The axiom of canonicity was introduced by the famous Polish logician Roman Suszko in 1951 as an explication of Skolem's Paradox and a precise representation of the axiom of restriction in set theory proposed much earlier by Abraham Fraenkel. We discuss the main features of Suszko's contribution and hint at its possible further applications.

This note discusses some problems concerning intended, standard, and nonstandard models of mathematical theories. We pay attention to the role of extremal axioms in attempts at a unique characterization of the intended models. We recall also Jan Woleński’s views on these issues.

This short note is a summary of the talk given at the Adam Mickiewicz University in Poznań during the conference on Philosophy of Mathematics, III , on October 17, 2011. We suggest to understand mathematical intuition as a collection of (verbalized) judgments constituting the core of the context of discovery in mathematics. Mathematical intuition is present not only in the axioms: it can be observed in mathematical research practice as well. A few examples of mathematical intuition in action are given. (...) We discuss the dynamic character of mathematical intuition, trying to reveal the sources of the corresponding changes of intuitive views in mathematics. There are several such sources, e.g.: paradoxes, new research programs (for instance, the program of arithmetization of analysis), explicit definitons of concepts understood so far in an intuitive way, and – of course – the development of the mathematical knowledge itself. We devote special attention to the distinction between standard, exception, and pathology. Finally, we say a few words about conflicts of intuitions in mathematics. (shrink)

Contents: Preface. SCIENTIFIC WORKS OF MARIA STEFFEN-BATÓG AND TADEUSZ BATÓG. List of Publications of Maria Steffen-Batóg. List of Publications of Tadeusz Batóg. Jerzy POGONOWSKI: On the Scientific Works of Maria Steffen-Batóg. Jerzy POGONOWSKI: On the Scientific Works of Tadeusz Batóg. W??l??odzimierz LAPIS: How Should Sounds Be Phonemicized? Pawe??l?? NOWAKOWSKI: On Applications of Algorithms for Phonetic Transcription in Linguistic Research. Jerzy POGONOWSKI: Tadeusz Batóg's Phonological Systems. MATHEMATICAL LOGIC. Wojciech BUSZKOWSKI: Incomplete Information Systems and Kleene 3-valued (...) Logic. Maciej KANDULSKI: Categorial Grammars with Structural Rules. Miros??l??awa KO??L??OWSKA-GAWIEJNOWICZ: Labelled Deductive Systems for the Lambek Calculus. Roman MURAWSKI: Satisfaction Classes - a Survey. Kazimierz _WIRYDOWICZ: A New Approach to Dyadic Deontic Logic and the Normative Consequence Relation. Wojciech ZIELONKA: More about the Axiomatics of the Lambek Calculus. THEORETICAL LINGUISTICS. Jacek Juliusz JADACKI: Troubles with Categorial Interpretation of Natural Language. Maciej KARPI??N??SKI: Conversational Devices in Human-Computer Communication Using WIMP UI. Witold MACIEJEWSKI: Qualitative Orientation and Grammatical Categories. Zygmunt VETULANI: A System of Computer Understanding of Texts. Andrzej WÓJCIK: The Formal Development of van Sandt's Presupposition Theory. W??l??adys??l??aw ZABROCKI: Psychologism in Noam Chomsky's Theory . Ryszard ZUBER: Defining Presupposition without Negation. PHILOSOPHY OF LANGUAGE AND METHODOLOGY OF SCIENCES. Jerzy KMITA: Philosophical Antifundamentalism. Anna LUCHOWSKA: Peirce and Quine: Two Views on Meaning. Stefan WIERTLEWSKI: Method According to Feyerabend. Jan WOLE??N??SKI: Wittgenstein and Ordinary Language. Krystyna ZAMIARA: Context of Discovery - Context of Justification and the Problem of Psychologism. (shrink)

This review discusses the content of Mateusz Hohol’s new book Foundations of Geometric Cognition. Mathematical cognition has until now focused mainly on human numerical abilities. Hohol’s work tackles geometric cognition, an issue that has not been described in previous investigations into mathematical cognition. The main strength of the book lies in its critical analysis of a huge amount of results from empirical experiments. The author formulates his theoretical proposals very carefully, avoiding radical and one-sided solutions. He claims that human geometric (...) cognition is based mainly on two core systems, both being phylogenetically hardwired, namely the system of layout geometry and the system of object geometry. The interaction of these systems becomes amplified in the individual development of the mind, which, in turn, is supported by the use of language. The second part of the review contains the reviewer’s remarks concerning the history of geometry, experiments related to spatial representations, and the role of geometry in mathematical education. (shrink)

We review the four recent monographs by Roman Murawski.

