Economic growth is mostly explained by investments and employment growth. Since the mid 1990s various social categories have been introduced into the economic growth analysis such as trust, crime and income inequality etc. According to sociology and psychology, it is the family that constitutes interpersonal ties and is an indicator of happiness and quality of life. It can be said that happy people better fulfil their social roles and also work better. We set a hypothesis that the family ties have (...) an influence on economic growth. More precisely: the more divorces (compared to newly couples), the slower economic growth. This hypothesis was confirmed in an analysis of Poland’s economy in the years 1967–2006. Due to the disintegration of family ties measured by the above mentioned divorce rate Poland’s annual economic growth was slowed by about a 0.6 percentage point on average. This estimation is based on a GDP growth model which, along with the divorce rate, also includes employment dynamics, invest rate and crime rate. (shrink)

Inequality of incomes is one of the significant factors forming the social capital. Two views dominate among economists dealing with the influence of inequality of income on economic growth. On the one hand, a too low inequality of income does not motivate people to increase the labour productivity. A low inequality of income might result from an extended social care system and overloading GDP with social transfers. A good example of it may be a situation when the unemployed refuses to (...) accept a job offer and prefers the unemployment benefit rather to a slightly higher salary. Moreover, a lack of incentives for the employee who fails to acknowledge the economic sense of increasing the productivity of his work might lead to the slower growth of economy. On the other hand, a contrary view suggests that an increase of the inequality of income has a negative impact on the economy. The accumulation of wealth by a small number of citizens raises doubts about good use of that wealth for investments necessary for the growth of the economy. An excessive inequality of income is confronted with disapproval of the significant part of society and regarded as unfair and unjustified. It may also increase the crime level and decrease the trust and, more generally, lead to the weakening of social capital. The arguments above lead to a hypothesis that the influence of the inequality of income on the growth of the economy has a non-linear character. We confirmed this hypothesis in growth models of the US and Swedish economies. We assess the historically optimal inequality of income measured by the Gini coefficient at 46% and 24% for the US and Sweden respectively. The optimal inequality of income in Poland was assessed previously at 29%. The dissimilarities may result from the cultural differences, educational level differences, ethnic differences and differences in diligence. (shrink)

Jan Salamucha was born on the 10th of June 1903 in Warsaw and murdered on the 11th of August 1944 in Warsaw during the Warsaw Uprising very early on in his scholarly career. He is the most original representative of the branch of the Lvov-Warsaw School known as the Cracow Circle. The Circle was a grouping of scholars who were interested in reconstructing scholasticism and Christian philosophy in general by means of mathematical logic. As Jan Lukasiewicz’s successor in the area (...) of logic and Konstanty Michalski’s student in the area of the history of medieval thought, Salamucha had an excellent preparation for this task. His main achievements include a masterful logical analysis of the proof _ex motu _for the existence of God, a modern interpretation of analogical notions and a comprehensive approach to the problem of essence. He also contributed several historical studies: he examined Aristotle’s theory of deduction (and found contradictions in it), he reconstructed William Ockham’s propositional logic and established the authenticity of his treatise on _insolubilia,_ and he identified the historical sources of the antinomies in Antiquity and the Middle Ages. He did not shy away from popularizing philosophy, and in that work he was able to elucidate rather than oversimplify the complexities of philosophy. (shrink)

The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of complexity 2. This is (...) the first example of an exact estimation of the degree of natural complex logics, i.e. logics whose deducibility relation cannot be represented by a single matrix. The remaining examples of complex logics are more artificial, having been constructed for the purpose of checking some theoretical possibilities. (shrink)

In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic with such a degree of complexity. The (...) results of the final part of the paper cast a new light on the scope of the Kripke-style semantics in comparison to the matrix semantics. (shrink)

The aim of this note is to give an example of application of model theory to the theory of logical matrices. . More precisely, we show that Wojtylak's representation theorem is an immediate consequence of a result due to Mal'cev . Throughout the present note we assume that matrices, and classes of matrices under consideration are of the same xed similarity type. Suppose that K is an arbitrary class of matrices, and M is a matrix . We say that M1 (...) 2 K is called a replica of M in the class K i there is a homomorphism h of M onto M1 such that for every homomorphism g of M into arbitrary N 2 K there exists a homomorphism f of M1 into N such that g = f h. (shrink)

x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.

. In our paper, presented here in abstract form, we consider the sentential logic with semi-negation. It should be stressed, however, that our main interest is not that logic itself but rather more general matters concerning the theory of matrix semantics for sentential logics. The logic with semi-negation provides a relevant example for elucidating such basic notions of matrix semantics as degree of complexity, degree of uniformity, and self-referentiality. Thus our paper being a contribution to the theory of matrix semantics (...) may be treated as a sequel to [1]. (shrink)

The notion of a conditionally distributive lattice was introduced by B. Wolniewicz while formally investigating the ontology of situations . In several of this lectures he has appealed for a study of that class of lattices. The present abstract is a response to that request.

The volume aims to show the variety of research currents of the Lvov-Warsaw School and the ways in which these currents are developed today. The content of the book is divided into three parts: “Logic and Semiotics”, “Metaphysics and Ontology”, and “Psychology and Sociology”.

