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.

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.

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)

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.

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.

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)

Translation of Lev Shestov's What is Philosophy?

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)

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)

Reviewed Works:Dick de Jongh, Franco Montagna, Provable Fixed Points.Dick de Jongh, Franco Montagna, Much Shorter Proofs.Alessandra Carbone, Franco Montagna, Rosser Orderings in Bimodal Logics.Alessandra Carbone, Franco Montagna, Much Shorter Proofs: A Bimodal Investigation.

Argument of this text is that: to develop aesthetics of sport, we should not begin with aesthetics as philosophy of art but with aesthetics of everyday life; to start with aesthetics of sport, we should not begin with beautiful of ‘pure aesthetics’ but with the dramatic; to analyze the dramatic in sport, we should not open the analysis with analogy between theater and sport, but with sport as a sort of performance; to get at the meaning of sport as a (...) drama, we have to discuss different meanings ‘drama’ has in theory and everyday communication; to map the dramatic in sport as performance, we have to discuss some features of sport which determine its dramatics first, and its potential as spectacle later. To proceed with the argument, we have to take into account contemporary state of aesthetics, recent development of aesthetics of everyday life, and theory of performance, together with Bernard Suits’ definition of game, Gadamer’s idea of play, and Lévy-Strauss’ account on conjunctive and disjunctive ritual. (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.

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.

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)

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.

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)

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, 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)

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)

Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys. 23, 987 (1993)] allow finding infinitely fragile objects without destroying them. Many experiments have been successfully performed showing that indeed, the original scheme and its modifications lead to reduction of the disturbance of the observed systems. However, there is a controversy about the validity of the term “interaction-free” for these experiments. Broad variety of such experiments are reviewed and the meaning of the interaction-free measurements is clarified.

The problem of neural memory storage is discussed, based on the results of studies of memory impairment after hippocampal lesions, motor learning, and electrophysiological research on “spinal memory. ” I support Shors & Matzel's major statements. The absence of reliable evidence on the LTP memory storage function and other data cast doubt on the synaptic theory of memory.

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)

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.

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)

“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)