We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as by characterising their combinatorial properties by means of their monads. This extends to arbitrary sets and properties methods previously used to study partition regular Diophantine equations on. Several applications are described by means of multiple examples.

We introduceself-divisibleultrafilters, which we prove to be precisely those$w$such that the weak congruence relation$\equiv _w$introduced by Šobot is an equivalence relation on$\beta {\mathbb Z}$. We provide several examples and additional characterisations; notably we show that$w$is self-divisible if and only if$\equiv _w$coincides with the strong congruence relation$\mathrel {\equiv ^{\mathrm {s}}_{w}}$, if and only if the quotient$(\beta {\mathbb Z},\oplus )/\mathord {\mathrel {\equiv ^{\mathrm {s}}_{w}}}$is a profinite group. We also construct an ultrafilter$w$such that$\equiv _w$fails to be symmetric, and describe the interaction between the (...) aforementioned quotient and the profinite completion$\hat {{\mathbb Z}}$of the integers. (shrink)

Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of labels, relating numerosities with the Kiesler field of Euclidean numbers. This approach allows us to easily introduce, by means of numerosities, ordinals and their natural operations, as well as the Lebesgue measure as a counting measure on the reals.

Dans la première partie de son article « Une morale est-elle compatible avec le scepticisme? », Jules Vuillemin propose une interprétation du scepticisme de Pyrrhon d’Élis et s’interroge sur sa compatibilité avec une vie morale. La présente contribution s’attache à resituer la lecture de Vuillemin dans l’histoire du pyrrhonisme ainsi que dans les débats récents à son sujet, et à la discuter en la comparant au néo-pyrrhonisme de Sextus Empiricus. À suivre Vuillemin, Pyrrhon suspend son jugement par rapport à tout, (...) y compris ses impressions. Cette suspension universelle provoquerait une impassibilité totale et fournirait une ligne de conduite, mais serait assez difficile à adopter. Nous suggérons que suspendre son jugement sur ses propres impressions n’est pas difficile, mais impossible ; que la façon dont, selon Vuillemin, cette suspension fournirait au sceptique une ligne de conduite implique une contradiction ; et qu’il existe une autre façon d’expliquer comment le sceptique peut, dans certaines limites, maintenir une ligne de conduite. (shrink)

La traduction est inséparable de l’histoire d’un peuple, de sa culture passée et présente, de la dimension politique qui, en définitive, délimite les cadres juridiques et sociaux où se déploie l’activité des personnes, mais aussi marque l’opinion et le débat idéologique dans une démocratie. Alors que la planète s’achemine vers le plurilinguisme d’une mondialisation économique et culturelle, en Catalogne, la politique se trouve en partie prise dans un combat visant à faire du catalan une langue majoritaire, voire, pour les nationalistes (...) radicaux et indépendantistes, la seule langue officielle. Dans un tel contexte, la traduction depuis et vers le catalan constitue le moyen culturel stratégique d’une revendication identitaire face à la langue de Cervantès. La question de la traduction et, plus précisément, celle de la langue catalane est inévitablement perçue comme politique, ce qui, d’une certaine manière, tend à laisser la réalité linguistique occultée derrière le contexte historique que la Catalogne a connu.Translation is inseparable from the history of a people, its culture past and present, and its political dimension which, ultimately, frames the legal and social context in which individuals act, but also sets its stamp on public opinion and ideological debate in a democracy. As multilingualism marches onward in an economically and culturally globalised world, politics in Catalonia have been caught up in a struggle to make Catalan the majority language – or, for radical nationalists and independence activists, even the only official language. In this context, translation from and into Catalan has become a strategic cultural vehicle for claims opposing Catalan identity to the language of Cervantes. The question of translation and, more specifically, translation of the Catalan language is inevitably perceived as political, so that the linguistic realities tend to be overshadowed by the historical context as experienced in Catalonia. (shrink)

God’s gesture. Nature and the origin of the sign in Spinoza. The Author provides the textual and conceptual elements to outline a thought of event in Spinoza’s philosophy. On the one hand necessitas and contingentia are known to exclude one another while, on the other, necessitas and contingere are not opposite. They are the same when seen in relation to the conception of libera necessitas and to the doctrine of the unity of intellect and will. Also, the unity of a (...) thought of concept and a thought of event appears in the definition of revelation, where the problem of the sign becomes crucial in separating philosophy from theology. A comparative study of the texts confirms the influence of Stoicism on the triadic model of the sign, showing that all interpreters give a pragmatic orientation to the sense of signs. The impossibility for any sign to be signum sui is not due to a defect in its nature. The idea of God, in fact, does not itself need any sign to be known, but it is also true that there is no lack of a sign for its linguistic communication. (shrink)

The pascalian use of indivisibles is here considered in the context of the theological and mathematical debates of the time, by distinguishing it clearly from this of Cavalieri. The combinatory and geometrical approaches are closely linked in Pascal’s work. His use of indivisibles has a heuristic, inventive character and not only a demonstrative one. Ontologically speaking, it stems out from the acceptance of actual infinite. The use of the symmetry axiom of Archimedes is the basis of the pascalian use of (...) the infinitesimals, which has, in other respects, some close connexions with the Leibnizian conception of infinitesimals. (shrink)

En la actualidad, la ética está excesivamente centrada en la reflexión y en el establecimiento de reglas, de normas. Muchos debates sobre ética empiezan o acaban en la reflexión sobre qué normas o reglas deben aceptarse pública o universalmente, sobre cuáles de ellas deben ser leyes civiles, sobre qué comportamientos la ley civil debería prohibir y por qué. A juicio del autor, este hecho supone un reduccionismo y hace olvidar que lo más importante de la ética es el desarrollo integral (...) del individuo. Las reglas tienen su importancia en ética, pero no son el factor más relevante en ella porque no son suficientes para ayudar al individuo al desarrollo de sus capacidades, para su vida buena. El artículo muestra cómo la virtud juega un papel fundamental en ese proceso. (shrink)

Automatic identification system is a vessel tracking system, which since 2004 has become a global tool for the detection and analysis of seagoing traffic. In this article, we look at how this technology, initially designed as a collision avoidance system, has recently become involved in debates concerning migration across the Mediterranean Sea. In particular, after having briefly discussed its emergence and characteristics, we examine how through different practices of appropriation AIS, and the data it generate, have been seized upon, both (...) to contest and to sustain the exclusionary nature of borders, and the mass dying of migrants at sea to which it leads. We do so by referring to forms of data activism we have contributed to in the frame of our Forensic Oceanography project as well as to situations in which AIS has been mobilized by xenophobic groups to demand even stronger exclusionary measures. At the same time, we point to the multiplicity of actors who participate in the politics of migration through AIS in unexpected ways. We conclude by highlighting the irreducible ambivalence of practices of appropriation and call for persistent attention to one’s own positioning within the global datascape constituted by AIS and other data. (shrink)