We will give a simple philosophical "proof" of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpinski and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in fact show (...) why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy--if you reject CH you are only two steps away from rejecting the axiom of choice (AC)--we will point out along the way some extensions of our intuition which contradict AC. (shrink)

Effective vaccines for COVID‐19 are already available to humankind. In Peru, 86 million doses were administered to cover the demand for 33 million Peruvian people. Hence, vaccination has been prioritized in groups: health personnel, subjects with pre‐existing health conditions and those over 65 years of age. However, given the social problems and the public health situation in Peru, this work defends that the priority of vaccination should be focused on the population living in extreme poverty. The method used was an (...) ethical argumentation on the distribution of scarce antiSARS‐CoV2 vaccine in Peru. This argument is based on the analysis of the Peruvian population living in extreme poverty, which presents different layers of vulnerability, and that, in the face of an eventual SARS‐CoV2 infection, these would be exacerbated one after the other, through a cascade effect. This scenario would give rise to new vulnerabilities to those already existing, causing greater damage. Vaccination efforts on this key population would give them the opportunity to continue to find ways to bring food to their homes, significantly reducing the risk of contagion in their environment and mitigating the devastating effect of the local diseases to which they are already exposed. Four objections related to this argument are raised with their corresponding responses. Priority access to the vaccine would significantly reduce the humanitarian harm to people living in extreme poverty, prevailing the principles of justice and equity. (shrink)

Banach introduced the following two-person, perfect information, infinite game on the real numbers and asked the question: For which sets $A \subseteq \mathbf{R}$ is the game determined????? Rules: The two players alternate moves starting with player I. Each move a n is legal iff it is a real number and $0 , and for $n > 1, a_n . The first player to make an illegal move loses. Otherwise all moves are legal and I wins iff ∑ a n exists (...) and ∑ a n ∈ A. We will look at this game and some variations of it, called Banach games. In each case we attempt to find the relationship between Banach determinancy and the determinancy of other well-known and much-studied games. (shrink)

La humanidad ya dispone de vacunas eficaces contra el COVID‐19. En Perú se administraron 86 millones de dosis para cubrir la demanda de 33 millones de peruanos. Para ello, se ha priorizado la vacunación en grupos clave: personal de salud, sujetos con condiciones de salud preexistentes y mayores de 65 años. Sin embargo, dada la problemática social y la situación de la salud pública en Perú, este trabajo defiende que la prioridad de la vacunación debe centrarse en la población que (...) vive en extrema pobreza. El método utilizado fue una argumentación ética sobre la distribución de la vacuna contra el COVID‐19 en Perú. Esta argumentación se basa en el análisis de la población peruana que vive en extrema pobreza, la cual presenta diferentes estratos de vulnerabilidad, y que, ante una eventual infección por SARS‐CoV‐2, se irían agravando uno tras otro, a través de un efecto en cascada. Este escenario daría lugar a nuevas vulnerabilidades de las ya existentes, causando mayores daños. Los esfuerzos de vacunación en esta población clave les brindaría oportunidad de seguir encontrando formas de llevar alimentos a sus hogares, reduciendo significativamente el riesgo de contagio en su entorno y mitigando el efecto devastador de las enfermedades locales a las que ya está expuesta. Se plantean cuatro objeciones relacionadas con este argumento, con sus correspondientes respuestas. El acceso prioritario a la vacuna reduciría significativamente el daño a las personas que viven en la extrema pobreza, haciendo prevalecer los principios de justicia y equidad. (shrink)

This isnotabout the symbolic manipulation of functions so popular these days. Rather it is about the more abstract, but infinitely less practical, problem of the primitive. Simply stated:Given a derivativef: ℝ → ℝ, how can we recover its primitive?The roots of this problem go back to the beginnings of calculus and it is even sometimes called “Newton's problem”. Historically, it has played a major role in the development of the theory of the integral. For example, it was Lebesgue's primary motivation (...) behind his theory of measure and integration. Indeed, the Lebesgue integral solves the primitive problem for the important special case whenfis bounded. Yet, as Lebesgue noted with apparent regret, there are very simple derivatives = 0,F=x2sinforx≠ 0) which cannot be inverted using his integral.The general problem of the primitive was finally solved in 1912 by A. Denjoy. But his integration process was more complicated than that of Lebesgue. Denjoy's basic idea was to first calculate the definite integralf dxover as many intervals as possible, using Lebesgue integration. Then, he showed that by using these results, the definite integral could be found over even more intervals, either by using the standard improper integral technique of Cauchy, or an extension technique developed by Lebesgue. (shrink)

