Olav Asheim: What is the concept horse if not a concept?

In this paper I look at Frege’s theory of concepts as functions, but also his categorical divide between concepts and objects. I discuss his paradoxical statement that «The concept horse is not a concept», employing his logico-semantic theory as a background. What is clear from Frege’s writings is that he sees an important difference between talking about an F and talking about the F (where «F» is any common noun). Used with the indefinite article and the copula, as is the second occurrence of the noun «concept» in Frege’s statement, it functions as a predicate, whose Fregean Bedeutung (reference) is always what Frege calls a «concept»; used with the definite article, as is the first occurrence of «concept» in Frege’s statement, it functions as a singular term, whose Fregean Bedeutung is always an object and therefore not a concept. The consequence of this is that it is impossible to refer with a singular term to a concept and thus for Frege to say what he intends to say. I go into this in some detail and also discuss the connection between Frege’s view of concepts as not being objects and his disastrous basic law V. In conclusion I concentrate on the question of which kind of object the singular term «the concept horse» actually refers to in Frege’s view. I reject the widely accepted answer that it is the extension of the concept word «horse». Rather, I propose that it is something that has no special place in Frege’s semantical ontology.

Keywords: Gottlob Frege, concept and object, basic law V, Russell’s paradox, the methexis problem, the ineffable