The work has two parts. The first part is about Peirce and his ideas about the continuum. There are considered the connection of his theory of continuity with his loic and his philosophy.

In the second part Peirce's ideas are compared with models of todays logic and mathematics. There is considerd constructive mathematics, the logic of perception from Bell, Blau's Logic of reflection and a model of Myrvold. Then there is developed a new model.