Unfortunately, Adam Smith’s undeserved legacy as a proponent of laissez-faire and liberal institutions at the international scope inhibits profiting from his refined analysis of international affairs. I argue that the Wealth of Nations’ chapter on colonies contains Smith’s discussion of the sovereign’s adaptation to ignorance in global politics. I examine the sense in which the sovereign is ignorant according to Smith and how sovereigns adapt to ignorance with varying success. His comparative analysis suggests that reduction of one’s share in ignorance (...) is not always desirable, and a priori rejection of ignorance is impractical because it deprives of a potentially advantageous resource. A careful reading of his work enables learning from his approach to global politics, without filtering it through his ideas on the free market. (shrink)

Multidrug resistance (MDR) is developed in a population of somatic mammalian cells in vivo or in vitro when they are selected for resistance to each of a large group of drugs (colchicine, adriamycin, actinomycin D, etc.). It is produced by the amplification of some unknown gene(s) whose product(s) evidently change(s) the plasma membrane permeability of a cell to a selective agent and to other unrelated compounds. A large specific genomic region (150–250 kbp) undergoes amplification in MDR cells selected for the (...) resistance to different drugs. Amplified DNA is located in homogeneously staining regions of chromosomes, double minute chromosomes and small chromatin bodies – episome‐like structures that replicate out of the S‐phase of a cell cycle. The selection of MDR cell variants is accompanied by regular karyotypic evolution specific for this type of drug resistance. (shrink)

Prominent thinkers such as Jurgen Habermas and Michael Sandel are warning that biomedical enhancements will undermine fundamental political values. Yet whether biomedical enhancements will undermine such values depends on how biomedical enhancements will function, how they will be administered and to whom. Since only few enhancements are obtainable, it is difficult to tell whether these predictions are sound. Nevertheless, such warnings are extremely valuable. As a society we must, at the very least, be aware of developments that could have harmful (...) consequences. Indeed, if important values were to be jeopardized, we should take appropriate measures to protect them. This paper focuses on four central values: solidarity, personal responsibility, equality and autonomy. It delineates the conditions under which biomedical enhancements would undermine these values. It also details the circumstances under which these values would be unaffected by enhancements as well as those under which they would be promoted. Specifying these conditions is valuable; it would enable society to prepare appropriate ethical guidelines and policy responses in advance. (shrink)

The main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment (...) experienced by the previous generation. (shrink)

Śiḥot maran ha-Mashgiaḥ Mohari Leṿinshṭain, zatsal -- Ḥidushe torato ʻa. Mas. B.ḳ. ṿe-liḳuṭim -- Leḳeṭ mi-maʼamraṿ mi-moreshet Daṿid Heber ṿe-ʻinyene ha-shaʻah.

To ascertain the context of Il’enkov’s philosophy, the author delves into the history of philosophy since the Sophists and Plato. For Il’enkov, philosophy is not an abstract science “about everything, ” but a study of ideas – forms which are identical for thinking and being. These objective and universal forms of thought are explained as products and schemes of human activity creating the world of culture and reified in its “smart” things.

To ascertain the context of Il'enkov's philosophy, the author delves into the history of philosophy since the Sophists and Plato. For Il'enkov, philosophy is not an abstract science "about everything," but a study of ideas -- forms which are identical for thinking and being. These objective and universal forms of thought are explained as products and schemes of human activity creating the world of culture and reified in its "smart" things.

