Halin in 1965 proved that if a graph has [Formula: see text] many pairwise disjoint rays for each [Formula: see text] then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin’s theorem and the construction proving it seem very much like standard versions of compactness arguments such as König’s Lemma. Those results, while not computable, are relatively simple. They only use (...) arithmetic procedures or, equivalently, finitely many iterations of the Turing jump. We show that several Halin-type theorems are much more complicated. They are among the theorems of hyperarithmetic analysis. Such theorems imply the ability to iterate the Turing jump along any computable well ordering. Several important logical principles in this class have been extensively studied beginning with work of Kreisel, H. Friedman, Steel and others in the 1960s and 1970s. Until now, only one purely mathematical example was known. Our work provides many more and so answers Question 30 of Montalbán’s Open Questions in Reverse Mathematics in 2011. Some of these theorems including ones in Halin in 1965 are also shown to have unusual proof theoretic strength as well. (shrink)

Artikkelen ønsker å gi et konstruktivt bidrag til forståelsen og anvendelsen av fair play i en kroppsøvingsfaglig kontekst. Dette er et tema som er blitt aktualisert i og med at fair play er kommet inn som et sentralt element i kroppsøvingsfagets nye reviderte læreplan. Fair play omhandler regler, normer og verdier som skal gjelde ved idrettsutøvelse, og det er et etablert verdikonsept innenfor organisert idrettsliv og idrettsetisk forskning. I skolen, derimot, er fair play mindre kjent. Kroppsøvingsplanen hevder fair play omfatter (...) aspekter ved idrettsspillet som å overholde regler, vise hverandre respekt og gjøre hverandre gode. Hva betyr så dette? Hva vil det si å gjøre hverandre gode? Rommer det bare en teknisk eller også en sosialetisk kvalitet? Dersom det siste er tilfelle, bør det diskuteres hvilke danningskvaliteter det så ligger i det å gjøre hverandre gode i faget, og om disse har noen tilknytningspunkt til Aristoteles' klassiske dyder om rettferdighet, måtehold, mot og klokskap. Dette er de sentrale spørsmålene artikkelen reiser og prøver å gi noen svar på. Artikkelen ser først på fair play i kroppsøvingsfagets planer, for deretter å gi begrepet en nærmere etymologisk og ideologisk-historisk avklaring, med utgangspunkt i begrepene «fair» og «play». Videre drøftes fair play i lys av de aristoteliske dydene, relatert til kroppsøvingsfaglig kontekst og diskurs.Nøkkelord: kroppsøving, fair play, idrett, lek og danningEnglish summary: Fair play in Physical Education in the light of Aristotelian virtue ethicsThe aim of this article is to give a constructive contribution to the understanding and the application of the concept of fair play in the Physical Education context. This is a topic that has come into focus since fair play has been introduced as a central element in the newest revision of the subject curriculum. Fair play concerns the rules, norms, and values that apply to sports activities, and constitutes an established value concept within organized sports and research related to sports ethics. In schools, however, fair play is less known. The Physical Education curriculum states that fair play concerns aspects of sports and games such as adhering to rules, showing each other respect, and helping each other achieve. What, then, does this mean? What does it mean to help each other achieve? Does it entail purely technical, or also socio-ethical qualities? If the latter is the case, a discussion is needed as to what ethical formation qualities are involved in helping each other achieve in the subject and whether these have any connection to Aristotle's classical virtues of justice, moderation, courage, and wisdom. These are the central issues the article raises and attempts to shed some light on. The article takes a closer look at fair play in the curricula of Physical Education, moving on to an etymological and ideological-historical clarification of the concept, taking the concepts of fair and play as starting points. Further, it discusses fair play in the light of Aristotelian virtues, related to a Physical Education context and discourse. (shrink)

Physicians frequently face ethical dilemmas when caring for patients. To help them to cope with these, biomedical ethics aims to implement moral norms for particular problems and contexts. As a means of studying the cognitive and neurobiological features underlying the respect for these norms, moral cognitive neuroscience could help us to understand and improve ethical questioning. The article reviews recent developments in the field and presents neurobiological arguments to highlight why some moral rules are universally shared and why some ethical (...) responses are very dependent on context. (shrink)

Volume 19, Issue 10, October 2019, Page 57-59.

