Author: Koepke Ireneusz Title: ANDRZEJ WALICKI AND “WARSAW SCHOOL OF THE HISTORY OF IDEAS” (Andrzej Walicki i „warszawska szkoła historyków (historii) idei”) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 259-276 Keywords: ANDRZEJ WALICKI, WARSAW SCHOOL OF THE HISTORY OF IDEAS Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:This article is an attempt of presenting Andrzej Walicki connections with the so called Warsaw School of the History of Ideas and his (...) research on basic methodological issues created by this “school”, which are linked with the history of ideas and the history of philosophy. The most important are research rules which has been used by A. Walicki, and their consequences on his intellectual work as well as some critical remarks. (shrink)

Kazimierz Ajdukiewicz: about cognition -- Roman Ingarden: about the existence of the world -- Józef Maria Bocheński: on communism -- Rev. Józef Tischner: about the ethics of solidarity -- Kazimierz Twardowski: about happiness.

In the paper, several data reduction techniques for machine learning from big datasets are discussed and evaluated. The discussed approach focuses on combining several techniques including stacking, rotation, and data reduction aimed at improving the performance of the machine classification. Stacking is seen as the technique allowing to take advantage of the multiple classification models. The rotation-based techniques are used to increase the heterogeneity of the stacking ensembles. Data reduction makes it possible to classify instances belonging to big datasets. We (...) propose to use an agent-based population learning algorithm for data reduction in the feature and instance dimensions. For diversification of the classifier ensembles within the rotation also, alternatively, principal component analysis and independent component analysis are used. The research question addressed in the paper is formulated as follows: does the performance of a classifier using the reduced dataset be improved by integrating the data reduction mechanism with the rotation-based technique and the stacking? (shrink)

RubisCO is Earth's main enzyme responsible for CO2 fixation via carboxylation of ribulose-1,5-bisphosphate into organic matter. Besides the carboxylation reaction, RubisCO also catalyzes the oxygenation of RuBP by O2, which is probably as old as its carboxylation properties. Based on molecular phylogeny, the occurrence of the reactive oxygen species -removing system and kinetic properties of different RubisCO forms, we postulated that RubisCO oxygenase activity appeared in local microoxic areas, yet before the appearance of oxygenic photosynthesis. Here, in reviewing the literature, (...) we present a novel hypothesis: the RubisCO early oxygenase activity hypothesis. This hypothesis may be compared with the exaptation hypothesis, according to which latent RubisCO oxygenase properties emerged later during the oxygenation of the Earth's atmosphere. The reconstruction of ancestral RubisCO forms using ancestral sequence reconstruction techniques, as a promising way for testing of RubisCO early oxygenase activity hypothesis, is presented. RubisCO catalyzes carboxylation and oxygenation of ribulose-1,5-bisphosphate. Carboxylating properties of RubisCO are an ancient way for CO2 fixation into organic matter. However, an evolutionary importance of oxygenase activity of RubisCO remains enigmatic. Here, we formulated RubisCO early oxygenase activity hypothesis. According to this hypothesis, RubisCO oxygenase activity appeared yet before the appearance of oxygenic photosynthesis. (shrink)

In the paper, several data reduction techniques for machine learning from big datasets are discussed and evaluated. The discussed approach focuses on combining several techniques including stacking, rotation, and data reduction aimed at improving the performance of the machine classification. Stacking is seen as the technique allowing to take advantage of the multiple classification models. The rotation-based techniques are used to increase the heterogeneity of the stacking ensembles. Data reduction makes it possible to classify instances belonging to big datasets. We (...) propose to use an agent-based population learning algorithm for data reduction in the feature and instance dimensions. For diversification of the classifier ensembles within the rotation also, alternatively, principal component analysis and independent component analysis are used. The research question addressed in the paper is formulated as follows: does the performance of a classifier using the reduced dataset be improved by integrating the data reduction mechanism with the rotation-based technique and the stacking? (shrink)

There are four main positions in the argument about whether God exists: atheism, theism, agnosticism, and scepticism. From an epistemological standpoint, scepticism is the most rational; even if a decisive argument which would settle the debate has not been discovered yet, one cannot exclude the possibility of finding it eventually. Agnosticism is too radical, but theism and atheism exceed the available data. However, from a practical standpoint, choosing theism or atheism seems to be more rational than scepticism ; one of (...) them is bound to be right, because there are only two possibilities, one of which has to be true: either God exists or not. (shrink)

Christianization of Polish territories, according to the Western rite, incorporated these lands into the Western European civilization and emerging there political and legal doctrines, which were used in creating Polish political-legal thought. At the time of establishing social bonds and structures of the state, the political elite came into being and the Polish political thought developed. It corresponded with the main political thought and ideas of the West, but the Polish ideas displayed characteristics, necessary for protecting the Polish raison d’etat. (...) Development of political thought, original and particular for Polish conditions, dissimilar from the main European trends, may be a testimony to richness of intellectual and political ideas of past Polish generations. It was this political thought, that allowed the Polish national identity to survive, and caused that the fight for political independence was successful. Many contemporary researchers, including those from Western Europe, see influences of the past political ideas in the contemporary attitudes of Poles. (shrink)

We generalize the Bolzano-Weierstrass theorem on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel's constructible universe L. This characterization can be used to prove the generalized continuum hypothesis in L.