ThevariationunderdomesticationhasbeenstudiedbyevolutionarybiologysincethebeginningoftheDarwinistrese archprogramme,highlightingartificialselectionasapartofthedevelopmentoftheconceptofnaturalselection.R ecently,nicheconstructiontheoryhasbeenusedtoanalyzetheprocessofdomesticationwhichhashistoricallybeen partofsociallifeforhumanbeings.Inthepresentworkwemakeanapproachtotheimplicationsofartificialselectio nasanelementinthelineofdialecticaltensionbetweennatureandsociety.WeanalyzefromaMarxistperspectivethe elementsofcontinuityanddiscontinuitythatthereproductionofa“secondnature”introducesintheprocessofnich econstruction.Wefocusonthepoliticdimensionofusevalue(Echeverría2001)asanemergingprocessinthere-produ ctionofasocialandculturalidentityinhumansocieties.Inthisworkwefocusondomesticatedplants.Theexistence ofatelosorsubjacentintentionalityconfiguresdistinctivefeaturesofhumannicheconstruction(Zeder2009)and centrallyofartificialselection.Thereproductionofasecondnatureisdirectedbyateloswhichisnotonlynornece ssarilyrelatedtothemagnitudeofresourcesappropriatedbyhumanbeings,butalsotothegenerationofusevalueada ptedtoacertainformofsociallifethatisrecreatedandgivenplace:apoliticdimension.

Analyzes principal forces that determined the direction of Camus' thought on ethics and political values.

Translation of Lev Shestov's What is Philosophy?

The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

I begin my eulogy to folly not in jest as did the illustrious Erasmus of Rotterdam in the old days, but in all sincerity and from all my heart. In this task Berdiaev's new book will be of great assistance to me. Had he wished to do so, he could have titled it, following his long-deceased colleague's example, In Praise of Folly, because its purpose is to challenge common sense. True, the book is a collection of articles written in the (...) last six years, hence, properly speaking, it does not and cannot serve some one purpose. Six years is a long time: not only a writer like Berdiaev, but any writer will change to some extent during so long a period. The book opens with an article written long ago, "The Struggle for Idealism" [Bor'ba za idealizm], in which the author still maintains a strictly Kantian viewpoint that admits, as we know, common sense and all its accompanying virtues. Then the author gradually evolves and, by the end of the book, he openly declares war on common sense, but what he opposes to common sense is not Folly, as is usually done, but Great Reason. Of course, one can express oneself in this way, calling Folly Great Reason, and, if you like, this has a deep meaning or, more precisely, a deep sting, for what can be more insulting and humiliating to common sense than to confer the honorific title of Great Reason on Folly? Until now common sense has been accepted as the father and closest friend of all minds, great and small. Now, Berdiaev, scorning genealogy and historically shaped heraldry, elevates "opposition to common sense," that is, Folly to the order of Great Reason. No doubt, this is very audacious, but Berdiaev is a writer who above all is daring and, in my opinion, this is his greatest strength. I would say that his gift, his philosophical and literary talent, lies in his audacity. As soon as it abandons him, the source of his inspiration evaporates, he has nothing to say, and he ceases to be himself. But I have run too far ahead. Let us return to his evolution or, rather, to the evolution of his idea. (shrink)

This is a philosophical paper in favor of the many-worlds interpretation of quantum theory. The necessity of introducing many worlds is explained by analyzing a neutron interference experiment. The concept of the “measure of existence of a world” is introduced and some difficulties with the issue of probability in the framework of the MWI are resolved.

This article compares the sections on the qualities desirable in a wife in Abū Ḥāmid al-Ghazālī’s Iḥyāʾ ʿulūm al-dīn and Bar Hebraeus’s Ethicon, which the West Syrian writer modeled on al-Ghazālī’s work. The article first establishes that al-Ghazālī based his profile of the ideal wife on a jurisprudential discussion of the topic by his teacher, Imām al-Ḥaramayn al-Juwaynī, expanding it, however, by adding anecdotes from Sufi literature and reasoned arguments on how “the good wife” will best facilitate her husband’s devotion (...) to God. The article then moves to consider how Bar Hebraeus appropriates, reconfigures, and reframes as Christian teaching al-Ghazālī’s discussion. Finally, the article argues that the similarity between the two texts demonstrates that both carve out a particular notion of male piety intelligible and resonant in their different religious traditions and in the broader monotheistic culture of the premodern Middle East. (shrink)

