Project description: Many philosophers will know the iterative conception of sets, according to which sets are successively formed from previously available objects. This conception has been a huge success, by explaining and motivating large parts of contemporary set theory. The project, Construction in the Formal Sciences, seeks to develop other, similarly powerful applications of an idealized and infinitary constructional approach. We aim, in particular, to develop a foundation for the study of intensional entities, e.g. propositions and properties, where a variety of paradoxes still arise, with no agreed-upon solution—nearly a century after set theory received its proper foundation. By building on my recent work on potentialism (which generalizes Aristotle’s notion of potential infinity) and some theoretical tools inspired by constructive mathematics, we will develop applications of the idealized constructional approach in philosophy, foundations of mathematics, formal semantics, and formal ontology.
An interview (in Norwegian) with Øystein Linnebo can be found here.