Kohlenbach, U., Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation, Annals of Pure and Applied Logic 64 27–94.We consider uniqueness theorems in classical analysis having the form u ε U, v1, v2 ε Vu = 0 = G→v 1 = v2), where U, V are complete separable metric spaces, Vu is compact in V and G:U x V → is a constructive function.If is proved by arithmetical means from analytical assumptions x (...) εXy ε Yx z ε Z = 0) only , then we can extract from the proof of → an effective modulus of uniqueness, which depends on u, k but not on v1,v2, i.e., u ε U, v1, v2 ε Vu, k εG, G 2-φuk→dv2-itk). Such a modulus φ can e.g. be used to give a finite algorithm which computes the zero of G on Vu with prescribed precision if it exists classically.The extraction of φ uses a proof-theoretic combination of functional interpretation and pointwise majorization. If the proof of → uses only simple instances of induction, then φ is a simple mathematical operation. (shrink)

The criticism of neoliberalism is omnipresent. The term is seemingly self-explanatory, but its original use in public has been forgotten. Its form originated in the international movement of ordoliberalism in the 1930s, which used neoliberalism to describe its distinction from laissez-faire capitalism. This conceptual confusion has created considerable consequential problems that overlay today’s debate on the future of the market economy. The fact that the neoliberalism of the ordoliberals is today equated by its critics with the capitalism of the libertarians (...) raises questions. Since the economic dogma of Milton Friedman, who was the inspiration for the so-called Chicago Boys in Chile, whose economic policy was first captured by today’s negatively connoted term neoliberalism, this approach needs to be looked at more closely. Should the ideas of the Chicago school of thought substantially distinguish themselves from the other currents of economic liberalism, a solution to the confusion of terms could be possible, giving a new twist to the debate on the market economy. Such a clarifiation would be of fundamental importance for the ethical question of the social orientation of the economic order, since ordoliberalism was in turn the godfather of the social market economy. Furthermore, this would have consequences for applied political ethics in the context of political theories of justice, whose theoretical constructs reflect the existing economic order as a fact of experience. (shrink)

Auf Thomas Hobbes geht die Feststellung zurück, Absurdität sei ein Privileg des Menschen: Nur ein rationales Wesen ist offensichtlich der Irrationalität fähig.

Der Band versammelt 29 Aufsätze, die Walter Haug in seinen letzten Lebensjahren geschrieben hat. In ihnen entwickelt er die großen Themen seines Lebenswerkes - insbesondere seine Beschäftigung mit dem höfischen Roman und der Mystik - weiter und führt sie zusammen unter dem titelgebenden Aspekt der Negativität, d.h. des Scheiterns, des Verlustes, der Trennung. Die erotische Liebe wie die mystische Gottesbegegnung, deren absoluten Anspruch die Wirklichkeit nie ganz zu erfüllen vermag, können durch Literatur in ihrem Scheitern dargestellt und gerade dadurch erfahrbar (...) gemacht werden. Literaturtheoretische und philosophiegeschichtliche Überlegungen bilden einen Schwerpunkt des Bandes, dessen Themenkreis über den höfischen Roman und die Mystik hinaus Heldenepik, Märendichtung, Lyrik und anderes mehr umfasst. Der Band spiegelt die Lebendigkeit und Vielseitigkeit von Haugs Denken und erlaubt zuletzt, über sechs Reden und Nachrufe, einen sehr persönlichen Blick auf diesen herausragenden Wissenschaftler und Menschen. (shrink)

In this paper a new method, elimination of Skolem functions for monotone formulas, is developed which makes it possible to determine precisely the arithmetical strength of instances of various non-constructive function existence principles. This is achieved by reducing the use of such instances in a given proof to instances of certain arithmetical principles. Our framework are systems ${\cal T}^{\omega} :={\rm G}_n{\rm A}^{\omega} +{\rm AC}$ -qf $+\Delta$ , where (G $_n$ A $^{\omega})_{n \in {\Bbb N}}$ is a hierarchy of (weak) subsystems (...) of arithmetic in all finite types (introduced in [14]), AC-qf is the schema of quantifier-free choice in all types and $\Delta$ is a set of certain analytical principles which e.g. includes the binary König's lemma. We apply this method to show that the arithmetical closures of single instances of $\Pi^0_1$ -comprehension and -choice contribute to the growth of extractable bounds from proofs relative to ${\cal T}^\omega$ only by a primitive recursive functional in the sense of Kleene. In subsequent papers these results are widely generalized and the method is used to determine the arithmetical content of single sequences of instances of the Bolzano-Weierstraß principle for bounded sequences in ${\Bbb R}^d$ , the Ascoli-lemma and others. (shrink)

