Ideal objects as models in science

Three main concepts of model in science are distinguished: (1) semantical model of a theory; (2) real model of another real thing; (3) mathematical model of a real thing. The last concept is the most important for the empirical sciences. The mathematical model is not identical with a theory: it is an ideal object which is directly described by the theory. We have here an intermediate level between reality and theory.     

From the Profession

Studies in East European Thought -     

Three contributions to the two-valued propositional calculus

Summary Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions. This paper appeard orginally under the title “Trois contributions an calcul des propositions bivalent” inStudia Societatis Scientiarum Torunensis, Toruń, Polonia, Sectio A, vol. I (1948), pp. 3–15.     

Concerning axiomatizability of the quasivariety generated by a finite Heyting or topological Boolean algebra

In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked in Rautenberg [10].     

Systemy S4 I S5 Lewisa a spójnik identyczności

Allatum est die 28 Septembris 1970     

O klasach normalnych i nienormalnych na terenie języka potocznego

Problematyka i glówne tezy tej pracy pochodz od pierwszego autora. Udzial drugiego autora sprowadza sie do propozycji utosamienia jeezyka potocznego z formalizmem logiki zda i logiki nazw oraz do pewnych sugestii odnonie systematyzacji materialuAllatum est die 2 Octobris 1965