Descartes' philosophy contains an intriguing notion of the infinite, a concept labeled by the philosopher as indefinite. Even though Descartes clearly defined this term on several occasions in the correspondence with his contemporaries, as well as in his Principles of Philosophy, numerous problems about its meaning have arisen over the years. Most commentators reject the view that the indefinite could mean a real thing and, instead, identify it with an Aristotelian potential infinite. In the first part of this article, I (...) show why there is no numerical infinity in Cartesian mathematics, as such a concept would be inconsistent with the main fundamental attribute of numbers: to be comparable with each other. In the second part, I analyze the indefinite in the context of Descartes' mathematical physics. It is my contention that, even with no trace of infinite in his mathematics, Descartes does refer to an actual indefinite because of its application to the material world within the system of his physics. This fact underlines a discrepancy between his mathematics and physics of the infinite, but does not lead a difficulty in his mathematical physics. Thus, in Descartes' physics, the indefinite refers to an actual dimension of the world rather than to an Aristotelian mathematical potential infinity. In fact, Descartes establishes the reality and limitlessness of the extension of the cosmos and, by extension, the actual nature of his indefinite world. This indefinite has a physical dimension, even if it is not measurable. La filosofía de Descartes contiene una noción intrigante de lo infinito, un concepto nombrado por el filósofo como indefinido. Aunque en varias ocasiones Descartes definió claramente este término en su correspondencia con sus contemporáneos y en sus Principios de filosofía, han surgido muchos problemas acerca de su significado a lo largo de los años. La mayoría de comentaristas rechaza la idea de que indefinido podría significar una cosa real y, en cambio, la identifica con un infinito potencial aristotélico. En la primera parte de este artículo muestro por qué no hay infinito numérico en las matemáticas cartesianas, en la medida en que tal concepto sería inconsistente con el principal atributo fundamental de los números: ser comparables entre sí. En la segunda parte analizo lo indefinido en el contexto de la física matemática de Descartes. Mi argumento es que, aunque no hay rastro de infinito en sus matemáticas, Descartes se refiere a un indefinido real a causa de sus aplicaciones al mundo material dentro del sistema de su física. Este hecho subraya una discrepancia entre sus matemáticas y su física de lo infinito, pero no implica ninguna dificultad en su física matemática. Así pues, en la física de Descartes, lo indefinido se refiere a una dimensión real del mundo más que a una infinitud potencial matemática aristotélica. De hecho, Descartes establece la realidad e infinitud de la extensión del cosmos y, por extensión, la naturaleza real de su mundo indefinido. Esta indefinición tiene una dimensión física aunque no sea medible. (shrink)

FDE, LP and K3 are closely related to each other and admit of an intuitive informational interpretation. However, all these logics are co-NP complete, and so idealized models of how an agent can think. We address this issue by shifting to signed formulae, where the signs express imprecise values associated with two bipartitions of the corresponding set of standard values. We present proof systems whose operational rules are all linear and have only two structural branching rules that express a generalized (...) Principle of Bivalence. Each of these systems leads to defining an infinite hierarchy of tractable approximations to the respective logic, in terms of the maximum number of allowed nested applications of the two branching rules. Further, each resulting hierarchy admits of an intuitive 5-valued non-deterministic semantics. (shrink)

The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of metaphysical accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, another (...) based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multi-dimensional properties. Our second aim is to demonstrate that the choice between these accounts can make a substantial metaphysical difference. To make this point, we rely on two case studies (involving quantum observables and values) in which we apply the accounts in order to model apparent cases of metaphysical gradedness. (shrink)

Accountability is a cornerstone of the governance of artificial intelligence (AI). However, it is often defined too imprecisely because its multifaceted nature and the sociotechnical structure of AI systems imply a variety of values, practices, and measures to which accountability in AI can refer. We address this lack of clarity by defining accountability in terms of answerability, identifying three conditions of possibility (authority recognition, interrogation, and limitation of power), and an architecture of seven features (context, range, agent, forum, standards, process, (...) and implications). We analyse this architecture through four accountability goals (compliance, report, oversight, and enforcement). We argue that these goals are often complementary and that policy-makers emphasise or prioritise some over others depending on the proactive or reactive use of accountability and the missions of AI governance. (shrink)

We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.

