We study versions of limit models adapted to the context of metric abstract elementary classes. Under categoricity and superstability-like assumptions, we generalize some theorems from 7, 15-17. We prove criteria for existence and uniqueness of limit models in the metric context.

Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained in this fashion (`unfoldable cardinals') lie in the boundary of the propositions consistent with `V = L' and the existence of 0 ♯ . We also provide an `embedding characterisation' of the unfoldable cardinals and study their preservation and destruction by various forcing constructions.

We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability‐like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.

We prove the following main theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ‐limits over M, for, are isomorphic over M.

In recent years, mathematical logic has developed in many directions, the initial unity of its subject matter giving way to a myriad of seemingly unrelated areas. The articles collected here, which range from historical scholarship to recent research in geometric model theory, squarely address this development. These articles also connect to the diverse work of Väänänen, whose ecumenical approach to logic reflects the unity of the discipline.

We provide here the first steps toward a Classification Theory ofElementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some λ greater than its Löwenheim-Skolem number. We study the degree to which amalgamation may be recovered, the behaviour of non μ-splitting types. Most importantly, the existence of saturated models in a strong enough sense is proved, as a first step toward a complete solution to the o Conjecture for these classes. Further (...) results are in preparation. (shrink)

A long series of conversations interweaving mathematical, historical and philosophical aspects of categoricity in model theory took place between the author and Saharon Shelah in 2016 and 2017. In this excerpt of that long conversation, we explore the relationship between explicit and implicit aspects of categoricity. We also discuss the connection with definability issues.

Theoria, Volume 87, Issue 4, Page 971-985, August 2021.

The existence of End Elementary Extensions of models M of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper, we further investigate the connection between the height of M and the existence of End Elementary Extensions of M. In particular, we prove that the theory `ZFC + GCH + there exist measurable cardinals + all inaccessible non weakly compact cardinals are possible heights of models with no End (...) Elementary Extensions' is consistent relative to the theory `ZFC + GCH + there exist measurable cardinals + the weakly compact cardinals are cofinal in ON'. We also provide a simpler coding that destroys GCH but otherwise yields the same result. (shrink)

In this article we present a notion of “logical perfection”. We first describe through examples a notion of logical perfection extracted from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver of ideas in model theory, both mathematically (stability theory may be regarded as a way of approximating categoricity) and philosophically. In the past two decades, categoricity notions have started to overlap with more classical notions of robustness and smoothness. These (...) have been crucial in various parts of mathematics since the nineteenth century. We postulate and present the category of logical perfection. We draw on various notions of perfection from mathematics of the 19th and 20th centuries and then trace the relation to the concept of categoricity in power as a logical notion of what a “mathematically perfect” structure is. (shrink)

We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah. We then study versions of the small index property for various non-elementary classes. In particular, we obtain the small index property for quasiminimal pregeometry structures.

Theoria, Volume 87, Issue 4, Page 870-873, August 2021.

The works of the early Greek philosophers are not only a fundamental source for understanding archaic Greek culture and the whole of ancient philosophy, but also a perennially fresh resource that has stimulated Western thought until the present day. This nine-volume edition presents all the major fragments from the sixth to the fourth centuries BC.

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (shrink)

This collection of five articles and two interviews, compiled by the author himself as a kind of political testament, focuses on the ecological thinking he pioneered in Europe.

I defend the view that circular definitions can be useful and illuminating by focusing on the fitting-attitudes analysis of value. This definition states that an item has value if and only if it is a fitting target of attitudes. Good items are the fitting targets of positive attitudes, and bad items are the fitting targets of negative ones. I shall argue that a circular version of this definition, defended by Rabinowicz and Rønnow-Rasmussen (2006), is preferable to its non-circular counterpart and (...) upholds reasonable standards of acceptability. The standards I will be discussing come from Humberstone (1997), who claims that definitions cannot be informative as long as they are inferentially circular. (shrink)

Lo psíquico, que no la psicología como ciencia, es un tema poco tratado en la filosofía de Polo. En este escrito se busca dar explicación de qué es lo psíquico y cuál es su importancia. Se defiende que lo psíquico tiene dos condiciones reduccionistas implícitas que se constituyen a partir de la crisis de la filosofía de Hegel. La primera es creer que la realidad es reductible a la percepción individual. La segunda consiste en que el pensamiento ya esté determinado (...) preconceptualmente. (shrink)

