58吃瓜

Abstract: Meinong’s object theory is thought by many to be inconsistent聽(or even trivial). Indeed, its most straightforward formalisation in聽second-order logic is. However, contemporary logicians have developed聽more subtle formalisations of Meinong’s ideas, the so-called聽neo-Meinongian logics, that are provably consistent. In this talk, I聽review two of the main approachs, Nuclear Meinongianism and Dual Copula聽Meinongianism, and I develop a new one, based on a Meinongian instinct聽about complex properties. I present a consistent formal system based on聽second-order logic augmented with lambda-abstraction (an operator聽constructing complex properties) and a Meinongian operator m (which聽constructs Meinongian objects). I then mention an application of this聽formal聽system in philosophy of mathematics. More precisely, I show how聽to derive a non-standard set theory within the formal system and present聽some of its properties. This serves as a first step towards Meinongian聽foundations of mathematics, resembling Frege’s logicism.