The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two di erent ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relation of (...) inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and proposed by B. Iwanuś, as well as a set of axioms WI of this arithmetic, modelled on the W axioms, PI and WI being also equivalent, categorical and consistent. We also discuss the problem of independence of sets of axioms, which were dealt with earlier. (shrink)

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

This paper seeks to define the main trends, arguments and problems regarding the question of method formulated by Twardowski and his students. In this regard, the aim of the paper is twofold. First, I situate Brentano’s project of descriptive psychology within the context of disputes in the school of Twardowski concerning the method of both psychology and phenomenology, arguing that descriptive-psychological analysis was dominant in this respect. Second, the study explores the notion of eidetic phenomenology, as founded on a methodological (...) procedure, which supposed to guarantee infallibility of its descriptions. To show this, I first reconstruct Brentano’s concept of descriptive psychology, its object, its method and aims. Second, I track the changes and reinterpretations provided by Twardowski in his view of descriptive-psychological analysis. Third, I explore Witwicki’s and Bandrowski’s—both early students of Twardowski—discussions of the descriptive approach. I try to show that the former accepted psychologism, while the latter overcame it by means of logical analysis. Fourth, I suggest that the only student of Twardowski who renounced the Brentanian method was Ingarden, who developed eidetic phenomenology. Finally, I present Blaustein’s—one of the last students of Twardowski—reappraisal of descriptive psychology and his critique of Ingarden’s method. This controversy over the method of descriptive psychology reveals how one can situate Twardowski’s legacy within early phenomenology in Poland. (shrink)

The article explores two phenomenologies of image consciousness that were formulated by Ingarden and Blaustein, both of whom were students of Husserl. Both philosophers analyze image consciousness in the context of the phenomenon of contemplating a painting. The article is divided into seven sections. Section 1 presents the historical background of Blaustein’s and Ingarden’s explorations. In Section 2, Ingarden’s description of a painting as different from an image is reconstructed. In Section 3, Ingarden’s analysis of Husserl’s image consciousness is discussed. (...) Section 4 concerns Blaustein’s theory of intentionality, which was formulated in a critical elaboration of Husserl’s philosophy. Section 5 discusses the detailed components of Blaustein’s theory of intentionality, i.e., his theory of psychic representations. This theory is then used in Section 6 in an analysis of Blaustein’s reading of § 111 of Husserl’s Ideas I. Section 7 summarizes both theories in order to draw parallels and differences between Ingarden and Blaustein. In this regard, it is argued that both philosophers refer to different theoretical contexts when discussing Husserl’s idea of image consciousness. (shrink)

1. Phenomenology is first and foremost about intentionality. As Husserl puts it, “Intentionality is the name of the problem encompassed by the whole of phenomenology”.1 Broadly understood, the phen...

The paper reconstructs the evolution of Hilary Putnam’s early, i.e. functionalist, views in the philosophy of mind. It distinguishes between the following two alternatives: weak functionalism, which asserts that traditional ontological questions about the mind are, in fact, pseudo-problems; and strong functionalism, the claim that the nature of mind can be discovered empirically if one acknowledges that mental states are defined relationally, without direct recourse to the properties of the brain. By analyzing Putnam’s reasons for rejecting weak functionalism and type (...) physicalism the author arrives at the conclusion that Putnam was wrong on both counts: weak functionalism was not an unstable position, and if one is willing to make some reasonable assumptions, strong functionalism is reducible to type physicalism. Finally, an attempt is made to isolate the causes of the premature success of strong functionalism. (shrink)

Summary The article explores psychological motives in Leopold Blaustein’s philosophy. Blaustein was educated in Lvov, Freiburg im Breisgau and Berlin. In his original explorations, he attempted to connect a phenomenological perspective with descriptive psychology. As trained by Twardowski, he took over some motives of understanding the method of philosophy (psychology), its objectives and aims. The author situates Blaustein also in a dialogue with Stumpf and next to the context of Dilthey’s humanistic psychology is examined. Finally, the article explores the influences (...) of Gestalt psychology on Blaustein. The ultimate thesis of the article is that Blaustein’s method can be grasped as a phenomenologically oriented descriptive psychology. (shrink)