Progressions of iterated reflection principles can be used as a tool for the ordinal analysis of formal systems. We discuss various notions of proof-theoretic ordinals and compare the information obtained by means of the reflection principles with the results obtained by the more usual proof-theoretic techniques. In some cases we obtain sharper results, e.g., we define proof-theoretic ordinals relevant to logical complexity Π1 0 and, similarly, for any class Π n 0 . We provide a more general version of the (...) fine structure relationships for iterated reflection principles (due to U. Schmerl [25]). This allows us, in a uniform manner, to analyze main fragments of arithmetic axiomatized by restricted forms of induction, including IΣ n , IΣ n − , IΠ n − and their combinations. We also obtain new conservation results relating the hierarchies of uniform and local reflection principles. In particular, we show that (for a sufficiently broad class of theories T) the uniform Σ1-reflection principle for T is Σ2-conservative over the corresponding local reflection principle. This bears some corollaries on the hierarchies of restricted induction schemata in arithmetic and provides a key tool for our generalization of Schmerl's theorem. (shrink)

Recently, the variety of the financial frauds have increased, while the number of victims became difficult to estimate. The purpose of this paper is to present the main profiles of financial frauds’ victims using a reviewing method. The analysis captures the main theoretical and empirical background regarding the motives and circumstances of becoming a victim, the dynamics of several social and demographical characteristics of this type of victims, as well as a sample of relevant case studies from some developing countries. (...) The main finding is that, in literature, most of the victims are male people of different ages, employed, married or single, regardless the level of education. For developing countries such as China, India and Nigeria, the majority of victims act out of naivety and desire to escape from poverty, while some victims from Latin America, China and Nigeria are influenced by greed and lack of empathy, without thinking of further consequences for their families and friends involved. Moreover, most of the victims are convinced to invest in financial schemes by family members, friends, or acquaintances. (shrink)

A well-known result states that, over basic Kalmar elementary arithmetic EA, the induction schema for ∑n formulas is equivalent to the uniform reflection principle for ∑n + 1 formulas . We show that fragments of arithmetic axiomatized by various forms of induction rules admit a precise axiomatization in terms of reflection principles as well. Thus, the closure of EA under the induction rule for ∑n formulas is equivalent to ω times iterated ∑n reflection principle. Moreover, for k < ω, k (...) times iterated ∑n reflection principle over EA precisely corresponds to the extension of EA by k nested applications of ∑n induction rule.The above relationship holds in greater generality than just stated. In fact, we give general formulas characterizing in terms of iterated reflection principles the extension of any given theory by k nested applications of ∑n or Πn induction rules. In particular, the closure of a theory T under just one application of ∑1 induction rule is equivalent to T together with ∑1 reflection principle for each finite Π2 axiomatized subtheory of T.These results have closely parallel ones in the theory of subrecursive function classes. The rules under study correspond, in a canonical way, to natural closure operators on the classes of provably recursive functions. Thus, ∑1 induction rule precisely corresponds to the primitive recursive closure operator, and ∑1 collection rule, introduced below, corresponds to the elementary closure operator. (shrink)

Provability logic GLP is well-known to be incomplete w.r.t. Kripke semantics. A natural topological semantics of GLP interprets modalities as derivative operators of a polytopological space. Such spaces are called GLP-spaces whenever they satisfy all the axioms of GLP. We develop some constructions to build nontrivial GLP-spaces and show that GLP is complete w.r.t. the class of all GLP-spaces.

We suggest an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture proof-theoretic information. We use this method to analyze Peano arithmetic and show how an ordinal notation system up to 0 can be recovered from the corresponding algebra in a canonical way. This method also establishes links between proof-theoretic ordinal analysis and the work which has been (...) done in the last two decades on provability logic and reflection principles. Because of its abstract algebraic nature, we hope that it will also be of interest for non-prooftheorists. (shrink)

It is argued that the many-worlds interpretation is by far the best interpretation of quantum mechanics. The key points of this view are viewing the wave functions of worlds in three dimensions and understanding probability through self-locating uncertainty.

