Frege e Peano sullo status matematico e logico delle definizioni

This thesis has as its subject the logical and mathematical status of definitions. Starting from the end of the XIXth century and the beginning of the XXth century such status has been put into question: how should we define? Which should be the rules when defining? How many kinds of definitions exist? In such a context we can find two of the most influential authors of the discussion: Gottlob Frege, a German philosopher, and Giuseppe Peano, a known Italian mathematician. We will tackle the above questions with reference to these two authors inasmuch as they represent two of the most influential thinkers of their subject: Frege is often considered to be the father of analytic philosophy, the author who brought mathematical rigour into philosophical thinking. In his writings the questions concerning definitions played a crucial role. His standard for definitions, as we will see, were rigorous and precise. 
On the other hand we have Giuseppe Peano, a known and recognised mathematician from the university of Turin. Peano is often considered to be one of the greatest Italian mathematicians; very important are his works on his axiomatic system (Peano’s axioms), his Formulary and the foundation of his school. 
As we will see, these two thinkers often discussed about the logical and mathematical status of definitions. Starting from their letters we will see how and why their view differed. The epistolary exchange will acquire great importance in our inquiry. During my thesis I will then discuss the role of the letters in such a context: in the letters we can see a well-formed overview of the positions of the two authors. 
Moving then to their public writings we will see some ontological and epistemological matters about the status of definitions; in such writings we will find further analysis and developments. 
Furthermore we will focus on some kinds of definitions, like, in particular, definitions by abstractions. Such definitions were highly debated by most mathematical thinkers at the time. From the point of view of Frege and Peano we will see the genesis of such definitions and how they were used by them. A special case of definitions, the definition of the equality relationship, will be examined separately. Towards the end of my thesis I will show how such a symbol was problematic and source of discussion.