The Polar Conception of Vagueness

In his 1990 lecture ‘Concepts without boundaries’, Mark Sainsbury presents a system that he calls the polar conception of vague concepts. In this paper, it is demonstrated that the polar conception naturally gives rise to a weaker than classical logic -- namely, a quantum logic characterised by the failure of the law of distribution -- based on the relation of proximity to polar cases. After the quantum account is presented, it is suggested that the rejection of the law of distribution is well motivated in the context of vagueness.