We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations (...) in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed. (shrink)

We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.

A generic extension L[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{L}[x]}$$\end{document} by a real x is defined, in which the E0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{E}_0}$$\end{document}-class of x is a lightface Π21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Pi}^1_2}$$\end{document} set containing no ordinal-definable reals.

The parameter-free part $$\textbf{PA}_2^*$$ of $$\textbf{PA}_2$$, second order Peano arithmetic, is considered. We make use of a product/iterated Sacks forcing to define an $$\omega$$ -model of $$\textbf{PA}_2^*+ \textbf{CA}(\Sigma ^1_2)$$, in which an example of the full Comprehension schema $$\textbf{CA}$$ fails. Using Cohen’s forcing, we also define an $$\omega$$ -model of $$\textbf{PA}_2^*$$, in which not every set has its complement, and hence the full $$\textbf{CA}$$ fails in a rather elementary way.

The small, the tiny, and the infinitesimal have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler’s book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley’s criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The (...) casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history. (shrink)

The Petrine-Pushkinian era lasted no more than two hundred years. It originated at the Battle of Poltava, where Russian troops first showed themselves not just equal to the Swedes, who were otherwi...

The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable to (...) most modal logics for which decidability with respect to admissibility is known and to many others, for instance, to the modal logicsK4,K4.1,K4.2,K4.3,S4.1,S4.2,GL.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logicsD n; to all intermediate Gabbay-De-Jong logicsD n; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well. (shrink)

The sum of all objects of a science, the objects’ features and their mutual relations compose the reality described by that sense. The reality described by mathematics consists of objects such as sets, functions, algebraic structures, etc. Generally speaking, the use of terms reality and existence, in relation to describing various objects’ characteristics, usually implies an employment of physical and perceptible attributes. This is not the case in mathematics. Its reality and the existence of its objects, leaving aside its application, (...) are completely virtual and yet clearly organized. This organization can be recognized in the creation of axioms or in the arrival at new theorems and definitions. It results either from a formalization of an intuitive idea or from a combinatorics that has not been guided by intuition. In all four possible cases—therefore, also in the two in which there is no intuitive “lead”, we can plausibly talk about a discovery of mathematical facts and thus support the Platonist view. (shrink)

Trata-se de discutir a centralidade do trabalho como categoria de reconhecimento através da problematização de sua natureza disciplinar. Isto nos levará a um duplo movimento: primeiro, a categoria de trabalho em Marx será relida à luz não apenas da temática da espoliação econômica da mais-valia, mas também da espoliação psíquica das relações de estranhamento entre sujeito e objeto; segundo, as modificações recentes no mundo do trabalho e as modalidades de sofrimento psíquico a elas associadas serão interpretadas a partir do impacto (...) social de tal forma de espoliação. (shrink)

El siguiente artículo aborda la crítica que manifiesta que John Stuart Mill incurrió en la falacia naturalista y en la falacia de composición. Esta temática se puede abordar de dos formas: una consistiría en analizar si Mill realmente desconoce la distinción entre lo deseado y lo deseable; otra sobre si su concepción de hedonismo, felicidad, conlleva la comisión de las falacias mencionadas. Esta última forma es el tema principal que se aborda; en otras palabras, se mencionará brevemente lo relativo a (...) si Mill confunde deseado/deseable, es/debe, y se puntualiza en cómo el hedonismo y la idea de felicidad millianos no llevan a caer en la falacia naturalista ni en la falacia de composición. En todo esto la educación jugará un papel valioso. (shrink)

This discussion note points to some verbal imprecisions in the formulation of the Enhanced Indispensability Argument. The examination of the plausibility of alternative interpretations reveals that the argument’s minor premise should be understood as a particular, not a universal, statement. Interpretations of the major premise and the conclusion oscillate between de re and de dicto readings. The attempt to find an appropriate interpretation for the EIA leads to undesirable results. If assumed to be valid and sound, the argument warrants the (...) rationality of the belief in an unusual variant of Platonism. On the other hand, if taken as it stands, the argument is either invalid or is unsound or does not support the mathematical Platonism. Thus, the EIA in its present form cannot serve as a useful device for the Platonist. (shrink)

