Marco Ruffino

The purpose of this paper is to discuss Frege’s view on vagueness, and to draw some relevant consequences of it. By examining what exactly Frege has in mind each time he complains about vagueness and advocates the sharpness requirement, I argue that he shows preoccupation with different kinds of vagueness in different periods of his thought. I also discuss the scope of the sharpness requirement, and argue that it is intended as applying primarily to mathematics and logic. Finally, I try and argue that some of Frege’s remarks on incomplete functions suggest a view that is close in spirit to the contemporary supervaluationist approach to vagueness

In this paper, I seek to clarify an aspect of Frege's thought that has been only insufficiently explained in the literature, namely, his notion of logical objects. I adduce some elements of Frege's philosophy that elucidate why he saw extensions as natural candidates for paradigmatic cases of logical objects. Moreover, I argue (against the suggestion of some contemporary scholars, in particular, Wright and Boolos) that Frege could not have taken Hume's Principle instead of Axiom V as a fundamental law of arithmetic. This would be inconsistent with his views on logical objects. Finally, I shall argue that there is a connection between Frege's view on this topic and the famous thesis first formulated in ‘Über Begriff und Gegenstand’ that ‘the concept horse is not a concept’. As far as I know, no due attention has been given to this connection in the scholarly literature so far.