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Logika racjonalności. W stronę modalnego platonizmu matematycznego

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Wilczek P.
Zagadnienia Filozoficzne w Nauce
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2011
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issue 49
98-122
PL
In this article Whitehead’s philosophy of mathematics is characterized as a Structural Second-Order Platonism and it is demonstrated that the Whiteheadian ontology is consistent with modern formal approaches to the foundation of mathematics. We follow the pathway taken by model-theoretically and semantically oriented philosophers. Consequently, it is supposed that all mathematical theories (understood as deductively closed set of sentences) determine their own models. These models exist mind-independently in the realm of eternal objects. From the metatheoretical point of view the hypothesis (posed by Józef Życiński) of the Rationality Field is explored. It is indicated that relationships between different models can be described in the language of modal logics and can further be axiomatized in the framework of the Second Order Set Theory. In conclusion, it is asserted that if any model (of a mathematical theory) is understood, in agreement with Whitehead’s philosophy, as a collection of eternal objects, which can be simultaneously realized in a single actual occasion, then our external world is governed by the hidden pattern encoded in the field of pure potentialities which constitute the above mentioned Field of Rationality. Therefore, this work can be regarded as the first step towards building a Logic of Rationality.
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A New Postulate of Set Theory – The Leibniz-Mycielski Axiom

100%
Wilczek P.
Filozofia Nauki
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2010
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vol. 18
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issue 3
79-103
PL
In this article we will present the Leibniz-Mycielski axiom (LM) of set theory (ZF) introduced several years ago by Jan Mycielski as an additional axiom of set theory. This new postulate formalizes the so-called Leibniz Law (LL) which states that there are no two distinct indiscernible objects. From the Ehrenfeucht-Mostowski theorem it follows that every theory which has an infinite model has a model with indiscernibles. The new LM axiom states that there are infinite models without indis-cernibles. These models are called Leibnizian models of set theory. We will show that this additional axiom is equivalent to some choice principles within the axio-matic set theory. We will also indicate that this axiom is derivable from the axiom which states that all sets are ordinal definable (V=OD) within ZF. Finally, we will explain why the process of language skolemization implies the existence of indis-cernibles. In our considerations we will follow the ontological and epistemological paradigm of investigations.
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Kanon literatury polskiej jako wyzwanie dla zagranicznego polonisty. Problem przekładu

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Wilczek P.
Wielogłos
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2008
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vol. 2
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issue 4
PL
POLISH LITERARY CANON AS A CHALLENGE FOR A FOREIGN SPECIALIST IN POLISH STUDIES: THE PROBLEM OF TRANSLATIONIn the article an attempt is made to answer the question why some Polish literary works are included in the world canon and some others, endorsed by Polish critics as excellent, are not. The author discusses The Western Canon of Harold Bloom and the criteria for including some literary works in Bloom’s canon and excluding  thers from this canon. There are only a few works of Polish literature on Bloom’s list. This is a starting point for the discussion about the presence of Polish literature in the world canon. As far as non-English literary works are concerned, the shape of the canon is infl uenced by several factors. Translation into English is only a prerequisite for a more important role in the world canon. Anthologies also play a decisive role in this process. However, there are a few other equally important factors: an infl uential, well known translator; a mainstream publishing house; recommendations of renowned critics; and reviews in prestigious journals and magazines. For that reason there are works and authors that can be found in the world canon, e.g. the latest translation of Ferdydurke, included as the only Polish literary work on a list of 501 Must-Read Books published by Bounty Books in 2007. This translation was included because it was published by Yale University Press, recommended by Susan Sontag and favourably reviewed by „The Observer”. This is also the case with the poetry Adam Zagajewski – he is in the canon not only because he is an excellent poet but also because he is a professor of prestigious American universities; his poetry and essays are present in magazines, such as „New Yorker”; he has an influential translator; his works are published by well known publishers and reviewed by „The New York Review of Books”. Only in such circumstances is there a chance to include a work of a minor literature in the world canon.
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Najnowsze tendencje w badaniach nad literaturą staropolską

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Wilczek P.
Świat Tekstów. Rocznik Słupski
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2007
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vol. 5
21-34
EN
The article is devoted to the most interesting aspects of research on Polish Medieval, Renaissance and Baroque literature in the last forty years. The most significant books, articles and research projects are discussed. The author focuses his attention on the following problems: Neo-Latin literature, studies on rhetoric, academic editing of Old Polish literature, research on religious literature and Baroque poetry, new methods of research inspired by thematology, philosophical hermeneutics, existentialism and phenomenology. The last two parts of the article are dedicated to research combining various disciplines (visual poetry, religious polemics, etc.) and to a significant development of Medieval studies from the 1990s. The author believes that studies on Old Polish literature form an essential part of literary studies in Poland and are interesting because of their interdisciplinary and comparative nature. There are still many important issues to be addressed. Neo-Latin studies have been long neglected and excluded from research on the history of Polish literature; there is a major shortage of specialists trained in the academic editing of old texts – both in Polish and Latin; there is a lack of serious academic monographs on major Renaissance and Baroque writers. Despite all these problems, achievements in this field are often spectacular.
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