In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...) the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct theories extending ZF are never bi-interpretable and models of ZF are bi-interpretable only when they are isomorphic. Nevertheless, for natural weaker set theories, we prove, including Zermelo–Fraenkel set theory $\mathrm {ZFC}^{-}$ without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. Specifically, there are well-founded models of $\mathrm {ZFC}^{-}$ that are bi-interpretable, but not isomorphic—even $\langle H_{\omega _1},\in (...) \rangle $ and $ \langle H_{\omega _2},\in \rangle $ can be bi-interpretable—and there are distinct bi-interpretable theories extending $\mathrm {ZFC}^{-}$. Similarly, using a construction of Mathias, we prove that every model of ZF is bi-interpretable with a model of Zermelo set theory in which the replacement axiom fails. (shrink)

Interpretations are generally regarded as the formal representation of the concept of translation.We do not subscribe to this view. A translation method must indeed establish relative consistency or have some uniformity. These are requirements of a translation. Yet, one can both be more strict or more flexible than interpretations are. In this article, we will define a general scheme translation. It should incorporate interpretations but also be compatible with more flexible methods. By doing so, we want to account for methods (...) that seem to imply a sense of translation but are not reducible to interpretations. The main example will be the relative consistent proof between ZF and NBG given by Novak (1950). Further, we will explore a way of combining interpretations. This should account for truth conditions discarded by interpretations in translated theories. (shrink)

In this article, instead of taking a particular method as translation, we ask: what does one expect to do with a translation? The answer to this question will reveal, though, that none of the first order methods are capable of fully represent the required transference of ontological commitments. Lastly, we will show that this view on translation enlarge considerably the scope of translatable, and, therefore, ontologically comparable theories.

A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including $\mathsf {PA}$ [39], $\mathsf {ZF}$, $\mathsf {Z}_2$, and $\mathsf {KM}$ [6]. In this article we extend Enayat’s investigations to subsystems of these latter two theories. We prove that restricting the Comprehension schema of $\mathsf {Z}_2$ and $\mathsf {KM}$ gives non-tight theories. Specifically, we show that $\mathsf {GB}$ and $\mathsf {ACA}_0$ each admit different bi-interpretable extensions, (...) and the same holds for their extensions by adding $\Sigma ^1_k$ -Comprehension, for $k \ge 1$. These results provide evidence that tightness characterizes $\mathsf {Z}_2$ and $\mathsf {KM}$ in a minimal way. (shrink)

Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide to (...) a platonist ontology. Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Bala-guer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. Balaguer's version of Platonism, Full-Blooded Platonism (FBP), is the view that "there are as many abstract mathematical objects as there could be-i.e., there actually exist abstract mathematical objects of all possible kinds" (Balaguer, 2017, p. 381). He continues: Since FBP says that there are abstract mathematical objects of all possible kinds, it follows that if FBP is true, then every purely mathematical theory that could be true-i.e., that is internally consistent-accurately describes some collection of actually existing abstract objects. Thus it follows from FBP that in order to acquire knowledge of abstract objects, all we have to do is come up with an internally consistent purely mathematical theory (and know that it is internally consistent). (Balaguer, 2017, p. 381) * To be published in 43rd International Wittgenstein Symposium proceedings. (shrink)

We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to emphasize the incomplete picture of both theories and treat models as their syntactical counterparts. Insisting on the incomplete picture will allow us to argue in favor of the revisability of the standard model interpretation. We then show that it is hopeless to expect that the (...) relative grounding provided by a standard interpretation can resist being revisable. We start briefly characterizing the expansion of arithmetic `truth' provided by the interpretation in a set theory. Further, we show that, for every well-founded interpretation of recursive extensions of PA in extensions of ZF, the interpreted version of arithmetic has more theorems than the original. This theorem expansion is not complete however. We continue by defining the coordination problem. The problem can be summarized as follows. We consider two independent communities of mathematicians responsible for deciding over new axioms for ZF and PA. How likely are they to be coordinated regarding PA’s interpretation in ZF? We prove that it is possible to have extensions of PA not interpretable in a given set theory ST. We further show that the probability of a random extension of arithmetic being interpretable in ST is zero. (shrink)