This chapter explores the influence of Artificial Intelligence (AI) on digital democracy, focusing on four main areas: citizenship, participation, representation, and the public sphere. It traces the evolution from electronic to virtual and network democracy, underscoring how each stage has broadened democratic engagement through technology. Focusing on digital citizenship, the chapter examines how AI can improve online engagement while posing privacy risks and fostering identity stereotyping. Regarding political participation, it highlights AI's dual role in mobilising civic actions and spreading misinformation. (...) Regarding representation, AI's involvement in electoral processes can enhance voter registration, e-voting, and the efficiency of result tabulation but raises concerns regarding privacy and public trust. Also, AI's predictive capabilities shift the dynamics of political competition, posing ethical questions about manipulation and the legitimacy of democracy. Finally, the chapter examines how integrating AI and digital technologies can facilitate democratic political advocacy and personalised communication. However, this also comes with higher risks of misinformation and targeted propaganda. (shrink)

This chapter examines the evolving debate on AI legal personhood, emphasizing the role of path dependencies in shaping current trajectories and prospects. Two primary path dependencies emerge: prevailing legal theories on personhood (singularist vs. clustered) and the impact of technological advancements. We argue that these factors dynamically interact, with technological optimism fostering broader rights-based debates and periods of skepticism narrowing discussions to limited rights. Additional influences include regulatory cross-linkages (e.g., data privacy, liability, cybersecurity) and historical legal precedents. Current regulatory frameworks, (...) particularly in the EU, generally resist extending legal personhood to AI systems. Case law suggests that without explicit legislation, courts are unlikely to grant AI legal personhood on their own. For this to happen, AI systems would first need to prove de facto legitimacy through sustained social participation. The chapter concludes by assessing near- and long-term prospects, from generative AI and AI agents in the next 5–20 years to transformative possibilities such as AI integration with human cognition via Brain-Machine Interfaces in a more distant future. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

The EU proposal for the Artificial Intelligence Act (AIA) defines four risk categories: unacceptable, high, limited, and minimal. However, as these categories statically depend on broad fields of application of AI, the risk magnitude may be wrongly estimated, and the AIA may not be enforced effectively. This problem is particularly challenging when it comes to regulating general-purpose AI (GPAI), which has versatile and often unpredictable applications. Recent amendments to the compromise text, though introducing context-specific assessments, remain insufficient. To address this, (...) we propose applying the risk categories to specific AI scenarios, rather than solely to fields of application, using a risk assessment model that integrates the AIA with the risk approach arising from the Intergovernmental Panel on Climate Change (IPCC) and related literature. This model enables the estimation of the magnitude of AI risk by considering the interaction between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We use large language models (LLMs) as an example. (shrink)

Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...) its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt. Many of us know and probably have used the Leibnizian formula: to .. (shrink)

The purpose of this paper is to analyze the relation between the synthesis of reproduction in imagination and the schematism. It is known that the synthesis of reproduction, according to Kant, can be considered as the transcendental imagination itself. Hence, if we take the transcendental imagination as the source of the schema, it is necessary to understand how the relation between the schema and the synthesis takes place.

Regulation is nothing without enforcement. This particularly holds for the dynamic field of emerging technologies. Hence, this article has two ambitions. First, it explains how the EU´s new Artificial Intelligence Act (AIA) will be implemented and enforced by various institutional bodies, thus clarifying the governance framework of the AIA. Second, it proposes a normative model of governance, providing recommendations to ensure uniform and coordinated execution of the AIA and the fulfilment of the legislation. Taken together, the article explores how the (...) AIA may be implemented by national and EU institutional bodies, encompassing longstanding bodies, such as the European Commission, and those newly established under the AIA, such as the AI Office. It investigates their roles across supranational and national levels, emphasizing how EU regulations influence institutional structures and operations. These regulations may not only directly dictate the structural design of institutions but also indirectly request administrative capacities needed to enforce the AIA. (shrink)