Certain mathematical objects bear the name “pathological”. They either occur as unexpected and unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the (...) problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas. (shrink)

In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks concerning the development of infinitary logic. I also stress the fact that the second axiomatization of set theory provided by Zermelo in 1930 involved the use of extremal axioms of a very specific sort.1.

This review discusses the content of Mateusz Hohol’s new book Foundations of Geometric Cognition. Mathematical cognition has until now focused mainly on human numerical abilities. Hohol’s work tackles geometric cognition, an issue that has not been described in previous investigations into mathematical cognition. The main strength of the book lies in its critical analysis of a huge amount of results from empirical experiments. The author formulates his theoretical proposals very carefully, avoiding radical and one-sided solutions. He claims that human geometric (...) cognition is based mainly on two core systems, both being phylogenetically hardwired, namely the system of layout geometry and the system of object geometry. The interaction of these systems becomes amplified in the individual development of the mind, which, in turn, is supported by the use of language. The second part of the review contains the reviewer’s remarks concerning the history of geometry, experiments related to spatial representations, and the role of geometry in mathematical education. (shrink)

The paper is devoted to the description of life and scientific achievements as well as the influence of Seweryna Łuszczewska-Romahnowa.

We consider structures of the form, where Φ and Ψ are non-empty sets and is a relation whose domain is Ψ. In particular, by using a special kind of a diagonal argument, we prove that if Φ is a denumerable recursive set, Ψ is a denumerable r.e. set, and R is an r.e. relation, then there exists an infinite family of infinite recursive subsets of Φ which are not R -images of elements of Ψ. The proof is a very elementary (...) one, without any reference even to e.g. the -theorem. Some consequences of the main result are also discussed. (shrink)

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

Journal Name: Philologus Issue: Ahead of print.

The old-fashioned concept of state is shown to be inadequate and misleading. Replacing it by a concept of information and taking advantage of the invariance of the mechanical description under time reversal puts the problems of the interpretation of quantum mechanics in a new light. A more realistic interpretation appears to be possible. Moreover, a new explanation of the Einstein-Podolsky-Rosen paradox is presented, too.

Las jako zespół przyrody o określonych właściwościach pełni szereg wielorakich funkcji gospodar­czych, pośrednio gospodarczych i pozagospodar­czych. Jako przyrodnicza całość jest mało stabilny i ulega wielu czynnikom biotycznym, abiotycznym i antropogenicznym. Z praktyki ochrony lasu w granicach admini­stracyjnych Regionalnej Dyrekcji Lasów Państwo­wych w Olsztynie wynika, że szczególnie niebez­pieczne bywają owady - z grupy szkodników pier­wotnych - żerujące na drzewach żywych i pozornie zdrowych, a osłabionych działaniem jednego lub kil­ku czynników, zwykle abiotycznych. Pojawy nie­których zmuszają do podejmowania zabiegów ratow­niczych. Sposoby sprowadzania liczebności (...) trzech moty­li, tzn. brudnicy mniszki, strzygoni choinówki i zwójki zieloneczki, do poziomu przed laty nazywanego „żelaznym zapasem” przedstawia niniejsze opracowanie. (shrink)

Jerzy Franczak comprehensively presents Jacques Rancière's thought by emphasizing the relations between politics and literature. The detailed analysis considers the context of modern aesthetics and political philosophy, which is why the book introduces further protagonists, such as Louis Althusser, Michel Foucault, Pierre Bourdieu, or Jean-François Lyotard. Franczak first reconstructs Rancière's original philosophy of literature so as to then immediately apply it in readings of select world literature masterpieces by Gustav Flaubert, Max Jacob, Bertold Brecht, Vladimir Nabokov, and Philip Roth.