It is held by many philosophers that it is a consequence of epistemic contextualism that speakers are typically semantically blind, that is, typically unaware of the propositions semantically expressed by knowledge attributions. In his ?Contextualism, Invariantism and Semantic Blindness? (this journal, 2009), Martin Montminy argues that semantic blindness is widespread in language, and not restricted to knowledge attributions, so it should not be considered problematic. I will argue that Montminy might be right about this, but that contextualists still face a (...) serious and related problem: that it is a consequence of epistemic contextualism that subjects are typically unaware of contents conveyed by knowledge attributions, independently of whether these are semantic or non-semantic contents. Even if semantic blindness is widespread in language, it does not seem that content unawareness of this sort is. (shrink)

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term “explanation” in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors’ claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also (...) provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label “understandable AI” to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following De Regt (2017) and Kuorikoski and Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent’s success in using the system. (shrink)

The book forms a balanced structure in which the three conceptual pillars of Spinoza's natural law theory (individuality, natural laws, and power) are first analyzed from the viewpoint of his ontology and then from the viewpoint of his ...

Rendre hommage à un auteur, ce n'est pas seulement célébrer ce qu'il fut mais c'est aussi alerter sur ce que son oeuvre apporte au présent et à l'avenir de la connaissance. C'est bien le sens donné à cet hommage à André-Jean Arnaud. Repenser le droit, c'était pou r cet auteur érudit : repenser les lieux, les conditions et les façons de l'étudier en dépassant les frontières géographiques en même temps que les frontières disciplinaires. En montrant en quoi André-Jean Arnaud fut, (...) hors des sentiers battus et des orthodoxies de la production et de la transmission des savoirs en la matière, un exceptionnel précurseur et l'infatigable artisan d'un nouveau régime de connaissance sur le droit, le présent ouvrage s'adresse à toutes celles et à tous ceux, enseignants, chercheurs, étudiants ou simples citoyens, pou r qui l'étude du droit permet de mieux comprendre ce que sont et ce que sont susceptibles de devenir nos sociétés. (shrink)

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

Trata-se de capítulo de um livro sobre a noção de "substância" na história da filosofia e contém uma discussão sobre a noção ordinária de "corpo" do ponto de vista da filosofia analítica.

Mathematical chemistry is often thought to be a 20th-century subdiscipline of chemistry, but in this paper we discuss several early chemical ideas and some landmarks of chemistry as instances of the mathematical way of thinking; many of them before 1900. By the mathematical way of thinking, we follow Weyl's description of it in terms of functional thinking, i.e. setting up variables, symbolizing them, and seeking for functions relating them. The cases we discuss are Plato's triangles, Geoffroy's affinity table, Lavoisier's classification (...) of substances and their relationships, Mendeleev's periodic table, Cayley's enumeration of alkanes, Sylvester's association of algebra and chemistry, and Wiener's relationship between molecular structure and boiling points. These examples show that mathematical chemistry has much more than a century of history. (shrink)

Recent attempts to develop and apply digital ethics principles to address the challenges of the digital transformation leave organisations with an operationalisation gap. To successfully implement such guidance, they must find ways to translate high-level ethics frameworks into practical methods and tools that match their specific workflows and needs. Here, we describe the development of a standardised risk assessment tool, the Principle-at-Risk Analysis (PaRA), as a means to close this operationalisation gap for a key level of the ethics infrastructure at (...) many organisations – the work of an interdisciplinary ethics panel. The PaRA tool serves to guide and harmonise the work of the Digital Ethics Advisory Panel at the multinational science and technology company Merck KGaA in alignment with the principles outlined in the company’s Code of Digital Ethics. We examine how such a tool can be used as part of a multifaceted approach to operationalise high-level principles at an organisational level and provide general requirements for its implementation. We showcase its application in an example case dealing with the comprehensibility of consent forms in a data-sharing context at Syntropy, a collaborative technology platform for clinical research. (shrink)

Mit seiner Theorie der vernünftigen Übereinkunft liefert André Olbrich die Grundlegung eines Kriteriums für moralische Urteile über richtig und falsch: Im Anschluss an klassische und moderne Vertragstheoretiker wird die Akzeptanz eines Urteils durch die Betroffenen zum obersten Rechtfertigungsmaßstab erhoben. Das vertragstheoretische Denken wird weiterentwickelt und konsequent als umfassende normative Theorie ausformuliert. Die Leserinnen und Leser erfahren, von welchem Standpunkt aus sich die Regeln unseres sozialen Miteinanders einer Kritik unterziehen lassen und auf welchen moralischen Grundlagen Recht und Politik aufbauen.

