A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

We survey recent developments in the theory of class forcing for- malized in the second-order set-theoretic setting.

It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal (...) concepts to be protected against defects because of their precise and stable nature. On the other, studies going back as far as Lakatos (1963) showcase the changeability of such concepts. -/- In this paper, I will investigate if and how defectiveness based on the occurrence of inconsistencies can appear with formal concepts. To make the case as strong as possible, I employ a strict notion of formal concept that assumes the concept to have a fixed and definite extension. I will show that there are indeed certain types of defectiveness that cannot occur with such concepts; but that there are other types of defectiveness that do occur. This means that while formal concepts have to be treated differently than non-formal concepts, questions about defectiveness---as raised in the conceptual engineering debate and philosophy of science---can still be applied to them. I will highlight this point by showing how formal sciences have special strategies available to them that allow them to resolve defectiveness of their concepts in a flexible and informative manner. (shrink)

Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...) aims of the Second Philosopher’s investigation into set-theoretic methodology; pro- vides a platform to analyze the Second Philosopher’s methods themselves; and can be applied to further questions in the philosophy of set theory. (shrink)

In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...) for operative logic and mathematics. In this article, we claim that this is in fact not the case. Rather, we argue for a shift that happened in Lorenzen’s treatment of the infinite from the early to the late 1950s. His early motivation for the development of operativism is concerned with a critique of the Cantorian notion of set and related questions about the notion of countability and uncountability; only later, his motivation switches to focusing on the concept of infinity and the debate about actual and potential infinity. (shrink)

An objective of thisthesis is to investigate whether philosophical tradition can justify or support some of the arguments that are at the basis of Leibniz’s system (for example, monads have no window to the exterior world, a phrase that summarises the structure of Monadology). I shall demonstrate how Leibniz reflects the concerns and the positions of his key predecessors. Thus, the aim of the thesis is to explore key antecedents to Leibniz’s central doctrines. The thesis argues that Leibniz carried out (...) a logical development of some principles in the eclectic system of Plotinus, which resulted in the structure of Monadology. Whether Leibniz’s project was successful or not will depend on how we view those principles. (shrink)

Ambient assisted living technologies are increasingly presented and sold as essential smart additions to daily life and home environments that will radically transform the healthcare and wellness markets of the future. An ethical approach and a thorough understanding of all ethics in surveillance/monitoring architectures are therefore pressing. AAL poses many ethical challenges raising questions that will affect immediate acceptance and long-term usage. Furthermore, ethical issues emerge from social inequalities and their potential exacerbation by AAL, accentuating the existing access gap between (...) high-income countries and low and middle-income countries. Legal aspects mainly refer to the adherence to existing legal frameworks and cover issues related to product safety, data protection, cybersecurity, intellectual property, and access to data by public, private, and government bodies. Successful privacy-friendly AAL applications are needed, as the pressure to bring Internet of Things devices and ones equipped with artificial intelligence quickly to market cannot overlook the fact that the environments in which AAL will operate are mostly private. The social issues focus on the impact of AAL technologies before and after their adoption. Future AAL technologies need to consider all aspects of equality such as gender, race, age and social disadvantages and avoid increasing loneliness and isolation among, e.g. older and frail people. Finally, the current power asymmetries between the target and general populations should not be underestimated nor should the discrepant needs and motivations of the target group and those developing and deploying AAL systems. Whilst AAL technologies provide promising solutions for the health and social care challenges, they are not exempt from ethical, legal and social issues. A set of ELSI guidelines is needed to integrate these factors at the research and development stage. (shrink)