In a small literary gem full of sardonic wit, brilliant insights, and provocative criticism Witold Gombrowicz discusses Kant, Hegel, Schopenhauer, Kierkegaard, Sartre, and Heidegger in six "one-hour" essays—and addresses Marxism in a "fifteen-minute" piece. "Who hasn't wished for a painless way to find out what the big shots of philosophy—Hegel and Kant, Nietzsche and Sartre—thought of the human condition? It has never been easy reading such formidable thinkers, and most explainers and textbooks either get it wrong or massacre the (...) language. So imagine my pleasure in opening Witold Gombrowicz's _Guide to Philosophy in Six Hours and Fifteen Minutes_, an exceptional effort at summarizing concepts in bold, declarative sentences.... [This book] is like the course in philosophy you wish you had taken."—David Lehman, _Bloomberg News_ "A must for every reader of Gombrowicz."—Denis Hollier, New York University. (shrink)

Theories of discursive integration form a group of theories that see the principles responsible for the integration of experience data (apperception) in the practices and schemes of discourse. These theories indicate that the use of language unites and organizes experience data. Their main assumption can be expressed as follows: this integration does not inhere in objects and cannot be derived from them; hence this integration cannot be secondarily expressed in language, but results exclusively from the use of language (or discourse). (...) In this article, Witold Marzęda gives an overview of narrativist theories, script theories, Gazzaniga and Dennett’s models, which refer to evolutionary psychology, and the theories of Lakoff and Johnson – all these being theories of discursive integration. Marzęda’s main objective is to formulate a paradox, which consists in a trap of self-referentiality into which these theories fall: they postulate some general properties of discourse, which, firstly, do not have to become at once the properties of individual models and which, secondly, do not admit of falsification. (shrink)

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

The paper sets out to prove that Leszek Kołakowski remained under a considerable influence of Friedrich Nietzsche’s ideas, which is evidenced by the way he poses and solves theoretical problems as well as his critical and often ironical detachment from the modern culture. He devoted a great deal of attention to nihilism, and searched for mythical conditioning of the thinking of the man of today; from the late 1950s, he was a follower of the philosophy of freedom and opposed philosophical (...) and historical determinism. He rejected systemic thinking and any fundamentalism in science. (shrink)

There seems to be something mysterious about applications of for- mal systems, including those of logic, to empirical reality 1 . If logic is to be applied to empirical situations, like those described in an ordinary lan- guage, then { it seems to some people { its statements cannot be necessary, or analytic, propositions. However, they are both applicable and necessary. This supposed puzzle constitutes a signicant part of the problem of philo- sophical foundations of logic 2 . To this (...) mind of the present writer, there is no mystery of applications, since any empirical, or even ostensive, predicate can be involved in cer- tain meaning postulates, e.g. \No red is green", which are both empirical and necessary propositions; empirical as they involve ostensibly dened predicated; necessary, as it is enough to know their meaning to state, their validity. The case of logical theorems can be considered at the same footing, logical constants being treated as dened ostensively. Nevertheless, not an individual state of mind but the actual state of scholarly discussions makes something a problem; in the present state of foundational discussions on logic, the \mystery of applications" preserves its vitality, hence any new way of dealing with it proves welcome. (shrink)

The main purpose of the article is to define the framework in which one can situate Leopold Blaustein’s philosophy. The author focuses on the question of the method which is used by Blaustein and he situates it in the historical-philosophical context. The article defends the thesis that Blaustein uses a method which can be labelled as a phenomenologically oriented descriptive psychology that is close to, though not identical with, Edmund Husserl’s project as formulated in the first edition of his Logical (...) Investigations and that is connected to Husserl’s 1925 lectures on the phenomenological psychology. The article is divided into four parts. In the first part, the author disputes the one-sided classifications of Blaustein’s philosophy either as a continuator of the analytical tradition of the Lvov-Warsaw School, or as a mere repetition of Husserl’s achievements. In the next part, the author sketches an intellectual biography of Blaustein and on this basis he defines the context in which one has to situate this thought. In this regard, two further parts of the article are devoted to two sources of inspiration for Blaustein. In the third part, a selection of methods and concepts of descriptive psychology are examined, and in the last part of the article, references to Husserl’s phenomenology are explored. (shrink)