André Tosel, décédé en mars 2017, était un philosophe engagé, attaché tout au long de son existence à faire vivre un marxisme critique puisant notamment dans le meilleur de la tradition italienne de ce courant de pensée ; il fut l'un des rares français à introduire et discuter les oeuvres majeures d'A. Labriola et surtout d'A. Gramsci, ainsi par ailleurs que celles de Vico dont il fut un fin connaisseur. Il consacra sa thèse de doctorat d'état aux rapports entre religion, (...) politique et philosophie chez Spinoza et contribua de façon décisive à de nouvelles lectures du philosophe en le mettant en miroir de Marx. Professeur de philosophie des universités de Besançon, Franche Comté, de Paris 1 Panthéon-Sorbonne et de Nice Sophia-Antipolis, dans lesquelles il occupa de nombreuses fonctions de directions administratives et scientifiques, il était un homme de collectif attaché à faire vivre le savoir, s'engageant dans la vie universitaire et politique, contribuant également de manière décisive au lancement et à l'animation de la revue Actuel Marx. Passionné par l'évolution des pensées contemporaines, il intervenait régulièrement dans des débats d'actualité, sous la forme de contributions dans L'Humanité ou dans des ouvrages destinés à un public large, tout particulièrement dans la dernière période sur les questions de sécularisation, de laïcité et de religion. Cet ouvrage entend lui rendre hommage en abordant les différentes facettes de son oeuvre, traversant un demi-siècle de vie intellectuelle. (shrink)

We analyze the connections of Lavoisier system of nomenclature with Leibniz’s philosophy, pointing out to the resemblance between what we call Leibnizian and Lavoisian programs. We argue that Lavoisier’s contribution to chemistry is something more subtle, in so doing we show that the system of nomenclature leads to an algebraic system of chemical sets. We show how Döbereiner and Mendeleev were able to develop this algebraic system and to find new interesting properties for it. We pointed out the resemblances between (...) Leibniz program and Lavoisier legacy, particularly regarding the lingua philosophica for understanding and thinking Nature, in this particular case, chemistry. In the second part we discuss, from the linguistic viewpoint, how Lavoisian algebraic system may be taken further to build a language. We study the constituents of such a chemical language. Finally, we formalize some of the ideas here presented by using elements of network theory and discrete mathematics. (shrink)

El uso de sistemas de machine learning en los procesos de selección laboral ha sido de gran utilidad para agilizarlos y volverlos más eficientes, pero al mismo tiempo ha generado problemas en términos de equidad, confiabilidad y transparencia. En este artículo comenzamos explicando los diferentes usos de la Inteligencia Artificial en los procesos de selección laboral en Estados Unidos. Presentamos los sesgos sexuales y raciales que han sido detectados en algunos de ellos y explicamos los obstáculos jurídicos y prácticos para (...) su detección y análisis. Un posible remedio jurídico a la discriminación algorítmica es el régimen de impacto diferencial sistémico utilizado en Estados Unidos. Usamos algunas características de este régimen para señalar los vacíos jurídicos frente a la discriminación en el acceso al empleo en el ámbito del derecho laboral colombiano, y ofrecemos algunas características generales que podría tener un régimen de esa naturaleza. (shrink)

Hegelians normally consider Hegel's philosophical system from two perspectives: metaphysics, interpreting this discipline as the central one to understand the work of the German philosopher, or non-metaphysics, being more relevant alternative interpretations that avoid it. This article presents a study on the senses of reflection. These senses can be extrinsic or absolute. These two senses are the backbones of the Hegelian system. Therefore, by means of a study of whether extrinsic and absolute reflection are notions that guide us towards metaphysical (...) or non-metaphysical readings, we try to give an answer to the debate between the possible interpretations of Hegel. (shrink)