Often ZF practice includes the use of the meta-theoretical notion of classes as shorthand expressions or in order to simplify the understanding of conceptual resources. NBG theory expresses formally the internalization of this feature in set theory; in this case, classes, before used metatheoretically, will also be captured by quantifiers of the first order theory. Never- theless there is a widespread opinion that this internalization of classes is harmless. In this context, it is common to refer to the conservativeness of (...) NBG in relation to ZF as a sufficient condition to understand those theories as “equivalent”, attributing a sense of virtuality to the use of classes quantified in NBG. We believe, however, that a technique used to estab- lish relationships between theories is not necessarily neutral in relation to its results - so a conservativeness established through models have different meaning and depth of that rela- tionship established by finitary interpretations. We believe, therefore, that the way in which relationships between theories are established influences the analysis result. In the case of the relationship between NBG and ZF, since NBG is finitely axiomatizible and ZF not, we believe that we have sufficient reasons to assert that the use of different analysis tools may re- veal differences such as expressiveness, ontological commitment and logical conservativeness. Therefore, this project aims to clarify the relationship between these two theories through triangulations between them and the different analysis tools. The use of finitary techniques, in this case, may prove greater expressiveness and ontological commitment of NBG in relation to ZF - relation obscured by an infinitary approach. We believe that, through this research, we can contribute to the debate on the basis of mathematics, denaturalizing the supposedly “equivalent” use of NBG and ZF for this purpose. (shrink)

In this review, I will discuss the historical importance of “The Significance of the New Logic” by Quine. This is a translation of the original “O Sentido da Nova Lógica” in Portuguese by Carnielli, Janssen-Lauret, and Pickering. The American philosopher wrote this book in the beginning of the 1940s, before a major shift in his philosophy. Thus, I will argue that the reader must see this book as an introduction to an important period in his thinking. I will provide a (...) brief summary of the chapters, remarking on valuable features in each of them and positions Quine abandoned in his later work. (shrink)

Apart from references to perception, words such as see and listen have shared, non-literal meanings across diverse languages. Such cross-linguistic meanings have not been systematically investigated as they appear in their natural home — informal spoken interaction. We present a qualitative examination of the semantic associations of perception verbs based on recorded everyday conversation in thirteen diverse languages. Across these diverse communities, spontaneous interaction provides evidence for two commonly-discussed extensions of perception verbs — perception~cognition, hearing~linguistic communication — as well as (...) illustrating other meanings and functions that have been less appreciated heretofore. The range of usage that is readily observable in informal conversation makes it clear that this type of data must take center stage for the empirically grounded study of semantics. Moreover, these data suggest that commonalities in polysemous meanings may rely not only on universal cognition, but also on the universal exigencies of social interaction. (shrink)

O texto apresenta e discute um entendimento de aprendizagem que se fundamenta na linguagem e na pesquisa. Defendendo que todo aprender constitui a reconstrução de algo já anteriormente aprendido, argumenta-se que a aceitação disso exige valorizar a linguagem e a pesquisa como elementos centrais nos processos de ensinar e de aprender. Mostra-se, ainda, que assumir esses entendimentos possibilita tornar as aprendizagens mais significativas, criando oportunidades aos alunos de se assumirem em suas autorias na reconstrução dos discursos sociais, e, assim, qualificar (...) politicamente todo o processo. (shrink)

Philosophers of perception frequently assume that we see actual states of affairs, or facts. Call this claim factualism. In his book, William Fish suggests that factualism is supported by phenomenological observation as well as by experimental studies on multiple object tracking and dynamic feature-object integration. In this paper, I examine the alleged evidence for factualism, focusing mainly on object detection and tracking. I argue that there is no scientific evidence for factualism. This conclusion has implications for studies on the phenomenology (...) and epistemology of visual perception. (shrink)