Emotional peer support systems have benefits for student-student relationships and allow for children and adolescents' participation in schools. For students with specific educational needs and disabilities, positive relationships seem to be more difficult to attain and these students are more vulnerable to suffer negative peer experiences such as bullying and social exclusion. Systems in which peers can show helpful behavior are beneficial for schools in order to create a positive, supportive climate. Emotional peer support entails social interaction through emotional or (...) practical help based on what these peers have in common and many times with benefits for both. This systematic review identified interventions of emotional peer support in schools for students with SEND. Twenty-three studies were identified that involved four types of befriending: circle of friends, peer buddying, peer networks, and social lunch clubs. Studies reported mainly positive outcomes for both focus students and peer supporters in terms of increased social interaction and social acceptance, as well as enhanced self-esteem and empathy on the individual level. Further bonding of the students by friendship was also perceived, but more precise data is required to draw further conclusions. Support by the school as an institution, the specific role of the teacher, and family participation are important factors related to the impact of peer support systems. Information on these aspects was scarce, and it is recommended to include variables of this nature in future research. Intervention descriptions revealed students' active participation through suggestions for activities, however their involvement in organizing the systems was limited. More research is needed to learn about the opportunities of emotional peer support to improve student-student relationships including the active involvement of the peers themselves in this support. (shrink)

Many of the computing systems programmed using Machine Learning are opaque: it is difficult to know why they do what they do or how they work. Explainable Artificial Intelligence aims to develop analytic techniques that render opaque computing systems transparent, but lacks a normative framework with which to evaluate these techniques’ explanatory successes. The aim of the present discussion is to develop such a framework, paying particular attention to different stakeholders’ distinct explanatory requirements. Building on an analysis of “opacity” from (...) philosophy of science, this framework is modeled after accounts of explanation in cognitive science. The framework distinguishes between the explanation-seeking questions that are likely to be asked by different stakeholders, and specifies the general ways in which these questions should be answered so as to allow these stakeholders to perform their roles in the Machine Learning ecosystem. By applying the normative framework to recently developed techniques such as input heatmapping, feature-detector visualization, and diagnostic classification, it is possible to determine whether and to what extent techniques from Explainable Artificial Intelligence can be used to render opaque computing systems transparent and, thus, whether they can be used to solve the Black Box Problem. (shrink)

To date, no definition of life has been unequivocally accepted by the scientific community. In frustration, some authors advocate alternatives to standard definitions. These include using a list of characteristic features, focusing on life’s effects, or categorizing biospheres rather than life itself; treating life as a fuzzy category, a process or a cluster of contingent properties; or advocating a ‘wait-and-see’ approach until other examples of life are created or discovered. But these skeptical, operational, and pluralistic approaches have intensified the debate, (...) rather than settled it. Given the failure of even these approaches, we advocate a new strategy. In this paper, we reverse the usual line of reasoning and argue that the “life problem” arises from thinking incorrectly about the nature of life. Scientists most often conceptualize life as a class or kind, with earthly life as a single instance of it. Instead, we advocate thinking about Earth’s Life as an individual, in the way that species are now thought to be. In this view, Life is a monophyletic clade that originated with a last universal common ancestor, and includes all its descendants. We can continue to use the category ‘life’ pragmatically to refer to similarities between various phenomena and Life. But the relevant similarities are a matter of interest and preference, not a matter of fact. The search for other life in the Universe, then, is merely a search for entities that resemble parts of Life in whatever sense astrobiologists find most appealing. This does not mean that the search for evolved complexity elsewhere in the universe or its creation in the lab are futile endeavors, but that debates over whether they count as ‘life’ are. Ironically, finally abandoning the concept ‘life’ may make our searches for evolved complexity more fruitful. We explain why. (shrink)

