Bartoszynski, T. and S. Shelah, Closed measure zero sets, Annals of Pure and Applied Logic 58 93–110. We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of (...) the ideal of meager sets. (shrink)

We prove that the cofinality of the smallest covering of R by meager sets is bigger than the additivity of measure.

The article reviews the book Einführung in die Erkenntnistheorie [Introduction to Theory of Knowledge], by Ernst Gerhard.

We construct a model of ZFC satisfying the Dual Borel Conjecture in which there is a set of size ℵ₁ that does not have measure zero.

We show that it is consistent with ZFC that the intersection of some family of less than ultrafilters have measure zero. This answers a question of D. Fremlin.

When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of (...) any teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers. (shrink)

Modern Polish philosophy has an impressive record as a powerful, innovating tradition, in many respects parallel to but independent of the development of analytical philosophy in Britain and America. Owing to an absence of adequate translations however, the work of its leading exponents has generally only been encountered second-hand. To remedy this, Quinton and Skolimowski have translated an introduction to philosophy written by Kazimierz Ajdukiewicz, probably the outstanding representative of the generation. Problems and Theories of Philosophy surveys concisely and, (...) so far as possible, systematically the main problems in epistemology and metaphysics and the most historically important of the solutions proposed to them. The book still reads freshly and displays many of the characteristic intellectual virtues of Polish philosophy: clarity and straightforwardness of presentation combined with a bracing rigour and precision. It is in no sense parochial to its Polish origins and can stand beside the classic English introductions to the subject as stimulating and lucid analysis of perennial philosophical problems and strategies. (shrink)

. ACT, CONTENT, AND OBJECT OF THE PRESENTATION It is one of the best known positions of psychology, hardly contested by anyone, that every mental phenomenon ...

In this paper we present two consistency results concerning the existence of large strong measure zero and strongly meager sets. RID=""ID="" Mathematics Subject Classification (2000): 03e35 RID=""ID="" The first author was supported by Alexander von Humboldt Foundation and NSF grant DMS 95-05375. The second author was partially supported by Basic Research Fund, Israel Academy of Sciences, publication 658.

The contemporary development of socialist economy is featured not only by high dynamics, but also by essential structural and qualitative changes. The economic policy and the socialist planning in particular tendtowards optimalization of economic growth, then to engage for its proper directions, structure and rythmicality. The every year growing national product ought to be, as it is possible, most suitable and useful for implementation of threefold objective: 1° the better satisfaction with the necessities of population, 2° the quicker modernization of (...) the national economy, and 3° the effective development of the foreign trade as well as the international cooperation.The superiority of a set of social criteria is becoming the general assumption of economic policy. A vision of the future human being and the mature society is determining prospective objectives and aims of the development as well is indicating ways and means for their realization by economic policy.The economic growth is not objective by itself, but has to serve for a comprehensive social advancement. At the same time the factors of social advancement advantageously impact the labour productivity and otherwisethey perform a role of additional stimulatives of the economic growth.The objectives of social advancement should be realized gradually basing on staging patterns of systematic raise of the living standards of the population. A hierarchy and a sequence of satisfaction with the both individual and collective necessities demand a skillful application of the criteria of the economic and social choice. We are using here the principle of social and economic rationality.Hence the factors of social advancement, involving the scientific and technical progress, belang to the fundumatel elements of the present economic and social policy. At the same time objectives and means of modern economic and social advancement are here strictly interlaced. (shrink)

OPER ACCESS. The correspondence between Meinong and Kazimierz Twardowski highlights the relationship between two philosophers who influenced the history of philosophy and psychology in Austria and Poland. The two correspondents discuss, among other things, their epistemological approach and the university politics of their times. In addition, there is an extensive introduction that places the correspondence in its proper historical and philosophical context.

We conclude the discussion of additivity, Baire number, uniformity, and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichon's diagram.

“The concept of Logos at Heraclitus. The analyze of B1 fragment”. “Logos” is the most important word in the Heraclitus’ philosophy. One can tell, that Heraclitusis the philosopher of logos. The way of interpretation of this notion influences the comprehention of all work of the Greek thinker.The word appears eleven times in the following fragments : B 1, B 2, B 31, B 39, B 45, B 50, B 72, B 87, B 108, B 115 [numeration of Diels-Kranz]. Logos contains (...) several notions, and it can not be reduced to one, as for exemple reason, speach, fire or god. The analyse of B1, where the logos apperas for the first time, shows the complexity of this term. (shrink)

Ziel des vorliegenden Aufsatzes ist es, die Existenz von eventuellen Berührungspunkten zwischen Wittgenstein und Ingarden nachzuweisen. Nach einer kurzen Einführung wird anfangs der Hintergrund der Analyse des Problems formuliert. Darauf hin werden die Positionen Wittgensteins Ontologie mit wenigen Begriffen und Ingardens dreistufige Ontologie jeweils skizzenhaft dargestellt und kritisch auf das Vorhandensein von gemeinsamen Grundlinien geprüft. Als Gesichtspunkte gelten dabei folgende Begriffe: Ontologie, Welt und Mensch, Sprache und Ästhetik. Abschließend werden die charakteristischen Merkmale von Berührungspunkten genannt.

In this paper I seek to analyse the following question: how is it that I am able, today, to succeed in fulfilling my goals? My analysis will, I hope, demonstrate that virtues are important because they facilitate this sort of fulfilment. An examination of the classical notion of virtue is thus called for, and this in turn suggests that, at least in certain cases, virtue is connected with luck—that these two belong together. This points towards a new form of contemporary (...) virtue ethics, whose distinctive character will be reflected in the particular significance it invests in the concepts of “qualification” and “competence.” Finally, we are led to Wittgenstein's assertion that “The world of the happy person is other than the world of the hapless person.”. (shrink)

We answer a question of Just, Miller, Scheepers and Szeptycki whether certain diagonalization properties for sequences of open covers are provably closed under taking finite or countable unions.

A set X⊆ℝ is strongly meager if for every measure zero set H, X+H ≠ℝ. Let [Formula: see text] denote the collection of strongly meager sets. We show that assuming [Formula: see text], [Formula: see text] is not an ideal.

During the first semester of the academic year 1930/31 in the John Casimir University in Lvov Kazimierz Ajdukiewicz delivered a series of lectures on logical semantics. In eight of them, now published for the first time, he presents - in the very clear manner - his fractional method of identifying syntactic categories, and he shows how to use this method to eliminate the antynomies of classes, relations and properties. The Ajdukiewiczian method had been appreciated among logicians and it is (...) considered widely one of the starting points of so-called categorial grammars. (shrink)

We prove that the following are consistent with ZFC. 1. 2 ω = ℵ ω 1 + K C = ℵ ω 1 + K B = K U = ω 2 (for measure and category simultaneously). 2. 2 ω = ℵ ω 1 = K C (L) + K C (M) = ω 2 . This concludes the discussion about the cofinality of K C.

We will construct several models where there are no strongly meager sets of size 2ℵ0.

Autor tworzy strukturę Peryta, która posiada tę właściwość, iż środkiem świata jest miejsce wybrane przez obserwatora co zmienia charakter zjawisk geometrycznych, w tym perspektywy.