In the first part of the article, Giuseppe Veronese’s concept of arithmetical constructivism is reconstructed from his dispersed remarks. It is pointed out that although for Veronese time is a necessary condition for the construction of natural numbers by an individual subject and the subject cognizes time in an a priori way, it is not a (proto-)intuition of the subject. This is a fundamental difference between the concept proposed by Veronese and the constructivism of Kant and Brouwer. Veronese’s justification of (...) the subject’s ability to cognize infinity, represented in his text by infinite sequences, is analyzed in the second part of the paper. The only condition for the cognition of the infinite sequence is to have a rule according to which its successive terms “follow one another.” The price of the ability to cognize the infinitive “whole” (sequence) may be the uncognizability of certain “parts” (terms of sequence). Infinite sequences, cognizable according to Veronese, are allowed as objects of mathematical research, although they do not meet the condition of constructability. (shrink)

Henryk Chmielewski is the author of a historical comic book devoted to the 100th anniversary of Poland regaining its independence. The comic book of Chmielewski is a subjective vision of Polish history, because every act of creation is first of all an act of destruction. Artist says about very difficoult moment of Polish history (the 19th century, the early 20th century). He creates original story, argues, that the idea of Poland as an independent state was never not lost. Polish people (...) were formed armyduring the Napoleonic Wars, and Polish organisations started major uprisings (the Polish–Russian War of 1830–1831 and the January Uprising of 1863-64). Chmielewski creates an interesting picture of the world with the use of many varying forms, different codes (e.g. picture, word, photography). He use various means of expression: semantic, linguistic, compositional (see values, compotents: metannaration, digression, opposition "we" - "they", stereotype, appropriate words - freedom, Poland, Poles, relationship: fiction - real world, illusion, colloquial language). (shrink)

W publikacji autor analizuje powszechność wdrażania określonych kategorii innowacji w przedsiębiorstwach funkcjonujących w krajach Unii Europejskiej. Analizy dokonano w dwóch przekrojach: 1) państw członkowskich Unii Europejskiej, 2) przynależności sektorowej przedsiębiorstw. Podstawą dla tej analizy są wyniki badań kwestionariuszowych przeprowadzonych w kwietniu 2009 r. przez the Gallup Organization wśród 5034 przedsiębiorstw. Respondentami byli przedstawiciele zarządów tych przedsiębiorstw. Celem publikacji jest dokonanie statystycznej analizy odpowiedzi respondentów na temat powszechności wdrażania innowacji.

The object of this paper is to suggest how the Frege–Dummettian notions of criterion of identity and criterion of application can be put to work within Putnam’s account of reference for natural kind terms in “Meaning of ‘Meaning’ ”. By doing so, some light can be shed on Putnam’s earlier views on “necessity relative to a body of knowledge” as well as his later views on sortal identity. If the Frege–Dummettian criteria are indeed at work within Putnam’s account, then we (...) must either give up rigidity or else give up the division of linguistic labor hypothesis. I will give an example from biological nomenclature that may sway us towards giving up the former. (shrink)

Autor niniejszego artykułu stawia tezę, iż w _Biblii Paulistów_, w szczególności zaś w tłumaczeniu Ewangelii i Psalmów, zastosowano tylko pozornie „język współczesny”, gdyż jej tekst w wielu wypadkach zapożycza pełne frazy z _Biblii Tysiąclecia_. Powstaje w ten sposób pewna hybryda językowa, mieszająca język potoczny i już utrwalony tradycją „polski styl biblijny”. Tezę tę ilustrują liczne przykłady oparte o analizowany tekst. Kolejną poruszaną kwestią jest teoretyczna i praktyczna zasadność samego faktu sięgania po język współczesny, a w istocie po język potoczny w (...) przekładzie Pisma Świętego. Z teoretycznego punktu widzenia jest to jednoznacznie sprzeczne z tradycją wyznaczoną przez _Wulgatę _św. Hieronima, którego przekładowy język naruszał kanony łaciny cycerońskiej (a więc języka naturalnie brzmiącego dla ówczesnego wykształconego odbiorcy) w trosce o jak największą wierność wobec oryginału. Święty Hieronim zderzał łacinę ze strukturami składniowymi języka hebrajskiego, w wyniku czego powstała pewna nowa jakość, odbierana jeszcze długi czas później jako „dobroczynny zgrzyt językowy” (sformułowanie A. Bermana), prowadzący również do poszerzenia zasobów języka docelowego. Ta zasada została przyjęta w późniejszych katolickich przekładach Biblii, w tym w przekładzie ks. Jakuba Wujka, i odrzucona dopiero przez nową tradycję protestancką zainaugurowaną przez Marcina Lutra. Z praktycznego natomiast punktu widzenia wolno zadać pytanie o duszpasterską skuteczność używania takiego języka i sięganie do tradycji protestanckiej w sytuacji, gdy kościoły protestanckie Europy pustoszeją mimo propozycji „chrześcijaństwa ułatwionego”. (shrink)

