GABRIEL PEDROSA DÓRIA

The formalist project aims to rethink theories by eliminating intuition, adopting a rigorous formal method of proof. Not only mathematicians followed the idea proposed by David Hilbert, but also theorists from the most different areas, from the most theoretical to the essentially empirical. Thus we rewrite theories on purely logical bases. It seems that Gödel has arrived to put an end to this project's biggest aspirations! This is proof that logic and all formal systems arising from it can be incomplete. The discovery of certain judgments that are not deductible. Is this a limit to the formalist project or its complete decline and failure? How far can we go using axiomatics to base the most diverse types of theories? The proposal is not only to study the proof of Gödel's incompleteness theorems, but also its philosophical implications for the formalist project in the sciences. Will we really have a future impasse and a limit to the use of the formal axiomatic method? We will try to find out.