The received view of dynamical explanation is that dynamical cognitive science seeks to provide covering law explanations of cognitive phenomena. By analyzing three prominent examples of dynamicist research, I show that the received view is misleading: some dynamical explanations are mechanistic explanations, and in this way resemble computational and connectionist explanations. Interestingly, these dynamical explanations invoke the mathematical framework of dynamical systems theory to describe mechanisms far more complex and distributed than the ones typically considered by philosophers. Therefore, contemporary dynamicist (...) research reveals the need for a more sophisticated account of mechanistic explanation. (shrink)

Models developed using machine learning are increasingly prevalent in scientific research. At the same time, these models are notoriously opaque. Explainable AI aims to mitigate the impact of opacity by rendering opaque models transparent. More than being just the solution to a problem, however, Explainable AI can also play an invaluable role in scientific exploration. This paper describes how post-hoc analytic techniques from Explainable AI can be used to refine target phenomena in medical science, to identify starting points for future (...) investigations of causal relationships, and to generate possible explanations of target phenomena in cognitive science. In this way, this paper describes how Explainable AI—over and above machine learning itself—contributes to the efficiency and scope of data-driven scientific research. (shrink)

In a context of pervasive digitalization of the social world, both before and during the COVID-19 pandemic, the field of education has undergone major changes with the development of digital practices and settings. However, the physical presence of the subjects and the body remain something primordial and irreplaceable in traditional educational processes. Thus, it is often assumed that virtuality is opposed to the corporeal reality of the subjects involved in teaching, learning and studying. In this paper we aim to critically (...) challenge this assumption by addressing the phenomenon of virtuality in a more original sense: as a fundamental dimension of corporeality itself. Drawing on Merleau-Ponty’s phenomenological insights, we argue that the experience of the virtual is inherently embodied and fully real. We understand corporeality and virtuality as entangled and multidimensional phenomena. At the same time, this leads us to rethink the digital as only one possible medium in which virtuality can appear as inherent to embodied experience. We develop our phenomenological approach in three instances. First, we question and bracket two common assumptions about corporeality. From our critical perspective, assumptions about a disembodied digitality and a devirtualized corporeality represent extremes within which educational discourses currently move. Second, we address the inherent virtuality of embodied experience. We outline the heuristic concept of the virtual body to describe corporeality and virtuality as entangled and multidimensional phenomena that encompass extension, intercorporeality and intermediality. Finally, we make some remarks on the relationships of corporeality and virtuality considering the challenges of digital education. (shrink)

"Epistola a Memeceo, Maximas capitales, Sentencias vaticanas, fragmentos y testimonios; texto griego y traduccion": p. [87]-161.

This paper discusses the varieties of capitalism in transitional societies in Latin America and Central / Eastern Europe. The intended purpose of these transitions from semi-closed import-substituting economies in the first case and state socialist ones in the second was to institutionalize open-market economies. Twenty or thirty years later, there is a variety of types of capitalism in these countries, which I classify into three: open-market, neo-mercantilist, and anemic. The question for sociology is whether these quite different variants represent temporary (...) stages or distortions in the same process of transition or whether, on the contrary, they may institutionalize as discrete forms of peripheral capitalism. Neither standard “legacy” argu­ments nor institutionalist theories offer satisfactory answers to this question. The multiple modernities approach, on the other hand, is more appropriate as a theoretical perspective, but it has not produced yet specific propositions applicable to this question. My paper makes two claims. First, the successful transfer of institutions depends on the congruence between these institutions and the broader institutional framework of the recipient economies, a point not developed by institutionalist theories. I offer a hypothesis in this regard: Two critical nodes of congruence are the regulatory and extractive capacity of the state and the strength of civil society. Second, market capitalism (as liberal democracy as well) is a complex institution, and some of its components “travel” more easily across societies and institutional frameworks, and therefore are easier to institutionalize. This is the source of the hybrid variants. (shrink)