The sensorimotor theory of vision and visual consciousness is often described as a radical alternative to the computational and connectionist orthodoxy in the study of visual perception. However, it is far from clear whether the theory represents a significant departure from orthodox approaches or whether it is an enrichment of it. In this study, I tackle this issue by focusing on the explanatory structure of the sensorimotor theory. I argue that the standard formulation of the theory subscribes to the same (...) theses of the dynamical hypothesis and that it affords covering-law explanations. This however exposes the theory to the mere description worry and generates a puzzle about the role of representations. I then argue that the sensorimotor theory is compatible with a mechanistic framework, and show how this can overcome the mere description worry and solve the problem of the explanatory role of representations. By doing so, it will be shown that the theory should be understood as an enrichment of the orthodoxy, rather than an alternative. (shrink)

This paper critically examines the debate between William of Ockham and his contemporary Peter Auriol on how to account for the intension and remission of forms. Peter Auriol denies that an added degree of a quality such as the theological virtue of charity could be anything other than something which is neither a universal nor an individual and which cannot be grasped by intuition, but must be posited in order to account for the possibility that an accidental form can vary (...) in intensity. Ockham aims at proving that Auriol’s account is inconsistent. In my opinion, Ockham does not succeed, nor does he succeed in defending a consistent account of the metaphysics underlying the intension and remission of forms. Indeed, he conceives of the degree of a quality as a part of the intensified quality which, while being an individual that is really distinct from the quality and can be picked out, forms a unity with it in such a way that the union of the degree and the quality is itself an individual. Ockham fails to distinguish the notion of maximal resemblance holding between a quality’s degree and the quality from the notion of maximal resemblance which holds between individuals of the same species. In the end, he is led to give up the idea that a degree is an individual that can be picked out in order to protect the core thesis of his nominalism about universals. (shrink)

La filosofía y el filosofar adquieren en la vida de Juan Bautista Ferro lasdimensiones propias de un auténtico pensar que se reflejó en cada acción,en el discurrir diario de la vida académica universitaria o en las "tertuliasrnonologantes" que el propio Ferro concertaba con sus amigos en su casao en plena calle. Ferro fue el ejemplo vivo de una tradición filosófica quecentra su acción sobre el propio filósofo, y el cultivo de la "oralidad" corno"método" para enseñar a aprender. El texto muestra (...) todo esto a través deuna reconstrucción testimonial. (shrink)

English summary: This book attests that a study on the history of philosophy has its place in contemporary debates. This book attempts to reconstruct William of Ockham's position on the nature and function of real definitions in order to show that nominalism does not oblige a particular position on essences. French description: Guillaume d'Ockham, defenseur bien connu du nominalisme, a manifeste un interet soutenu pour les definitions reelles. Cet ouvrage s'efforce de reconstruire sa position sur la nature et la fonction (...) des definitions reelles. Un examen de ce qu'est une definition reelle appelle une etude de ce qu'est une essence et de la nature du lien a poser entre l'essentiel et le necessaire. Cet ouvrage a pour objectif de montrer que le nominalisme ne contraint pas a une position determinee sur les essences. Saul Kripke nous dit que l'essentiel se reduit au necessaire. Kit Fine, par contre, affirme qu'il faut revenir a Aristote et soutenir que l'essentiel est irreductible au necessaire. Notre examen atteste qu'une etude en histoire de la philosophie a toute sa place dans les debats contemporains. L'essentialisme de Guillaume d'Ockham incite a rendre a Aristote ce qui lui revient et a faire preuve de circonspection. En definitive, les deux positions en presence ne sont peut-etre pas incompatibles. (shrink)

