We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among others, this gives some true co-analytic sets. The case where the dictionary is finite is studied and gives a natural example of a set at level ω of the Wadge hierarchy.

We show that there is an antichain basis for neither the class of non-potentially closed Borel subsets of the plane under Borel rectangular reducibility nor the class of analytic graphs of uncountable Borel chromatic number under Borel reducibility.

Let ξ ≥ 1 be a countable ordinal. We study the Borel subsets of the plane that can be made [Formula: see text] by refining the Polish topology on the real line. These sets are called potentially [Formula: see text]. We give a Hurewicz-like test to recognize potentially [Formula: see text] sets.

We prove that, for each countable ordinal ξ≥1, there exist some -complete ω-powers, and some -complete ω-powers, extending previous works on the topological complexity of ω-powers [O. Finkel, Topological properties of omega context free languages, Theoretical Computer Science 262 669–697; O. Finkel, Borel hierarchy and omega context free languages, Theoretical Computer Science 290 1385–1405; O. Finkel, An omega-power of a finitary language which is a borel set of infinite rank, Fundamenta informaticae 62 333–342; D. Lecomte, Sur les ensembles de (...) phrases infinies constructibles a partir d’un dictionnaire sur un alphabet fini, Séminaire d’Initiation a l’Analyse, 1, année 2001–2002; D. Lecomte, Omega-powers and descriptive set theory, Journal of Symbolic Logic 70 1210–1232; J. Duparc, O. Finkel, An ω-Power of a Context-Free Language Which Is Borel Above , in: S. Bold, B. Löwe, T. Räsch, J. van Benthem , in the Proceedings of the international conference foundations of the formal sciences V : Infinite Games, November 26th to 29th, 2004, Bonn, Germany, in: Studies in Logic, vol. 11, College Publications at King’s College, 2007, pp. 109–122]. We prove effective versions of these results; in particular, for each recursive ordinal there exist some recursive sets A2<ω such that , where and denote classes of the hyperarithmetical hierarchy. To do this, we prove effective versions of a result by Kuratowski, describing a set as the range of a closed subset of the Baire space ωω by a continuous bijection. This leads us to prove closure properties for the pointclasses in arbitrary recursively presented Polish spaces. We apply our existence results to get better computations of the topological complexity of some sets of dictionaries considered in [D. Lecomte, Omega-powers and descriptive set theory, Journal of Symbolic Logic 70 1210–1232]. (shrink)

We prove that, for any natural number \, we can find a finite alphabet \ and a finitary language L over \ accepted by a one-counter automaton, such that the \-power $$\begin{aligned} L^\infty :=\{ w_0w_1\ldots \in \Sigma ^\omega \mid \forall i\in \omega ~~w_i\in L\} \end{aligned}$$is \-complete. We prove a similar result for the class \.

We prove that, for any natural number n≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 1$$\end{document}, we can find a finite alphabet Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} and a finitary language L over Σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Sigma $$\end{document} accepted by a one-counter automaton, such that the ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document}-power L∞:={w0w1…∈Σω∣∀i∈ωwi∈L}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} (...) L^\infty :=\{ w_0w_1\ldots \in \Sigma ^\omega \mid \forall i\in \omega ~~w_i\in L\} \end{aligned}$$\end{document}is Πn0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Pi }}^0_n$$\end{document}-complete. We prove a similar result for the class Σn0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\Sigma }}^0_n$$\end{document}. (shrink)

The Oyapock River has been the border between France and Brazil since the Treaty of Bern came to resolve a centuries-old dispute between the two states. Only populated by indigenous communities and a few adventurers, the two banks of the river are untouched by any lasting colonial and national settlement before the second half of the 19th century. Penal colonization is the formula adopted by the two states to fill the "void" of a border to be formalized. The criminal models (...) circulate and are reinterpreted by participating with great intensity in the making of the territory. (shrink)

In the past forty years, Bruno Latour’s claim that Science Is Politics By Other Means (SIPBOM) has been the underlying creed of Science and Technology Studies (STS), most of us simply taking it for granted. In contrast, this special issue is predicated on the observation of an enduring lack of exegesis of this catchphrase so remarkable that is has caused an outcry among natural scientists, echoed in some social science quarters. If SIPBOM has been a resource for decades, by turning (...) it into a topic this special issue revisits one of the most exciting and challenging insights of contemporary thought. (shrink)

To students and practitioners of anamorphic art, the name of Jean-François Niceron is more than preeminent; it has become iconic. La Perspective Curieuse was first published in 1638. An augmented version was then translated into Latin by Mersenne in 1646. A newly amended and augmented version was retranslated into French by Roberval in 1652. This book is an English translation of the 1652 text, with reference to the 1638 and 1646 versions. Considering the continued high reputation of the book, the (...) mathematics have been checked for correctness and consistency, and the authors have provided a full commentary, pointing out the most difficult turns of the 17th-century French, the respective contributions of Niceron, Mersenne and Roberval, and explaining Niceron's greatest insights and weaknesses. (shrink)

