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.

“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)

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)

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)

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)

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.

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)

What is the most important reason for using Computer Vision methods in humanities research? In this article, I argue that the use of numerical representation and data analysis methods offers a new language for describing cultural artifacts, experiences and dynamics. The human languages such as English or Russian that developed rather recently in human evolution are not good at capturing analog properties of human sensorial and cultural experiences. These limitations become particularly worrying if we want to compare thousands, millions or (...) billions of artifacts—i.e. to study contemporary media and cultures at their new twenty-first century scale. When we instead use numerical measurements of image properties standard in Computer Vision, we can better capture details of a single artifact as well as visual differences between a number of artifacts–even if they are very small. The examples of visual dimensions that numbers can capture better then languages include color, shape, texture, contours, composition, and visual characteristics of represented faces, bodies and objects. The methods of finding structures and relationships in large numerical datasets developed in statistics and machine learning allow us to extend this analysis to very big datasets of cultural objects. Equally importantly, numerical image features used in Computer Vision also give us a new language to represent gradual and continuous temporal changes—something which natural languages are also bad at. This applies to both single artworks such as a film or a dance piece and also to changes in visual characteristics in millions of artifacts over decades or centuries. (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)

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.

Two recently proposed quantum experiments are analyzed. The first allows to find an object without "touching" it. The second allows to teleport quantum states, transmitting a very small amount of information. It is shown that in the standard approach these experiments are in conflict with the intuitive notions of causality and locality. It is argued that the situation is less paradoxical in the framework of the many-worlds interpretation of quantum theory.

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 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)

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.

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)

Cover -- Contents -- Introduction to the Second Edition -- Prefatory Note -- Introduction -- Foreword -- I Parmenides in Chains -- II In the Bull of Phalaris -- III On the Philosophy of the Middle Ages -- IV On the Second Dimension of Thought -- Lev Shestov-Biographical Timeline -- Notes -- Bibliography -- Index.

An attempt to solve the collapse problem in the framework of a time-symmetric quantum formalism is reviewed. Although the proposal does not look very attractive, its concept - a world defined by two quantum states, one evolving forwards and one evolving backwards in time - is found to be useful in modifying the many-worlds picture of Everett’s theory.

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.

We investigate the bimodal logics sound and complete under the interpretation of modal operators as the provability predicates in certain natural pairs of arithmetical theories . Carlson characterized the provability logic for essentially reflexive extensions of theories, i.e. for pairs similar to . Here we study pairs of theories such that the gap between and is not so wide. In view of some general results concerning the problem of classification of the bimodal provability logics we are particularly interested in such (...) pairs that is axiomatized over by ∏1-sentences only, and, for each n 1, proves the n-times iterated consistency of . A complete axiomatization, along with the appropriate Kripke semantics and decision procedures, is found for the two principal cases: finitely axiomatizable extensions of this sort, like e.g. ), ), etc., and reflexive extensions, like ¦n 1\s}), etc. We show that the first logic, ICP, is the minimal and the second one, RP, is the maximal within the class of the provability logics for such pairs of theories. We also show that there are some provability logics lying strictly between these two. As an application of the results of this paper, in the last section the polymodal provability logics for natural recursive progressions of theories based on iteration of consistency are characterized. We construct a system of ordinal notation , which gives exactly one notation to each constructive ordinal, such that the logic corresponding to any progression along coincides with that along natural Kalmar elementary well-orderings. (shrink)

For “natural enough” systems of ordinal notation we show that α times iterated local reflection schema over a sufficiently strong arithmetic T proves the same Π 1 0 -sentences as ω α times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at ε-numbers. We also derive the following more general “mixed” formulas estimating the consistency strength of iterated local reflection: for all ordinals α ⩾ 1 and all β, β ≡ Π 1 0 (...) T ω α · , α ≡ Π 1 0 T β + ω α . Here T α stands for α times iterated local reflection over T , T β stands for β times iterated consistency, and ≡ Π 1 0 denotes mutual Π 1 0 -conservativity. In an appendix to this paper we develop our notion of “natural enough” system of ordinal notation and show that such systems do exist for every recursive ordinal. (shrink)

We characterize the bimodal provability logics for certain natural (classes of) pairs of recursively enumerable theories, mostly related to fragments of arithmetic. For example, we shall give axiomatizations, decision procedures, and introduce natural Kripke semantics for the provability logics of (IΔ 0 + EXP, PRA); (PRA, IΣ 1 ); (IΣ m , IΣ n ) for $1 \leq m etc. For the case of finitely axiomatized extensions of theories these results are extended to modal logics with propositional constants.

A brief review of the attempts to define “elements of reality” in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post- selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.

Translation of Lev Shestov's What is Philosophy?