El presente artículo analiza la etapa denominada arqueológica de Michel Foucault. Puntualizando principalmente cómo en esta etapa es entendido el concepto de libertad desde la noción foucaultiana de discurso. Se aborda, en este sentido, la etapa arqueológica de Foucault desde tres áreas. La primera, nos habla de cómo se erige lo diferente, lo anormal. La segunda, expone cómo se construye lo aparente, lo indiscutible. Por último, a partir de un marco teórico previamente expuesto, reflexionamos respecto del concepto de libertad.

In two occasions a Bibliography of Structuralism has been published in Erkenntnis (1989, 1994). Since then a lot of water has flowed under the bridge and the structuralist program has shown a continuous development. The aim of the present bibliography is to celebrate the 25th anniversary of the publication of An Architectonic for Science –structuralism’s main reference work– and of its recent translation into Spanish by updating the previous bibliographies with titles which have appeared since 1994 as well as before (...) that year but which are not included in them. As in the former deliveries, this bibliography only covers books and articles that are concerned directly with the structuralist approach in the philosophy of science. We would like to thank the many colleagues who have helped us in collecting all the information. Notwithstanding we apologize in advance for the possible entries that we missed to include in this third Bibliography of Structuralism. (shrink)

The EU Artificial Intelligence Act (AIA) defines four risk categories for AI systems: unacceptable, high, limited, and minimal. However, it lacks a clear methodology for the assessment of these risks in concrete situations. Risks are broadly categorized based on the application areas of AI systems and ambiguous risk factors. This paper suggests a methodology for assessing AI risk magnitudes, focusing on the construction of real-world risk scenarios. To this scope, we propose to integrate the AIA with a framework developed by (...) the Intergovernmental Panel on Climate Change (IPCC) reports and related literature. This approach enables a nuanced analysis of AI risk by exploring the interplay between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We further refine the proposed methodology by applying a proportionality test to balance the competing values involved in AI risk assessment. Finally, we present three uses of this approach under the AIA: to implement the Regulation, to assess the significance of risks, and to develop internal risk management systems for AI deployers. (shrink)

To Wittgenstein’s late thought is often attributed a form of cultural or epistemic relativism, according to which truths are relative to the criteria of justification valid within a linguistic community. This paper aims to show that this attribution lies largely on a misinterpretation of Wittgenstein’s ideas on the relation between language-games and forms of life. In the first section are presented the grounds for some relativist readings of Wittgenstein’s thought. In the second section, through the analysis of some passages of (...) the Tractatus and On Certainty, it is argued that, although Wittgenstein insisted on the “ungroundedness” of our language-games, he did not mean that any epistemic attitude, as long as it is endorsed by a community, is as valid as any other one. Rather, it is possible to show that some games better apply to our world and appear thus as more objective, so that there can be a difference in the validity of world-picures, contrary to what the epistemic relativist holds. In the third and final section, it is claimed that the different communities that appear in Wittgenstein’s examples are not actual or existing alternative possibilities, but an imaginary anthropology that Wittgenstein uses to enlighten how we, humans, work with our language-games. So, it is not possible to attribute him the idea that different games underly different forms of life, as some relativist authors do. It is concluded that Wittgenstein was not likely to be a cultural relativist. (shrink)

In recent years, several strategies have been proposed to tackle social controversies about topics in which science is settled, among which one of the most influential is that of Elizabeth Anderson, who argues that any lay person with access to the Internet and basic education can reliably assess the acceptability of various claims involving expert knowledge. In particular, the author shows that this procedure can be successfully applied to the case of anthropogenic global warming. In this article we will try (...) to argue why, even if we concede that Anderson's proposal is satisfactory in that particular case, it fails to generalize when applied to other controversies. In this article, we illustrate it with the cases of flat-Eartherism and anti-vaxxerism. (shrink)

L’articolo esamina la proposta europea di regolamento sull’intelligenza artificiale, AI Act (AIA). In particolare, esamina il modello di analisi e valutazione del rischio dei sistemi di IA. L’articolo identifica tre potenziali problemi di implementazione del regolamento: (1) la predeterminazione dei livelli di rischio, (2) la genericità del giudizio di significatività del rischio e (3) l’indeterminatezza della valutazione sull’impatto dei diritti fondamentali. Il saggio suggeriscealcune soluzioni per affrontare questi tre problemi.