Normal 0 21 false false false PT-BR X-NONE X-NONE MicrosoftInternetExplorer4 O estudo tem caráter qualitativo e busca em referenciais teóricos . C ontempla uma reflexão aberta a respeito do alvorecer da razão na modernidade, que lança o ser humano ao centro do universo . Ao fazê-lo, fragmenta a formação do ethos, vórtice que alcança a contemporaneidade. Na sequência traz suportes teóricos, com base, principalmente nas concepções de Agamben, Bauman,Vaz, entre outros, acerca da ainda possibilidade formativas de construção da comunidade humana. (...) Apesar dos numerosos e diversos conhecimentos produzidos, na atualidade, crescem as dificuldades de compreensão da condição humana e do significado dos fazeres humanos. A aposta na subjetividade como uma essência, marca da metafísica, também pos em questão a identidade pessoal . A contemporaneidade ampla e complexa clama por contextos educacionais capazes de dinamizar bases ontológicas com diferentes bases conceptuais e vivenciais. Dessa forma a problemática orientadora da reflexão é: como constituiu-se a formação do ethos contemporâneo e, quais são os desafios à educação? Como resultados destacamos que a racionalidade técnico-científica gerou despreocupação com a vivência de valores éticos voltados ao bem comum; a individualização fomentou a descrença em políticas democráticas e ceifou a esperança na formação de um ethos contemporâneo solidário. Concluimos que existe uma necessidade urgente de repensar a constituição ontológica do ser humano, como pressuposto imprescindível na reconstituição da relação entre o EU/TU ou EU/HUMANIDADE; a compreensão do Outro requer aceitar a pluralidade de perspectivas de novas vivências e formas relacionais; educar é vivenciar laços de sensibilidade social para construir comunidades nas quais a amizade seja o esteio político. Palavras-chaves: Educação. Ética. Comunidade. Amizade THE FORMATION OF CONTEMPORARY ETHOS: CHALLENGES TO EDUCATION: The study is qualitative and search for theoretical frameworks. Contemplates an open reflexion about the dawn of reason in modernity, which throws the human to the center of the universe . fragments forming the ethos vortex that reaches the contemporary. Following brings theoretical supports, based mainly on the concepts of Agamben, Bauman, Vaz, among others, about the possibility of building further training of the human community. Despite numerous and diverse knowledge produced, in actuality, there are growing difficulties in understanding the human condition and the meaning of human doings. The focus on subjectivity as an essence, brand of metaphysics, also calls into question the personal identity. The broad and complex contemporary calls for educational contexts capable of stimulating ontological bases with different conceptual and experiential bases. Thus the problem of guiding reflection is: how was the formation of the contemporary ethos and what are the challenges for education? The results highlight that the scientific-technical rationality generated unconcern with the experience of ethical values ​​directed to the common good; individualization fostered disbelief in democratic politics and claimed the hope of forming a contemporary ethos supportive. We conclude that there is an urgent need to rethink the ontological constitution of the human being as an indispensable prerequisite to rebuild the relationship between I / YOU or I / HUMANITY; understanding of the Other requires accepting the plurality of perspectives and experiences of new relational forms; educate social ties is experiencing sensitivity to build communities in which friendship is political mainstay . Keywords: Education. Ethics. Community. Friendship. (shrink)

La recepción europea de Gómez Dávila comenzó a desplegarse de manera más amplia a partir de la lectura y difusión realizada por Franco Volpi. Este artículo alude a la manera como dicha lectura concretó las interpretaciones del colombiano, principalmente a la luz de una filosofía práctica y una perspectiva crítica. De dichas posturas, el italiano destaca la vocación vital y el carácter provocador del pensamiento de Gómez Dávila.

The Critique of Pure Reason—Kant’s First Critique—is one of the most studied texts in intellectual history, but as Alfredo Ferrarin points out in this radically original book, most of that study has focused only on very select parts. Likewise, Kant’s oeuvre as a whole has been compartmentalized, the three Critiques held in rigid isolation from one another. Working against the standard reading of Kant that such compartmentalization has produced, The Powers of Pure Reason explores forgotten parts of the First (...) Critique in order to find an exciting, new, and ultimately central set of concerns by which to read all of Kant’s works. Ferrarin blows the dust off of two egregiously overlooked sections of the First Critique—the Transcendental Dialectic and the Doctrine of Method. There he discovers what he argues is the Critique’s greatest achievement: a conception of the unity of reason and an exploration of the powers it has to reach beyond itself and legislate over the world. With this in mind, Ferrarin dismantles the common vision of Kant as a philosopher writing separately on epistemology, ethics, and aesthetics and natural teleology, showing that the three Critiques are united by this underlying theme: the autonomy and teleology of reason, its power and ends. The result is a refreshing new view of Kant, and of reason itself. (shrink)

