This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group:,,, ⌜∨ ☐q⌝,and for any n > 0 a formula ⌜ ∨ ⌝, where has not the atom ‘q’, and and have no common atom. We generalize Pollack’s result from [12],where (...) he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities. (shrink)

This chapter focuses on the aims and challenges of the creative ageing policy. It tries to provide an integrated summary of discussions undertaken in the field of the arts and ageing. The chapter also underlines associations of this discourse with health care, social services, and other topics such as social and technological innovations for ageing societies.

The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.

Argumentem indukcyjnym w retoryce jest paradygmat ; paradygmat jednak nie polega na przechodzeniu od wielu szczegółowych przypadków do pewnego uogólnienia, czyli uniwersalizacji wszystkich poszczególnych przypadków — jak normalnie w argumentacji z indukcji — lecz jest przejściem od jednego szczegółu do szczegółu innego, podobnego, przy czym wymaganym warunkiem jest to, że jeden i drugi konkretny przypadek należą do tego samego rodzaju. Paradygmat zatem nie jest indukcją w znaczeniu ścisłym, ale wydaje się bardziej spełniać warunki analogii. W artykule zostaje sformułowana teza, że (...) u Arystotelesa występują trzy rodzaje wnioskowań: dedukcja, indukcja i wnioskowanie z przykładu; dla zaprezentowania specyfiki wnioskowania przez paradygmat są także analizowane różne typy wnioskowań, tzn. sylogizm apodeiktyczny, dialektyczny, indukcyjny, aby na tym tle wykazać odrębność wnioskowań przez paradygmat, które wydają się być pewnym rodzajem analogii. Prezentowany więc artykuł jest próbą podania charakterystyki i specyfiki argumentacji przez paradygmat u Arystotelesa w świetle jego Retoryki oraz pism logicznych. (shrink)

The aim of this essay is to create a coherent theistic model of a solution to the problem of evil. To this end, it is shown that the differences in Kierkegaard’s and Plantinga’s accounts of the problem of evil can be reconciled if looked at from a broader theistic perspective. This requires, on the one hand, that Plantinga’s immanent and logical vision be extended to include Kierkegaard’s spiritual and existential view of evil, and, on the other hand, that a correction (...) be made to Kierkegaard’s view thereof, as a result of the way in which Plantinga presents the relationship between good and moral evil in the world. Consequently, in Plantinga’s Free Will Defense the existence of God is consistent with the existence of evil, not because God has a reason to permit evil in the world, but because evil as a real element of the temporal world does not come from God. In Kierkegaard’s Free Spirit Offense, in turn, the interpretative model applied demonstrates that the existence of moral good must be independent of the existence of spiritual evil, for otherwise the moral evil of immanence would not be able to be forgiven by the spiritual good of transcendence. (shrink)

Unitary, irreducible representations of the proper, orthochronous Lorentz group comprise the main series and the supplementary series. The main series is spanned by the complete set of eigenstates of the self-adjoint Casimir operator C 1=−(1/2)M μν M μν , where M μν are generators of Lorentz transformations. The supplementary series has no such interpretation; moreover it is spurious from the point of view of functional analysis as it does not enter into the integral representation of an arbitrary test function. The (...) author describes the physical context within which the supplementary series arises, nevertheless, in a natural way: it arises if we exponentiate a massless scalar quantum field living in three-dimensional de Sitter space-time and if the appropriate coupling constant is small enough. (shrink)

In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...) courses in logic can be used for testing arguments with strict implications, strict equivalences and other operators which may represent connectives from natural language. (shrink)

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.