At least since Kuhn’s Structure, philosophers have studied the influence of social factors in science’s pursuit of truth and knowledge. More recently, formal models and computer simulations have allowed philosophers of science and social epistemologists to dig deeper into the detailed dynamics of scientific research and experimentation, and to develop very seemingly realistic models of the social organization of science. These models purport to be predictive of the optimal allocations of factors, such as diversity of methods used in science, size (...) of groups, and communication channels among researchers. In this paper we argue that the current research faces an empirical challenge. The challenge is to connect simulation models with data. We present possible scenarios about how the challenge may unfold. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

This article discusses the relation between empirical and normative approaches in bioethics. The issue of dwarf tossing, while admittedly unusual, is chosen as a point of departure because it challenges the reader to look with fresh eyes upon several central bioethical themes, including human dignity, autonomy, and the protection of vulnerable people. After an overview of current approaches to the integration of empirical and normative ethics, we consider five ways that the empirical and normative can be brought together to speak (...) to the problem of dwarf tossing: prescriptive applied ethics, theoretical ethics, critical applied ethics, particularist ethics and integrated empirical ethics. We defend a position of critical applied ethics that allows for a two-way relation between empirical and normative theories. Against efforts fully to integrate the normative and the empirical into one synthesis, we propose that the two should stand in tension and relation to one another. The approach we endorse acknowledges that a social practice can and should be judged both by the gathering of empirical data and by normative ethics. Critical applied ethics uses a five stage process that includes: (a) determination of the problem, (b) description of the problem, (c) empirical study of effects and alternatives, (d) normative weighing and (e) evaluation of the effects of a decision. In each stage, we explore the perspective from both the empirical (sociological) and the normative ethical point of view. We conclude by applying our five-stage critical applied ethics to the example of dwarf tossing. (shrink)

The philosophical conception of mechanistic explanation is grounded on a limited number of canonical examples. These examples provide an overly narrow view of contemporary scientific practice, because they do not reflect the extent to which the heuristic strategies and descriptive practices that contribute to mechanistic explanation have evolved beyond the well-known methods of decomposition, localization, and pictorial representation. Recent examples from evolutionary robotics and network approaches to biology and neuroscience demonstrate the increasingly important role played by computer simulations and mathematical (...) representations in the epistemic practices of mechanism discovery and mechanism description. These examples also indicate that the scope of mechanistic explanation must be re-examined: With new and increasingly powerful methods of discovery and description comes the possibility of describing mechanisms far more complex than traditionally assumed. (shrink)

Our understanding of the universe has grown rapidly in recent decades. We’ve discovered evidence of water in nearby planets, discovered planets outside our solar system, mapped the genomes of thousands of organisms, and probed the very origins and limits of life. The scientific perspective of life-as-it-could-be has expanded in part by research in astrobiology, synthetic biology, and artificial life. In the face of such scientific developments, we argue there is an ever-growing need for universal biology, life-as-it-must-be, the multidisciplinary study of (...) non-contingent aspects of life as guided by biological theory and constrained by the universe. We present three distinct but connected ways of universalizing biology—with respect to characterizing aspects of life everywhere, with respect to the explanatory scope of biological theory, and with respect to extending biological insights to the structure of nonbiological entities. For each of these, we sketch the theoretical goals and challenges, as well as give examples of current research that might be labeled universal biology. (shrink)

This chapter subsumes David Marr’s levels of analysis account of explanation in cognitive science under the framework of mechanistic explanation: Answering the questions that define each one of Marr’s three levels is tantamount to describing the component parts and operations of mechanisms, as well as their organization, behavior, and environmental context. By explicating these questions and showing how they are answered in several different cognitive science research programs, this chapter resolves some of the ambiguities that remain in Marr’s account, and (...) shows that many different areas and traditions of cognitive scientific research can be unified under the mechanistic framework. (shrink)