My basic research question – well beyond the scope of this book – is what the relationships between cognitive processes and cultural structures and practices are. Here, I get closer to answering this question in the following five steps: (1) I present cognitive ecology as a research tradition in cognitive science, characteristic of the approaches to wide cognition, i.e., embodied, embedded, extended, ecological psychology, enactivism, etc. (2) I distinguish two dimensions of the distributed cognition approach: as a theoretical framework and (...) as a task model, focusing on the former. This distinction has so far eluded cognitive science theorists, and this approach has not been sufficiently analysed as a potential theory of cognitive science in general and the basis for its integration, being reduced to the dimension of the task model. (3) I discuss approaches in research on interactions in distributed cognitive systems, focusing more on the notion of external representations, and mostly on the notion of affordance. When assessing the potential of the latter, I look for consistency in what is crucial for understanding the interactions, between ecological psychology and design research. (4) I analyze the up to now underestimated potential of the distributed cognition approach in the dispute over the bounds of cognitive processes. (5) I identify and assess the analogies between the distributed cognition approach and the neo-mechanistic model of explanation that has become popular in cognitive science, and indicate possible benefits for the integration of the latter. As one can see, I am not trying to fully answer the question about the relationship between cognition and culture, but rather assess to what extent cognitive science in its current form is capable of. (shrink)

The paper is a short introduction to the article 'Affordances for robots' by Thomas E. Horton, Arpan Chakraborty and Robert St. Amant, in the context of applications of ecological psychology.

For a free filter F on $$\omega $$ ω, endow the space $$N_F=\omega \cup \{p_F\}$$ N F = ω ∪ { p F }, where $$p_F\not \in \omega $$ p F ∉ ω, with the topology in which every element of $$\omega $$ ω is isolated whereas all open neighborhoods of $$p_F$$ p F are of the form $$A\cup \{p_F\}$$ A ∪ { p F } for $$A\in F$$ A ∈ F. Spaces of the form $$N_F$$ N F constitute the (...) class of the simplest non-discrete Tychonoff spaces. The aim of this paper is to study them in the context of the celebrated Josefson–Nissenzweig theorem from Banach space theory. We prove, e.g., that, for a filter F, the space $$N_F$$ N F carries a sequence $$\langle \mu _n:n\in \omega \rangle $$ ⟨ μ n : n ∈ ω ⟩ of normalized finitely supported signed measures such that $$\mu _n(f)\rightarrow 0$$ μ n ( f ) → 0 for every bounded continuous real-valued function f on $$N_F$$ N F if and only if $$F^*\le _K{\mathcal {Z}}$$ F ∗ ≤ K Z, that is, the dual ideal $$F^*$$ F ∗ is Katětov below the asymptotic density ideal $${\mathcal {Z}}$$ Z. Consequently, we get that if $$F^*\le _K{\mathcal {Z}}$$ F ∗ ≤ K Z, then: (1) if X is a Tychonoff space and $$N_F$$ N F is homeomorphic to a subspace of X, then the space $$C_p^*(X)$$ C p ∗ ( X ) of bounded continuous real-valued functions on X contains a complemented copy of the space $$c_0$$ c 0 endowed with the pointwise topology, (2) if K is a compact Hausdorff space and $$N_F$$ N F is homeomorphic to a subspace of K, then the Banach space C(K) of continuous real-valued functions on K is not a Grothendieck space. The latter result generalizes the well-known fact stating that if a compact Hausdorff space K contains a non-trivial convergent sequence, then the space C(K) is not Grothendieck. (shrink)

Most discussions of the reproducibility crisis focus on its epistemic aspect: the fact that the scientific community fails to follow some norms of scientific investigation, which leads to high rates of irreproducibility via a high rate of false positive findings. The purpose of this paper is to argue that there is a heretofore underappreciated and understudied dimension to the reproducibility crisis in experimental psychology and neuroscience that may prove to be at least as important as the epistemic dimension. This is (...) the communication dimension. The link between communication and reproducibility is immediate: independent investigators would not be able to recreate an experiment whose design or implementation were inadequately described. I exploit evidence of a replicability and reproducibility crisis in computational science, as well as research into quality of reporting to support the claim that a widespread failure to adhere to reporting standards, especially the norm of descriptive completeness, is an important contributing factor in the current reproducibility crisis in experimental psychology and neuroscience. (shrink)

We argue that Yarkoni's proposed solutions to the generalizability crisis are half-measures because he does not recognize that the crisis arises from investigators' underappreciation of the roles of theory in experimental research. Rather than embracing qualitative analysis, the research community should make an effort to develop better theories and work toward consistently incorporating theoretical results into experimental practice.