In 1891, Hilbert came to the conclusion that geometry is not a science of the physical space but is an abstract science. Hilbert’s new position was repeated in the introduction to Grundlagen der Geometrie in 1899. The aim of this paper is to show the sources of change of Hilbert’s position in 1891. We showed that the di-rect source of the change was having heard a lecture by Wiener on projective geome-try. Wiener presented there a project of geometry as a (...) science of abstract objects i.e. objects as sets of minimal number of – only relational – properties. We showed that this idea was derived by Wiener from Dedekind’s arithmetic of natural numbers, pre-sented in 1888 in Was sind und was sollen die Zahlen? Thus – and this is the essential thesis of our paper – the original source of Hilbert’s idea of geometry as a abstract science is included in Dedekind’s concept of arithmetic. (shrink)

Book review: Lukas Benedikt Kraus, Der Begriff des Kontinuums bei Bernard Bolzano, Beiträge zur Bolzano-Forschung, vol. 25, Academia Verlag, Sankt Augustin 2014, pp. 112.

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)

The main purpose of the present paper is to demonstrate that as early as 1904 pre-eminent American mathematician Maxime Bôcher was an adherent to the presently relevant argument of reasonableness, or even necessity of parallel development of two philosophical methods of reflection on mathematics, so that its essence could be more fully comprehended. The goal of the research gives rise to the question: what two types of philosophical deliberation on mathematics were proposed by Bôcher?

In this paper incomplete data sets, or data sets with missing attribute values, have three interpretations, lost values, attribute-concept values and ‘do not care’ conditions. Additionally, the process of data mining is based on two types of probabilistic approximations, global and saturated. We present results of experiments on mining incomplete data sets using six approaches, combining three interpretations of missing attribute values with two types of probabilistic approximations. We compare our six approaches, using the error rate computed as a result (...) of ten-fold cross validation as a criterion of quality. We show that for some data sets the error rate is significantly smaller (5% level of significance) for lost values, for some data sets the smaller error rate is associated with attribute-concept values, and sometimes with ‘do not care’ conditions. Again, for some approaches the error rate is significantly smaller for saturated probabilistic approximations than for global probabilistic approximations, while for some approaches it is the other way around. Thus, for an incomplete data set, the best approach to data mining should be chosen by trying all six approaches. (shrink)

This Special Issue brings a selection of peer-reviewed papers that were presented at the 12th Principia International Symposium: Models and Modeling in the Sciences, Florianópolis, Brazil, online, August 2021. In this preface, the chair and the secretary of the organizing committee comment the symposium's context and briefly present the issue.

This article is drafted on the basis of three complementary essays by Professor Jerzy Janik. The author takes a look at selected issues in the field of quantum mechanics – especially the problem of quantum superposition and supersymmetry – from perspective of great philosophical systems. The author draws attention to the fact that some of these issues reflect old philosophical problems, and – in some cases – philosophical perspective may save interpretations of quantum mechanics from paradoxes.

Jerzy Perzanowski s ideas were based on an original blend of logic and ontology in what he called onto/logic, where the slash is meant to suggest a quotient of ontology by logic. Perzanowski began as a logician, his early works being on modal logic, then gradually shifted his interest to logical philosophy, meaning not so much philosophy of logic as philosophy informed by logic. Perzanowski was a rare breed of analytical philosopher who thought that a philosophical theory of everything (...) was worthwhile. In this systematic spirit, he began with method. He presented his method of total analysis and synthesis quite simply: reduce the object of research to its simplest possible constituents, and then combine them in some way. Better still, combine them in every possible way, thereby producing a space of possibilities analogous to (and in certain cases identical with) the logical space. Thus, analysis and synthesis differ from a trivial disassembly and reassembly.". (shrink)

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.

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)

Etyka transhumanizmu jest etyką utylitarystyczną. Celem transhumanistycznego projektu ulepszania człowieka jest zwiększenie jego dobrostanu fizycznego, psychicznego i społecznego, czyli zwiększenie sumy szczęścia jednostki i społeczności, której jest ona częścią. Treścią niniejszych rozważań jest wskazanie i opisanie tego, co stanowi ostateczną podstawę etyki transhumanistycznej i wyznacza zarazem granicę, poza którą nie mogą wykroczyć transhumanistyczne projekty ulepszającego modyfikowania człowieka. Twierdzimy, że tą podstawą i zarazem wyznacznikiem granicy moralnej akceptacji działań jest zachowanie tożsamości osobowej podmiotu. Tożsamość tę rozumiemy w sensie kartezjańskim, czyli jako (...) relację, w jakiej samoświadomość podmiotu pozostaje do jego cielesności. Transhumanistyczne ulepszanie człowieka staje się zatem niemoralne, jeśli może prowadzić do utraty pamięci jednostki o przeszłych relacjach między jej samoświadomością a cielesnością. (shrink)