Chciałem Go pożegnać. Kilkakrotnie próbowałem napisać choć parę słów. O Nim samym. Okazało się, że nie potrafię. Udało mi się tylko przedstawić Jego poglądy na reizm Tadeusza Kotarbińskiego, ale uczyniłem to gdzie indziej. Muszę tu poprzestać na ofiarowaniu Mu tego, co napisałem na Jego dziewięćdziesiąte urodziny, w osiemdziesięciolecie naszej przyjaźni.

We would like to begin a series of translations of outstanding articles [published previously in FP], mainly by Jesuit philosophers. Our first choice is a paper by Franciszek Bargieł, an eminent scholar of Jesuit philosophy who taught and lectured in philosophy at the Faculty of Philosophy of the Society of Jesus in Kraków/Cracow for many years. This article, published in the journal “Forum Philosophicum,” vol. 2, 1997 (245–54), was originally written and published in Latin and has been translated from that (...) language. (shrink)

The kernel of this volume is an English translation of Jan Łukasiewicz’s classic work on the concept of cause (1906). It is the starting point for analytical considerations on causality of two generations of philosophers belonging to the tradition of the Lvov-Warsaw School.

Jan Paweł II wielokrotnie odnosił się do relacji między Kościołem a sztuką. Dostrzegał, że dialog między Kościołem i sztuką wygasł lub został naznaczony sprzecznościami na przełomie XIX i XX wieku. W niniejszym studium koncentruję się na dwóch kluczowych kwestiach: czy Kościołowi potrzebna jest sztuka oraz czy sztuka potrzebuje Kościoła? Odpowiedź na drugie pytanie nie jest ewidentna i odnosi się do innej kwestii sformułowanej przez Jana Pawła II:,,Czy sztuka ulega ograniczeniu lub zostaje pozbawiona istotnego znaczenia, jeżeli pomija rzeczywistość Kościoła?”. Sztuka w (...) istocie potrzebuje Kościoła, jeśli ma lepiej rozumieć prawdziwe powołanie człowieka oraz jeśli ma rozumieć, że jej ostateczny cel nie tkwi w prezentacji tego, co złe i niemoralne. (shrink)

The subject of the article is the contacts of Polish queens with the sanctuary of Our Lady of Częstochowa at Jasna Góra Monastery. The considerations are based on the archival materials stored in the Archives at Jasna Góra and the literature on the subject. In the Jasna Góra archives, books were used, in which votive gifts donated by the faithful to the Jasna Góra sanctuary were entered. The analytical method was used in the work. Most of the Polish queens had (...) contacts with the Jasna Góra sanctuary. Some of the queens made pilgrimages to the sanctuary in person, others offered devotional gifts and votes. The most frequent contacts with Jasna Góra were: Ludwika Maria, spouse of Władysław IV and Jan Kazimierz, Maria Kazimiera, spouse of Jan III Sobieski, Maria Eleonora, spouse of Michał Korybut Wiśniowiecki, and Maria Józefa, spouse of August III Wettin. The other queens had more modest contacts with Jasna Góra. All the rulers offered liturgical vestments, jewelery and financial donations. Ludwika Maria and Maria Józefa showed the greatest attention to the Jasna Góra sanctuary. However, the piety of the rulers resulted not only from their personal faith, but also from the norms and principles adopted in a given era in expressing religiosity. (shrink)

Artykuł prezentuje ustalenia na temat majątku ziemskiego syna i spadkobiercy wojewody krakowskiego Mikołaja Zebrzydowskiego – Jana, miecznika krakowskiego (1620–1621). Artykuł powstał na podstawie niewykorzystanych dotąd źródeł z krakowskich ksiąg grodzkich pierwszej połowy XVII wieku. Ustalono, że część dóbr ziemskich, w tym dobra rodowe, odziedziczył po ojcu, część natomiast kupił. Przed śmiercią zgromadził dobra prywatne, na które składał się zamek w Pieskowej Skale, miasto i części w dwóch innych miastach, 28 wsi, części w 9 wsiach, 22 folwarki oraz 4 nieruchomości w (...) miastach. Dobra te położone były na terenie Małopolski, w której w pierwszej połowie XVII wieku był jednym z najbogatszych właścicieli ziemskich. Dochody z tego majątku powiększał o dobra królewskie. (shrink)

Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.

The author presents Leszek Kołakowski from the perspective of his private acquaintanceship, lasting for about 47 years, as a witty man and a workaholic. L. Kołakowski never formed a classic “school”, but there is something all his disciples share: a thesis, key to understanding his ideas, which holds that “THERE IS MORE THAN ONE CORRECT OPINION IN THE HUMANITIES”, i.e. we will ALWAYS have opinions for and against, which goes against any dogmatism, wherever it may appear; this also bears consequences (...) in diagnosing the socio-political reality past and present. (shrink)

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable.

In this paper the notion of unifier is extended to the infinite set case. The proof of existence of the most general unifier of any infinite, unifiable set of types (terms) is presented. Learning procedure, based on infinite set unification, is described.

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

Stephenson (2022) has argued that Kant’s thesis that all transcendental truths are transcendentally a priori knowable leads to omniscience of all transcendental truths. His arguments depend on luminosity principles and closure principles for transcendental knowability. We will argue that one pair of a luminosity and a closure principle should not be used, because the closure principle is too strong, while the other pair of a luminosity and a closure principle should not be used, because the luminosity principle is too strong. (...) Stephenson’s argument also depends on a factivity principle for transcendental knowability, which we will argue to be false. (shrink)