Positive Universally Held Properties are Necessarily Universally Held

The well-known Principle of Plenitude has it that everything that exists in some possible world exists in the actual world. I argue for an amended version of this principle: If there’s a possible world in which something lacks some positive property, then there’s an object in the actual world that lacks that property. That is, all positive universally held properties in the actual world are necessarily universally held. This rules out that for some positive property, everything in the actual world merely happens to have it. After having presented and defended the argument, I show that it has a wide range of corollaries, such as that there are mereologically simple and composite things, physical and non-physical things, caused and uncaused things, and contingent and necessarily existing things. The argument has three premises. The first premise is the thesis that there are no things that do not exist. The second premise is a Fregean theory of linguistic meaning. According to the third premise, two meanings coincide if and only if their reference sets coincide. The notion of a reference set is defined in the paper