The aim of the paper is to consider the situation with the social class stratification in Latvia. The focus is on the middle social class, due to the significance of this class both for the economic growth and the achievement of the sustainable, long-term development of the country. The subject of sociological research is the formation of class stratification in the region (estimated on the basis of cluster analysis), the main characteristics of the selected clusters based on the analysis of (...) the volumes and structure of total resources and aggregate capital. In the conclusion of the article, the controversial issues of classes in modern societies are analyzed. (shrink)

This paper argues against Galen Strawson’s criticism of the narrativist identity thesis. Strawson points out that the narrativist thesis fails to portray those with an episodic perception of themselves. I claim that episodicity is rather problematic and that we should question the validity of this notion. The first step in this goal is to decipher Strawson’s basis of the self which is an amalgam between the cultural and social and is perceived differently by different people. Afterwards, I will try to (...) use the claims derived from Strawson’s basis and apply the critique of his method. I pose a question about the relationship between episodic and diachronic and, ultimately, argue that both culturally and biologically, assuming the diachronic aspect of the self is necessary, apart from the very small number of cases. In this sense, the main conclusion is that Strawson’s thesis is limiting but does not pose a valid alternative to the narrativist identity thesis. (shrink)

Understanding has usually been seen as a method of hermeneutics. Until recently, philosophers of science paid little attention to the topic of scientific understanding because they came to the conclusion that understanding can be nothing more than a psychological by-product of scientific activity. However, many scientists believed that understanding was an important aim of science. The article states that understanding is a universal cognitive phenomenon applicable to the knowledge of not only cultural and historical phenomena, but also natural objects and (...) processes. Understanding does not oppose explanation; some types of the latter produce scientific understanding. In the course of criticism of the standard model of scientific explanation, the first concepts of “scientific understanding” arose – unifying and causal-mechanistic. A pragmatic approach to scientific understanding is also considered, linking it to the cognitive skills of a scientist or a group of scientists. (shrink)

The article draws a conceptual distinction the (French) structuralism of the 50’s–60’s and the post-structuralism of the 70’s, which are discussed as overlapping in their intellectual paths; their mutual dynamics is defined as a reaction of the intelligence to the pressure of depersonalized unified schemes within the logic of structuralism against free improvisation and loose interpretation instead of total explanations in the post-structuralism interpretation. The article establishes a conceptual identity of the paradoxical nature between post-structuralism (and deconstructionism, which is homogeneous (...) and identical thereto in a number of aspects), on the one hand, and constructionism with its specific process of language dismantling – social/ideological languages, social group dialects, on the other hand, which naturally leads the authors to the analysis of the paradoxicality principles, defined by post-structuralism (five principles of paradoxicality of Gilles Deleuze – paradox of regress, paradox of sterile reiteration, paradox of neutrality, paradox of absurd, paradox of Levi-Strauss); poststructuralists’ paralogisms are examined through paradoxical denotation; the late Roland Barthes’ phenomenon of paradoxicality, becoming a plot-forming principle of narration, is analyzed. Poststructuralism is conceptualized in the article as the first decisive step of post-modernism; the affinity of post-structuralist and postmodernist commitment to parody, game and irony is stated; the theory of language games in post-modern interpretation is explored; one of those games – a game of carnival – is explored within the diachronic retrospective; the affinity of parody and carnival tradition of post-structuralism and post-modernism to the romantic irony of the XIXth century and its inconsistency with the popular culture of laugh is established. The genesis of poststructuralism and post-modernism is connected with the ideological restart of the Western society before the “very end” of the Resistance ideas and the disappointment of the left European intellectuals in the “great legends” and illusions of Marxism. The blurred concepts of relativism are connected with the mutual disproportion of different layers of historical experience. (shrink)