Although we may find the concept of anomie in Greek thought, it is since Durkheim that the concept begins to be used specifically as a sociological concept. However, a theory of anomie only becomes consolidated since “Social Structure and Anomie” by Robert K. Merton (Merton 1938). The theory becomes important and conquers its space in the rest of the century as one of the most productive theories about deviance. In this study, based on a contemporary conception of scientific theory, that (...) of the structuralist metatheory, a reconstruction of Merton’s approach is proposed, allowing to make explicit the deep structure of the theory. (shrink)

Fragmentalism was originally introduced as a new A-theory of time. It was further refined and discussed, and different developments of the original insight have been proposed. In a celebrated paper, Jonathan Simon contends that fragmentalism delivers a new realist account of the quantum state—which he calls conservative realism—according to which: the quantum state is a complete description of a physical system, the quantum state is grounded in its terms, and the superposition terms are themselves grounded in local goings-on about the (...) system in question. We will argue that fragmentalism, at least along the lines proposed by Simon, does not offer a new, satisfactory realistic account of the quantum state. This raises the question about whether there are some other viable forms of quantum fragmentalism. (shrink)

We propose a formal framework to examine the relationship between models and observations. To make our analysis precise,models are reduced to first-order theories that represent both terminological knowledge – e.g., the laws that are supposed to regulate the domain under analysis and that allow for explanations, predictions, and simulations – and assertional knowledge – e.g., information about specific entities in the domain of interest. Observations are introduced into the domain of quantification of a distinct first-order theory that describes their nature (...) and their organization and takes track of the way they are experimentally acquired or intentionally elaborated. A model mainly represents the theoretical knowledge or hypotheses on a domain, while the theory of observations mainly represents the empirical knowledge and the given experimental practices. We propose a precise identity criterion for observations and we explore different links between models and observations by assuming a degree of independence between them. By exploiting some techniques developed in the field of social choice theory and judgment aggregation, we sketch some strategies to solve inconsistencies between a given set of observations and the assumed theoretical hypotheses. The solutions of these inconsistencies can impact both the observations – e.g., the theoretical knowledge and the analysis of the way observations are collected or produced may highlight some unreliable sources – and the models – e.g. empirical evidences may invalidate some theoretical laws. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

One might suppose that Everettian quantum mechanics (EQM) is inhospitable to metaphysial indeterminacy (MI), given that, as A. Wilson (2020) puts it, "the central idea of EQM is to replace indeterminacy with multiplicity" (77). But as Wilson goes on to suggest, the popular decoherence-based understanding of EQM (henceforth: DEQM) appears to admit of indeterminacy in both world number and world nature, where the latter indeterminacy---our focus here---is plausibly metaphysical. After a brief presentation of DEQM (S1), we bolster the case for (...) there being MI in world nature in DEQM (S2). The remainder of the paper is devoted to a comparative assessment of the two main approaches to MI for purposes of accommodating this MI---namely, a metaphysical supervaluationist approach (as per Barnes and Williams 2011) and a determinable-based approach (as per Wilson 2013 and Calosi and Wilson 2018 and 2021). We briefly describe each approach (S3), then offer arguments in favour of a determinable-based approach to world nature MI in DEQM (S4). (shrink)

