In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation (...) is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably-based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (shrink)

The basic concept of Type-2 Theory of Effectivity to define computability on topological spaces or limit spaces are representations, i. e. surjection functions from the Baire space onto X. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 Complexity Theory on the represented spaces. For each of these properties, we give a nice characterization of the (...) class of spaces that are equipped with a representation having the respective property. (shrink)

The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way that relative computability (...) of functions is preserved. Thus the use of admissible representations rather than of non–admissible ones does not decrease the class of relatively computable functions. (shrink)

Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...) is needed. But there may be no computable points in X. By converging sequences of basis sets instead of Cauchy sequences of points we construct a metric completion of a space together with a canonical representation equation image, equation image. We show that there is a computable embedding of in with computable inverse. Finally, we construct a notation of a dense set of points in with computable mutual distances and prove that the Cauchy representation of the resulting computable metric space is equivalent to equation image. Therefore, every computably regular space has a computable homeomorphic embedding in a computable metric space, which topologically is its completion. By the way we prove a computable Urysohn lemma. (shrink)

Matthias Schröder has asked the question whether there is a weakest discontinuous problem in the topological version of the Weihrauch lattice. Such a problem can be considered as the weakest unsolvable problem. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schröder’s question sensitively depends on the axiomatic framework that is chosen, and it is a positive answer if we (...) work in Zermelo–Fraenkel set theory with dependent choice and the axiom of determinacy $\mathsf {AD}$. On the other hand, using the full axiom of choice, one can construct problems which are discontinuous, but not effectively so. Hence, the exact situation at the bottom of the Weihrauch lattice sensitively depends on the axiomatic setting that we choose. We prove our result using a variant of Wadge games for mathematical problems. While the existence of a winning strategy for Player II characterizes continuity of the problem (as already shown by Nobrega and Pauly), the existence of a winning strategy for Player I characterizes effective discontinuity of the problem. By Weihrauch determinacy we understand the condition that every problem is either continuous or effectively discontinuous. This notion of determinacy is a fairly strong notion, as it is not only implied by the axiom of determinacy $\mathsf {AD}$, but it also implies Wadge determinacy. We close with a brief discussion of generalized notions of productivity. (shrink)

Defined narrowly, epistemology is the study of knowledge and justified belief. As the study of knowledge, epistemology is concerned with the following questions: What are the necessary and sufficient conditions of knowledge? What are its sources? What is its structure, and what are its limits? As the study of justified belief, epistemology aims to answer questions such as: How we are to understand the concept of justification? What makes justified beliefs justified? Is justification internal or external to one's own mind? (...) Understood more broadly, epistemology is about issues having to do with the creation and dissemination of knowledge in particular areas of inquiry. This article will provide a systematic overview of the problems that the questions above raise and focus in some depth on issues relating to the structure and the limits of knowledge and justification. (shrink)

Developments in Non-Invasive Prenatal Testing (NIPT) and cell-free fetal DNA analysis raise the possibility that antenatal services may soon be able to support couples in non-invasively testing for, and diagnosing, an unprecedented range of genetic disorders and traits coded within their unborn child’s genome. Inevitably, this has prompted debate within the bioethics literature about what screening options should be offered to couples for the purpose of reproductive choice. In relation to this problem, the European Society of Human Genetics (ESHG) and (...) American Society of Human Genetics (ASHG) tentatively recommend that any expansion of this type of screening, as facilitated by NIPT, should be limited to serious congenital and childhood disorders. In support of this recommendation, the ESHG and ASHG cite considerations of distribution justice. Notably, however, an account of justice in the organization and provision of this type of screening which might substantiate this recommendation has yet to be developed. This paper attempts to redress this oversight through an investigation of Norman Daniels’ theory of Just health: meeting health needs fairly. In line with this aim, the paper examines what special moral importance (for Just health) screening for the purpose of reproductive choice might have where concerning serious congenital and childhood disorders in particular. The paper concludes that screening for reproductive choice where concerning serious congenital and childhood disorders may be important for providing women with fair opportunity to protect their health (by either having or not having an affected child). (shrink)

One of the most common arguments in favour of the state's authority is that without the coordinating hand of political institutions, we could not achieve important moral benefits. I argue that if we understand authority correctly, then coordination cannot even in principle establish that coordinators have political authority.

We investigate interpolation properties of many-valued propositional logics related to continuous t-norms. In case of failure of interpolation, we characterize the minimal interpolating extensions of the languages. For finite-valued logics, we count the number of interpolating extensions by Fibonacci sequences.

