We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract (...) properties and are preserved and reflected by translations under suitable conditions. (shrink)

The paper presents Polish culture from the X century to the present time inspected from a special perspective, namely that determined by the opposition universal-native. It is shown that in Poland the native, at times slightly modest artistic styles and forms as well as the more cosmopolitan and universal European trends always served the best-possible expression of the essence of the Polish people and their national traditions, unbrokenly preserved over ages.

The aim of the paper is to determine why copernicus made a personal seal of the ancient intaglio with the image of apollo playing a lyre, A representation illustrating the myth of phoebus the sun-God and his music as the source of the harmony of the universe. The reasons seem to be: a remarkable role played by the ancient opinions concerned with the harmony of the world in the creative process of copernicus' cosmological theory (his acceptance of "plato's axiom"), The (...) fact that in his theory the sun became the centre of the universe, And that a harmony of sounds, Supposed to be produced by the spheres moving under the rule of phoebus' music, Became--In his opinion--The real although not acoustical harmony of the simple circular spheres on which planets move in a uniform way around the sun. (shrink)

In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model theoretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of interpolation and definability, as they appear in the literature of institutional model theory. Both case studies illustrate a considerable extension of the original scopes of the two classical (...) theorems. Our presentation is rather narrative with the relevant logic and institution theory concepts introduced and explained gradually to the non-expert reader. (shrink)