This chapter analyses the philosophical views on mathematics and logic of scientists connected with the Cracow Centre, i.e. the views of Jan Sleszyński (his last name is also given by the Polish "Śleszyński"), Stanisław Zaremba and Witold Wilkosz. Let us add that for a certain period Zygmunt Zawirski and Leon Chwistek worked within the Cracow Centre. However, for several reasons (cf. Introduction) we have decided to discuss their works and views in the other chapters (namely, Zawirski's works in Chap.  3 and Chwistek's in Chap.  2).