It is a matter of fact that Europe is facing more and more crucial challenges regarding health and social care due to the demographic change and the current economic context. The recent COVID-19 pandemic has stressed this situation even further, thus highlighting the need for taking action. Active and Assisted Living technologies come as a viable approach to help facing these challenges, thanks to the high potential they have in enabling remote care and support. Broadly speaking, AAL can be referred (...) to as the use of innovative and advanced Information and Communication Technologies to create supportive, inclusive and empowering applications and environments that enable older, impaired or frail people to live independently and stay active longer in society. AAL capitalizes on the growing pervasiveness and effectiveness of sensing and computing facilities to supply the persons in need with smart assistance, by responding to their necessities of autonomy, independence, comfort, security and safety. The application scenarios addressed by AAL are complex, due to the inherent heterogeneity of the end-user population, their living arrangements, and their physical conditions or impairment. Despite aiming at diverse goals, AAL systems should share some common characteristics. They are designed to provide support in daily life in an invisible, unobtrusive and user-friendly manner. Moreover, they are conceived to be intelligent, to be able to learn and adapt to the requirements and requests of the assisted people, and to synchronise with their specific needs. Nevertheless, to ensure the uptake of AAL in society, potential users must be willing to use AAL applications and to integrate them in their daily environments and lives. In this respect, video- and audio-based AAL applications have several advantages, in terms of unobtrusiveness and information richness. Indeed, cameras and microphones are far less obtrusive with respect to the hindrance other wearable sensors may cause to one’s activities. In addition, a single camera placed in a room can record most of the activities performed in the room, thus replacing many other non-visual sensors. Currently, video-based applications are effective in recognising and monitoring the activities, the movements, and the overall conditions of the assisted individuals as well as to assess their vital parameters. Similarly, audio sensors have the potential to become one of the most important modalities for interaction with AAL systems, as they can have a large range of sensing, do not require physical presence at a particular location and are physically intangible. Moreover, relevant information about individuals’ activities and health status can derive from processing audio signals. Nevertheless, as the other side of the coin, cameras and microphones are often perceived as the most intrusive technologies from the viewpoint of the privacy of the monitored individuals. This is due to the richness of the information these technologies convey and the intimate setting where they may be deployed. Solutions able to ensure privacy preservation by context and by design, as well as to ensure high legal and ethical standards are in high demand. After the review of the current state of play and the discussion in GoodBrother, we may claim that the first solutions in this direction are starting to appear in the literature. A multidisciplinary debate among experts and stakeholders is paving the way towards AAL ensuring ergonomics, usability, acceptance and privacy preservation. The DIANA, PAAL, and VisuAAL projects are examples of this fresh approach. This report provides the reader with a review of the most recent advances in audio- and video-based monitoring technologies for AAL. It has been drafted as a collective effort of WG3 to supply an introduction to AAL, its evolution over time and its main functional and technological underpinnings. In this respect, the report contributes to the field with the outline of a new generation of ethical-aware AAL technologies and a proposal for a novel comprehensive taxonomy of AAL systems and applications. Moreover, the report allows non-technical readers to gather an overview of the main components of an AAL system and how these function and interact with the end-users. The report illustrates the state of the art of the most successful AAL applications and functions based on audio and video data, namely lifelogging and self-monitoring, remote monitoring of vital signs, emotional state recognition, food intake monitoring, activity and behaviour recognition, activity and personal assistance, gesture recognition, fall detection and prevention, mobility assessment and frailty recognition, and cognitive and motor rehabilitation. For these application scenarios, the report illustrates the state of play in terms of scientific advances, available products and research project. The open challenges are also highlighted. The report ends with an overview of the challenges, the hindrances and the opportunities posed by the uptake in real world settings of AAL technologies. In this respect, the report illustrates the current procedural and technological approaches to cope with acceptability, usability and trust in the AAL technology, by surveying strategies and approaches to co-design, to privacy preservation in video and audio data, to transparency and explainability in data processing, and to data transmission and communication. User acceptance and ethical considerations are also debated. Finally, the potentials coming from the silver economy are overviewed. (shrink)

In this position paper, we have used Alan Cooper’s persona technique to illustrate the utility of audio- and video-based AAL technologies. Therefore, two primary examples of potential audio- and video-based AAL users, Anna and Irakli, serve as reference points for describing salient ethical, legal and social challenges related to use of AAL. These challenges are presented on three levels: individual, societal, and regulatory. For each challenge, a set of policy recommendations is suggested.

