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.

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)

We study the fragment of Peano arithmetic formalizing the induction principle for the class of decidable predicates, $I\Delta_1$ . We show that $I\Delta_1$ is independent from the set of all true arithmetical $\Pi_2-sentences$ . Moreover, we establish the connections between this theory and some classes of oracle computable functions with restrictions on the allowed number of queries. We also obtain some conservation and independence results for parameter free and inference rule forms of $\Delta_1-induction$ . An open problem formulated by J. (...) Paris is whether $I\Delta_1$ proves the corresponding least element principle for decidable predicates, $L\Delta_1$ (or, equivalently. the $\Sigma_1-collection$ principle $B\Sigma_1$ ). We reduce this question to a purely computation-theoretic one. (shrink)

Due to evidence that traumatic experience impacts the brain, the body (concerning sensory sensitivity), and the mind, a recent study that attempted to answer the question of whether the effects of CSA can be reversed by using a multidisciplinary approach consisting of dual treatments: hyperbaric & psychotherapy, was conducted. Its results showed that in addition to improvement of brain functionality, symptoms of distress were significantly reduced. The current paper aims to present the process as experienced by the 40 female childhood (...) sexual abuse survivor participants. Data included participants’ daily journals and drawings, and participants’ summaries presented verbally and written, 6-months after the study ended. A phenomenological analysis was used. Results showed three phases, the initial phase – remembering the trauma from both physical and cognitive aspects, the second phase - physiological relaxation as well as positive memories emerge; and, the third phase – bouncing back to life. The results are discussed in light of the study theoretical model and Lev-Wiesel (2014) childhood sexual abuse conceptualization. (shrink)

The first volume in the new critical edition of Lev Shestov's work in English, which I have been asked to coordinate. The volume includes my preface and annotations.

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)

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)

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)

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.

Review text: "A specialist collection, but fascinating in its sociological insights."John Turnbull in: New Directions 3/2010.

Introduction A good example of emergentism - interpreted by M. Siderits [1] as - Buddhist reductionism) is an excerpt from the dialogue between King Milinda[4] and the monk Nāgasena[5] about the self, which is part of the text close to the Abhidhamma tradition entitled "Milindapaha". The text was published by V. Trenckner in 1880 in [2] and translated into English by T.W. Rhys Davids [3] in the series "Sacred Books of the East". Furthermore, there is an English translation by I. (...) B. Horner [4] and Bhikkhu Pesala [5] and into Russian by A.V. Paribok [6]. There are also German [7] and French translations [8; 9]. Yet the classical translation by Rhys Davids is currently largely obsolete. Paribok's translation into Russian is not convenient for practical use as it would need to be further translated into English, and this double translation, which is not very good from the point of view of the philological approach to the text. We have therefore decided to make our own, new translation of the passage from "Milindapaha", in which the dialogue about the self is being held. (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.

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)

“All Things Are Possible” is a 1920 English translation of the 1905 work by the Ukrainian/Russian existentialist philosopher Shestov. It draws on the aphoristic style of Nietzsche and deals with as diverse issues as science, rationalism and religion. This edition also includes an interesting foreword by D. H. Lawrence. Highly recommended for those with an interest in philosophy, and particularly existentialism. Contents include: “Lev Shestov”, “Note”, “Foreword”, “Zu Fragmentarish Ist Welt Und Leben”, and “Nur Für Schwindelfreie”. Many vintage books such (...) as this are increasingly scarce and expensive. It is with this in mind that we are republishing this volume now in an affordable, modern, high-quality edition complete with a specially-commissioned new biography of the author. (shrink)

At IAPS Ljubljana conference (September 2007) Dag Vidar Hanstad and Sigmund Loland presented a paper on elite-level athletes' duty to provide information on their whereabouts, to decide between two opposing positions: is this WADA demand justifiable anti-doping work or an indefensible surveillance regime? They concluded that on moral grounds this regime is conditionally acceptable, the condition being the acceptability of a general framework and objectives embodied in anti-doping global legislative foundations (the World Anti-Doping Code). But, as they said, principled objections (...) against the system have more universal relevance, which has to be taken seriously . To take this ambiguous and intriguing conclusion a step further, I propose a legal rather than ethical approach, from the aspect of constitutional and international human rights law, and the possible clash of two legally acknowledged values - the concept of elite sport without doping, and the concept of individual human rights. This conflict between ideological or moral values and the legality of individual rights is not a novelty. This paper presents three instances of this conflict: Bernard de Mandeville's differentiation between public and private values; Eug ne Sue's parallel legal and civil morals; and the contemporary moralisation of law which conflates legality into morality. The subordination of legality to morality has potentially dangerous consequences: here, Agamben's 'state of exception' comes to mind, with his analysis of potestas and auctoritas. However, in the case of sport and the war against doping, the origin of power is not in the nation state; it originates in civil society's non-governmental national and international bodies recognised as autonomous sources of legal order. (shrink)

A recent claim by Meehan that quantum mechanics has a new “control problem” that puts limits on our ability to prepare quantum states and revises our understanding of the no-cloning theorem is examined. We identify flaws in Meehan’s analysis and argue that such a problem does not exist.