The study provides an insight into the structural features of the famous VIII century Buddhist treatise Tattvasaṅgrāha by Śāntarakṣita with regard to the text’s main purpose ( prayojana ) as it is treated in Kamalaśīla’s commentary Pañjikā. Any text along with its referential (representational) function of conveying message - meaning to the addressee, or its expressive function, reflecting the author's attitude to what is communicated, also performs the ‘appellative’ function, encouraging the recipient of the message to act. This function which (...) could also be called praxiological was always significant in Indian text culture, since from the times of Veda-s it was embedded in its very core. This function is of paramount importance in the case of Indian religious and philosophical texts, whose main aim is to convince and transform the consciousness of their percipients. Along with linear models of message transfer, Sanskrit texts could demonstrate non-linear semantic structures, transmitting the main idea of the text indirectly. It is exactly how one should perceive the message of Śāntarakṣita’s Tattvasaṅgrāha according to the suggested by Śāntarakṣita’s prominent student Kamalaśīla in his Pañjikā -commentary to the treatise. He proposes to consider Tattvasaṅgrāha not as a thematically heterogeneous encyclopaedic or doxographic work, whose main objective is to refute different non-Buddhist views (as it is often treated by scholars now), but as a text, which by its very design exposes one of the most important Buddhist principles - the law of the dependent origination ( pratītyasamutpāda ). The themes, discussed in a number of the chapters of Tattvasaṅgrāha, indeed, appear to have direct correlation with the characteristics of pratītyasamutpāda given to it in Śālistamba-sūtra - an early Mahāyāna text, which explains this universal law. Kamalaśīla suggests looking at Tattvasaṅgrāha as at one big unit-sentence - mahāvākya, with the exposition of pratītyasamutpāda as its unitary purpose-meaning ( abhidheya ). In this context, the treatise functions as a praxiological tool for the ‘installing’ into the consciousness of the text’s addressee the knowledge of ‘true principles’ (tattva-s) of pratītyasamutpāda. This interpretation of the main message of the text raises also a question of the adequate translation of the name of the treatise into other languages, because, according to Kamalaśīla, ‘ Tattvasaṅgrāha’ means the ‘Assembly of Principles-(tattva’-s)’ which specify precisely pratītyasamutpāda (pratītyasamutpāda-viśeṣaṇāni tattvāni). (shrink)

This paper deals with the notion of intelligibility crisis in terms of conflict and harmony. Namely, we will analyze the notion of intelligibility from MacIntyre’s philosophical opus and apply it to the historical case. Intelligibility, according to MacIntyre, is the notion which provides us with contextual meaning and embeds our actions with sense within the specific tradition. Intelligibility crisis is the term that is coined to provide a descriptive account of the phenomenon when we cannot connect ourselves with a new (...) social context in which we find ourselves in. To further elaborate on this and apply it onto an example, we shall use the historical case of the Yugoslavian nation. We will provide analysis between three different contextual narratives – pre-Yugoslav narrative, Yugoslav narrative, and post-Yugoslav narrative. After applying the notion of intelligibility crisis onto this historical case study, we will notice how people of one social narrative lose intelligibility by going into another social narrative. Furthermore, we shall consider the notions of conflicts and harmony as those that are connected to intelligibility. The main argument from the descriptive state of things which was offered would be the following – conflicting sentiments arise when we are not in harmony with the narrative within which we have attained intelligibility. (shrink)

This article involves a qualitative research undertaken to elucidate how Ukraine’s European identity is constructed by Carl Bildt, Sweden’s Minister for Foreign Affairs. Specifically, the paper’s aim is to identify conceptual metaphors used by Carl Bildt in his political online discourse concerning Ukraine within the timeframe from 1 April 2013 until 1 April 2014. In addition to this objective, the article explores whether or not concepts SELF as the EU and OTHER as non-EU respectively are embedded in conceptual metaphors identified (...) in Bildt’s discoursal space involving Ukraine’s European identity. Results of the data analysis reveal several types of conceptual metaphors which are present in the corpus of Bildt’s online discourse involving Ukraine: “EU as a Path”, “EU as a Nurturant Parent”, “EU as a House”, “Ukraine’s Politics towards EU as a Stock Market Crash”, “Ukraine’s Path to EU as Poland’s EU Path” and “The EU Flag as a Symbol of the Better Future”, respectively. These conceptual metaphors seem to be exacerbated by the presence of the concept SELF. (shrink)

У статті розглядаються антропологічні аспекти японського вчення «шляху воїна» (бусідо). Обґрунтовується правомірність історико-філософського підходу до вивчення бусідо як філософської антропології, у центрі якої – тип людини-воїна (homo militans). Проаналізовано основні екзистенціали бусідо – смерть, свобода, служіння.