The so-called weak König's lemma WKL asserts the existence of an infinite path b in any infinite binary tree . Based on this principle one can formulate subsystems of higher-order arithmetic which allow to carry out very substantial parts of classical mathematics but are Π 2 0 -conservative over primitive recursive arithmetic PRA . In Kohlenbach 1239–1273) we established such conservation results relative to finite type extensions PRA ω of PRA . In this setting one can consider also a uniform (...) version UWKL of WKL which asserts the existence of a functional Φ which selects uniformly in a given infinite binary tree f an infinite path Φf of that tree. This uniform version of WKL is of interest in the context of explicit mathematics as developed by S. Feferman. The elimination process in Kohlenbach [10] actually can be used to eliminate even this uniform weak König's lemma provided that PRA ω only has a quantifier-free rule of extensionality QF-ER instead of the full axioms of extensionality for all finite types. In this paper we show that in the presence of , UWKL is much stronger than WKL: whereas WKL remains to be Π 2 0 -conservative over PRA, PRA ω ++ UWKL contains full Peano arithmetic PA. We also investigate the proof–theoretic as well as the computational strength of UWKL relative to the intuitionistic variant of PRA ω both with and without the Markov principle. (shrink)

Individuals who experience stereotype threat – the pressure resulting from social comparisons that are perceived as unfavourable – show performance decrements across a wide range of tasks. One account of this effect is that the cognitive pressure triggered by such threat drains the same cognitive resources that are implicated in the respective task. The present study investigates whether mindfulness can be used to moderate stereotype threat, as mindfulness has previously been shown to alleviate working-memory load. Our results show that performance (...) decrements that typically occur under stereotype threat can indeed be reversed when the individual engages in a brief mindfulness task. The theoretical implications of our findings are discussed. (shrink)

In this note we show that the so-called weakly extensional arithmetic in all finite types, which is based on a quantifier-free rule of extensionality due to C. Spector and which is of significance in the context of Gödel"s functional interpretation, does not satisfy the deduction theorem for additional axioms. This holds already for Π0 1-axioms. Previously, only the failure of the stronger deduction theorem for deductions from (possibly open) assumptions (with parameters kept fixed) was known.

LetA H be the Herbrand normal form ofA andA H,D a Herbrand realization ofA H. We showThere is an example of an (open) theory ℐ+ with function parameters such that for someA not containing function parameters Similar for first order theories ℐ+ if the index functions used in definingA H are permitted to occur in instances of non-logical axiom schemata of ℐ, i.e. for suitable ℐ,A In fact, in (1) we can take for ℐ+ the fragment (Σ 1 0 -IA)+ (...) of second order arithmetic with induction restricted toΣ 1 0 -formulas, and in (2) we can take for ℐ the fragment (Σ 1 0,b -IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers.On the other hand, $$PA^2 \vdash A^H \Rightarrow PA \vdash A,$$ wherePA 2 is the extension of first order arithmeticPA obtained by adding quantifiers for functions andA∈ℒ(PA). This generalizes to extensional arithmetic in the language of all finite types but not to sentencesA with positively occurring existential quantifiers for functions. (shrink)

Existe uma tendência evidente de computadorizar cada vez mais atividades do dia-a-dia. Ferramentas de IA, de tomada de decisão e aprendizado de máquina são algumas destas tecnologias. Neste artigo analisamos como a modelagem de aplicações de bancos de dados deve evoluir para atender a estes requisitos. Coisas estruturais e ocorrêncais adequadas são consideradas e, para cada conceito, têm que ser definidas regras que garantem a integridade do sistema como um todo. Caracteristicas específicas de sistemas complexos ativos e/ou reativos, questões de (...) autonomia, aspectos espaciais e temporais, assim como informações imprecisas, devem ser levados em consideração. (shrink)

The eminent 20th-century Polish philosopher Tadeusz Kotarbiński (1886–1981) is the author of a novatory philosophy of combating global suffering. Kotarbiński’s theory states that although humans are by nature rational, and additionally endowed with goodwill, human life nonetheless offers an endless stream of pain and suffering. Some of this suffering results from the essence of the human condition and can not be helped, mostly, however, it is the effect of the meanderings of the human mind and can be eliminated by education. (...) More than by anything else, the human mind is brought to err by so-called phantasmats, or emotion-laden intellectual mirages, mainly of a religious, national and political nature. Such phantasmats are the source and fundament of humanity’s divisions into hostile cultures, nations and political systems, which in turn gives rise to conflict between civilizations, countries and ideologies, inadvertently accompaniedby mounting mistrust, suspiciousness, xenophobia, hatred, armaments—and ultimately war. All this means an ocean of suffering for countless individuals. Both in philosophy and praxis Kotarbiński strove to eliminate all sources of suffering, including that stemming from differences in culture, development, nationality, and politics. He believed in the motivating powers of reason and the creative powers of persuasion, and consequently sought to attain his goal by rationalization, or focusing solely on the logic-driven and common experiencing of the human fate in a bid to eradicate cultural, national and political difference. Thus united, humanity would melt into one big human state devoted to lingering inevitable suffering. Today similar views are promoted as “global humanism”—which makes Kotarbiński a pioneer of the Humanistic Manifesto 2000. An Appeal for New Global Humanism brochure. (shrink)

