ETD

• Alfred N. Whitehead
• axiom of reducibility
• Bertrand Russell
• Cantor
• Frank Ramsey
• Gottlob Frege
• logic
• logicism
• logicist thesis
• mathematics
• paradoxes
• Principa Mathematica
• ramified theory of types
• Richard's paradox
• Russell's paradox
• set theory
• theory of types

This dissertation aims to explain Russell's ramified theory of types. Beginning with the explanation of the situation of the mathematics at the end of the XIX century - focusing in particular on Cantor's set theory and on the logicist thesis -, the author paints the situation of the emerging of the paradoxes that generated the crisis of the foundations of mathematics, and illustrates the attempt made by Bertrand Russell in order to overcome this difficulty. The dissertation firstly discusses the simple theory of types, and then analyzes the ramified theory and the reasons that brought Russell to its elaboration: the aim of the work is clarifying such a complicated theory. Finally, the author explains the historical reasons of the rejection of the theory.