"Ise monogatari" is a remarkable monument of Japanese classical literature, dated around the end of the XIX - the beginning of the tenth century. The author of this piece is not known, although the most common traditional version states that it is one of the leading poets of Heaven's years of Arrivar-Narihira. "Ise monogatari" occupies an important place in the classical hierarchy of texts - deep knowledge of it was obligatory for an educated person; in addition, this work includes a (...) review of the life of the Heianan aristocrat, and therefore has the character of "encyclopedic" self-writing culture. (shrink)

Richard Browring called "Isi monogatari" one of the most important and at the same time one of the most mysterious texts of Japanese culture. Created at the beginning of the tenth century, at a turning point, at the dawn of the early and mature phases of Hayan's days, this work was one of the first written in classical Japanese, one of the first works of the genre of monogatari, the first work of the genre Uta-monogatari, and others like that. He (...) then laid down standards for the entire development of the Japanese literary tradition. However, we are not interested in the philological aspect of the problem, and such an aspect that was still on the periphery of the studios "Isi monogatari", namely, the religious and philosophical interpretation of the work. A vivid example of such an interpretation is one of the most ancient commentary on this work, "Isa monogatari zuiṇo:". Next, for convenience, we will call it just "Zuino". (shrink)

Early Heyen is interesting for religious scholars for at least two reasons. First, at this time in Japan there is an independent professional philosophy. Second, at this time the formation of the first of three religious-cultural-sociopolitical syntheses, which highlights in the history of the religions of Japan Dzh.Kitagava - the synthesis of Ritsurio: "paradigmatic form of immanent theocracy", ends. The religious and philosophical culture of early Heyana is a complex, multi-layered phenomenon. Its basis was the linguistic conceptualization of the world (...) of classical Japanese and, to some extent, classical Chinese, as well as mythological representations, inherited mostly from archaic times. On this basis, ideas developed from the continent in the previous period - Confucian, Buddhist, Taoist, who managed to get well here for three hundred years Developed. (shrink)

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.

The article reports the results from the developmentof four data-driven discovery systems, operating inlinguistics. The first mimics the induction methods ofJohn Stuart Mill, the second performs componentialanalysis of kinship vocabularies, the third is ageneral multi-class discrimination program, and thefourth finds logical patterns in data. These systemsare briefly described and some arguments are offeredin favour of machine linguistic discovery. Thearguments refer to the strength of machines incomputationally complex tasks, the guaranteedconsistency of machine results, the portability ofmachine methods to new tasks and (...) domains, and thepotential machines provide for our gaining newinsights. (shrink)

In one of the first genetic screens aimed at identifying induced developmental mutants, Nadine Dobrovolskaïa-Zavadskaïa, working at the Pasteur Laboratory in the 1920s, isolated and characterized a mutation affecting Brachyury, a gene that regulates tail and axial development in the mouse. Dobrovolskaïa-Zavadskaïa's analysis of Brachyury and other mutations affecting tail development were among the earliest attempts to link gene action with a tissue-specific developmental process in a vertebrate. Her analyses of genes that interacted with Brachyury led to the discovery of (...) the t-haplotype chromosome of mouse. After 70 years, Brachyury and the multiple genes with which it interacts continue to occupy a prominent focus in developmental biology research. A goal of this review is to identify the contributions that Dobrovolskaïa-Zavadskaïa made to our current thinking about Brachyury and how she helped to shape the dawn of the field of developmental genetics. BioEssays 23:365–371, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