El objetivo de este trabajo es poner al descubierto los principales valores cognitivos y epistemológicos desde los que Warren Weaver puso en marcha el Programa de Biología Experimental, un programa que llevado a cabo desde la presidencia de la división de ciencias naturales de la Fundación Rockefeller, marcó y condicionó en buena medida el posterior desarrollo de la investigación biológica. Para tal fin se mostrará, en primer lugar, cómo fue la llegada de Weaver a la Fundación Rockefeller, así como las (...) razones bajo las cuáles el consejo de esa institución decidió entre 1932 y 1933 dar prioridad a las investigaciones biomédicas, y la manera por la cual lo hicieron. En un segundo momento, el más extenso e importante, veremos algunos de los elementos más significativos de la perspectiva epistemológica y cognoscitiva de de Weaver. Finalizaremos viendo cómo esa perspectiva, desarrollada en conexión con el Programa de Biología Experimental, inter-actuó con la visión reduccionista de la biología a la que el programa parecía apuntar. The aim of this article is to uncover the main cognitive and epistemological values that influenced Warren Weaver in starting the Experimental Biology Program, a program carried out from the time that he became president of the Natural Sciences Division of the Rockefeller Foundation, and which significantly marked and conditioned the subsequent development of biological research. To this end, we first describe the arrival of Warren Weaver at the Rockefeller Foundation, and the reasons for which the Board of this Foundation, between 1932 and 1933, decided to prioritize biomedical research, and the manner in which they did so. Then, secondly, in the largest and most important part of the article, we will present some of the most significant elements of Weaver's epistemological and cognitive perspective. Finally, we will show how this perspective, developed in connection with the Experimental Biology Program, interacted with the reductionist view of biology to which the program seemed to point. (shrink)

καλὸν δ᾽ ἐπὶ σήματι σῆμασκέπτεσθαι, μᾶλλον δὲ δυοῖν εἰς ταὐτὸν ἰόντωνἐλπωρὴ τελέθοι, τριτάτῳ δέ κε θαρσήσειας. It is a good idea to observe one sign after another, and if two agree, it is more hopeful, while with a third you can be confident. Appropriately for a poet who is ‘subtly speaking’, the epithet applied to him by Ptolemy III Euergetes, Aratus does not cease offering unexpected material to explore. This statement holds true also for the famous passage containing the acrostic (...) ΛΕΠΤΗ. (shrink)

The term “transcendental” means something which is a necessary and a priori condition of knowledge. In other words, “the transcendental” refers to all presuppositions of a knower who is ready for knowing. These presuppositions are sometimes called “epistemic assumptions”. The paper presents author’s interpretation of the knowledge necessary conditions. The theoretical background for this interpretation is Kazimierz Twardowski’s theory of actions and products, and John Searle’s theory of human action.

Cognitive activity, which essentially consistsof the use of signs, does not only depend onthe internal (mental, or brain) processes. Thefirst part of the paper presents severalversions of the idea of the external andcultural organization of individual''s mentalprocesses. The second part of the paperconsiders a future development of cognitivescience as a science of the extended andsocially constructed mind. KazimierzTwardowski''s theory of intentionality and histheory of actions and products provide theconceptual framework of the undertaken analysis.