The idea of rejection of some sentences on the basis of others comes from Aristotle, as Jan Łukasiewicz states in his studies on Aristotle's syllogistic [1939, 1951], concerning rejection of the false syllogistic form and those on certain calculus of propositions. Short historical remarks on the origin and development of the notion of a rejected sentence, introduced into logic by Jan Łukasiewicz, are contained in the Introduction of this paper. This paper is to a considerable extent a summary of papers (...) which are not easily available, even to the Polish reader: (1) J. Słupecki, Funkcja Łukasiewicza (Łukasiewicz’s function), Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, nr 3 (1959), 33-40; (2) U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131; (3) G. Bryll, Kilka uzupełnień teorii zdań odrzuconych (Some supplements to the theory of rejcted sentences), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Mnografie, Nr 22 (1969), 153-154. The paper also contains a good number of results which have not been published yet. Chapter I contains results presented in the papers (1)-(3). It provides an extension of Alfred Tarski’s theory of deductive systems presented by him in the papers [1930]: Fundamentale Begriffe der Methodologie der deduktiven Wssenschaften, I and Über einige fundamentale Begriffe der Metamathematik. The enriched theory is marked with T. The most essential new concept in T is the function Cn-1, whose definition was given by Słupecki in (1) on the basis of the so-called Tarski’s general theory of deductive systems. It has the form: y e Cn-1X iff Ex e X (x e Cn {y}), where Cn is Tarski’s consequence operation. In accordance with the definition: A sentence y is rejected on the basis of the sentences of the set X iff at least one of sentences of X is a consequence of y (is deducible from y). The intuitive meaning of the rejection function Cn-1: on the basis of false sentences we can reject false sentences only (while by means of the consequence operation Cn on the basis of true sentences we can deduce true sentences only). The function Cn-1 is a generalization of the notion of rejected sentences which was introduced into logic by Łukasiewicz. The essential property of the rejection function Cn-1 is that it satisfies the axioms of general Tarski’s consequence Cn, so it is a consequence operation, called the rejection consequence. In addition, it is an additive and normal operation. In Chapter I, there are given notions analogous to those of the theory of deductive systems, but they are written down by means of the symbol ‘Cn-1’ and not ‘Cn’. There are established the properties of introduced notions and differences and analogies taking place between them and properties of respective notions of the theory T. There are also given generalizations of the notions of ‘decidable system’ and ‘consistent system’ used by Łukasiewicz. The short Chapter II contains axioms of the system T’ which is equivalent to the system T. The only difference between sets of primitive notions of these systems consists in the appearance of the function Cn-1 in the system T’ instead of the function Cn. This chapter reproduces the results given in (2), but they are partially simplified. (shrink)

Among numerous songs written by Wasowski and Przybora for the tv and radio show Old Gentlemen’s Cabaret two: Piosenka jest dobra na wszystko from the Fifth Evening of the Cabaret and Mambo Spinoza from the Eighth Evening might be considered autothematic. They represent an idea of ‘a song about a song’ — a common theme or motif in Polish popular music. In reaction to ideological degeneration of different forms of mass entertainment between 1949 and 1955, Wasowski and Przybora decided to (...) ‘redefine’ a song, writing these two pieces full of humour and allusions. (shrink)

Contents: INTRODUCTION. Kazimierz TWARDOWSKI: The Majesty of the University. I. Zygmunt ZIEMBI??N??SKI: What Can Be Saved of the Idea of the University? Leszek KO??l??AKOWSKI: What Are Universities for? Leon GUMA??N??SKI: The Ideal University and Reality. Zygmunt BAUMAN: The Present Crisis of the Universities. II. Kazimierz AJDUKIEWICZ: On Freedom of Science. Henryk SAMSONOWICZ: Universities and Democracy. Jerzy TOPOLSKI: The Commonwealth of Scholars and New Conceptions of Truth. Klemens SZANIAWSKI: Plus ratio quam vis. III. Leon KOJ: Science, Teaching and Values. Klemens (...) SZANIAWSKI: The Ethics of Scientific Criticism. Jerzy BRZEZI??N??SKI: Ethical Problems of Research Work of Psychologists. IV. Janusz GO??L??KOWSKI: Tradition in Science. Jerzy KMITA: Is a "Creative Man of Knowledge" Needed in University Teaching? Leszek NOWAK: The Personality of Researchers and the Necessity of Schools in Science. RECAPITULATION. Jerzy BRZEZI??N??SKI: Reflections on the University. (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)

