We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is (...) continuous in model class topology). (shrink)

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.

Klein’s Erlangen program contains the postulate to study thegroup of automorphisms instead of a structure itself. This postulate, takenliterally, sometimes means a substantial loss of information. For example, thegroup of automorphisms of the field of rational numbers is trivial. Howeverin the case of Euclidean plane geometry the situation is different. We shallprove that the plane Euclidean geometry is mutually interpretable with theelementary theory of the group of authomorphisms of its standard model.Thus both theories differ practically in the language only.

The monograph of Jacek Zieliński, The Concept of Creatio ex Nihilo in the Thought of the Greek Apologists of the 2nd century, published by Wroclaw’s Atut in 2013, discusses an important problem of the theory of creation from nothing. It also asks an important question, how far the elements of the concept, articulated in its final form only by Augustine of Hippo can be found in the writings of the Christian apologists of the 2nd century. It is an important question, (...) especially that the Bible in its canonical form, the early extra-biblical Jewish literature or – even more – Greek tradition does not unambiguously advocate the concept creatio ex nihilo. Hence the question how, when and why the concept was articulated, since it played such an important role in the Christian thought of later centuries. In addition, the book of Jacek Zielinski is important in Polish market, because there are only a few serious publications dealing with the issue. The article gives a description and short analysis of the book, pinpointing its strong sights and showing areas, which could be strengthened in this and — hopefully — following publications on creatio ex nihilo by Jacek Zieliński. (shrink)

The article refers to the issue of freedom from a philosophical perspective. First of all, it discusses Plato’s metaphor of the cave in Politeia, in which the philosopher writes of freedom in its individual and collective forms. Then the article indicates how the metaphor was read by such contemporary philosophers as Martin Heidegger and Hannah Arendt, who interpret Plato’s metaphor from existential-phenomenological and political perspectives. Heidegger stresses the freedom of a human being, who in the light of the subjective existential (...) experience begins to live objectively in an authentic way. He frees himself up from the impersonal-I. A person, who experienced the truth as un-concealment, is not enslaved anymore to the impersonality of the crowd. He is able to face his own mortality and to take responsibility for his own fate. A special expression of freedom is shown in his care for others, even if it means risking one’s life. Hannah Arendt interprets Plato’s metaphor from the perspective of political philosophy. Her assessment becomes some kind of memento. What if the prisoners of the cave simply do not want to leave their place? Does the philosopher have a right forcefully to pull them out of the cavern? What is better, the attitude of Socrates, who dialogues with people or the attitude of Plato, who simply lectures the mob? In this way Arendt refers to the concept of freedom, as it is sketched in Plato’s cave. At the same time, she argues with Heidegger’s interpretation of the Platonic metaphor. Heidegger stresses the freedom of a human being, who in the light of the subjective existential experience begins to live objectively in an authentic way. He frees himself up from the impersonal-I. Human, who experienced the truth as un-concealment and freedom, is not enslaved anymore with the impersonality of the crowd, which reject individualism and authenticity. He is able to face his own mortality and to take responsibility for his own fate. A special expression of so understood freedom is shown in his care for others, even if this way he risks his own life. Hannah Arendt interprets Plato’s metaphor rather from the perspective of political philosophy. Her assessment, rooted in the very foundation of the political-philosophical thought becomes some kind of memento. What if the prisoners of the cave, simply do not want to leave their place? Does the philosopher have a right to forcefully pull them out of the cave of shadows? What is better, the attitude of Socrates, who dialogues with people and treats them as equal partners or the attitude of Plato, who simply lectures the mob? (shrink)

The article analyzes the concept of universal scope of salvation in the thought of Friedrich Schleiermacher especially with the references to his early Speeches on Religion and the later treatise The Christian Faith. It moves from Schleiermacher’s understanding of religion per se to his soteriological and eschatological theories. It can be said that he understands the nature of religion apophatically as the feeling and intuition and points to an aspect of mystery, which religion contains. He rejects in the Speeches on (...) Religion the anthropomorphic understanding of God and speaks of God-universum. Finally, in the treatise Christian Faith, he reinterprets the theological concept of the original sin and depravation, and points to a natural process of development of humankind from the Godless-consciousness to the God-consciousness. This leads the German thinker to universalistic beliefs. From the Protestant-reformed tradition Schleiermacher adopts the concept of predestination. However, he rejects the so called “double predestination” to salvation and condemnation. According to him, all people are chosen to be saved “in Christ”. This way, Schleiermacher continues the Reformed tradition, however he understands the election in the universal categories. He rejects the God, who choses for salvation only some people, but accepts God-universum, who maintains the unity of humanity and leads people to the perfect, eschatological communion. In the convictions pointing to the final unity of humankind, Schleiermacher exposes his deep humanism. He assumes that it is impossible to reconcile the traditional view of the eternal hell with God’s love. Divine punishment can serve as an aspect of overall paidagogia, leading to the maturing of humanity. However, it cannot be understood as a retribution, based on God’s wrath and cruel lex talionis. Such an understanding of God is for Schleiermacher unacceptable. (shrink)

This article analyzes the notion of apokatastasis, first as it appears in the Greek philosophical tradition and then in the context of Christian thought. It shows how the cosmic theory of eternal return unfolded within early currents of Hellenic philosophy, and subsequently how the personal dimension of apokatastasis grew out of those traditions, where questions about the fate of humanity became primary. The article then points to the fundamental philosophical assumptions of apokatastasis in its cosmic and personal forms. Christian thought, (...) in the process of its evolution, made significant use of Greek methodology and concepts. One of the theories transferred to the Christian context concerned the notion of universal salvation (apokatastasis). Such thinkers as Origen, Gregory of Nyssa and John Scotus Eriugena developed the concept into its mature form. Although apokatastasis has been condemned on numerous occasions, it has survived in Christian teaching. From a secular perspective, it can be regarded as a symbol of the equity of all people, beckoning us in the direction of the notion of religious inclusion. As such, it ought to be construed as translating into respect and care for the other person sic et nunc. (shrink)