In this article, I argue that there is philosophy of science since philosophy existed. Thus, the idea that the philosophy of science was born with neopositivism is historically wrong and detrimental to the development of the philosophy of science itself. Neopositivism tried to found the philosophy of science as an anti-philosophical discipline, as a field of study that came to replace simple philosophy. The attempt was maintained for thirty years, but failed. Now, this does not mean that we cannot make (...) good philosophy of science today, but that the philosophy of science has returned to the common house of philosophy, it is gradually recovering the connection that it should never have lost with the main philosophical traditions and disciplines. (shrink)

Este artículo es parte de un trabajo de investigación bastante más amplio, que llevó casi cinco años de duración, en el cual nos propusimos una lectura rigurosa como singular del concepto de sujeto en Alain Badiou y Jacques Lacan. En vistas a delimitar claramente el tema de estudio, la pregunta que nos formulamos como punto de partida fue la siguiente: ¿qué lugar ocupa el concepto de sujeto en la articulación lógica del pensamento de ambos autores, particularmente en sus dimensiones ontológicas (...) y políticas? Como se podrá apreciar a continuación, dicho trabajo despliega una topología conceptual que a su vez presenta ciertos hitos históricos. Pues es sabido que uno de los temas centrales en torno al cual ha girado la fi losofía política contemporánea ha sido la cuestión del sujeto, y así también, correlativamente, de los saberes y verdades que lo fundamentan. Se ha interrogado por ejemplo ¿cuál puede ser el lugar de este sujeto? ¿Es posible especifi car a priori su existencia? ¿De dónde deriva su estatuto? ¿Se trata de una función trascendental o sustancial, vacía o refl exiva? Estas preguntas responden, en cierta forma, a una concepción de sujeto más bien propia de la metafísica moderna que intentaremos desplazar. (shrink)

Since antiquity, philosophers have investigated how change works. If a thing moves from one state to another, when exactly does it start to be in its new state, and when does it cease to be in its former one? In the late Middle Ages, the "problem of the instant of change" was subject to considerable debate and gave rise to sophisticated theories; it became popular and controversial again in the second half of the twentieth century. The studies collected here constitute (...) the first attempt at tackling the different aspects of an issue that, until now have been the object of seminal but isolated forays. They do so in through a historical perspective, offering both the medieval and the contemporary viewpoints. (shrink)

A method for the recursive identification of physiological models of the cardiovascular baroreflex is proposed and applied to the time-varying analysis of vagal and sympathetic activities. The proposed method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictors and the results show a close match between experimental and simulated signals. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and the obtained estimators of vagal and sympathetic activities were (...) compared to traditional markers associated with baroreflex sensitivity. High correlations were observed between traditional markers and model-based indices. (shrink)

Many artists, art critics, and poets suggest that an aesthetic appreciation of artworks may modify our perception of the world, including quotidian things and scenes. I call this Art-to-World, AtW. Focusing on visual artworks, in this paper I articulate an empirically-informed account of AtW that is based on content-related views of aesthetic experience, and on Goodman’s and Elgin’s concept of exemplification. An aesthetic encounter with artworks demands paying attention to its aesthetic, expressive, or design properties that realize its purpose. Attention (...) to these properties make percipients better able to spot them in other entities and scenes as well. The upshot is that an aesthetic commerce with artworks enlarges the scope of what we are able to see and has therefore momentous epistemic consequences. (shrink)

El objetivo del presente texto es llegar a una descripción clara y comprensiva de la forma budista de abordar la cuestión cognitiva. La palabra cognición se refiere aquí al proceso por el cual se desenvuelve la convicción de que algo es "verdadero". El examen budista de la cognición puede, a su vez, ser encarado como una forma de buscar mayor libertad y distanciamiento frente a los pensamientos, opiniones y tendencias propios.