El objetivo de este artículo es presentar una reconstrucción de la teoría de los grupos dereferencia. La teoría, desarrollada por Robert K. Merton, ha sido largamente utilizada enlos más variados campos de las ciencias sociales, aunque con escasa o nula consideraciónmetateórica hasta ahora. La reconstrucción atenderá a la presentación que de la misma serecoge en sendos artículos de su libro Social Theory and Social Structure, de 1968, a saber:“Contributions to the theory of reference group behavior” y “Continuities in the theory (...) ofreference groups and social structure”. Para presentar esta reconstrucción me apoyaré en elinstrumental de la Metateoría Estructuralista. Después de una consideración informal de lateoría, serán presentados sus modelos potenciales, modelos, modelos potenciales parciales,sus aplicaciones intencionales y algunos comentarios acerca de la noción de “grupo de referencia”en lo que respeta su carácter relacional y disposicional. (shrink)

The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when conditioning on the action of some underlying common cause. The extended interpretation of the principle, by contrast, urges that common causes should be called for in order to explain positive deviations between the estimated correlation of two events and the expected value of their correlation. (...) The aim of this paper is to provide the extended reading of the principle with a general probabilistic model, capturing the simultaneous action of a system of multiple common causes. To this end, two distinct models are elaborated, and the necessary and sufficient conditions for their existence are determined. (shrink)

In this paper, I argue that if one is already an advocate of scientific realism, then one would be also a realist about laws of nature. To show this, I argue that only scientific realists would accept that non-accidental regularities require explanation and that their genuine explanation is given by laws of nature. Then, from this conclusion, it seems that scientific realists have reason to believe that there are laws of nature in an objective sense. If this is correct, the (...) conclusion is that there are no reasons for advocates of scientific realism to be skeptics about laws of nature. (shrink)

The article argues that AI can enhance the measurement and implementation of democratic processes within political parties, known as Intra-Party Democracy (IPD). It identifies the limitations of traditional methods for measuring IPD, which often rely on formal parameters, self-reported data, and tools like surveys. Such limitations lead to partial data collection, rare updates, and significant resource demands. To address these issues, the article suggests that specific data management and Machine Learning techniques, such as natural language processing and sentiment analysis, can (...) improve the measurement and practice of IPD. (shrink)

The complexity and emergent autonomy of Generative AI systems introduce challenges in predictability and legal compliance. This paper analyses some of the legal and regulatory implications of such challenges in the European Union context, focusing on four areas: liability, privacy, intellectual property, and cybersecurity. It examines the adequacy of the existing and proposed EU legislation, including the Artificial Intelligence Act (AIA), in addressing the challenges posed by Generative AI in general and LLMs in particular. The paper identifies potential gaps and (...) shortcomings in the EU legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models. (shrink)

The Vehicle Routing Problem (VRP) has been extensively studied by different researchers from all over the world in recent years. Multiple solutions have been proposed for different variations of the problem, such as Capacitive Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Time Windows (VRP-TW), Vehicle Routing Problem with Pickup and Delivery (VRPPD), among others, all of them with deterministic times. In the last years, researchers have been interested in including in their different models the variations that travel times may (...) experience when exposed to all kind of phenomena, mainly vehicle traffic. This article addresses the VRP from this perspective, proposing the design and implementation of a genetic algorithm based on neutrosophic theory for calculating the fitness function of each route, considering the variability and uncertainty present in travel times. A deterministic genetic algorithm is also implemented with the average travel times to compare it with the neutrosophic algorithm using simulation. As conclusion, a deterministic algorithm does not necessarily generate the best solution in the real world, full of uncertainty. Also, the quantification of uncertainty using neutrosophic theory can be used in route planning, opening a broad and interesting field of research for future investigations. (shrink)

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements (...) (H-axioms) in countable transitive models, the collection of which constitutes the `hyperuniverse' (H), has remarkable 1st-order consequences, some of which we review in section 5. (shrink)

Cancel culture is a form of societal self-defense that becomes prominent particularly during periods of substantial moral upheaval. It can lead to the polarization of incompatible viewpoints if it is indiscriminately demonized. In this brief editorial letter, I consider framing cancel culture as an essentially contested concept (ECC), according to the theory of Walter B. Gallie, with the aim of establishing a groundwork for a more productive discourse on it. In particular, I propose that intermediate agreements and principles of reasonableness (...) can help refocus the debate on cancel culture towards democratic discourse, without blanket justification for every instance. In this context, asserting that cancel culture is an ECC does not dismiss the potential of achieving consensus on its shared core meaning or societal role. Like other similar ECCs, such as democracy or rule of law, it highlights the importance of contestations in shaping our collective understanding of the concept. (shrink)

Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics.

FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...) linear operational rules and only two branching structural rules, the latter expressing a generalized rule of bivalence. This system naturally leads to defining an infinite hierarchy of tractable depth-bounded approximations to FDE. Namely, approximations in which the number of nested applications of the two branching rules is bounded. (shrink)

Forests, cars and orchestras are very different ontological entities, and yet very similar in some aspects. The relationships they have with the elements they are composed of is often assumed to be reducible to standard ontological relations, like parthood and constitution, but how this could be done is still debated. This paper sheds light on the issue starting from a linguistic and philosophical analysis aimed at understanding notions like plurality, collective and composite, and propos- ing a formal approach to characterise (...) them. We conclude the presentation with a discussion and analysis of social groups within this framework. (shrink)

En este trabajo nos referiremos al debate entre internismo y externismo epistemológicos a partir del episodio que constituye el debate entre Michael Williams y Alvin Goldman, que se expresa en el intercambio de trabajos presente en el volumen del año 2016 Goldman and his critics. Enmarcaremos esta discusión señalando que, mientras una serie de autores (en particular Laurence BonJour y, siguiendo su influencia, Jennifer Lackey y Fernando Broncano) extrae del debate internismo/externismo la consecuencia “dualista” de que el conocimiento no puede (...) analizarse según un único eje, sino que hallamos al menos dos -el de la razonabilidad subjetiva y el de la conductividad a la verdad-, Goldman se presenta como un externista de “línea dura” para el cual el internismo es simplemente insostenible y la justificación epistémica ha de comprenderse exclusivamente en términos confiabilistas. Sobre este trasfondo, analizaremos la propuesta de Williams, quien por un lado busca probar que las críticas de Goldman al internismo quedan restringidas a una versión “mentalista” o “subjetivista”, y, por el otro, busca ratificar una epistemología internista moderada apoyándose en el señalamiento de que el conocimiento humano es indisociable de consideraciones de responsabilidad (accountability). Buscaremos probar que la réplica de Goldman, que se centra en denunciar una presunta confusión por Williams entre el problema del “estar justificado” y el del “justificar”, no hace justicia a la amplitud del problema de la justificación epistémica, una vez que este es abordado, no a partir de presuntas “intuiciones” sobre el significado de “conocimiento” en el lenguaje ordinario, sino a partir de las prácticas en las que nociones como esta pueden hacerse funcionar. -/- . (shrink)

L’Ipotesi del Continuo, formulata da Cantor nel 1878, è una delle congetture più note della teoria degli insiemi. Il Problema del Continuo, che ad essa è collegato, fu collocato da Hilbert, nel 1900, fra i principali problemi insoluti della matematica. A seguito della dimostrazione di indipendenza dell’Ipotesi del Continuo dagli assiomi della teoria degli insiemi, lo status attuale del problema è controverso. In anni più recenti, la ricerca di una soluzione del Problema del Continuo è stata anche una delle ragioni (...) fondamentali per la ricerca di nuovi assiomi in matematica. L’articolo fornisce un quadro generale dei risultati matematici fondamentali, e un’analisi di alcune delle questioni filosofiche connesse al Problema del Continuo. (shrink)

This article discusses Rik Peels's response to Williams's argument against voluntary belief. Williams argues that voluntary beliefs must be acquired independently of truth-considerations, so they cannot count as beliefs after all, since beliefs aim at truth. Peels attempted to reply by showing that in cases of self-fulfilling beliefs, a belief can indeed be voluntarily acquired in conditions which retain the necessary truth-orientation. But even if we make two crucial concessions to Peels’s proposal, his argument ultimately fails. The first concession is (...) that beliefs can be weakly voluntary-namely, we can acquire them at will though we do not preserve them at will but on the basis of evidence. Conceding this, however, only lands us in the “acquisition problem”: how a belief can be acquired qua belief when we still do not think we have justification for it. This leads us to the second concession: that knowing in advance that a certain belief is self-fulfilling provides us with such a justification. However, this concession lands us in the ultimate obstacle: that, precisely because such a justification is available both before and at the moment of forming the belief, the cognitive perspective of the subject is identical at both moments, which obscures what it even means to say that at a certain moment she started to have a belief. (shrink)

