Frege's Category of Unsaturatedness

Abstract

Frege's category of unsaturatedness (incompleteness) is a central concept of his ontology. By means of it Frege divides the realm of all entities into functions and objects. In this paper I try to show some fundamental difficultes relevant to the concept in hand. First of all I am interested in difference between incompleteness of the propositional functions (especially concepts) and incompleteness of the non-propositional functions (particularly arithmetical functions). I also discuss a few other problems closely conected with the above, namely: 1) distinction between unsaturatedness of expressions and unsaturatedness of entities to which these expressions refer; 2) possibility of ontological and epistemological interpretation of incompleteness; 3) interpretation of Fregean semantical category of sense from Frege's dualistic ontology point of view.