Translation of Lev Shestov's What is Philosophy?

Plotinus represent a constant reference in all of Šestov's philosophy. For the Russian philosopher Plotinus is, on the one hand, the one who thought up thesynthesis of Greek philosophy, on the other, the one who first broke with that same tradition precisely when it was at its peak. However, Šestov does lift from the Enneadi certain passages which he marries - as if in a sort of contrapuntal rewriting exercise - to others in which Plotinus seems to contradict himself. What (...) interests Šestov are precisely those discontinuities in the thought of the last great philosopher of old in an anti-Greek function. That of Šestov is once again a marked criticism of Rationalism as creator of an autonomous set of ethics that he judges according to an intellect which everything is subject to. Autonomousethics, affirms Šestov, is a fruit of Greek schools of thought to the extent that it shows distrust for what is mutable, unforeseen and arbitrary, of everything which, in short, is irrational, as it is not inserted in the One/All necessitating, justifying, regulating. In the alternative between Athens and Jerusalem, between the Rationalism and the Bible, Šestov opts to assume a stance, in no uncertain terms, on the side Jerusalem, taking with him the Plotinus of the awakening andheading towards a greater reality capable of overturning the throne occupied for too long by reason. That Plotinus who at a certain point was obliged to say thatin this other dimension "the intellect before God represents a reckless, ungodly apostate" (VI.9.5). That Plotinus, who ultimately, in one of those most particularmoments, realized that he was predestined for something loftier with respect to the world of evil and death. (shrink)

The article reviews the book L' esperienza tragica come iniziazione: Lev Šestov [Tragic Experience as Initiation: Lev Shestov], by Aleksander Posacki.

The article reviews the book L' esperienza tragica come iniziazione: Lev Šestov [Tragic Experience as Initiation: Lev Shestov], by Aleksander Posacki.

Lev Isakovic Sestov e annoverato fra gli eccezionali filosofi del XX secolo. Questo pensatore di origine giudea, e un continuatore della corrente esistenziale del pensiero religioso di Pascal e Kierkegaard. Viene, pero annoverato pure - del resto insieme ai filosofi menzionati - alla corrente del pensiero tragico. Questo non e contradditorio perche ambedue le trame sono presenti alla riflessione di Sestov, anzi esse sono Ii, cosi inseparabilmente intrecciate, che fino ad oggi la riflessione del pensatore russo essenzialmente sfugge (...) da ogni interpretazione univoca. Nel frammento seguente del teste sto dimostrando che per Sestov l'esperienza tragica non e soltanto un inizio deU'esperienza religiosa, ma anche la sua condizione indispensabile, come un'IIniziazione. Sestov cerca l'esemplificazione di questa coincidenza particolare - l'esperienza tragica come un'iniziazione religiosa - sugli esempi dei vari pensatori di cui ha scrutato non soltanto le opere ma anche le biografie, partendo dalla premessa che esse sono delle realta collegate inseparabilmente. Sestov cerca l'affermazione di questa verita studiando la vita e le opere dei pensatori non soltanto tragici come Shakespeare, Ibsen, Nietzsche o Dostoevskij, ma sopratutto dei pensatori religiosi come Pascal o Lutero e Kierkegaard. In questi ultimi quel collegamento del tragico e della reiigiosita si e fatto evidente, mentre negli altri esso era soltanto parziale e embrionale. (shrink)

Lev Isakovic Sestov e annoverato fra gli eccezionali filosofi del XX secolo. Questo pensatore di origine giudea, e un continuatore della corrente esistenziale del pensiero religioso di Pascal e Kierkegaard. Viene, pero annoverato pure - del resto insieme ai filosofi menzionati - alla corrente del pensiero tragico. Questo non e contradditorio perche ambedue le trame sono presenti alla riflessione di Sestov, anzi esse sono Ii, cosi inseparabilmente intrecciate, che fino ad oggi la riflessione del pensatore russo essenzialmente sfugge (...) da ogni interpretazione univoca. Nel frammento seguente del teste sto dimostrando che per Sestov l'esperienza tragica non e soltanto un inizio deU'esperienza religiosa, ma anche la sua condizione indispensabile, come un'IIniziazione. Sestov cerca l'esemplificazione di questa coincidenza particolare - l'esperienza tragica come un'iniziazione religiosa - sugli esempi dei vari pensatori di cui ha scrutato non soltanto le opere ma anche le biografie, partendo dalla premessa che esse sono delle realta collegate inseparabilmente. Sestov cerca l'affermazione di questa verita studiando la vita e le opere dei pensatori non soltanto tragici come Shakespeare, Ibsen, Nietzsche o Dostoevskij, ma sopratutto dei pensatori religiosi come Pascal o Lutero e Kierkegaard. In questi ultimi quel collegamento del tragico e della reiigiosita si e fatto evidente, mentre negli altri esso era soltanto parziale e embrionale. (shrink)

Plotinus represent a constant reference in all of Šestov's philosophy. For the Russian philosopher Plotinus is, on the one hand, the one who thought up thesynthesis of Greek philosophy, on the other, the one who first broke with that same tradition precisely when it was at its peak. However, Šestov does lift from the Enneadi certain passages which he marries - as if in a sort of contrapuntal rewriting exercise - to others in which Plotinus seems to contradict himself. What (...) interests Šestov are precisely those discontinuities in the thought of the last great philosopher of old in an anti-Greek function. That of Šestov is once again a marked criticism of Rationalism as creator of an autonomous set of ethics that he judges according to an intellect which everything is subject to. Autonomousethics, affirms Šestov, is a fruit of Greek schools of thought to the extent that it shows distrust for what is mutable, unforeseen and arbitrary, of everything which, in short, is irrational, as it is not inserted in the One/All necessitating, justifying, regulating. In the alternative between Athens and Jerusalem, between the Rationalism and the Bible, Šestov opts to assume a stance, in no uncertain terms, on the side Jerusalem, taking with him the Plotinus of the awakening andheading towards a greater reality capable of overturning the throne occupied for too long by reason. That Plotinus who at a certain point was obliged to say thatin this other dimension "the intellect before God represents a reckless, ungodly apostate" (VI.9.5). That Plotinus, who ultimately, in one of those most particularmoments, realized that he was predestined for something loftier with respect to the world of evil and death. (shrink)

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

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)

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)

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)

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)

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)

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.

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)

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)

First English-language translation of Lev Shestov's early writings on faith, ancient philosophy and biblical revelation.

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)

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)

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.

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.

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.

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 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)