Anna Pietryga

Tradycyjna sylogistyka proponuje wysnuwanie wniosku o relacji między dwoma zbiorami z dwóch przesłanek kategorycznych, z których każda stwierdza coś o relacji łączącejjeden z tych zbiorów z trzecim (którego nazwa stanowi tzw. termin średni). Od średniowiecza znana jest metoda sprawdzania poprawności formalnej sylogizmu na podstawie wnikliwej oceny jego składni, a od XIX wieku również metoda graficznego przedstawiania przesłanek na diagramie Venna dla trzech zbiorów, których wzajemne relacje stanowią temat sylogizmu. W diagramie tym pewną trudność stanowi pojawiająca się w wielu przypadkach niepusta suma obszarów. W przedstawianym artykule proponuje się nową metodę przedstawienia przesłanek sylogizmu, polegającą na prezentacji obszarów, w których mogą lub muszą według przesłanek znajdować się elementy zbiorów, i tych obszarów, które z pewnością są puste. W szczególności dla niepustej sumy obszarów proponuje się wykorzystanie relacji rotalnej między dwoma obszarami tworzącymi niepustą sumę i możliwe ujednoznacznienie tej relacji przez wskazany w przesłance pusty obszar diagramu. Rotal relation and an empty region as a tool for deciding the validity of traditional sylogism moods as exemplified by selected third figure ones Traditional syllogistics sugests inferring a result about the binary relation between sets from the two categorical premisses each of which state something about a relation between one of them to a third set (whose name is called the middle term). Since the Middle Ages it is known how to check the formal correctness of a syllogism by the detailed analysis of its syntax, and since the 19th century also how to present the premisses graphically on the Venn diagram for three sets, whose mutual binary relations consttute the subject of syllogistics. The non-empty sum of subregions is sometimes not very comfortable to deal with. In the paper a new method is described for presenting syllogisms premisses, which consists in indicating the subregions, in which the premisses say some elements may or have to be located and those subregions which are announced empty. In particular, for the non-empty sum of two regions the rhotal relation is suggested together with the the possible corresponding empty region, had it been suitably indicated by one ot he premisses.

The formal principle of inconsistency in logic, in the form in which it comes from Aristotle, asserts that two contradictory judgments are not both true. Since the 20th century logic has progressed towards ever higher formality, it might be more suitable to say that inconsistent sentences, rather than judgments, cannot be both true.1 The universally accepted and lectured classical calculus of sentences2 adopts this principle without reservations. Some of the more recent logical systems are limiting the scope of its applicability, and also the natural language in which we daily express our judgments and inferences accepts in some cases a simultaneous occurrence of contradictory sentences. This text sets out to present a brief and simplified outline of this state of affairs. The systems of logic that accept inconsistencies and the related issues concerning natural language will be presented against the background of classical logic.

”The Logic of Complementarity” by Costa and Krause is a system of paraconsistent logic designed for theories that include complementary descriptions of their fields, which are considered to be a source of contradiction. In fact, in such cases contradictions arise not due to complementarity itself, but as a result of a taciturn agreement on semantics. For this reason, it may be proposed that a modification of lexical semantics of the complementary descriptions is needed as an addition to the new consequence introduced in the logic of complementarity.

There is no need to introduce Gottfried Wilhelm Leibniz, a great philosopher, theologian, diplomat, creator of the infinitesimal calculus and founder of the Academy of Sciences in Berlin. He also planned the development of the so-called Lingua characteristica. Literally taken, the name of the language means a language of letters, a graphic language, also called a characteristica universalis. It was meant to be a way of expressing meanings, as modeled after methods used in arithmetic and geometry and having unusual properties.

The works by Graham Priest that I'm most familiar with are those of the 1980’s. I understand they belong to the logical part of his writing, as presented by the organizers of the “Towards Graham Priest” meeting at Szczecin University on 20 June, 2012. Myself, I read Priest’s works to be imprecise, to say the least. Thelack of precision is to be traced particularly in his interpretations of Alfred Tarski’s heritage. This applies to Tarski’s main points, namely: semantically closedlanguages, the T-scheme, and the appreciation of natural language. The strange thing about it is that Priest does not mind other people expressing views opposite to his own, but admits he cannot determine which contradictions are true and gives only vague indications about how to judge the criticisms.