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

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)

The environment in which humans evolved is strongly and positively autocorrelated in space and time. Probabilistic judgments based on the assumption of independence may not yield evolutionarily adaptive behavior. A number of “faults” of human reasoning are not faulty under fuzzy arithmetic, a nonprobabilistic calculus of reasoning under uncertainty that may be closer to that underlying human decision making.

Naturalist aestetics, strictly speaking, is a move to establish naturalist explanation of aesthetic phenomena. It was nearly forgotten, at least in the history of aesthetics, where, if mentioned, it was put aside as something dead and despised. Its reappearance in recent years, among other occasions at the XIVIVth International Congress of Aesthetics (Rio de Janeiro, 2004), came as a surprise and a challenge. Its second modernity has predecessors in the first modernity, and Darwin is only one of the many, and (...) its background in contemporary naturalist proposals in social and human sciences (biosociology, evolutionary psychology, cognitive science, etc.). Contemporary proposals to explain some basic aesthetic preferences of taste, and aesthetic pleasure itself in terms of evolution, may be illuminated by historical background. We can also understand them (in Ulrich Beck's vocabulary) as second modernity, as a move to deal with uncertainties of aesthetics. What still makes contemporary naturalist aesthetics a continuation of aesthetic modernity, however, is its inability to take (contemporary) art seriously. (shrink)

We criticize the synaptic theory of long-term memory and the inappropriate usage of physical notions such as in motor control theories. Motor control and motor memory hypotheses should be based on explicitly specified hypothetical control variables that are sound from both physiological and physical perspectives. [HOUK et al.; SMITH; THACH].

The article brings under scrutiny an understudied dialogical account about the deposition of the patriarch of Constantinople Nicholas IV Mouzalon (1147-51). A close reading shows that this is not an official record of the proceedings but a piece of fiction that deliberately inverts the generic conventions of the two types of texts indicative of the 12th-century literary landscape, namely 1) minutes of church councils and 2) syllogistic theological dialogues. The anonymous author invites the reader to recognize the all-familiar scheme of (...) the Socratic interrogation but eventually departs from it investing the protagonists (Manuel I Komnenos and Mouzalon) with features that distance them from their Platonic models. The text seems to be inextricably linked to Mouzalon’s canonical dilemma: can an archbishop who previously voluntarily fled from his office be appointed archbishop once again? In fact, the author’s primary concern is not the patriarch but the emperor, a judge-logician who is at one and the same time Socrates and more than Socrates, and the new language able to reflect the changing balance between the imperial and ecclesiastical powers in mid- 12th-century Byzantium. (shrink)

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)

The article examines the historiosophical reflections of F. I. Tyutchev, presented in his treatises, letters, poems, and substantiates the idea that Tyutchev does not proclaim slogans of either Slavophil or Westernist doctrines, but creates an original imperial ideology. Tyutchev views Russia as an equal and integral part of Europe, linking the existence of the empire with the development of the European spirit in Russia. The main criterion for the existence of the empire is unity. If it does not exist, then (...) the state as an empire cannot exist. Tyutchev treated Orthodoxy as a historiosophical category. He bases his concept of the historical process on the traditions of Eastern Christianity and the legacy of the Byzantine Empire. In the idea of an empire based on Christian principles, Tyutchev sees the best system of statehood. For Tyutchev, the Russian people and Orthodoxy play a major role in the transformation of the world. In the concept of state and power, the categories of Christian ethics are especially important for Tyutchev, which, in his opinion, were not really relevant for the upper strata of society and representatives of the Russian government. The poet calls power "godless", claiming that it does not come from God, but is based on its material power, without recognizing a higher Divine authority over itself. The reason for the "godlessness" of the authorities was the separation from the Russian people and their national traditions and the departure from the historical past of "Holy Russia". This, from Tyutchev's point of view, is the main existential problem of Russia. Tyutchev's concept of empire was not a reproduction of the realities of the political life of Russia in the XIX century, but was an attempt to answer how the state should be built. Tyutchev's ideal of the Russian state is based on a society united by a single Christian faith. (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)

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)

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)

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)

It is argued that Lewis's approach to Elga's Sleeping Beaty problem is untenable and, therefore, the universality of the betting approach to probability has not been breached.

It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no ``probability'' for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: a). A ``sleeping pill'' gedanken experiment which makes correspondence between an illegitimate question: ``What is the probability of an outcome of a quantum measurement?'' with a legitimate question: ``What is the probability that ``I'' am in the world corresponding to that (...) outcome?''; b). A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and c). Relativistic causality, which together with explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and ``caring measure'' replacing probability measure are discussed. (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.