This paper describes two quotation strategies employed by speakers of Nanti, one involving grammaticalized quotatives and another involving complement-taking verbs of saying, and examines the consequences of the pragmatic differences between these strategies for two key questions in the study of evidentiality: first, the importance of degree of grammaticalization in delimiting ‘evidentials’; and second, the importance of the analytical distinction between epistemic modal and ‘source of information’ evidential meanings. Nanti use of the two quotation strategies is specifically analyzed in the (...) context of self-quotation practices in order to isolate specific aspects of their pragmatics. This analysis shows that the lexical quotative strategy expresses that the quoted party is not only the source of the content of the utterance, but is also an ‘illocutionary source’, who is committed to the interactional force of the utterance, while the grammaticalized quotative strategy does not indicate such a commitment. The functional difference between lexical and grammatical quotative strategies in Nanti is compared with differences between lexical and grammaticalized quotative and reportive strategies found in other languages, and the Nanti results are found to be consistent with cross-linguistic tendencies towards functional differentiation of lexical quotative and reportives, on the one hand, and their grammaticalized counterparts, on the other. These facts, it is argued, motivate a distinction on functional grounds between grammaticalized reportives and quotatives and their lexical counterparts, supporting the use of grammaticalization as a criterion for distinguishing evidentials proper from evidential strategies. The commitment-augmenting function of the lexical quotative construction in Nanti self-quotation is then examined in light of the commitment-diminishing function commonly attributed to quotatives and reportives. It is argued that both types of commitment-modulating effects emerge as implicatures from the basic information and illocutionary source semantics of Nanti lexical quotatives, and from pragmatic reasoning based on whether the quoted party is first person or third person. The fact that both commitment-modulating functions of Nanti lexical quotatives are derived from semantics of lexical quotatives elements is argued to show that the distinction between information source and epistemic modal meanings, often taken to be a pivotal notional distinction in defining evidentiality as a grammatical category, is also essential to the proper analysis of the pragmatics of evidential strategies in discourse. (shrink)

Le messianisme fait à la fois partie des principaux articles de foi du Judaïsme et appelle en même temps son renversement lorsqu’il se réalise de manière effective. Le messianisme s’exprime alors à travers une critique de la loi comme impératif catégorique, étatique et particulariste exercée par une instance transcendante. Saint-Paul incarne très certainement le fer de lance de cette révolution messianique au fondement de l’universalisme. Cette inauguration d’une loi immanente au sujet destinée à supplanter la loi transcendante du Judaïsme se (...) prolonge à travers un certain nombre de figures de la modernité, notamment celles de Spinoza et Freud. Le messianisme n’est pas à entendre ici comme pure et simple trahison de la loi juive mais au contraire comme révélation d’une fracture qui lui appartient originellement. (shrink)

A well-known polymodal provability logic inlMMLBox due to Japaridze is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic. This system plays an important role in some recent applications of provability algebras in proof theory. However, an obstacle in the study of inlMMLBox is that it is incomplete w.r.t. any class of Kripke frames. In this paper we provide a complete Kripke semantics for inlMMLBox . First, we isolate a certain subsystem inlMMLBox (...) of inlMMLBox that is sound and complete w.r.t. a nice class of finite frames. Second, appropriate models for inlMMLBox are defined as the limits of chains of finite expansions of models for inlMMLBox . The techniques involves unions of n -elementary chains and inverse limits of Kripke models. All the results are obtained by purely modal-logical methods formalizable in elementary arithmetic. (shrink)

We introduce the logics GLP Λ, a generalization of Japaridze’s polymodal provability logic GLP ω where Λ is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall provide a reduction of these logics to GLP ω yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP Λ and the decidability of GLP Λ for recursive orderings Λ. Further, we give a restricted axiomatization of the variable-free fragment (...) of GLP Λ. (shrink)