The concept of dignity is notoriously vague. In this paper it is argued that the reason for this is that there are three versions of dignity that are often confused. First we will take a short look at the history of the concept of dignity in order to demonstrate how already from Roman Antiquity two versions of dignity can be distinguished. Subsequently, the third version will be introduced and it will be argued that although the three versions of dignity hang (...) together, they should also be clearly distinguished in order to avoid confusion. The reason for distinguishing the three versions is because all three of them are only partially effective. This will be demonstrated by taking the discussion about voluntary ‘dying with dignity’ as an example. Inspired by both Paul Ricoeur’s concept of ethics and the ethics of care a proposition will be done as to how the three versions of dignity may sustain each other and help achieve what neither one of the versions can do on its own. (shrink)

The concept of evidence has gone unanalysed in much of the current debate between proponents and critics of evidence-based medicine. In this paper I will suggest that part of the controversy rests on an understanding of the word “evidence” that is too broad, and therefore contains the contradictions that allow both camps to defend their position and charge their adversaries. I will argue that reconciling the different meanings of the word ‘evidence’ in “evidence-based medicine” should help put EBM in its (...) rightful place. (shrink)

Whereas most branches of neuroscience are thought to provide mechanistic explanations, systems neuroscience is not. Two reasons are traditionally cited in support of this conclusion. First, systems neuroscientists rarely, if ever, rely on the dual strategies of decomposition and localization. Second, they typically emphasize organizational properties over the properties of individual components. In this paper, I argue that neither reason is conclusive: researchers might rely on alternative strategies for mechanism discovery, and focusing on organization is often appropriate and consistent with (...) the norms of mechanistic explanation. Thus, many explanations in systems neuroscience can also be viewed as mechanistic explanations. (shrink)

The so-called “intentional object” occupies a central position in the debates about intentionality in Brentano and the Brentano School. How does it relate to the correlate, the content, or the intended, possibly external, transcendent object? Does it perhaps even coincide with one of these? There was no clear consensus on this neither in Brentano’s time nor today. In order to develop a new perspective on the problem of the intentional object, I would like to introduce a deliberately radical interpretation and (...) related terminological change: what if we were to avoid any talk of “object” in this context altogether? Perhaps this could help avoid the ambiguities and misunderstandings associated with talk of “intentional objects.” In my contribution I would like to sketch such an interpretation and consider whether this attempt could be useful to reframe the debate. (shrink)

This paper considers the way mathematical and computational models are used in network neuroscience to deliver mechanistic explanations. Two case studies are considered: Recent work on klinotaxis by Caenorhabditis elegans, and a longstanding research effort on the network basis of schizophrenia in humans. These case studies illustrate the various ways in which network, simulation and dynamical models contribute to the aim of representing and understanding network mechanisms in the brain, and thus, of delivering mechanistic explanations. After outlining this mechanistic construal (...) of network neuroscience, two concerns are addressed. In response to the concern that functional network models are non-explanatory, it is argued that functional network models are in fact explanatory mechanism sketches. In response to the concern that models which emphasize a network’s organization over its composition do not explain mechanistically, it is argued that this emphasis is both appropriate and consistent with the principles of mechanistic explanation. What emerges is an improved understanding of the ways in which mathematical and computational models are deployed in network neuroscience, as well as an improved conception of mechanistic explanation in general. (shrink)

This volume is a broad anthology addressing many if not most major topics in phenomenology and philosophy in general: from foundational and methodological ...

The book is a comprehensive introduction to the work of the Estonian-German biologist Jakob von Uexküll. After a first introductory chapter by Morten Tønnessen and a second chapter on Uexküll's life and philosophical background, it contains four chapters devoted to the analysis of his main works; they are followed by a vast eighth chapter which deals with the influence Uexküll had on other philosophers and scientists, and by a conclusions focused on the possibility of updating Uexküll's work. The monograph combines (...) a careful reconstruction of the historical context in which the Uexküllian concepts emerged (the debate between mechanism and vitalism, contemporary scientific studies) and a thorough analysis of the philosophical contents of the Uexküllian views. As far as the key issue is concerned, Uexküll's notion of Umwelt refers to the perceptive and operative world which surrounds animal species; it is a subjective species-specific construction which provides living organisms with great security and behaviour stability. Moreover, the relationship that the animal carries out with its environment proves to be a complex system of semiotic interactions: its behaviour is not a set of mechanical reactions, but the result of a spontaneous attribution of meaning to the outside world, whose environmental elements are actively interpreted by the subject. The environment of animal species becomes a field of meaning, an exceedingly complex subjective elaboration; this can lessen the distance between animals and men, crediting both with the cognitive ability to grasp meanings and to use signs. (shrink)

