In my dissertation, I analyze primitive numerical individuation. According to classical Haecceitism, there are non-qualitative facts of the world that are not analyzed, determined, or reduced to qualitative facts of the world. One of the typical non-qualitative facts is an exemplification of a non-qualitative property, a haecceity or thisness. Thisness is often described as the property of being identical with a particular entity. I argue, instead, that there is another way to understand thisness, thisness in terms of numerical individuation, as a property of being numerically individuated as a single individual. Unlike the classical understanding of thisness via identity, this thisness is not an essential property of a particular entity. This thisness purely individuates an entity. It neither constitutes any characteristics of the entity nor explains what the entity is. For an entity to exemplify this property means that it is counted as a single individual. Haecceitism with this thisness implies that the existence of an entity as a single individual and the number of individuals in a world should be primitively and fundamentally given. Numerical individuation minimally requires two processes, singling out an entity from others and avoiding double-counting. There are many ways to avoid double-counting. One of the easiest ways is to eliminate the singled-out entity. We don't need any information as to which entity is which when singling it out and/or eliminating it. Numerical individuation can be determined independently of the process of identifying entities.

There is a fact of the matter in a world that can be revealed by the existence of mere numerical individuation, a symmetrical and irreflexive relation: for a relation R, R(x, y) & R(y, x) where x≠y. Consider any indiscernible but numerically distinct entities as standing in the symmetrical and irreflexive relation. This fact of the matter is determined only by the primitive numerical individuation of the relata. One important and opposite theory to this kind of primitive individuation has been a reductive analysis of individuation in terms of the intrinsic qualities of an entity. Recently, another kind of reductive individuation has been proposed, structural individuation. This kind of individuation is developed from a radical version of structuralism that maintains a structure/relation has ontological primacy and objects are ontologically secondary in the sense that an object's individuation is derived from its standing in the structure/relation. However, I argue that even a purely structuralist entity, such as a graph, requires the ennumeration of its nodes/vertices, in addition to the relational descriptions of vertices, in order for the graph to be determined. I also argue that any attempt to establish a metaphysical language without terms, variables, or quantifiers, seems to fail in that it seems impossible to get rid of one of the semantic roles of a variable, its encoding the sameness or distinctness of an individual for predicates to apply. Numerical individuation still appears to be one of the nonreductive fundamental facts of the world.