We prove constructively that the weak König lemma and quantifier-free number-number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. Furthermore, (...) we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

Dini's theorem says that compactness of the domain, a metric space, ensures the uniform convergence of every simply convergent monotone sequence of real-valued continuous functions whose limit is continuous. By showing that Dini's theorem is equivalent to Brouwer's fan theorem for detachable bars, we provide Dini's theorem with a classification in the recently established constructive reverse mathematics propagated by Ishihara. As a complement, Dini's theorem is proved to be equivalent to the analogue of the fan theorem, weak König's lemma, in (...) the original classical setting of reverse mathematics started by Friedman and Simpson. (shrink)

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

The question in the background of this article is what kind of epistemology can emerge on the basis of the philosophy of life. To answer this question, the theories of Georg Misch and Josef König have been analysed. Both authors differentiate between the analytic discourse of theoretical approaches to the world and the synthetic discourse of non-theoretical objectifications of life which create a human semantic environment. For Misch, the former is constituted with “discursive” and the later with “evocative” utterances. (...) For König as developed in his work “Sein und Denken”, “determining” and “modifying” predicates oppose each other as cardinally different cognitive and epistemological entities. The article focuses on König′s analysis of the genesis and logics of “determining” and “modifying” predication following the strategy of his book. In conclusion some controversies between Misch′s and König′s conceptions of a language constitution of the world are represented and discussed. (shrink)

The article poses the question to what extend Josef Koenig’s aesthetic approach represents a continuation of the Kantian approach by means of philosophy of language. Its starting point is Kant’s notion of aesthetic ideas for which concepts – in their metaphorical use – are an indespensable condition. Both authors presuppose the free play of cognitive faculties as a foundational principle of aesthetic experience. While for Kant beauty immediately results from pleasure concerning a perception, for Koenig this pleasure is mediated (...) by the purposiveness of a description of an aesthetic impression. A description is purposeful if it is expressed by an appropriate metaphor. Hence its interpersonal validity is only verifiable by resonance. (shrink)

A growing literature is taking an institutionalist and governance perspective on how algorithms shape society based on unprecedented capacities for managing social complexity. Algorithmic governance altogether emerges as a novel and distinctive kind of societal steering. It appears to transcend established categories and modes of governance—and thus seems to call for new ways of thinking about how social relations can be regulated and ordered. However, as this paper argues, despite its novel way of realizing outcomes of collective steering and coordination, (...) it can nevertheless be grasped with an old and fundamental figure in political philosophy: that of Thomas Hobbes’ Leviathan. Comparing algorithmic governance with this figure serves to highlight their similarities as socio-political arrangements, and specifically to clarify how algorithmic governance parallels the apolitical traits of the Leviathan—it eliminates the political as it requires compliance and forgoing contestation to best fulfill its role and to produce satisfying outcomes. (shrink)

We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.

Existentialist philosophy offers an understanding of how trying to eliminate ambiguities that inevitably mark the human condition only seemingly leads to freedom. This existentialist outlook can also serve to shed light on how democratic politics may similarly show tendencies which aim at overcoming immanent tensions. Such tendencies in democratic politics can be clarified using Sartre’s notion of ignorance – and truth as its counterpart. His concept of ignorance goes beyond merely facts or knowledge and refers to a mode of being. (...) It expresses a subject’s desire to avoid, rather than confront, resistances stemming from the world. Based on a distinction of different forms in which this orientation can manifest itself, this article shows how democratic politics, too, can be threatened by ignorance as a way of doing politics. This ignorance comes in different guises which all express a desire to eliminate tensions that democratic politics cannot overcome without undermining itself. (shrink)

Between 1983 and 1990, at least 163 Western drugs were tested in the GDR. On the basis of archival documentation, relevant literature, and interviews we examined the clinical trials of five drugs more thoroughly; two of these individual case studies are introduced in this article. In the case of the clinical trials of the synthetic human growth hormone Saizen we found extensive trial and patient documentation, which allows for a detailed analysis of ethical aspects such as parent information and informed (...) patient consent. In the case of the clinical trials of the „abortion pill“ Mifepristone for the World Health Organization we uncovered irregularities with regard to the ethical evaluation. However, taken together, we could not find any serious violation of ethical norms in connection with our cases studies. (shrink)

We document outcome bias in situations where an agent makes risky financial decisions for a principal. In three experiments, we show that the principal’s evaluations and financial rewards for the agent are strongly affected by the random outcome of the risky investment. This happens despite her exact knowledge of the investment strategy, which can, therefore, be assessed independently of the outcome. The principal thus judges the same decision by the agent differently, depending on factors that the agent has no influence (...) on. The effect of outcomes persists in a setting where principals communicate a preferred investment level. Principals are more satisfied with the agent after a random success when the agent did not follow the requested investment level, than after a failed investment that followed their explicit request. (shrink)