Potrzeba uzasadnienia zdań w sensie logicznym pŀynie z faktu, iż uznają one swą funkcją stwierdzenia zachodzenie stanu rzeczy, wyznaczonego przez ich sens, i to zachodzenie niezależne od nich samych, a zarazem jako twory czysto sygnitywne (językowe) nie są zdolne pokazać bezpośrednio tego zachodzącego stanu rzeczy.Uzasadnienie pośrednie przez odwoŀanie się do innych zdań, które tymi samymi cechami się odznaczają i same z natury swej wymagają uzasadnienia, nie może być nigdy definitywne i jako takie domaga się uzupeŀnienia przez uzasadnienie “bezpośrednie”.Uzasadnienie (...) bezpośrednie może być uzyskane jedynie w aktach bezpośredniego doświadczenia, tzn. w aktach, w których przedmiot poznania jest dany samoosobiście.Należy odróżnić dwa rozumienia “uzasadnienia”:uzasadnienie “ontyczne”: jest nim zachodzący niezależnie od zdaniastan rzeczy zgodny w swej zawartości, formie i sposobie zachodzenia z tym, jakim go wyznacza uzasadniane zdanie. Uzasadnienie w tym znaczeniu jestbytową podstawą prawdziwości zdania i przez swe zachodzenie konstytuuje tę prawdziwość. Każdy sąd prawdziwy jest ipso facto w tym znaczeniu “uzasadniony”, a każdy w tym znaczeniu uzasadniony jest prawdziwy, ale “być prawdziwym” i “stanowić podstawę prawdziwości” zdania to dwie różne, choć przynależne do siebie sprawy.“Uzasadnienie” w rozumieniu pewnejoperacji poznawczej (“uzasadniania”) wykazuje zachodzenie stanu rzeczy będącego podstawą ontyczną prawdziwości pewnego zdania.Uzasadnianie przez odwoŀanie się do tzw. “doświadczenia” dokonuje się przy jednostkowych zdaniach kategorycznych a zarazem empirycznych przez odwoŀanie się do odpowiedniego spostrzeżenia zewnętrznego lub wewnętrznego, w którym przedmiot oznaczony przez przedmiot zdania uzasadnianego dany jest a zarazem spostrzeżony w cesze przypisywanej mu w danym zdaniu. Jednakże samo to spostrzeżenie nie wystarcza, trzeba bowiem dokonać na podŀożu tego spostrzeżenia przedjęzykowo przebiegającej predykacji, która dopiero prowadzi do utworzenia odpowiedniego zdania. Stwierdzenie tożsamości sensu zdania uzasadnianego i zdania utworzonego w procesie uzasadniania na podstawie wymienionych czynności poznawczych jest końcową fazą procesu, w którym dany sąd jednostkowy kategoryczny staje się empirycznie uzasadniony.W końcowej części artykuŀu omówiono szereg trudności, jakie przy uzasadnianiu sądów wzmiankowanego typu się nasuwają. (shrink)

Using a comprehensive quotation from a book of Władysław Krajewski a characteristic of moderate scientism (to be called scientism below) is given. That is the stance I share with Krajewski. I complement the characteristic presenting scientism as an approved by me "naive trust in science". In the main part of the paper I discuss, however, the limitations imposed by contemporary science on the traditional epistemological optimism of scientism.

Hermann Grassmann’s 1861 work [2] was probably the first attempt at an axiomatic approach to arithmetic. The historical significance of this work is enormous, even though the set of axioms has proven to be incomplete. Basing on the interpretation of Grassmann’s theory provided by Hao Wang in [4], I present its detailed discussion, define the class of models of Grassmann’s arithmetic and discuss a certain axiom system for integers, modeled on Grassmann’s theory. At the end I propose to modify the (...) set of axioms of Grassmann’s arithmetic, which consists in adding an elementary sentence and removing a non-elementary one. I prove that after this modification the only model of the theory up to isomorphism is the standard model. (shrink)

Primary object of interest of mathematicians can be identified as a „mathematical matter”, the concept analogous to „physical matter” or „biological matter”. The „mathematical matter” is the soil upon which mathematics grows. One can distinguish three levels of it: some abstract but not necessarily clear conceptions, operational notions (like number) but not necessarily openly defined, theories not necessarily axiomatic. The „mathematical matter” originates in the abstract reflection upon events and forms in time and space. Its important elements are notions formed (...) mostly in the process of idealization and/or abstraction. Once formed, notions usually evolve being, e.g., simplified or complexified. Mathematics is a mirror of the world, most abstract and therefore fundamental. Although it is a free activity of human mind, mathematics reflects some deep ideas (beauty, simplicity etc.) while most interesting notions come up in tension fields between pairs of poles: the notion of a function can be seen as a bridge connecting variability and immutability, while that of a limit – connecting finiteness and infinity. A fusion of freedom and internal restrictions leads to mathematics which is simple, beautiful and effective. (shrink)

