The law of negation of the negation as it appears in the economic writings of Marx in general, and in Capital in particular, has repeatedly been treated in our philosophical literature in one way or another. To this day, however, as judged from the literature, attention has not been directed to the principle of negation of the negation as it is manifested not only in Marx's historical but also in his logical analysis. Negation of the negation has been examined primarily (...) as a form of expression of historical analysis . In the present article the emphasis is upon negation of the negation in logical analysis, upon the function of this principle considered as form of motion dealt with by historical analysis. All the examples of negation of the negation in historical analysis that have already been treated in the literature are omitted quite consciously, to avoid repetition. Nor is anything said about the structure of Capital as a "dialectically subdivided whole" in connection with negation of the negation, as that question has been splendidly handled in the book by L. A. Man'kovskii referred to in the footnote. (shrink)

Frant︠s︡uzskiĭ materializm XVIII veka -- Frant︠s︡uzskie istoriki vremen Restavrat︠s︡ii -- Sot︠s︡ialisty-utopisty -- Idealisticheskai︠a︡ nemet︠s︡kai︠a︡ filosofii︠a︡ -- Sovremennyĭ materializm.

Timlul ṿe-teʻud ṿideʼo shel 13 shaʻot pulmus.

This article looks at Lev P. Karsavin’s experience with the heritage of early Christian Gnosticism, from his attempts at stylization based on his study of genuine Gnostic texts and his systematic presentation of Gnostic systems in art almanacs published in the Soviet Union, to his perception of Gnosticism as a kind of “other principle” in his original religious–philosophical texts. We show that, following Silver-Age traditions, Karsavin uses myth as a form of philosophical thinking. He teeters on the edge of Gnosticism, (...) applying certain Gnostic concepts, but he generally turns to Gnostic thought only to distinguish it from his own, which he presents as authentic to the Christian tradition. He criticizes both ontological and anthropological postulates of Gnosticism: the hierarchization of intradivine life, the introduction of the cosmic feminine into the bosom of the Divine, the interpretation of the Fall as the kenosis of God in time, and the explanation of the perfect God from the imperfect world, as well as the type of religious personhood that leads to a rupture in theory and personal faith. We examine Karsavin’s reception of Gnosticism against the background of interest in Gnosticism in post-revolutionary Russia, as expressed by Kropotkinite anarchists, A. Karelin, V. Murav’ev, Yu. Danzas, and M. Kuzmin. (shrink)

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

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)

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)

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

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)

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)

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.