Frege's objects of a quite special kind

Abstract

In his article '?ber Begriff und Gegenstand' (BG) of 1892 Frege treats expressions of the form "the concept F" as genuine proper names which designate "objects of a quite special kind". He claims that, if we wish to assert something about a (first-level) concept F and to express this in the form usual for such assertions, the concept must first be represented by such an object, as in the sentence "The concept prime number is not empty". In addition, he points out that the two sen? tences (I) "There is at least one square root of 4" and (II) "The concept square root of 4 is realized" express the same thought. In (I) we have an assertion about a (first-level) concept that preserves its predicative nature, whereas in (II) something is (allegedly) asserted about an object. The assertion that something is realized as the word is being taken in (II) "can be truly made only about objects of a quite special kind, viz. such as can be designated by proper names of the form 'the concept F'" (KS, p. 174, TF, p. 50). Earlier in his book Die Grundlagen der Arithmetik (GLA) of 1884, Frege had expressed his belief that in the definition "The Number which belongs to the concept F is the extension of the concept equinumerous with the concept F" one could say for "extension of the concept" simply "concept" (GLA and FA, p. 80n). I refer to this substitution by means of "Sub". Sub yields an alternative definition of the term "the Number of the concept F". Now Frege's motive for considering Sub was obviously this: he realized that his explicit definition of "the Number of the concept F" rested on the question? able assumption that we intuitively know what the extension of a concept is.1 At one place in BG Frege mentions the alternative definition of "the Number of the concept F"; he does so in the course of repudiating one of the objections which Benno Kerry had raised to his use of the word "concept":