Social scientists have traditionally attempted to avoid extending strategies for acquiring experimental knowledge to the sphere of the social. Bruno Latour, however, has introduced a notion of the collective experiment, an experiment conducted by and with us all. In this short paper I seek to explore, by way of elucidating the talk of collective experiments, that Latour's notion has long since existed in the theory and practice of ecological design and restoration. Practitioners in ecological restoration projects find themselves in a (...) situation of double contingency, since neither do they know how nature will respond to their intervention nor is their interpretation of these responses already certain. Experimental practice in society then becomes the proceduralization of this contingency. (shrink)

I distinguish between Old Contextualism, New Contextualism, and the Multiple Concepts Theory. I argue that Old Contextualism cannot handle the following three problems: (i) the disquotational paradox, (ii) upward pressure resistance, (iii) inability to avoid the acceptance of skeptical conclusions. New Contextualism, in contrast, can avoid these problems. However, since New Contextualism appears to be a semanticized mirror image of MCT, it remains unclear whether it is in fact a genuine version of contextualism.

Helmholtz's theory of space had significant impact on Schlick's early ?critical realist? point of view. However, it will be argued in this paper that Schlick's appropriation of Helmholtz's ideas eventually lead to a rather radical transformation of the original Helmholtzian position.

This study examined whether parents’ attribution of their child’s emotions (internalizing, externalizing) to dispositional causes is associated with children’s problem behaviour (internalizing, externalizing). The mediating roles of parents’ emotion-dismissing and -coaching reactions and the moderating role of child’s gender was also examined. Participants were 241 US parents with a child (43% girls) between the ages of 5 and 7. Parents were presented with vignettes in which a gender-neutral child displayed internalizing and externalizing emotions and were asked to imagine their own (...) child in the vignettes. Subsequently, parents indicated whether they attributed the child’s emotion to dispositional causes and the likelihood of reacting in an emotion-dismissing and -coaching way in each situation. Child problem behaviour was measured using the CBCL. Results show that parental dispositional attributions were associated with child internalizing and externalizing problems, and this association was consistently mediated by emotion-dismissing reactions. The association between parental dispositional attributions and emotion-dismissing, as well as its indirect effect on child internalizing problems, was stronger for boys than for girls, whereas the indirect effect via emotion-coaching was stronger for girls than for boys. Thus, the parental attribution process seems to be different for boys and girls. (shrink)

Das Gerucht, Gott sei tot, scheint ubertrieben gewesen zu sein. An dessen Verbreitung haben die Naturwissenschaften einen wesentlichen Anteil gehabt. Gegenwartig fuhren dagegen gerade sie Gott wieder im Munde. Massgeblichen Anteil daran hat die Entdeckung des Phanomens der Feinabstimmung Wenn Naturkonstanten, die die Gestalt unseres Universums bestimmen, nur wenig andere Werte angenommen hatten, hatte es bewusstes Leben nie gegeben. Matthias Schleiff entwickelt daraus das teleologische Feinabstimmungsargument. In der Nachfolge traditioneller Gottesbeweise, aber mit den wissenschaftlichen Einsichten unserer Zeit, argumentiert er (...) dafur, dass sich die Annahme eines kosmischen Schopfers auf rationale Grunde stutzen kann. Er setzt sich dabei intensiv mit alternativen Erklarungshypothesen auseinander - etwa der Erklarung durch den Zufall, das Anthropische Prinzip oder die Theorie des Multiversums - und bringt so Naturwissenschaften, Philosophie und Theologie wieder in ein Gesprach uber den Anfang der Welt. (shrink)

We consider the following problem: Given a proof of the Skolemization of a formula F, what is the length of the shortest proof of F? For the restriction of this question to cut-free proofs we prove corresponding exponential upper and lower bounds.

A t-tautology is a propositional formula which is a tautology in all fuzzy logics defined by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

This study examines the specificvalues held by consumers towards organic andconventionally produced meat, with particularreference to moral issues surrounding foodanimal production. A quota sample of 30 femalesfrom both a rural and an urban area of Scotland, were interviewed. Overall, there was lowcommitment towards the purchase of organicmeats and little concern for ethical issues.Price and product appearance were the primarymeat selection criteria, the latter being usedas a predictor of eating quality. Manyattitude-behavior anomalies were identified,mainly as a result of respondents' cognitivedissonance and (...) lack of understanding regardingmeat production criteria underpinning meatquality marks, e.g., Soil Association label.Responsibilities for ethical issues appeared tobe delegated by the consumer to the meatretailer or government. This raises issuesabout educating consumers and bringingconsumers closer to understanding meatproduction systems. A conceptual framework isproposed that illustrates the significance ofconsumer involvement in how meat-purchasingdecisions are approached in terms of theevaluation of tangible and or intangiblequality attributes. The results also point tothe need for further research into thoseaspects of quality that individuals tend toaddress at the level of the citizen,rather than at the point of purchase. (shrink)

