A noção fregiana de objeto abstrato e a crítica ao psicologismo

Abstract

The objective of this dissertation is to present Gottlob Frege s criticism of psychologism in Mathematics and Logic. Our working hypothesis is that Frege s criticism is based on his notion of an "abstract object". In order to investigate this hypothesis we will contrast the pre and post paradox phases of Fregean s philosophy. We will try to show that there is a continuity between these two periods, and that this continuity depends on Frege s insistence in maintaining the notion of an "abstract object", even if in a somewhat weakened version. Our dissertation will be divided into three chapters. In the first chapter, we will make a brief characterization of psychologism in order to circumscribe the exact focus of Frege s criticism. In the second chapter we will discuss the notion of an "abstract object" in the pre-paradox period of Frege s philosophy and its connection to Frege s main concern: that of defining number upon a pure logical basis. Eventually, in the third chapter, we will show how, even without a logically unassailable method of introducing logical objects, due to Russell s paradox, the philosopher does not give up his main theses concerning the nature of logic and mathematics. They are still grounded on the notion of an "abstract object", even thought in a somewhat feebler form.