The Ontology of Group Agency

We present an ontological analysis of the notion of group agency developed by Christian List and Philip Pettit. We focus on this notion as it allows us to neatly distinguish groups, organizations, corporations – to which we may ascribe agency – from mere aggregates of individuals. We develop a module for group agency within a foundational ontology and we apply it to organizations

Flexible involutive meadows

We investigate a notion of inverse for neutrices inspired by Van den Berg and Koudjeti's decomposition of a neutrix as the product of a real number and an idempotent neutrix. We end up with an algebraic structure that can be characterized axiomatically and generalizes involutive meadows. The latter are algebraic structures where the inverse for multiplication is a total operation. As it turns out, the structures satisfying the axioms of flexible involutive meadows are of interest beyond nonstandard analysis

Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.