In two occasions a Bibliography of Structuralism has been published in Erkenntnis (1989, 1994). Since then a lot of water has flowed under the bridge and the structuralist program has shown a continuous development. The aim of the present bibliography is to celebrate the 25th anniversary of the publication of An Architectonic for Science –structuralism’s main reference work– and of its recent translation into Spanish by updating the previous bibliographies with titles which have appeared since 1994 as well as before (...) that year but which are not included in them. As in the former deliveries, this bibliography only covers books and articles that are concerned directly with the structuralist approach in the philosophy of science. We would like to thank the many colleagues who have helped us in collecting all the information. Notwithstanding we apologize in advance for the possible entries that we missed to include in this third Bibliography of Structuralism. (shrink)

Review of Balzer, Wolfgang, Moulines, C. Ulises e Joseph Sneed,Una arquitectónica para la ciencia. El programa estructuralista, Quilmes:Universidad Nacional de Quilmes, 2012, 498 pp. Translation by Pablo Lorenzanoof Balzer, Wolfgang; Moulines, C. Ulises e Joseph Sneed, An Architectonicfor Science. The Structuralist Program, Dordrecht: Reidel, 1987, 440 pp.

A la fecha, la academia hispanohablante ha abordado el pensamiento de Stefan Lorenz Sorgner analizando, casi exclusivamente, su intento de comprender a Nietzsche como un precursor del transhumanismo. Más allá de los alegatos a favor o en contra de tal lectura, este debate olvida que el pensamiento de Sorgner efectivamente se ha apropiado de varias intuiciones nietzscheanas, hasta el punto de crear su propio transhumanismo nietzscheano débil o bien, Metahumanismo. Con este contexto en mente, el presente artículo tiene tres objetivos (...) específicos:(1) ofrecer una caracterización que diferencia al Metahumanismo de Sorgner tanto del trans-como del post-humanismo;(2) señalar cómo se modulan las ideas de Nietzsche en el metahumanismo de Sorgner; y finalmente (3) ilustrar cuáles son algunas de las propuestas con las que el metahumanismo enfrenta los debates contemporáneos—una perspectiva anti utópica y una propuesta por una educación metahumanista—. De esta manera, el objetivo general de este artículo es ofrecer una introducción al pensamiento del filósofo metahumanista Stefan Lorenz Sorgner. (shrink)

Th e contemporary right to freedom of thought together with all its further declinations into freedom of speech, religion, conscience and expression, had one of its earliest historical recognitions at the end of the Wars of Religion with the Edict of Nantes (1598). In several respects one can saythat the right to freedom of thought is virtually “co-original” with the endof the Wars of Religion. Following this thought further, one might think that human rights defi ne the boundaries of our (...) social coexistence and are inextricably connected to the “fact” of cultural pluralism. (shrink)

Having a body is one of those unquestionable certainties of which we could not really understand the negation: the latter would not be a legitimate doubt in our linguistic, and therefore the epistemic game. In facts, according to Wittgenstein, contravening certain cornerstones of our language game implies that the used combination of words is being excluded from the game, withdrawn from circulation. The idea of this paper is that the external labelling of a behaviour as a mental illness, prima facie, (...) comes from here. Seriously questioning whether someone else controls my actions or my thoughts or whether I am actually dead, then, are not just doubts, as Wittgenstein's critique of G.E. Moore shows: such believes are constitutively excluded from our way of seeing the world and characterized as illnesses, anomalies; otherwise, it would the complete destruction of the language game we inhabit and therefore of the world as we know it, because we would not know on which bases something could be said truthfully or falsely if we did not even know that "this one is my hand". Therefore, even if mental illnesses objectify themselves in correlative physiological dysfunctions, such a discovery comes only after the external recognition of some symptoms, and to recognize the external symptoms of an illness we have to treat them as such; hereby is suggested that we do treat something this way when it threatens the certainties around which the language game we play revolves. (shrink)

