49(2013)1 
Papers

Janusz Wesserling Edward Nieznański
On the concept of truth in an intended model of the logic of beliefs
Summary
First of all the article looks at the building of an a posteriori logic of beliefs i.e. observation developed on the principle of how, people usually think, what kind of judgments they make about reality and what actually is described by the truth of the judgments under the influences of beliefs. In this situation, we have to depart from the customary practice of a priori semantics of possible worlds in favour of semantics for models intended. Secondly, we find that in practice, human judgments indirectly accept a logic of thinking generally, which leads us  thirdly  to define this logical system as an extension of intuitionistic logic. Fourthly, and finally, our empirically generated logic of beliefs, proves to be logic of hypotheses and suppositions, because judgments made on the basis of intuitionistic logic are not assertive judgments.

47(2011)1 
Dissertations

Edward Nieznański
World models in formalized systems of theodicy
Summary
The article illustrates various images of the world described by selected formalized systems of theodicy. The first of the formalizations discussed reconstruct the argument ‘ex motu’ and present reality as a finite chain of the relation of moving. They also indicate the existence of ‘primum movens’ or ‘movens immobile’. The idea of a chain was questioned by Francesca RivettiBarbo, who regarded the coherence axiom in the relation of moving as false. Peter Geach suggested, however, that the relation of becoming of the later material world from the previous ones was total. This relation is a chain. Korneliusz Policki advocated the view that the world is a partial order of the relation of moving. Also, he used the KuratowskiZorn lemma in proving the existence of ‘primum movens immobile’. RivettiBarbo and Ivo Thomas viewed the world as a multiplicative quasi halflattice. Kurt Gödel assumed that the world is Boole’s algebra, in which the generator of the ultrafilter of positive attributes is ‘summum bonum’. Finally, there were formalizations presenting Leibniz’ world which is governed by the principle of the sufficient reason of being. 
47(2011)4 
Science versus Utopia. Limits of Scientific Cognition

Edward Nieznański
On notions of assertion, knowledge and opinion in epistemic logic
Summary
In the article there is presented a formalized theory in frame of which there are compared three stages of convictions (S – I am (firmly) convinced, D – I admit, P  I suppose), W operator understood as “I know, that” and M operator reads as “I believe, that”. The theory is characterized both on syntactic and semantic level. In frame of a syntactic description there are noticed certain logical square connections between S and D, e.g.: S(p) is contrary to D(Np) and S(p) is opposite to S(Np). S(Np) is contrary to D(p). Expressions: D(p) and D(Np) are subopposite. Operators P and S are introduced axiomatically. Operators D, W, and M are characterized by definitions, which are understood in the following way:
Def 1: I admit, that p iff I am not firmly convinced, that not–p
Def 2: I know, that p iff p and I am firmly convinced, that p
Def 3: I believe, that p iff I suppose that p and I admit, that not–p.
On semantic level we consider a structure (T, <, ≤ ), where T is a set of time points, < is a relation of being earlier than, and ≤ is a relation of being not later than. 
46(2010)2 
Dissertations

Edward Nieznański
Third Way with double quantification
Summary
In the paper there are introduced two kinds of quantifiers, each of which includes different scope of the changeability of variables. The matter is expounded in two parts: first, it is described a language with the double quantification, second, a formalized theory of the Absolute is constructed. Using philosophical inspirations of St. Thomas Aquinas and Leibniz the aim of the discourse is to determine logical and ontological grounds for the acceptance of the fact of the existence and the uniqueness of the Absolute.


