Property modifiers and intensional essentialism

Abstract

In this paper, I deal with property modifiers defined as functions that associate a given root property P with a modified property [M P]. Property modifiers typically divide into four kinds, namely intersective, subsective, privative and modal. Here I do not deal with modal modifiers like alleged, which appear to be well-nigh logically lawless, because, for instance, an alleged assassin is or is not an assassin. The goal of this paper is to logically define the three remaining kinds of modifiers together with the rule of left subsectivity that I launch as the rule of pseudo-detachment to replace the modifier M in the premise by the property M* in the conclusion, and prove that the rule of pseudo-detachment is valid for all kinds of modifiers. Furthermore, it is defined in a way that avoids paradoxes like a small elephant being smaller than a large mouse.