The Naturalness and Structure of Relations
Abstract
This dissertation contributes to a theory of naturalness of properties and relations and to a view on the internal structure of relations. On naturalness, I develop and defend a new theory according to which it is position-relative and category-relative. Relations have object-positions. For example, the loving relation has the lover-position and the beloved-position, and the set-member relation has the set-position and the member-position. Position-relativism allows for attributions of naturalness to positions of relations. Category-relativism allows for attributions of naturalness to properties and (positions of) relations relative to categories of objects. For example, the lover-position of the loving relation can be more natural than its beloved-position, and the set-position of set-membership can be natural relative to the category of sets while failing to be natural relative to the category of physical objects. In the first two papers of this dissertation, I argue that position- and category-relative naturalness can help in accounts of similarity, especially regarding existential derivatives of relations (such as perhaps loving something) and negative totality properties (such as perhaps having no members); that it can help in accounts of intrinsicality, real change, and haecceistic properties; that it can account for negation as privation and real category mistakes; that it entails a distinction between characterizing and non-characterizing fundamental facts; and that it generates multiple orderings of naturalness, which, I suggest, has further applications. In the third paper, I apply a version of this view to improve sparse modalism, the view that analyzes concepts of essence in terms of necessity and naturalness. In the fourth paper, I defend positionalism, the view that takes positions to be irreducible aspects of the internal structure of non-directed relations. I formulate two main versions of this view and argue that they can accommodate relations with any symmetries.
