Continuous reducibilities are a proven tool in Computable Analysis, and have applications in other fields such as Constructive Mathematics or Reverse Mathematics. We study the order-theoretic properties of several variants of the two most important definitions, and especially introduce suprema for them. The suprema are shown to commutate with several characteristic numbers.

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have (...) bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness. (shrink)

We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f$ is R-random, then x is R-random as well. If additionally f is known to have (...) bounded variation, then we show f has Luzin’s if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness. (shrink)

In this work we investigate the Weihrauch degree of the problem Decreasing Sequence of finding an infinite descending sequence through a given ill-founded linear order, which is shared by the problem Bad Sequence of finding a bad sequence through a given non-well quasi-order. We show that $\mathsf {DS}$, despite being hard to solve, is rather weak in terms of uniform computational strength. To make the latter precise, we introduce the notion of the deterministic part of a Weihrauch degree. We then (...) generalize $\mathsf {DS}$ and $\mathsf {BS}$ by considering $\boldsymbol {\Gamma }$ -presented orders, where $\boldsymbol {\Gamma }$ is a Borel pointclass or $\boldsymbol {\Delta }^1_1$, $\boldsymbol {\Sigma }^1_1$, $\boldsymbol {\Pi }^1_1$. We study the obtained $\mathsf {DS}$ -hierarchy and $\mathsf {BS}$ -hierarchy of problems in comparison with the Baire hierarchy and show that they do not collapse at any finite level. (shrink)

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far $\mathrm {ATR}_0$ has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

Max Horkheimer, the founder of the critical theory of the ‘Frankfurt School’, died in July 1973. In his essay dedicated to this great thinker, sociologist and philosopher, the author attempts to uncover the theoretical roots of this critical thinking in the philosopher's early work. He analyses Horkheimer's early commitment to the cause of the victims of social, economic and political oppression as well as all systems that trample on the freedom and dignity of the individual and that discriminate against and (...) persecute minorities. He also pays special attention to Horkheimer's struggle against the authoritarian state, against totalitarianism as well as anti-Semitism. (shrink)

Thesis--Fribourg. Cf. Das Schweizer Buch. Serie B. 1966.

Name der Zeitschrift: Kant-Studien Jahrgang: 108 Heft: 1 Seiten: 19-54.

Background: Gait analysis after total ankle replacement and ankle arthrodesis is usually measured barefoot. However, this does not reflect reality. The purpose of this study was to compare patients barefoot and with footwear. Methods: We compared 126 patients (total ankle replacement 28, ankle arthrodesis 57, and tibiotalocalcaneal arthrodesis 41) with 35 healthy controls in three conditions (barefoot, standardized running, and rocker bottom shoes). Minimum follow-up was 2 years. We used dynamic pedobarography and a light gate. Main outcome measures: relative midfoot (...) index, forefoot maximal force, walking speed. Findings: The relative midfoot index decreased in all groups from barefoot to running shoes and again to rocker bottom shoes (p < 0.001). The forefoot maximal force increased wearing shoes (p < 0.001), but there was no difference between running and rocker bottom shoes. Walking speed increased by 0.06 m/s with footwear (p < 0.001). Total ankle replacement and ankle arthrodesis were equal in running shoes but both deviated from healthy controls (total ankle replacement/ankle arthrodesis smaller RMI p = 0.07/0.017; increased forefoot maximal force p = 0.757/0.862; slower walking speed p < 0.001). In rocker bottom shoes, this ranking remained the same except the relative midfoot index merged to similar values. Tibiotalocalcaneal arthrodesis were inferior in both shoes. Interpretation: Runners are beneficial and the benefit is greater for fusions and replacements. Rocker bottom shoes have little added benefit. Total ankle replacement and ankle arthrodesis were equal but inferior to healthy controls. Tibiotalocalcaneal arthrodesis has an inferior outcome. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The comic book hero Superman grew from a social crusader and a “champion of the oppressed” in the 1930s, to a patriotic and paternalistic fighter for “Truth, Justice, and the American way” in the 1940s and 1950s, to a compassionate Christ‐like savior in the latter part of the twentieth century – and always defending the Judeo‐Christian values upheld by the American majority. Friedrich Nietzsche’s “superman,” on the other hand, firmly rejects the very same values its superhero namesake upholds. While it (...) has been a common trope in the superhero genre and popular culture in general to characterize figures explicitly based on Nietzsche’s Übermensch as inhuman monsters, this chapter argues that Nietzsche’s concept can be reinstated through the character of Superman himself. Like Übermensch, Superman is strong, creative, noble, independent, and life‐affirming, but unlike him, Superman is compassionate and looks out for the little guy. (shrink)

Exploration of the political roles firms play in society is a flourishing stream within corporate social responsibility research. However, few empirical studies have examined multiple levels of political CSR at the same time from a critical perspective. We explore both how the motivations of managers and internal organizational practices affect a company’s choice between competing CSR approaches, and how the different CSR programs of corporate and civil society actors compete with each other. We present a qualitative interpretative case study of (...) how a French children’s clothing retailer develops CSR practices in response to accusations of poor working conditions and child labor in its supply chain. The company’s CSR approach consists of superficial practices, such as supplier audits by a cooperative business-organized nongovernmental organization and philanthropic activities, which enable managers to silence more radical alternative models defended by other NGOs, activists, and trade unions. By this approach, the core business model based on exploitative low-cost country sourcing remains intact through self-regulated CSR. Through the case study, we develop a framework of dynamism in competing CSR programs. We discuss the implications of our study for CSR researchers, company managers, and policy makers. (shrink)

Arno Bammé geht es in diesem Buch darum, die sozialhistorischen Wurzeln der gegenwärtigen Problematik im Verhältnis Natur/Gesellschaft/Wissenschaft/Technik deutlich zu machen. Ausgangspunkt seiner Argumentation ist David Bloors Edinburgh Strong Programme, demzufolge auch der”hard core“der Wissenschaft sozialen Ursprungs ist. Sein Ziel ist es, der tatsächlichen historischen Entwicklung, die sehr chaotisch verlaufen ist, soziologisch eine Struktur zu geben - in Form dreier Zäsuren, wobei das Wechselverhältnis von Wissenschaft, Technik und Gesellschaft im Vordergrund steht.

