Jari Palomäki

There are three conditions which an item has to fulfill in order to be listed into an inventory. Based on those three conditions, the logically basic entities are introduced: they are points, sets, and collections. These logically basic entities are related with three different logical relations, i.e., “is an element of”, “is a subset of”, and “is a part of” –relations, to constitute concepts. Those three logical relations have different relational properties, and thus they are to be distinguished. The logically basic entities are said to exist whereas the concepts constituted by them are said to subsist. One of the most important results is that we should not mix two inventories together, since otherwise inconsistencies follow.

In this paper three different solutions to Grelling’s paradox, also called the heterological paradox, are given. Firstly, after given the original formulation of the paradox by Grelling and Nelson in 1908, a solution to this paradox offered by Frank Plumpton Ramsey in 1925 is presented. His solution is based on the different meanings of the word “meaning.” Secondly, Grelling himself advocated the solution proposed by Uuno Saarnio in 1937. Saarnio’s solution is based on the exact definitions of the concept of word, and the concept of denoting. Thirdly, a solution to this paradox was proposed also by Georg Henrik von Wright in 1960, but his solution consists of saying that the word “heterological” does not name a concept—or it names a concept only up to a singular point.