Lists of species underpin many fields of human endeavour, but there are currently no universally accepted principles for deciding which biological species should be accepted when there are alternative taxonomic treatments (and, by extension, which scientific names should be applied to those species). As improvements in information technology make it easier to communicate, access, and aggregate biodiversity information, there is a need for a framework that helps taxonomists and the users of taxonomy decide which taxa and names should be used (...) by society whilst continuing to encourage taxonomic research that leads to new species discoveries, new knowledge of species relationships, and the refinement of existing species concepts. Here, we present 10 principles that can underpin such a governance framework, namely (i) the species list must be based on science and free from nontaxonomic considerations and interference, (ii) governance of the species list must aim for community support and use, (iii) all decisions about list composition must be transparent, (iv) the governance of validated lists of species is separate from the governance of the names of taxa, (v) governance of lists of accepted species must not constrain academic freedom, (vi) the set of criteria considered sufficient to recognise species boundaries may appropriately vary between different taxonomic groups but should be consistent when possible, (vii) a global list must balance conflicting needs for currency and stability by having archived versions, (viii) contributors need appropriate recognition, (ix) list content should be traceable, and (x) a global listing process needs both to encompass global diversity and to accommodate local knowledge of that diversity. We conclude by outlining issues that must be resolved if such a system of taxonomic list governance and a unified list of accepted scientific names generated are to be universally adopted. (shrink)

Jean Cavaillès (15 mai 1903-17 février 1944) était un philosophe français, héros et l'un des organisateurs de la Résistance, avant d'être fusillé à 40 ans par les nazis. Une journée d'hommage lui a été consacrée le 17 février 2014 à l'Ecole normale supérieure de Paris. Pierre-Yves Canu, Tommy Murtagh, Hourya Benis Sinaceur, Paul Cortois, Alya Aglan, Baptiste Mélès, Gerhard Heinzmann et Jacques Lautman présentent un Cavaillès indissociablement philosophe et Résistant, explorent les racines de sa pensée, montrent l'actualité de ses concepts. (...) Jean-Jacques Szczeciniarz et Christian Houzel proposent une analyse du Mouvement de la jeunesse allemand, un historique de la société Les Amis de Jean Cavaillès, éditrice du présent recueil, et deux hommages à celui qui la présida de 1989 à 1995, le mathématicien Henri Cartan. (shrink)

The definition of a perfect gas mixture varies substantially within the chemistry textbook literature. A recent International Union of Pure and Applied Chemistry (IUPAC) definition is here criticised as being insufficient to cover properties traditionally associated with such mixtures. Possible supplements to the definition to rectify the deficiency are considered. An alternative definition in molecular terms is shown to be comprehensive. The paper should serve as a summary of the properties of a perfect gas mixture and of essential components of (...) its definition. (shrink)

Theorems of hyperarithmetic analysis occupy an unusual neighborhood in the realms of reverse mathematics and recursion-theoretic complexity. They lie above all the fixed iterations of the Turing jump but below ATR $_{0}$. There is a long history of proof-theoretic principles which are THAs. Until the papers reported on in this communication, there was only one mathematical example. Barnes, Goh, and Shore [1] analyze an array of ubiquity theorems in graph theory descended from Halin’s [9] work on rays in graphs. They (...) seem to be typical applications of ACA $_{0}$ but are actually THAs. These results answer Question 30 of Montalbán’s Open Questions in Reverse Mathematics [19] and supply several other natural principles of different and unusual levels of complexity.This work led in [25] to a new neighborhood of the reverse mathematical zoo: almost theorems of hyperarithmetic analysis. When combined with ACA $_{0}$ they are THAs but on their own are very weak. Denizens both mathematical and logical are provided. Generalizations of several conservativity classes are defined and these ATHAs as well as many other principles are shown to be conservative over RCA $_{0}$ in all these senses and weak in other recursion-theoretic ways as well. These results answer a question raised by Hirschfeldt and reported in [19] by providing a long list of pairs of principles one of which is very weak over RCA $_{0}$ but over ACA $_{0}$ is equivalent to the other which may be strong or very strong going up a standard hierarchy and at the end being stronger than full second-order arithmetic. (shrink)