate means with which to treat them, avoiding recourse to historical descriptions, which are unable to yield social laws. He applied Hilbertism to economics and ethics in order to build an axiomatic and formalized model of the individual behavior and the dynamics of social groups.