Há atualmente um debate interdisciplinar profícuo sobre a noção de sofrimento social (social suffering). Pensadores e pensadoras como Barrington Moore Jr., Emmanuel Renault e Rahel Jaeggi desenvolvem o assunto a partir de um pressuposto elementar: sofrimento social diferencia-se de sofrimento individual na medida em que as causas do primeiro não são aturais (desejos básicos insatisfeitos, doenças, catástrofes naturais), mas resultam do agir humano; e, mais ainda, não resultam anto de relações interpessoais imediatas, mas de relações sociais mais amplas, como (...) a guerra, a pobreza, a exploração etc. No artigo Schopenhauer e a sociedade, Horkheimer afirmou que “no intransigente nominalismo de Schopenhauer em relação à sociedade estriba a raiz de sua grandeza” (p. 47). Para o pai da Teoria Crítica, a acepção schopenhaueriana de que apenas os indivíduos e o curso de suas vidas são reais, enquanto os povos são meras abstrações, não implicaria contrapor a sociedade e o Estado à pessoa singular ou esta àqueles. A sociedade se origina e se transforma a partir de indivíduos socialmente vinculados; o indivíduo não é uma ilha. Com essa chave de leitura, Horkheimer, como discípulo herético, consegue destacar e valorizar em Schopenhauer o aparato social da noção metafísica de sofrimento. O objetivo deste artigo é (i) mostrar em que medida a diferenciação entre sofrimento individual e social estaria implicitamente indicada em Schopenhauer e (ii) até que ponto a leitura de Horkheimer sobre o nominalismo de Schopenhauer em relação à sociedade permitiria sugerir elementos schopenhauerianos para os debates contemporâneos sobre sofrimento social. (shrink)

En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paraconsistencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...) y lógica), que necesitan decidirse por unt cómo realmente usar palabras en contextos concretos. Cuando tenemos claro sobre qué juego de idiomas estamos jugando, estos temas son vistos como preguntas científicas y matemáticas ordinarias como cualquier otra. Las percepciones de Wittgenstein rara vez se han igualado y nunca superado y son tan pertinentes hoy como lo fueron hace 80 años cuando dictó los libros azul y marrón. A pesar de sus fallas — realmente una serie de notas en lugar de un libro terminado —, esta es una fuente única de la obra de estos tres eruditos famosos que han estado trabajando en los bordes sangrantes de la física, las matemáticas y la filosofía durante más de medio siglo. Da Costa y Doria son citados por Wolpert (ver abajo o mis artículos sobre Wolpert y mi reseña de ' los límites de la razón ' de Yanofsky) desde que escribieron en el cómputo universal, y entre sus muchos logros, da Costa es pionera en paraconsistencia. Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punto de vista puede consultar mi libros Talking Monkeys 3ª ed (2019), Estructura Logica de Filosofia, Psicología, Mente y Lenguaje en Ludwig Wittgenstein y John Searle 2a ed (2019), Suicidio pela Democracia 4ª ed (2019), La Estructura Logica del Comportamiento Humano (2019), The Logical Structure de la Conciencia (2019, Entender las Conexiones entre Ciencia, Filosofía, Psicología, Religión, Política y Economía y Delirios Utópicos Suicidas en el siglo 21 5ª ed (2019), Observaciones sobre Imposibilidad, Incompletitud, Paraconsistencia, Indecidibilidad, Aleatoriedad, Computabilidad, Paradoja e Incertidumbre en Chaitin, Wittgenstein,. (shrink)

In this paper I apply the concept of _inter-Model Inconsistency in Set Theory_ (MIST), introduced by Carolin Antos (this volume), to select positions in the current universe-multiverse debate in philosophy of set theory: I reinterpret H. Woodin’s _Ultimate L_, J. D. Hamkins’ multiverse, S.-D. Friedman’s hyperuniverse and the algebraic multiverse as normative strategies to deal with the situation of de facto inconsistency toleration in set theory as described by MIST. In particular, my aim is to situate these positions on the (...) spectrum from inconsistency avoidance to inconsistency toleration. By doing so, I connect a debate in philosophy of set theory with a debate in philosophy of science about the role of inconsistencies in the natural sciences. While there are important differences, like the lack of threatening explosive inferences, I show how specific philosophical positions in the philosophy of set theory can be interpreted as reactions to a state of inconsistency similar to analogous reactions studied in the philosophy of science literature. My hope is that this transfer operation from philosophy of science to mathematics sheds a new light on the current discussion in philosophy of set theory; and that it can help to bring philosophy of mathematics and philosophy of science closer together. (shrink)