What is the Task of Frege’s Criteria of Referentiality?

Abstract

It is generally assumed that Frege’s solution to the problem of referential indeterminacy in the first volume of Grundgesetze is based on a contextualist conception of reference that is spelt out by his criteria of referentiality. The present paper argues that this assumption is hardly consistent with Frege’s remarks on the task of the criteria in the second volume. They leave no doubt that the criteria are not to be understood as explanations of the concept of reference, but as explanations of the requirement that in the exact sciences all concepts must have sharp boundaries. The crux of the problem of referential indeterminacy is that, to sharply delimit the boundaries of a vague or ambiguous concept, we have almost only concepts at our disposal that also lack sharp boundaries. To solve it, we need a non-inductive method for the complete determination of concepts. It is provided by Frege’s criteria of referentiality. They define a kind of “holistic” method for the complete determination of concepts according to which vague and ambiguous concepts must be completely determined in a reciprocal manner