Im Alter von 21 Jahren hat W. Pauli einen Handbuchartikel zur Relativitätstheorie verfaßt, der bis heute gelesen und zitiert wird. Er ist wohl der berühmteste Text zum Thema und wurde nicht zuletzt von A. Einstein begeistert gewürdigt. Die vorliegende Neuausgabe enthält den Originalartikel sowie weitere, teilweise recht ausführliche Ergänzungen, die Pauli im Jahre 1956 für die englische Ausgabe schrieb. Eine Reihe von Anmerkungen des Herausgebers dienen darüber hinaus als Lesehilfen und zeigen Verbindungen zu modernen Entwicklungen auf.

Contract cheating – outsourcing student assignments for a fee – presents a growing threat to the integrity of higher education. As contract cheating is based on students purchasing assignments that are original, traditional plagiarism detection tools remain insufficient to detect contract cheating. Part of the problem is that proving contract cheating is difficult. As a result, instructors may find it hard to prosecute students. To help address the problem, this conceptual paper builds upon extant scholarship on contract cheating and argues (...) that a novel evidence-based approach is needed. Such an approach should allow instructors to detect and prosecute cases of contract cheating effectively and efficiently. The paper then presents an outline of such an approach and calls it the “Doping Test” approach as it mimics some aspects of doping testing in professional sport. (shrink)

Einleitung: Die französischen Materialisten des 18. Jahrhunderts, von A. Baruzzi.--La Mettrie, von A. Baruzzi.--Helvétius, von E. Voegelin und P. Leuschner.--Diderot, von T. Schabert.--Sade, von A. Baruzzi.--Bibliographisches Stichwort (p. 168-174).

Ernst Cassirer's philosophy of culture has been much discussed in recent years. However, it remains unclear how it evolved from his older theory of knowledge. This study deals with this question on the basis of Cassirer's 'disposition' of a 'philosophy of the symbolic', reconstructed here for the first time. This text shows that the 'symbolic' refers to culture as a whole and to its inherent diversity. Therefore, 'the symbolic' includes the relationship between the general transcendental conditions of culture and its (...) empirical specificities in language and languages, art and the arts, myth and myths, science and disciplines. Cassirer does not comprehend this empirical and specific reality of symbolization depending on pre-existing transcendental conditions. Instead, he proceeds from the empirical diversity of the symbolisations and reflects on their simultaneously general and specific conditions. Thus, Cassirer embarks on a path that he finds paved in Kant's "Critique of Judgement": He consequently defines 'the symbolic' as the horizon for a reflective approach based on empirical findings - and not as the foundation of a systematic derivation of the diversity of culture in the style of the idealistic tradition. (shrink)

Although machine learning has been successful in recent years and is increasingly being deployed in the sciences, enterprises or administrations, it has rarely been discussed in philosophy beyond the philosophy of mathematics and machine learning. The present contribution addresses the resulting lack of conceptual tools for an epistemological discussion of machine learning by conceiving of deep learning networks as ‘judging machines’ and using the Kantian analysis of judgments for specifying the type of judgment they are capable of. At the center (...) of the argument is the fact that the functionality of deep learning networks is established by training and cannot be explained and justified by reference to a predefined rule-based procedure. Instead, the computational process of a deep learning network is barely explainable and needs further justification, as is shown in reference to the current research literature. Thus, it requires a new form of justification, that is to be specified with the help of Kant’s epistemology. (shrink)

We define and investigate a family of local–global principles for fields involving both orderings and p-valuations. This family contains the PAC, PRC and PpC fields and exhausts the class of pseudo classically closed fields. We show that the fields satisfying such a local–global principle form an elementary class, admit diophantine definitions of holomorphy domains, and their orderings satisfy the strong approximation property.

This paper reviews the debate on the notion of biological function and on functional explanation as this takes place in philosophy. It describes the different perspectives, issues, intuitions, theories and arguments that have emerged. The author shows that the debate has been too heavily influenced by the concerns of a naturalistic philosophy of mind and argues that in order to improve our understanding of biology the attention should be shifted from the study of intuitions to the study of the actual (...) practice of biological inquiry. (shrink)

The work [11] deals with questions of first-order definability in algebraic function fields. In particular, it exhibits new cases in which the field of constant functions is definable, and it investigates the phenomenon of definable transcendental elements. We fix some of its proofs and make additional observations concerning definable closure in these fields.

The term “translation” has three meanings: the practice of the translator, the textual outcome of this practice, and the relationship it creates between texts and languages. In this article, I would like to draw attention to this third aspect, translation as a relation. To do so, I will first propose a historical overview of the first two meanings, as well as of the normative or descriptive aims associated to them. Secondly, I identify three motives for thinking about translation that are (...) primarily concerned with its relational dimension: the lack of a language to speak about the relationship between languages, i.e. about what’s incomparable and what gets subtracted. I conclude this article with the hypothesis that translation as a relation constitutes a refuge event for the plurality of languages. (shrink)