Sesto Empirico e la dimostrazione matematica: momenti di una ricerca

Ancient Scepticism, particularly Sextus Empiricus’s Scepticism, gives us some passages about the conception of geometry and arithmetic: these are relative things, like the demonstration, and nothing is certain, not even the demonstration of the non-existence of demonstration. Although this, Greek Scepticism remains supported by realism: this realism can be a starting point for the thought. Some centuries later, skepticism appeared again: between the XVII and the XVIII centuries and between the XIX and the XX centuries, skepticism joined the sciences differently. It seems impossible, nowadays, to deny the way Skepticism helps empirical research. Still, it is difficult to defend a position that might fall in an extreme negation of possibilities of knowledge. The solution can be to resume ancient realism, in the perspective of ancient Sophia, in a dialogue between sciences and philosophy which maintains the common reference to reality