Andrzej Szostek believes the new evangelization to be one of the most important tasks of the modern catholic church. He reminds as that Poland in 15th century was a very tolerant country for people of various religious denominations. The modern catholic church should base on this tradition and strive for humanity and more universal outlook. The idea of the new evangelization is an essential message involved in the Gospel.

Basic theses of the article are the following: 1) Politics is inexplicable without relating it to the category of commonweal. 2) Acceptation of this category has some philosophical and ethical implications: it involves universalism, rationalism, personalistic character of participation. Finally, politics is defined as,,a wise endeavour after commonweal”.

In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin's Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.