A theoretical analysis of the concept of lifetime and mean life of unstable elementary particles is presented. New analytic formulas for lifetime and mean life as a function of decay width Γ and the mass of unstable particle are derived for Breit-Wigner and Matthews-Salam energy distributions. It is demonstrated that, for unstable particles with a larger width or decay energy threshold, the deviation from the generally accepted mean life τ m =Γ −1 is significant. The behavior of the decay law (...) P(t) for small times is analyzed, and it is shown that the Breit-Wigner distribution violates the condition P(t = 0) = 0, whereas the Matthews-Salam distribution satisfies it. (shrink)

W studium dokonano rekonstrukcji i analizy procesu pisania dwóch opowiadań Włodzimierza Odojewskiego (1930–2016) powstałych w latach 1976–1993. Autor bada bruliony (rękopisy i maszynopisy) przechowywane w archiwum pisarza na Wydziale Filologii Polskiej i Klasycznej UAM w Poznaniu. Praca nad dokumentacją genezy opowiadań odbywa się przy pomocy narzędzi zaproponowanych przez francuskich genetyków tekstu (P-M. de Biasi, J. Bellemin Noël) i amerykańskiego badacza J. Bryanta (pojęcie płynnego tekstu /fluid text/). Analiza dotyczy wybranych skupisk zmian w brulionach utworów Odojewskiego – redakcje tytułu, początkowych akapitów, (...) a także skreślenia, poprawki, uzupełnienia. Punktem dojścia studium jest stwierdzenie, że toku długotrwałego aktu twórczego pisarz dąży do konstrukcji, które w sposób maksymalnie precyzyjny oddają niuanse stanów psychicznych bohaterów oraz scenerii akcji opowiadań. Akt twórczy w wykonaniu Odojewskiego jest przykładem niestabilności pisania, którego efektem są kreacje płynnych postaci. (shrink)

The so-called ‘type method’ widely employed in biological taxonomy is often seen as conforming to the causal-historical theory of reference. In this paper, I argue for an alternative account of reference for biological nomenclature in which taxon names are understood as descriptive names. A descriptive name, as the concept came to be known from the work of Gareth Evans, is a referring expression introduced by a definite description. There are three main differences between the DN and the causal account. First, (...) according to the DN account, rather than fixing a name to a referent, the assignment of a type specimen to serve as the name-bearer for a taxon should be seen as performatively establishing a synonymy between a name and a definite description of the form “the taxon whose type is t”. Each taxon name is therefore associated with a criterion of application, a semantic rule that establishes the connection between the name and the descriptive content. This is the second major difference from the causal account: taxon names do have some descriptive content associated with them. The final locus of dissent concerns the strength of the modality resulting from the usage of taxon names. In order to address this point, I use the DN account to focus on the debate between Matt Haber and Joeri Witteveen concerning misidentification of type specimens, misapplication of names, and the truth conditions of Joseph LaPorte’s de dicto necessary sentence “Necessarily, any species with a type specimen contains its type specimen”. Using a pragmatic variant of the distinction between attributive and referential uses of descriptions, I argue that a metalinguistic version of the de dicto sentence is in fact falsified, as previously argued by Haber. (shrink)

Author: Sawicki Jerzy Title: THELEOGICAL PRINCIPLE IN KANT’S METHODOLOGY (Zasada teleologiczna w metodologii Kanta) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 281-292 Keywords: KANT, THELEOGICAL PRINCIPLE, FINALISM, MECHANICISM Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The work contains a concise of I. Kant’s views on the problem of the laws of nature and the theleological principle presented in this context, which Kant proposes in the character of a regulative methodological postulate. (...) The analysis of fundamental philosophical notions (the law of nature, necessity, causality, purpose) carried out from the position of an extreme aprioristic rationalism leads Kant to the conclusion about the basic impossibility of educing the conception of purpose (in relation to nature) from aprioristic transcendental laws, ie. such laws which the theoretical reason imposes to the nature by necessity. However, the fact of a total functioning of an organism does not fit, according to Kant, into the frames of a mechanically understood causality. Kant tries to solve this problem choosing the way of conclusion by analogy and finally he suggests to introduce into the living nature a specific causal relation in which the purposes constitute a particular kind of causes and results at the same time. That conception oscillates between mechanicism and theological finalism, and the fitting of a science system into the frames of aprioristic categories does not permit a finally decide about the supremacy of one or the other way of seeing the world. However, nevertheless, the perceiving and stressing of the peculiarity of organic symptoms, the formulation of the postulate about their unreductability to the law of a mechanical type constitute unquestionable and great merit of the author of the Criticism of the Judgment Authority. The idea of the totality of organism, though involved in subjective idealistic non consequences of Kant’s conceptions has in the given historical period all features of a deep and progressive thought, outpacing and inspiring several later research ideas, both in philosophy and in natural science. (shrink)