The travelling salesman problem (TSP) belongs to the class of NP-hard problems, in which an optimal solution to the problem cannot be obtained within a reasonable computational time for large-sized problems. To address TSP, we propose a hybrid algorithm, called GA-TCTIA-LBSA, in which a genetic algorithm (GA), tour construction and tour improvement algorithms (TCTIAs) and a list-based simulated annealing (LBSA) algorithm are used. The TCTIAs are introduced to generate a first population, and after that, a search is continued with the (...) GA. The problem of premature convergence of the GA to local optimum is tackled by a method called social disaster technique. Afterwards, the LBSA is applied to generate a new population based on one of two proposed operators called packing and judgement day. The proposed algorithm is implemented in the MATLAB environment, and its two variants, called GA-TCTIA-LBSA packing and GA-TCTIA-LBSA judgement day, are tested on symmetric and asymmetric instances from TSPLIB. The overall results demonstrate that the proposed GA-TCTIA-LBSAs offer promising results, particularly for small-sized instances. (shrink)

The paper discusses various aspects of the concept of “cultural memory” coined by Jan Assmann and related both to the problem of determining the categories of culture that became the first objects of philosophical reflection in the era of the Axial Age and to the issues of the modern crisis of the ideology of globalism and multiculturalism. Using the example of some categories of an archaic myth that have not lost their cultural and social relevance at present, the variability of (...) the genesis of philosophy in various civilizations of the epoch of the “Axial Age” is demonstrated - both those in which it arises as an independent form of worldview and those where this process stops at the stage of a highly speculative myth. Special attention is paid to the cultural and social aspects of memory and recollection of the past as forms of spiritual “resistance” to external cultural influences and the preservation of religious and ethnic identity, which is equally relevant both during the genesis of philosophy and in modern post-industrial society during the crisis of globalist ideology and the philosophy of multiculturalism. (shrink)

This article aims to discuss the aesthetic autonomy as a model for social emancipation. It starts from the contemporary challenges for the defense of aesthetic autonomy, using autonomy for criticizing discourses that seems to sustain a possible conciliation between life and art that not take into account the problems resulting from the connection between culture and capitalistic production.

Although the type‐I interferon (IFN‐I) response is considered vertebrate‐specific, recent findings about the Intracellular Pathogen Response (IPR) in nematode Caenorhabditis elegans indicate that there are similarities between these two transcriptional immunological programs. The IPR is induced during infection with natural intracellular fungal and viral pathogens of the intestine and promotes resistance against these pathogens. Similarly, the IFN‐I response is induced by viruses and other intracellular pathogens and promotes resistance against infection. Whether the IPR and the IFN‐I response evolved in a (...) divergent or convergent manner is an unanswered and exciting question, which could be addressed by further studies of immunity against intracellular pathogens in C. elegans and other simple host organisms. Here we highlight similar roles played by RIG‐I‐like receptors, purine metabolism enzymes, proteotoxic stressors, and transcription factors to induce the IPR and IFN‐I response, as well as the similar consequences of these defense programs on organismal development. (shrink)

This brief paper is a polemical response to Mikhail Epstein’s review of the Palgrave Handbook of Russian Thought, and especially to his claim that the widely acknowledged tendency of Russian philosophy towards holistic thinking is akin to political totalitarianism, not to say its underlying cause. My argument is that philosophical and political or ideological thought are fundamentally different in their nature and purpose, and cannot be usefully identified with one another as Epstein does. Epstein’s claim is, I argue, a manifestation (...) of the modern outlook at large, incapable of grasping the difference and, worse, offering precisely the opposite of a solution to the problems posed by totalitarianism. (shrink)

Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values xi ∈ {0,1}, which resulted in a philosophical standpoint known as Suszko’s Thesis. Three-valued truth tables were created corresponding to Priest’s tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with the four (...) original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn’s 4-valued truth tables are compared with our 4-valued truth tables. De Morgan’s laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan’s laws. (shrink)

We generalize, on higher projective levels, a construction of “incompatible” generic Δ1 3 real singletons given by Jensen and Johnsbråten.