Thiago Xavier de Melo

In this paper, I develop two versions of naı̈ve positionalism, the view that an n-adic relation has at most n positions and applies to some objects under an assignment of its positions to these objects. I argue that both versions can escape the problem of limited symmetries, raised by Kit Fine and Maureen Donnelly against naı̈ve positionalism. More specifically, I show that the problem of limited symmetries assumes that each application of a relation to some objects corresponds to one relational state, and I develop many-one positionalism, according to which many applications correspond to just one state whenever the nature of the relation determines that they are necessarily co-obtaining. Moreover, I develop a second version, localist positionalism, according to which, even though the number of applications and of relational states are the same, the identity of applications is determined locally by a symmetry structure that is part of the nature of the relation. Orthogonal to the distinction between the two views above, I also draw a distinction between structuralism and platonism about the identity of positions, and I argue that even though structuralism can provide a distinctive account of the symmetry of some relations, to account for all relations, any of these views on positions is better if combined with one of the two versions of positionalism above.

I develop and defend a new theory of naturalness according to which relations can be natural to different degrees relative to their different positions. Set-membership, for example, is more natural relative to its set-position than to its member-position. I call this view position-relativism. The alternative view, position-absolutism, implies that existential derivatives of the same non-symmetric relation—such as being a member of something, and having something as a member—must always have the same degree of naturalness. But this is false. Position-relativism avoids this problem and promises to do more.

I develop a theory of naturalness according to which properties are natural relative to categories of objects. This new theory avoids a problem that, I argue, afflicts standard theories: whereas standard theories allow for only one ordering of properties, considerations of the similarity and dissimilarity made by some negative properties—like having no parts, having no members, having no determinate mass, reflecting no visible light—require admitting more than one. Additionally, I argue that my view accounts for genuine categories, category mistakes, and negation as privation, and that it accounts for a distinction between characterizing and non-characterizing fundamentality.

According to sparse modalism, the notion of essence can be analysed in terms of necessity and naturalness. In this paper, I develop and defend a version of sparse modalism that is equipped with a non-standard, relativized conception of naturalness. According to this conception, properties and relations can be natural to different degrees relative to different kinds of things, and relations can be natural to different degrees relative to different slots. I argue that this relativized version of sparse modalism can accommodate various cases that the standard, non-relativized version can’t. The alternative version can accommodate cases where a relation is essential to a relatum but merely necessary to another, cases where a property is essential to an object but merely necessary to another, and cases where a less-than-perfectly natural property is essential to an object.