El estallido social en Chile desafı́a a las humanidades a abordar un fenómeno social inédito por sus formas, a través de un ejercicio reflexivo situado más allá de las tomas de posición en el debate público. Si bien, ha habido un sinnúmero de académicos del espectro nacional que han asumido posturas claras en esta coyuntura, las respuestas y justificaciones contingentes dejan incólumes otras dudas sobre cuestiones de principio. Sabı́amos que Chile vivı́a en una democracia de baja intensidad, con instituciones ancladas (...) al orden constitucional diseñado durante la dictadura cı́vico-militar y continuado por los gobiernos democráticos, con enormes áreas institucionales corrompidas por el fuero de la impunidad, con una clase polı́tica acostumbrada a los privilegios y bajo un modelo estructuralmente desigual en lo económico, social y cultural. Sabı́amos que todo lo anterior, en alguna medida, fue horadando las bases de las instituciones democráticas. Por eso, para muchos, las protestas que comenzaron en octubre son la continuidad de un dilatado proceso de acumulación del malestar que, debido a lo agudas de sus causas, tardaron más de lo que muchos imaginaron en llegar. (shrink)

In the first half of the 20 th century, philosophers of science used to sustain that the correct theory acceptance in science derived from their conforming to certain rules. However, from the historicist and practical turn in the philosophy of science, the theory acceptance started to be analyzed based on values rather than on a priori established rules. In this article, I will present four paradigmatic positions on the role of values in science. The first position, articulated by Hugh Lacey, (...) defends a regulative ideal of 'impartiality' in the acceptance of scientific theories as established. The other positions convey arguments that seem to conflict with this ideal. I characterize them as 'blind spot argument', 'inductive risk argument' and 'trust-based acceptance argument'. Based on this analysis, I will defend two main theses. My first thesis is that the ideal of impartiality is compatible with the arguments just mentioned. My second thesis is that the defense of impartiality has the advantage of providing a support for the epistemic authority of properly established scientific knowledge. Following Lacey, I will argue that theories can only be accepted as established under specified domains of phenomena. However, theories are accepted for other purposes, for example, when they are adopted to develop research or when they are endorsed to inform the legitimacy of an action. In such cases of theory acceptance, impartiality is neither possible nor desirable, which requires the support of other ideals. (shrink)

El presente artículo se enmarca en el contexto de la alternativa ofrecida por Quentin Meillassoux a la cuestión de la pregunta canónica ¿por qué hay algo y no más bien nada? (2018f) y pretende reflexionar sobre las condiciones que posibilitan la solución del dilema espectral (2016b) en el marco de una ontología extra científica (2020). Concebir el advenimiento de una entidad divina implicaría comprender, al menos, tres conceptos claves para el pensamiento del filósofo, a saber, el correlacionismo, factualidad y contingencia (...) absoluta. De esta manera, el objetivo principal de este artículo es esbozar una lectura introductoria a los cimientos de la filosofía de Meillassoux a fin de comprenderla como una ontología capaz de dar cuenta de la inexistencia divina. -/- The present article takes place in the context of the alternative offered by Quentin Meillas-soux to the question of the canonical question “why is there something and not rather nothing?” (2018f) and aims to reflect on the conditions that make the solution of the spectral dilemma possible (2016b) within the framework of an extra-scientific ontology (2020). To conceive of the advent of a divine entity would imply understanding at least three key concepts for the philos-opher’s thought, namely, correlationism, factuality and absolute contingency. Thus, the main objec-tive of this article is to outline an introductory reading of the fundamentals of Meillassoux’s phi-losophy in order to understand it as an ontology capable of accounting for divine non-existence. -/- . (shrink)