We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zermelo-Fraenkel axioms ZFC. This allows the following characterization of computable sets: a set of ordinals is ordinal register (...) computable if and only if it is an element of Gödel’s constructible universe L. (shrink)

Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor steps are determined by standard register machine commands. At limit times register contents are defined by appropriate limit operations. In this paper, we examine the ITRMs introduced by the third and fourth author (Koepke and Miller in Logic and Theory of Algorithms LNCS, pp. 306–315, 2008), where a register content at a limit time is (...) set to the lim inf of previous register contents if that limit is finite; otherwise the register is reset to 0. The theory of these machines has several similarities to the infinite time Turing machines (ITTMs) of Hamkins and Lewis. The machines can decide all ${\Pi^1_1}$ sets, yet are strictly weaker than ITTMs. As in the ITTM situation, we introduce a notion of ITRM-clockable ordinals corresponding to the running times of computations. These form a transitive initial segment of the ordinals. Furthermore we prove a Lost Melody theorem: there is a real r such that there is a program P that halts on the empty input for all oracle contents and outputs 1 iff the oracle number is r, but no program can decide for every natural number n whether or not ${n \in r}$ with the empty oracle. In an earlier paper, the third author considered another type of machines where registers were not reset at infinite lim inf’s and he called them infinite time register machines. Because the resetting machines correspond much better to ITTMs we hold that in future the resetting register machines should be called ITRMs. (shrink)

We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the (...) algorithmic approach to admissible recursion theory by indicating how the proof of the Sacks–Simpson theorem, i.e., the solution of Post’s problem in α-recursion theory, could be based on α-machines, without involving constructibility theory. (shrink)

The book is not only dedicated to linguists, but also to readers who are not familiar with notations developed in linguistics. The first part of the study presents philosophical justifications for linguistic settlements. These are based on the phenomenological reduction of Edmund Husserl, Karl R. Popper's falsificationism, the moderate rationalism of science of Izydora Dąmbska and Andrzej Bogusławski's lack of the nomological explanation in linguistics. The second part presents a re-examination of the solutions proposed in the field of linguistics, some (...) new philosophical explanations and a discussion of the truth of linguistic propositions. (shrink)

Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by $\mathscr{P}(\omega)/\mathrm{finite}$. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are \emph{no} intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality (...) of the associated measures. (shrink)

By using the notion of a simplified (κ,1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.

We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals . The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ω ω , and (...) a non-closure property of elementary embeddings of the universe. In some cases, equiconsistencies are obtained. (shrink)

Using the Friedman-Koepke Hyperfine Structure Theory of [2], we provide a short construction of a gap 1 morass in the constructible universe.

We give a proof ofTheorem 1. Let κ be the smallest cardinal such that the free subset property Fr ω (κ,ω 1)holds. Assume κ is singular. Then there is an inner model with ω1 measurable cardinals.

We propose a simple notion of "extender" for coding large elementary embeddings of models of set theory. As an application we present a self-contained proof of the theorem by D. Martin and J. Steel that infinitely many Woodin cardinals imply the determinacy of every projective set.

We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals. Without the Axiom of Choice, successor cardinals may be almost Ramsey. From fairly mild supercompactness assumptions, we construct a model of ZF + ${\neg {\rm AC}_\omega}$ in which every infinite cardinal is almost Ramsey. Core model arguments show that strong assumptions are necessary. Without successors of singular cardinals, we can weaken this to an equiconsistency of the following theories: “ZFC + There is a proper class of regular almost (...) Ramsey cardinals”, and “ZF + DC + All infinite cardinals except possibly successors of singular cardinals are almost Ramsey”. (shrink)

We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...) all sufficiently large m<ω, the class of measurables λ with oM≥ωm is, in V, stationary below m+2. (shrink)

We prove that every homogeneously Souslin set is coanalytic provided that either (a) 0long does not exist, or else (b) V = K, where K is the core model below a μ-measurable cardinal.

We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom of Choice (AC). By the new notion of parallel Prikry forcing that we introduce, we obtain surjective failures of SCH using only one measurable cardinal, including a surjective failure of Shelah's pcf theorem about the size of the power set of $\aleph _{\omega}$ . Using symmetric collapses to $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ , (...) or $\aleph _{\omega _{2}}$ , we show that injective failures at $\aleph _{\omega}$ , $\aleph _{\omega _{1}}$ , or $\aleph _{\omega _{2}}$ can have relatively mild consistency strengths in terms of Mitchell orders of measurable cardinals. Injective failures of both the aforementioned theorem of Shelah and Silver's theorem that GCH cannot first fail at a singular strong limit cardinal of uncountable cofinality are also obtained. Lower bounds are shown by core model techniques and methods due to Gitik and Mitchell. (shrink)

We show that for all natural numbers n, the theory “ZF + DC $_{\aleph_n}$ + $\aleph_{\omega}$ is a Rowbottom cardinal carrying a Rowbottom filter” has the same consistency strength as the theory “ZFC + There exists a measurable cardinal”. In addition, we show that the theory “ZF + $\aleph_{\omega_1}$ is an ω 2-Rowbottom cardinal carrying an ω 2-Rowbottom filter and ω 1 is regular” has the same consistency strength as the theory “ZFC + There exist ω 1 measurable cardinals”. We (...) also discuss some generalizations of these results. (shrink)