Deviendrai-je le héros de ma propre vie ou ce rôle sera-t-il tenu par un autre? Cette question, inspirée de la littérature, nous interpelle : tout être humain doit trouver sa propre voie, sa manière personnelle de participer à l’aventure humaine. Or, aucun de nous n’est vraiment préparé à se lancer dans un tel périple. Nous n’avons pas choisi notre milieu familial et culturel. Notre corps est fragile, notre pensée faillible. Puis, la route sera parsemée d’embûches de toutes sortes : précipitation, (...) erreur de calcul, malentendu, abandon, chagrin d’amour, injustice, ressentiment, maladie, conflit. Pourtant, nous espérons tous et toutes vivre en paix et avec un minimum de liberté. Pour y parvenir, nous suivrons les chemins qui nous semblent les meilleurs. Comment les choisir? Quelle sera notre boussole? Cet ouvrage porte sur notre quête philosophique d’unité ou d’harmonie. L’auteur y ouvre dix fenêtres sur diverses expériences de vie, de notre premier à notre dernier souffle. (shrink)

Diversität ist eines der zentralen Themen unserer Zeit. Sie durchdringt alle Lebensbereiche unserer Gesellschaften. Das Nachdenken über Diversität reicht von den Naturwissenschaften über die Geschichtswissenschaften, die Gesellschaftswissenschaften, die Philosophie bis zu den Künsten. Diversität ist zudem politisch und emotional beladen. Man denke an gesellschaftliche Minderheiten und ihre Rechte oder an das massive Artensterben unserer Tage. In diesem Buch wird nicht nur über Einzelaspekte von Diversität berichtet, es wird auch eine Synthese versucht. Drei einleitende Kapitel der HerausgeberInnen führen verständlich in komplexe (...) interdisziplinäre Problemzusammenhänge ein. Der Band versammelt 17 Beiträge namhafter Autorinnen und Autoren aus den Bereichen Kunst-, Kultur- und Wissenschaftsgeschichte, Medizin und Gesellschaftstheorie.00. (shrink)

La musique comme chemin d'existence et pour la penser... En effet, les moments d'intervention de la musique, de toutes les musiques, au fil des jours et au long de la vie ne manquent pas d'être signifiants. Ils instruisent autant sur la musique elle-même que sur la pensée et sur l'existence. Il serait prétentieux d'en produire une théorie générale. Toutefois, la voie de la chronique, jour après jour, aura tissé des fils permettant de s'attarder sur le sens, nécessairement ponctuel et subjectif (...) (chacun pourra substituer son écoute et ses pratiques propres), de l'Adieu en musique, des affinités qu'elle manifeste et peut-être révèle, de ses rapports avec telle image ou peinture, plus étonnamment avec la photographie, avec le son en général, la vérité ou encore le style. On verra aussi comment la musique s'entend dans le rêve et comment elle nous porte à considérer les animaux. Des oeuvres, des musiciens, et quelques philosophes et écrivains s'imposeront (Le Voyage d'Hiver, Le Boléro, Le Sacre du Printemps, Pelléas ; Haydn, Schubert, Mahler, Chostakovitch ; Descartes, Nietzsche, Adorno ; Goethe, Gerhard Meier, Sandor Maraï...). C'est pourtant davantage une vie dans la musique et par elle que la théorisation sur la musique qui inspire chacun des textes présentés ici. En s'efforçant de relever et de piquer leur objet, donc en le séparant et le thématisant staccato, peut-être la chance sera-t-elle donnée d'entrevoir l'existence dans sa continuité, legato. (shrink)

El pluralismo religioso trata de presentar lugares comunes en los que establecer diálogos entre diferentes religiones sin intención de persuadir. En esta investigación se aborda el pluralismo religioso en los periodos de Tubinga y Berna de Hegel. Esto es, en la filosofía del joven Hegel, periodo en el que se dedicó especialmente a la reflexión sobre la política y la religión. En este periodo, menos estudiado por la academia que su madurez, encontramos que hay al menos tres lugares comunes que (...) pueden facilitar el diálogo interreligioso: el sentimiento, la universalidad ética y la libertad. En esta investigación se presenta estos tres tópicos que Hegel descubre para el diálogo entre diferentes religiones para, finalmente, conectarlos con la discusión cronológicamente posterior sobre el pluralismo religioso. (shrink)

Pourquoi Averroès? Pourquoi Averroès juriste? Parce que dans le cadre du débat avec ceux qui soutiennent le caractère indubitable du texte sacré, Averroès affirme la primauté de la raison. Il a ainsi mis en avant le questionnement, le doute dans la recherche de la vérité. Ce doute toléré dans le cercle restreint des philosophes était inacceptable en droit (la charia) qui s'applique à tous les membres de la communauté des musulmans. D'où sa condamnation et son exil. La redécouverte de la (...) pensée d'Averroès pourrait permettre au monde arabo-musulman de s'extraire du chaos. (shrink)