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)

The paper is devoted to analysis of P. Benacerraf’s argument against set-theoretic reductionist realism which is a fragment of a broader argument, know as the “identification problem”. The analyzed fragment of P. Benacerraf’s argument concerns the possibility of reducing of mathematical notions to set-theoretic notions. The paper presents a reconstruction of P. Benacerraf’s original argumentation, its analysis and also several possible objections proposed by P. Benacerraf himself about 30 years later after the original publication. Namely, he claimed (1) that a (...) set-theoretic definition of natural numbers in G. Frege’s fashion can serve as a proper and unique set-theoretic definition, (2) that his argument doesn’t undermine eliminative reductionsts’ position, (3) that even if there are no argument possible in favor of some particular set-theoretic definition of natural numbers one may take set-theoretic realism for granted. An analysis of the mentioned possible objections shows their dependence on a number of additional premises. The paper demonstrates that P. Benacerraf’s objections on his own argument against set-theoretic realism either have a pragmatic character themselves or essentially rely on additional arguments that are justified pragmatically or require additional argumentation. For example, his possible objections require that set theory is considered as the only true foundational theory in mathematics, and that it has several important pragmatic virtues, like convenience of use to formalize other mathematical theories. In some cases, P. Benacerraf’s objections on their own, or the indicated additional principles may well be called into question, which demonstrates the insufficiency of P. Benacerraf’s objections against his original argument. Without the mentioned pragmatic arguments P. Benacerraf’s objections become a kind of belief in mysticism. Accordingly, his doubts about his own argument against set-theoretical realism seem insufficient to reject the problem of identification and save the position of set-theoretical realism from collapse. (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)

The article presents an analysis of the existential paradigm of M. Lermontov's creativity in the light of the existential theories of S. Kierkegaard and K. Jaspers, which is considered in the context of the cultural transition in Russian literature of the 1830s-1840s. It is argued that Lermontov radically changed the nature of his literary activity by the mid-1830s, overcoming his own existential ambivalence and abandoning the subjective emotionality and exoticism of his youthful poetry in favor of objective observations and research (...) of the surrounding world. Lermontov was aware of his existential ambivalence and sought to overcome this state in order to achieve cultural integrity, which should be considered as one of his main values. Lermontov's works reflect the concept of integrity as the integration of culture through a set of prevailing norms and ideals, as well as the feeling that this integrity was disintegrating in transitional times. This state of affairs caused a sense of disintegration in Lermontov, which is similar to the borderline situation of Jaspers. Lermontov's works illustrate the loss of cultural ideals with the decline of Romanticism. But rejecting the ideals of Romanticism, Lermontov conveys the feeling that post-Romantic disappointment generated cynicism and distorted thinking. The novel "The Hero of Our Time" has become the embodiment of such shortcomings. Lermontov's works do not belong to romanticism, nor to protorealism, nor to any combination of both. But Lermontov played his transitional role superbly. Not only did he raise questions about Romanticism that realism would later make its own, he also shed light on Romanticism itself and how it was fading. Lermontov showed how difficult it is for an artist who is aware of his own existential ambivalence to create and live in a transitional time devoid of a unifying sense of cultural integration and integrity, illustrating how badly a creative personality needs such integration and integrity. (shrink)

Successful communication is important for both society and people’s personal life. Here we show that people can improve their communication skills by interacting with multiple others, and that this improvement seems to come about by a greater tendency to take the addressee’s perspective when there are multiple partners. In Experiment 1, during a training phase, participants described figures to a new partner in each round or to the same partner in all rounds. Then all participants interacted with a new partner (...) and their recordings from that round were presented to naïve listeners. Participants who had interacted with multiple partners during training were better understood. This occurred despite the fact that the partners had not provided the participants with any input other than feedback on comprehension during the interaction. In Experiment 2, participants were asked to provide descriptions to a different future participant in each round or to the same future participant in all rounds. Next they performed a surprise memory test designed to tap memory for global details, in line with the addressee’s perspective. Those who had provided descriptions for multiple future participants performed better. These results indicate that people can improve their communication skills by interacting with multiple people, and that this advantage might be due to a greater tendency to take the addressee’s perspective in such cases. Our findings thus show how the social environment can influence our communication skills by shaping our own behavior during interaction in a manner that promotes the development of our communication skills. (shrink)

Traditionally, biomedical research has been devoted to improvement in the understanding and treatment or prevention of disease. Building on the knowledge generated by the long history of disease-oriented research, the next few decades will witness an explosion of biomedical enhancements to make people faster, stronger, smarter, less forgetful, happier, prettier, and live longer (Turner et al. 2003; Vastag 2004; Rose 2002). As with other biomedical interventions, research to assess the safety and efficacy of these enhancements in humans should be conducted (...) before their introduction into clinical practice.1 However, various concerns regarding the ethics of enhancement research could be raised. Those who .. (shrink)

Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is considered and a novel time-symmetric definition of quantum counterfactuals is proposed. This definition is applied for analyzing several controversies related to quantum counterfactuals.