Est ici publiée une stèle inédite, composée de deux fragments découverts en 2012 et 2017 et portant sept catalogues militaires de la cité de Chorsiai en Béotie du Sud‑Ouest. Ces documents, gravés sans doute par le même lapicide, s’échelonnent, d’après la nouvelle chronologie des archontes fédéraux, entre 223/222 et ca. 194/193 av. J.‑C. On compte un nouvel archonte, Kalliklès, qui peut être daté de 196/195. L’analyse de ces documents est l’occasion d’une réflexion portant principalement sur deux points : d’une part, (...) les modalités d’application de la possible réforme militaire intervenue en Béotie dans le dernier quart du iiie s. malgré la présence d’éphèbes thyréaphores sous l’archonte Hippias I (221/220), alors que sous le même archonte à Aigosthènes ils sont classés parmi les peltophores ; d’autre part, le nombre de conscrits (entre un et sept) et la manière dont ce polisma contribuait, selon ses forces, à l’effort militaire du koinon béotien. (shrink)

Ernest Nagel was one of the first philosophers of science who reflected systematically on the methodology of the social sciences. His cooperation with Paul F. Lazarsfeld at Columbia University proved to be instructive in this regard. Moreover, Nagel stood in close contact with representatives of sociological functionalism and published, in 1956, a contribution on the prospects of a formalization of functionalism. In his seminal The Structure of Science from 1961, Nagel devoted two long chapters to methodological and explanatory problems of (...) the social sciences. The aim of the present chapter is to rationally reconstruct this 1961 account. I will proceed in three steps: first, I shall shed some light on Nagel’s discussion of the problem of a clear-cut demarcation between the natural and the social sciences; then Nagel’s interpretation of the presumptive ‘immaturity’ of the social sciences will be taken into account; finally, two case studies will be provided in order to illustrate the implications of Nagel’s particular analysis. (shrink)

Facts such as the fact that Donald Trump is the US president or the fact that Germany won the 2014 world cup final are commonly referred to as “institutional facts” (“IFF”). I advocate the view that the nature of these facts is comparatively simple: they are facts that exist by virtue of collective recognition (CR), where CR can be direct or indirect. The leading account of IFF, that of John Searle, basically conforms with this definition. However, in his writings Searle (...) has considered or defended several other conditions as potentially necessary for the existence of IFF. In particular, he has considered whether (a) IFF necessarily involve deontic powers, (b) IFF are necessarily so-called “status functions”, (c) IFF require speech acts of Declaring for their existence, (d) IFF require language for their existence. Each of these considerations, if valid, would seem to render the nature of IFF less simple. In this paper, I argue that none of these considerations stand up to scrutiny. Being unaware of any other serious considerations of this kind, I conclude that the nature of IFF is simple as captured by my definition. There is a respect, however, in which my view is possibly less simple than Searle’s, for he suggests that CR is always direct, and never indirect. I reject this suggestion. Indeed, I think that most of the facts existing by virtue of CR exist by virtue of indirect CR. Some authors have (or at least might be construed as having) objected that CR is not even necessary for the existence of IFF. I argue that the account defended here is immune to these objections. (shrink)

The New Testament, while rejecting any superficial connection between illness and sin, does not reject a possible connection between illness and a person's relationship with God. An example can be seen in the story of the young blind man who was healed. His blindness does not result from any fault he or his parents had committed but apparently from God's wish to reveal his own healing power. The inner blindness of the Pharisees is a different type of blindness far more (...) difficult to heal. The blind young man was actually healed, not only in body but also in soul. Such miraculous healings are rare nowadays. However, if one takes a closer look at modern genetics and psycho-neuro-immunological findings, one may come to a better understanding of how miracle healings are linked to man's inner life and therefore also to his religiousness. Many diseases have genetic backgrounds. Defective genes, however, do not necessarily lead to subsequent illness. Genes have to be switched on or off. Only activated genes trigger pathological change. The human brain and all of man's thinking and feeling are intimately connected with such activations. We may thus conclude that both inner life and religious outlook on life are relevant to the origin and development of diseases. (shrink)

Freges Kontextprinzip "Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas" hat auch nach der von ihm vollzogenen Angleichung von Behauptungssätzen an Eigennamen Gültigkeit für die formale Sprache der "Grundgesetze". Der Bedeutungsvollständigkcitsbeweis, den er für sein Logiksystem anstrebt, schließt eine unmittelbare Anwendung dieses Prinzips nicht nur auf die unvollständigen Funktionsausdrücke, sondern auch auf die leerstellenfreien Wertverlaufsnamen ein. Wahrheitsnamen (Sätze) zeichnen sich vor anderen symbolsprachlichen Eigennamen in mehrfacher Hinsicht, insbesondere durch ihre semantische Selbständigkeit aus. Wertverlaufsnamen haben nur im Zusammenhang eines Wahrheitswertnamens (...) eine Bedeutung. Ihre Bedeutung besteht in ihrem Beitrag zur Bestimmung der Bedeutung von Wahrheitswertnamen, in denen sie vorkommen. (shrink)