Abstract

In the dissertation I seek to clarify an aspect of Frege's thought that has been insufficiently explained in the literature, namely, his notion of logical object. It is well known that the core of Frege's philosophical enterprise up to Grundgesetze der Arithmetik was the reduction of arithmetic to logic. Since Frege regarded numbers as objects, logic must have an ontological basis, i.e., an adequate class of objects to which numbers are reducible. These objects are, for Frege, extensions of concepts and truth-values. ;In the dissertation I adduce some elements of Frege's philosophy that elucidate why he saw these as natural candidates for paradigmatic cases of logical objects. In particular, I argue 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. First, I try to explain what are the general criteria for qualifying objects as logical, and why extensions of concepts have to be seen as the paradigmatic case of logical objects according to these criteria. There is, in my view, a connection between Frege's view on this topic and the famous thesis first formulated in ""Uber Begriff und Gegenstand " that "the concept horse is not a concept." ;Next, I examine Frege's introduction of truth-values as objects in his writings from 1891-92. As I shall argue, Frege's ontologization of truth-values is basically motivated and justified by the technical advantages that this step brought for the formalism of Grundgesetze der Arithmetik. ;Finally, I examine Frege's arguments in section 10 of Grundgesetze der Arithmetik, since this is the place in Frege's writings where extensions and truth-values are identified. I argue that Frege did not mean to employ a generalized version of the context principle in this section. Moreover, I argue that there is no incompatibility between Frege's procedure in this section and his realism regarding mathematical entities