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)

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

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)

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.

In this article ‡ we show how the universe of HST, Hrbaček set theory admits a system of subuniverses which keep the Replacement, model Power set and Choice, and also keep as much of Saturation as it is necessary. This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.

Knowledge representation, which lies at the core of artificial intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The aims are to help readers make their computer smarter, handle qualitative and uncertain information, and improve computational tractability.

. 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 third collection in this series includes the same combination of scarce and not so well-known texts as well as more important and popular works.

In continuation of our study of HST, Hrbaek set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st--language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe.We show that, given a standard cardinal , any set R * generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class (...) L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain -version of HST including the principle of +-saturation; moreover, in this case L[S(R)] is an elementary extension of L[S(R)] in the st--language whenever sets R R satisfy the requirements. (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)

Trata-se de analisar os usos da racionalidade mimética em Jacques Lacan e Theodor Adorno, isto a fim de mostrar como, nos dois casos, encontramos uma estratégia de reflexão sobre a mimesis que a eleva à condição de elemento fundamental para uma teoria do reconhecimento que não se esgote na temática da intersubjetividade. Neste sentido, este estudo insere-se em uma pesquisa mais ampla a respeito dos modos de aproximação entre psicanálise lacaniana e Escola de Frankfurt no que diz respeito ao problema (...) dos destinos da categoria de sujeito e dos processos de reconhecimento. (shrink)

During the late Soviet era, science fiction was one of the first zones of its ideological cosmos, registering the exhaustion of the communist utopia precisely within the literary genre aimed at its representation. In this article I consider the history of the “editing to death” of the Strugatsky brothers’ short novel Roadside Picnic as a representative case of the anti-utopian “uneasiness in civilization” of late actually existing socialism. Simultaneously with the censorship taming of the uneasiness, the Strugatsky’s science fiction dystopia (...) underwent a radical interpretation in Andrei Tarkovsky’s film adaptation Stalker as a Hegelian “good music with text”. In comparison to the censored edition, which is barely a timid emendation, ultimately yearning modestly for a good life during the most consumeristic and moderately repressive years of Soviet power, Tarkovsky’s aesthetically singular re-reading is truly a “Zone” of editing to death. (shrink)

Reproductive biotechnologies, also known as assisted reproductive technologies (ART), have undergone significant development over time, reaching a remarkable level of evolution in the 20th century. Currently, several biotechnologies stand out, among which Artificial Insemination (AI), widely spread globally, Embryo Production (EP) both in vivo and in vitro for embryo transfer, Intracytoplasmic Sperm Injection (ICSI), sexing, among other innovations. In Vitro Production (IVP) of embryos has emerged as the biotechnology that has experienced the greatest development and evolution in recent decades, covering (...) various fields such as research in assisted human reproduction, obtaining transgenic animals for biomedicine, preservation of endangered species and conservation of animals of high genetic value. This research aims to analyze the relevance of IVP, as well as the fundamental elements that make up this complex process. IVP of embryos involves several stages, from oocyte procurement, oocyte selection and in vitro maturation, sperm preparation, in vitro fertilization, to the culture of the resulting zygotes to blastocysts. These blastocysts, once transferable to recipients, culminate in the birth of a new being. However, this process has both advantages and disadvantages, which motivates continuous innovation in the field. (shrink)

Representative models are considered parts of real scientific theories.

In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their connections and give dividing examples. Also (...) we find algorithms recognizing these properties for some particular cases. (shrink)

This book aims to recover the disruptive nature of the dialectical tradition by means of a severe critique of the dominance of an anthropology of the individual identity in contemporary theories of recognition. This critique implies a thorough rethinking of basic concepts such as desire, negativity, will and drive, with Hegel, Lacan and Adorno being our main guides."--Back cover.

Trata-se de abordar o problema da teoria hegeliana da linguagem a partir do ponto onde pragmática e ontologia se articulam. Isto exige uma reflexão sobre a maneira com que Hegel organiza as dinâmicas da pragmática da linguagem levando em conta os modos de manifestação de uma negação ontológica no interior do campo de experiências lingüísticas da consciência.