In this article I will begin by discussing recent criticism, by Mauro Antonelli and Werner Sauer, of the ontological interpretation of Franz Brentano’s concept of intentionality, as formulated by i.a. Roderick Chisholm. I will then outline some apparent inconsistencies of the positions advocated by Antonelli and Sauer with Brentano’s formulations of his theory in several works and lectures. This new evaluation of (unpublished) sources will then lead to a sketch of a new approach to Brentano’s theory of intentionality. Specifically, it (...) will be argued that the notion of “intentional object” is inherently and un- avoidably ambiguous in every act of external perception, due to the fact that we can only have improper intentions directed at the external world. (shrink)

In the article Husserl’s view of the infinite around 1890 is analysed. I give a survey of his mathematical background and other important influences (especially Bolzano). The article contains a short exposition on Husserl's distinction between proper and symbolic presentations in the "Philosophie der Arithmetik" and between finite and infinite symbolic collections. Subsequently Husserl’s conception of surrogate presentations in his treatise "Zur Logik der Zeichen (Semiotik)" is discussed. In this text Husserl gives a detailed account of infinity, using surrogate presentations. (...) The conclusion is that with surrogates we can only operate according to blind psychological rules. (shrink)

A descriptive-exploratory analysis of assurance practices is presented in this paper, by analysing the patterns of sustainability assurance reporting in two national contexts with different levels of assurance activity over a period of 11 years. The study is based on theoretical insights drawn from institutional sociology and normativity production. It is framed both in the Italian situation, where assurance statements consistently include a narrow set of formal and procedural communications, and in an unsettled situation in the U.S., where assurance activity (...) is more incipient, but where experimentation in substantial assurance disclosure practices has more room to develop. Its main implication is that the diffusion of sustainability assurance and the creation of sustainability assurance disclosure norms are not without its cost: information quality does not increase with patterned practice. The results also point towards the noteworthy role of specific professionals in the earlier and later stages of assurance practice norms. They reveal a significant influence of non-Big4 firms in the diffusion of sustainability assurance disclosure norms. In contrast, the Big4 firms appear to be positively associated with the narrowing down of the assurance focus to a selected subset of this activity in later stages of the development of the assurance norm. In this regard, this study provides insight into the circumstantial—but relevant—carrier role of the Big4 firms in determining what “assurance” means. (shrink)

The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...) our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)

Franz Brentano is not usually associated with mathematics. Generally, only Brentano’s discussion of the continuum and his critique of the mathematical accounts of it is treated in the literature. It is this detailed critique which suggests that Brentano had more than a superficial familiarity with mathematics. Indeed, considering the authors and works quoted in his lectures, Brentano appears well-informed and quite interested in the mathematical research of his time. I specifically address his lectures here as there is much less to (...) be found about mathematics in his published works. Besides Brentano’s own work, it is quite remarkable to see that practically all of his better-known students sooner or later produced a work on the philosophy of mathematics. This also encourages the supposition not just of a common interest in the matter, but of a common theoretical core. All this prompts the question: Can we speak of a Brentanist philosophy of mathematics? (shrink)

This new textbook is an exceptionally clear and concise introduction to the philosophy of action, suitable for students interested in the philosophy of mind and the philosophy of social sciences. Moya begins by considering the problem of agency: how are we to understand the distinction between actions and happenings, between actions we perform and things that happen to us? Moya outlines and examines a range of philosophical responses to this problem. He also develops his own original view, treating the analysis (...) of meaningful action as the basis for understanding the distinctive interplay of agency, intention and commitment. Subsequent chapters examine recent attempts to integrate our understanding of action with the view of the world provided by the natural sciences. The work of Donald Davidson is examined in detail. Moya also discusses the views of many other authors who have contributed to recent debates in the philosophy of action, including Anscombe, Churchland, Harman, Hornsby, Goldman and O'Shaughnessy. (shrink)