By 'positivism' its contemporary critics mean either (a) the comte-Mill views of science, Or (b) methodological naturalism, Or (c) phenomenalism and/or instrumentalism. However, Most philosophers of science are positivists on some of these criteria and antipositivists otherwise. For example, (b) may be combined with the rejection of (c), E.G., Popper; neo-Wittgensteinians, E.G., Wright, Toulmin, Kuhn, Winch, Like nineteenth century neo-Kantians and conventionalists hold instrumentalist views of language, Theories and explanation; 'positive economics' may be either instrumentalist, E.G., Friedman, Or realist; instrumentalism, (...) Contrary to popper's account, Occurs with any admixture of realism and has pioneered anti-Inductivism, Hypotheticism and theoretical pluralism. (shrink)

The paper defends a dynamic view of reality which is founded on the assumption of the existence of the flow of time. This vindication makes use of a metaphysical theory of the flow of time developed by the author which is based on the notion of dynamic existence. It is shown that such a conception allows one to explain the fundamental phenomena connected with the flow of time, namely the continuous changing of the present, the endurance of things, and the (...) asymmetry of time. It is also argued that the proposed approach may be of some virtue for the empirical sciences because it explains the ubiquitous interest of scientists in the evolution of dynamic systems of different kinds, and provides us with an arrow of time which is lacking in theories describing fundamental physical interactions. The argument is advanced which aims to show that physics is unable to provide us with a theory of the flow of time and that we should look for such a theory in metaphysics. Thus, an approach to the relation between metaphysics and physics is vindicated that may help to overcome the difficulties blocking our understanding of reality as a dynamic one. (shrink)

The paper examines the relations between presentism and the thesis concerning the existence of the flow of time. It tries to show that the presentist has to admit the existence of the passage of time and that the standard formulation of presentism as a singular thesis saying that only the present exists is insufficient because it does not allow the inference of the existence of the passage of time. Instead of this, the paper proposes a formulation of presentism with the (...) aid of the notion of becoming; not only does a formulation state the existence of the flow of time in such a way as to avoid the question of the rate of the passage of time, it also allows the inference of the existence of only present things and events. The paper demonstrates that the proposed conception of presentism also has other virtues, such as homogeneity, non-triviality, and ability to express dynamicity of presentists’ image of the world which testify for it. (shrink)

This paper is a continuation of Part I under the same title. Its Chapter III contains results given in the following publications: U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131. G. Bryll, Związki logiczne pomiędzy zdaniami nauk empirycznych (Logical relations between sentences of empirical sciences). Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia (...) i Monografie, Nr 22 (1969), 155-216. This chapter contains an attempt to formalize some questions of methodology of empirical sciences. The theory T is enriched here not only by new definitions but also by a new primitive term and new axioms. The most important notion defined in this chapter is the set IndX of all inductive conclusions obtained on the basis of sentences of the set X. The function CnI defined by the equality: CnI X = X u IndX, satisfies the axioms of the general theory of deductive systems. The set CnI X can be understood as a system of empirical sciences in a narrower sense. This paper is a development of the considerations of G. Bryll, included in the above-listed article by this author. (shrink)

The aim of this paper is to make presentism a dynamic view of reality by basing it on a notion of dynamic existence, that is, on a notion of existence which has a dynamic character. The paper shows that both of the notions of existence which are used in metaphysical theories of time have a static character and, while such a notion is useful for eternalists, it is useless for presentists if they want to make their view able to remain (...) in agreement with our everyday experience and self-consistent. It is demonstrated that both empirical and theoretical arguments indicate that the presentist should replace the notion of this static existence with the notion of a dynamic existence and that this maneuver allows the presentist to treat his/her existential thesis as equivalent to the thesis that time flows. Not only does this strategy allow us to express presentism in a simple, homogenous way which remains in agreement with our experience, but also permits us to solve some of the difficult problems which presentism faces, such as, for example, the objection of triviality and the question about the rate of time passage. Moreover, such an approach to presentism allows us to solve fundamental metaphysical problems concerning time such as the problem of the openness of the future and the fixity of the past, direction of causation, and relations between presentism and persistence through time by endurance. (shrink)