We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant ‘true’ by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform reflection schemata in arithmetic, possibly of unrestricted logical complexity. We formulate an arithmetically complete calculus with modalities labeled by natural numbers and ω, where ω corresponds to the full uniform reflection schema, whereas n<ω corresponds to its restriction to arithmetical Πn+1-formulas. This (...) calculus is shown to be complete w.r.t. a suitable class of finite Kripke models and to be decidable in polynomial time. (shrink)

We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$$\end{document} in question, d > 1, we fix a natural extension of Peano Arithmetic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T \supseteq \sf{PA}}$$\end{document}, that proves the corresponding second-order sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{WPO}\left({\rm (...) S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$$\end{document}. Having this we consider the following parametrized first-order slow well-partial-ordering sentence \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \forall K > 0 \right) \left( \exists M > 0\right) \left( \forall x_{0},\ldots,x_{M}\in {\rm S}\text{\textsc{eq}}^{d}\right)$$\end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \left( \forall i\leq M\right) \left( \left| x_{i}\right| 1}$$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$$\end{document} is not provable in T.Moreover, by the well-known proof theoretic equivalences we can just as well replace T by PA or ACA0 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta _{1}^{1}\sf{CA}}$$\end{document}, if d = 2 and d = 3, respectively.In the limit case d → ∞ we replaceEFA-provably computable reals r by EFA-provably computable functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f: \mathbb{N} \rightarrow \mathbb{R}_{+}}$$\end{document} and prove analogous theorems. (In the sequel we denote by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}_{+}}$$\end{document} the set of EFA-provably computable positive reals). In the basic case T = PA we strengthen the basic phase transition result by adding the following static threshold clause\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1\right)}$$\end{document} is still provable in T = PA (actually in EFA). Furthermore we prove the following dynamic threshold clauses which, loosely speaking are obtained by replacing the static threshold t by slowly growing functions 1α given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1_{\alpha }\left( i\right)\,{:=}\,1+\frac{1}{H_{\alpha }^{-1}\left(i\right) }, H_{\alpha}}$$\end{document} being the familiar fast growing Hardy function and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H_{\alpha }^{-1}\left( i\right)\,{:=}\,\rm min \left\{ j \mid H_{\alpha } \left ( j\right) \geq i \right\}}$$\end{document} the corresponding slowly growing inversion. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha < \varepsilon _{0}}$$\end{document}, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1_{\alpha}\right)}$$\end{document} is provable in T = PA. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sf{SWP}\left( {\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2},1_{\varepsilon _{0}}\right)}$$\end{document} is not provable in T = PA. We conjecture that this pattern is characteristic for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T\supseteq \sf{PA}}$$\end{document} under consideration and their proof-theoretical ordinals o (T ), instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon _{0}}$$\end{document}. (shrink)

By a result of Paris and Friedman, the collection axiom schema for $\Sigma_{n+1}$ formulas, $B\Sigma_{n+1}$ , is $\Pi_{n+2}$ conservative over $I\Sigma_n$ . We give a new proof-theoretic proof of this theorem, which is based on a reduction of $B\Sigma_n$ to a version of collection rule and a subsequent analysis of this rule via Herbrand's theorem. A generalization of this method allows us to improve known results on reflection principles for $B\Sigma_n$ and to answer some technical questions left open by Sieg (...) [23] and Hájek [9]. We also give a new proof of independence of $B\Sigma_{n+1}$ over $I\Sigma_n$ by a direct recursion-theoretic argument and answer an open problem formulated by Gaifman and Dimitracopoulos [8]. (shrink)

Historically, appearance of the quantum theory led to a prevailing view that Nature is indeterministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is argued that ontic interpretations of the quantum wave function provide simpler and clearer physical explanation and that the many-worlds interpretation is the most attractive since it provides a deterministic and local theory for our physical Universe explaining the illusion of (...) randomness and nonlocality in the world we experience. (shrink)

From the institutional inauguration of the discipline in 1972, philosophy of sport tends to expand, spreading itself around the world from one country to another, and including new philosophical in...