This paper seeks to find possibilities forreconciliation of the implementation of theprecautionary principle and the promotion ofinternational trade of genetically modified organisms,based on the assumption that a sustainabledevelopment is a right objective to strive for. Itstarts with an explanation of the background and therole of the precautionary principle, and describes inwhat way measures based on the precautionary principlecan easily lead to the creation of trade barriers. Thearticle then examines to what extent the WTO (WorldTrade Organisation) Agreements allow theimplementation of the (...) precautionary principle. Inaddition, structural conflicts between the perceptionof the precautionary principle and the concept oftrade liberalisation will be evoked. The last sectionof the paper analyses to what extent the WTO rulesprovide possibilities to avoid or solve theseconflicts in order to attempt to answer the mainquestion: are the precautionary principle and theinternational trade of genetically modified organismsreconcilable? (shrink)

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the necessity (...) of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a "noncommutative pregeometry", and only when crossing this threshold does the usual space-time geometry emerges. (shrink)

Around 1716, the French astronomer and academician Joseph-Nicolas Delisle took up a new project: the twinned topics of Chinese chronology and astronomy. Unable to access Chinese sources and not knowing any fellow savants who shared this particular interest, Delisle methodically made extracts and compiled data from the existing European literature. Among Delisle's papers at the Observatoire de Paris still exist the results of this research, including a list of the books he found relevant. This paper develops a close reading of (...) Delisle's notes from this period to stage his journey into a recondite arena of technical and textual analysis, and to examine the scholarly practices and generic conventions through which early modern European savants confronted the Chinese astronomical tradition. (shrink)

Bulletin de Philosophie Médiévale, Volume 62, Issue, Page 430-436, January 2020.

Bulletin de Philosophie Médiévale, Volume 62, Issue, Page 430-436, January 2020.

Klara and the Sun, the latest novel by Nobel-prize winner Kazuo Ishiguro, forces one to reckon with one's own anxieties about the future of emerging technologies and confront deep questions about the nature of dignity, existence, and humanity. The novel also provides one with complex characters and a speculative future through which to live new lives, experience novel worlds, and see through different eyes. At the same time, the novel’s world offers us an uncanny distance from our own, making us (...) prone to pass judgments on the characters’ moral faults that we later come to recognize are also our own. (shrink)

There is no direct, constant relationship between the anthropological and cultural aspects of modernity. Anthropologically modern peoples display a certain heterogeneity that is not unconnected with earlier peoples, and the culture produced by modern humans, which is also heterogeneous, is differentiated diachronically and according to territory. Though paleogenetic research seems to point us to a single, African source for modern peoples, who had replaced the pre-sapiens populations in Eurasia, this view is not completely proven or accepted. On the other hand, (...) paleo-genetic research has contributed to our relinquishing the hypothesis of a multiregional ‘total continuity’ of local pre-modern populations in the Old World. Indeed the theory of a partial replacement, by a migration ‘out of Africa’, appears to be getting increasingly plausible. This article deals with the problems of the origins of modern man from the points of view of anthropological, paleogenetic, paleoenvironmental and cultural approaches. (shrink)

Research in recent years suggests that fairness concerns could mitigate hold-up problems. In this study, we report theoretical analysis and experimental evidence on an opposite possibility: that fairness concerns could also induce hold-up problems. In our setup, hold-up problems will not occur with purely self-interested agents, but theoretically could be induced by demand for distributional fairness among agents without sufficiently strong counteracting factors such as intention-based reciprocity. We observe a widespread occurrence of hold-up in our experiment. Relationship-specific investments occurred less (...) than half of the time, resulting in significant inefficiencies. Moreover, whenever a relationship-specific investment was made: (a) it was typically not reciprocated by the partner; (b) nor did the investor’s offers at the bargaining stage exhibit expectations for reciprocity. Consequently, the partner extracted all the additional expected payoff from relationship-specific investments. Further experimentation suggested that our results were driven by a fundamental lack of intention-based reciprocity in fairness concerns, rather than self-serving bias. (shrink)

Pour Thomas d’Aquin, la Trinité n’est pas d’ordre philosophique mais théologique, dépendant de la révélation biblique. Les controverses trinitaires sont déjà loin, les résolutions conciliaires aussi, mais Thomas, à plusieurs reprises et à chaque fois de manière différente, expose un traité des plus délicats. Il s’agit de poser trois personnes dans une seule substance. L’un de ses principaux apports est d’enrichir les relations d’origine qui distinguent les trois personnes en relations substantielles. Thomas tire les concepts au-delà de leur acception ordinaire, (...) manifestant ainsi la manière qui est la sienne d’entrecroiser philosophie et théologie. (shrink)

Ce volume reprend le problème sociologique de l'Etat pour le reformuler dans des termes au croisement des développements récents d'une philosophie politique soucieuse d'intégrer l'apport des sciences sociales et d'une sociologie politique prête, à partir de ses enquêtes, à questionner ses propres catégories. Deux traductions, tirées de conjonctures qui ont rendu particulièrement saillant le problème sociologique de l'Etat, constituent le point de départ de la réflexion. Celle-ci se poursuit dans une série de contributions, philosophiques et sociologiques, voulant découvrir un concept (...) d'Etat propre à une science sociale du politique. L'enjeu de ce volume n'est pas seulement d'interroger la nécessité de l'Etat pour les formes modernes - entendons démocratiques - de l'organisation politique. Il est de contribuer à spécifier l'Etat dans ce qui le rend socialement nécessaire. Cette démarche ouvre la possibilité d'identifier des critères sur la base desquels l'Etat existant peut être évalué et critiqué à nouveaux frais, à l'écart du cadre libéral dans lequel la critique de l'Etat est ordinairement condamnée à s'enfermer. (shrink)