I shall outline the topic from a historical perspective, placing the main emphasis on the hundred years’ period spanning 1870–1970.

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

Metafizyczny kreacjonizm a paradoksy teizmu ewolucyjnego: przyczynek do dyskusji w ramach współczesnego tomizmu Autor artykułu dowodzi, że metafizyczny kreacjonizm, z którym spotykamy się w filozofii św. Tomasza z Akwinu, w odróżnieniu od kreacjonizmu amerykańskiego oraz teologiczno-‑biblijnego, jest teorią, która wyrasta z czysto filozoficznego wyjaśnianie początków świata i człowieka. Nie jest zatem ideą biblijną przeniesioną na teren filozofii. Podobnie jak teizm metafizyki Arystotelesa, a także teizm metafizyki św. Tomasza z Akwinu nie jest teizmem religijnym, lecz teizmem czysto filozoficznym, gdyż wyrasta z (...) metafizycznego wyjaśniania rzeczywistości. Kreacjonizm metafizyczny jest ostatecznym wyjaśnieniem źródła istnienia bytów, które dane są nam w doświadczeniu, jako niekonieczne w istnieniu i zmienne. Natomiast kreacjonizm amerykański, jest interpretacja biologiczno-kosmologiczną biblijnej prawdy o stworzeniu świata w określonym przedziale czasowym i w punkcie wyjścia odwołuje się do danych Objawienia, które chce naukowo potwierdzić Artykuł został podzielony na dwie części. W części pierwszej zostały przedstawione węzłowe elementy metafizycznej teorii stworzenia ex nihilo i jej rozumienie. W drugiej zaś części artykułu zostały przywołane elementy teizmu ewolucyjnego, które z punktu metafizycznego kreacjonizmu są źródłem różnych paradoksów, a niekiedy i absurdów oraz domagają się ponownego przemyślenia. (shrink)

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T 0-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T 0-closure spaces. By this theorem we obtain the following characterization of the consequence (...) operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X. (shrink)

Dynamical Grammar explores the consequences for language acquisition, language evolution, and linguistic theory of taking the underlying architecture of the language faculty to be that of a complex adaptive dynamical system. It contains the first results of a new and complex model of language acquisition which the authors have developed to measure how far language input is reflected in language output and thereby get a better idea of just how far the human language faculty is hard-wired.

The article attempts to define the concept of “post-neo-Kantianism” based on the nature of its relationship to the concept of “neo-Kantianism”. Concerning this matter, the author poses the following tasks: to characterize the phenomenon of neo-Kantianism, to point out the problems of its definition, to identify the relevance of the term “post-neo-Kantianism” and its relation to the philosophy of I. Kant in particular. The author emphasizes the need to introduce this term in the classification of philosophy of the XX century (...) with the appropriateness of building the model of “Kantianism - Neo-Kantianism - Neo-Neo-Kantianism - Post-Neo-Kantianism”, where each new stage is determined by the nature of the reflection of thinkers of a certain period over the fundamental philosophical problems articulated in Kant's “Critics”. Among the post-Neo-Kantians, A. Noras names thinkers traditionally considered to be german phenomenologists, such as E. Husserl and M. Heidegger: it is from the philosophical concept of Husserl that one can speak of the emergence of post-Neo-Kantianism, and the semantically correct interpretation of Heidegger, according to author, is most clearly understood in the framework of Baden Neo-Kantianism. Investigating the phenomenon of post-Neo-Kantianism, the need is established for answering a question regarding the preceding Neo-Kantian tradition, within which there is still a number of contradictions unresolved in the history of philosophy regarding the classification of Neo-Kantian schools and the distinction between the two periods of Neo-Kantianism: early and late. Neo-Kantianism shows the relevance of Kantian philosophy, highlighting the ongoing debate about understanding the Kantian “Critique of Pure Reason”. Post-Neo-Kantianism plays an important role in terms of the perspectives of modern Kant studies, which include Gottfried Martin, Manfred Brelage, or Hans-Michael Baumgartner. (shrink)

Searching for what is common to all Henryk Elzenberg’s works, the author of the paper wishes to reveal the uniqueness of his ways of thinking. For this purpose, the author points at a variety of intellectual ways Elzenberg explored, considers the links between thinking and action, and asks a question about the aim of thinking and its relation to what was thought earlier. The independence of Elzenberg’s thinking, his diligence and seriousness grounded on the importance of issues he touched on (...) render his philosophizing a case of ethical action. The firmness of the analyses that the Polish philosopher performed—particularly in the field of axiology—comes together with responsibility for the subject matter of his thinking. Strict mental discipline he managed to maintain in the face of values as well as his determination to hold onto them in his own life make Elzenberg a Master who is himself an instantiation—exemplum—of integrity in thinking. Maybe, we also could learn something from him, and, however difficult challenge it may seem, maybe it would be worthwhile to take it on and go our own way. (shrink)

A. Klimczuk, Rekonwersja i outplacement nauczycieli i instruktorów praktycznej nauki zawodu, [in:] M. Juchnicka, Doradcze i edukacyjne aspekty reorientacji zawodowej i wsparcia zatrudnienia zwalnianych pracowników oświaty, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2015, pp. 157-233.