This paper discusses what kind of quantitative information one can extract under which circumstances from proofs of convergence statements in analysis. We show that from proofs using only a limited amount of the law-of-excluded-middle, one can extract functionals , where L is a learning procedure for a rate of convergence which succeeds after at most B-many mind changes. This -learnability provides quantitative information strictly in between a full rate of convergence and a rate of metastability in the sense of Tao (...) . In fact, it corresponds to rates of metastability of a particular simple form. Moreover, if a certain gap condition is satisfied, then B and L yield a bound on the number of possible fluctuations. We explain recent applications of proof mining to ergodic theory in terms of these results. (shrink)

Our understanding of epithelial development in Drosophila has been greatly improved in recent years. Two key regulators of epithelial polarity, Crumbs and DE‐cadherin, have been studied at the genetic and molecular levels and a number of additional genes are being analyzed that contribute to the differentiation of epithelial cell structure. Epithelial architecture has a profound influence on morphogenetic movements, patterning and cell‐type determination. The combination of embryological and genetic/molecular tools in Drosophila will help us to elucidate the complex events that (...) determine epithelial cell structure and how they relate to morphogenesis and other developmental processes. (shrink)

For the first time in his Doctrine of Right, Kant employs an expanded, three dimensional concept of public law. In addition to constitutional law, it also includes international law and cosmopolitan law. Each of these concepts of law is assigned its own principle of reason: constitutional law declares that a republic is the only rightful constitution for an individual state; international law requires at least an association of states with higher level instruments of coercion; and cosmopolitan law primarily defines the (...) basic rights of stateless peoples or individuals with respect to existing states. For the principles of reason for constitutional and international law, Kant formulates permissive laws, which allow for imperfections in an effort to promote the optima which the legal principles of reason dictate. Kant justifies these less perfect solutions not only with pragmatic considerations but also with reasons relating to the theory of the sovereignty of nations. Kants Rechtslehre verwendet erstmals einen erweiterten, dreidimensionalen Begriff des öffentlichen Rechts, der neben dem Staatsrecht nun auch das Völkerrecht und das Weltbürgerrecht umfaßt. Jeder dieser Begriffssphären wird ein eigenes vernunftrechtliches Prinzip zugeordnet: das Staatsrecht erklärt die Republik zur einzig rechtmäßigen Verfassung, während das Völkerrecht mindestens eine Staatenassoziation mit höherstufiger Zwangsgewalt erfordert und das Weltbürgerrecht in der Hauptsache die elementaren Rechte von staatslosen Völkern oder Einzelpersonen gegenüber Staaten definiert. Für das staatsrechtliche und das völkerrechtliche Prinzip formuliert Kant Erlaubnisgesetze, die zur Beförderung der vernunftrechtlichen Optima Minderformen zulassen, zu deren Rechtfertigung Kant nicht allein pragmatische, sondern ebenso volkssouveränitätstheoretische Gründe anführt. (shrink)

The notion of societal boundaries aims to enhance the debate on planetary boundaries. The focus is on capitalist societies as a heuristic for discussing the expansionary dynamics, power relations, and lock-ins of modern societies that impel highly unsustainable societal relations with nature. While formulating societal boundaries implies a controversial process – based on normative judgments, ethical concerns, and socio-political struggles – it has the potential to offer guidelines for a just, social-ecological transformation.

While border surveillance produces geopolitical realities and distinctions between types of human life, Richard Mosse’s video installation INCOMING (2017) uses a military high-grade thermal camera to challenge this onto-political project. Recording refugee camps and crossings via the Mediterranean into Europe, his techno-images’ specific mosaic structure, tactility, and luminous flatness evoke the visual mode of Byzantine icons, thus switching from a paranoid, invasive world/view to an economy of mediation and contact with the Other.

Summary: "Ein Bild sagt mehr als tausend Worte?" Worin gründet diese besondere "Sagkraft" der Bilder, wie sind epistemische Gehalte von Bildern denkbar, die sich einer sprachlichen Vermittlung entziehen, ja: ein genuin bildliches, nicht-sprachliches Erkenntnispotential für sich einfordern?