Remarks on the handbook Logic and Argumentation by Andrzej KisielewiczThe paper contains some critical comments on Andrzej Kisielewicz’s handbook of critical thinking Logika i argumentacja. Praktyczny kurs krytycznego myślenia, Warszawa 2017. The comments generally refer to two main topics of the handbook: a the definite rejection of formal logic as a tool of critical thinking, and b the support for the so-called analysis of reasonable possibilities as an essential method of critical thinking. The paper shows that these topics are not (...) suf ficiently clearand the support is not convincing enough. (shrink)

As it is well known, Jan Lukasiewicz invented his three-valued logic as a result of philosophical considerations concerning the problem of determinism and the status of future contingent sentences. In the article I critically analyse the thesis that the sentential calculus introduced by Lukasiewicz himself actually fulfills his philosophical assumptions. I point out that there are some counterintuitive features of Lukasiewicz three-valued logic. Firstly, there is no clear explanation for adopting specific truth-tables for logical connectives, such as conjunction, disjunction and (...) first of all implication. Secondly, it is by no means clear, why certain classical logical principles should be invalid for future contingents. And thirly, I show that within Lukasiewicz logic it is possible to construct a „paradoxical” sentence, namely a conditional which changes in time its logical value from truth to falsity. This fact obviously contradicts Lukasiewicz's philosophical reading of his three truth values, according to which true sentences are already positively determined, false sentences are negatively determined, and possible sentences are neither positively, nor negatively determined. Above-mentioned facts justify in my opinion the thesis that Lukasiewicz's three-valued logic does not satisfy his philosophical intuitions. For this purpose more appropriate seems to be sentential calculus based on the so-called supervaluation. It is three-valued, non-extentional calculus, which nevertheless preserves all tautologies of the classical logic. At the end of the article I consider the possibility of introducing to this calculus modal operators. (shrink)

The mathematical Platonism is the most popular standpoint amongst mathematicians. The Platonism better than other conceptions explains the fact, that mathematicians discover some properties of the mathematical objects, which are independent of them and exceed the boundary of our intuition and experience. On the other hand Platonism generates some difficulties. In spite of this the Platonism is the idea worth the defence. In the paper I modify the traditional formulation of Platonism, which avoids some of the difficulties.

The paper is devoted to the history of considerations on the denotation of propositions, or on that which is denoted, or described by propositions. n the first part of the paper, aside to the views of ancient authors (Plato, Aristotle, Stoics) concerning this issue, the debate about the existence and nature of the denotation of propositions has been presented. It was alive especially in the later scholastic philosophy (two objectivistic standpoints – among others – Gregory of Rimini, and one subjectivistic). (...) The second part of the paper discusses the position of modern and contemporary authors, i.e. two ways with which the question of the denotation of propositions was reconstructed in the 19th century, the so-called Brentano’s schools (Twardowski, Meinong), Frege’s thought and his followers. The texts of many authors have been analysed in order to present (and compare) all the more important views in the question of the denotation of propositions, starting from antiquity until the contemporary times. (shrink)

The author begins by asking the question: what kind of justification, if any, can be given in support of a normative system? Within the category of normative systems he allows for a variety of theories, ethical and legal. The are cross-classified, in particular they are divided into open and closed systems with regard to their normative, axiological and informative content.

This article is the analysis of the logical system-E (entailment) proposed in work ‘Entailment’, vol 1 i 2 [1975, 1992] by R. A. Aderson and N. D. Belnap Jr. The First part presents a brief history of notion ‘entailment’ and the application of logical systems of entailment. The Second part contains any characterization of reasons of construction of this logical system. The Third part presents logical system-E, and the last part focuses on the weak points of this type of the (...) formalization of the relations between sentences of a formal language. The purpose of this paper is to explore and explicate the realtion of entailment from the point of view of a logical pragmatic. (shrink)

In the initial part of the article texts of some authors are analyzed concerning material implication. In the further part of the article the proposition is justified that the operator of material implication differs in quality from other truth-functional operators. The final part of the article is devoted to considerations aiming at presenting what the thesis of the classical propositional calculus, in which the main operator is the operator of material implication, denote.