Um esboço sobre a natureza dos objetos da matemática Resumo: A natureza dos objetos da Matemática é um dos temas que reflete posicionamentos distintos em relação ao processo de ensino da disciplina. A partir dessa premissa, o presente texto tem como objetivo discutir o processo histórico-lógico de desenvolvimento da Matemática, na especificidade de seus objetos, a partir de concepções realistas e antirrealistas. Além disso, atenta para as manifestações de uma inversão metafísica da compreensão desses objetos. Esse objetivo surgiu a partir (...) do seguinte questionamento: Como se expressa a compreensão sobre a natureza dos objetos da Matemática no processo de desenvolvimento dessa ciência a partir de concepções materialistas e idealistas, realistas e antirrealistas? A discussão inicia pela caracterização dos objetos da Matemática a partir de suas manifestações realistas e antirrealistas, com ênfase nos processos de entificação realizados pelos pitagóricos, por Platão e por Aristóteles. Em seguida, realiza-se um movimento de caracterização da compreensão dos objetos da Matemática a partir do idealismo e do materialismo. Tais abordagens são realizadas a partir de uma outra, a filosófico-histórica, com o intuito de desnudar a essência pela qual se expressa o entendimento sobre os objetos matemáticos como necessário em processos de educação escolar. Palavras-chave: Filosofia da matemática; Concepções de Matemática; Educação Matemática. The nature of mathematical objects outlined Abstract: The nature of mathematical objects is one of the themes in the process of teaching mathematics that reflects distinctive positions. Based on this premise, the present article aims to discuss the historical-logical process of development of Mathematics, taking into account the specifics of its objects, found on unrealistics and realistics concepts. Furthermore, it considers the manifestations in the comprehension of metaphysics inversion of these objects. This objective emerges from the following question: How is the comprehension of the nature of mathematical objects in the process of development of this science based on materialistic and idealistic, realistic and unrealistic concepts expressed? The discussion begins with the characterization of the mathematical objects from the realistics and unrealistics manifestations, with an emphasis on the process of entification which was carried out by pythagoreans, such as Plato and Aristotle. Subsequently, it provides the characterization of the comprehension of the mathematical objects based on idealism and materialism. The approaches applied are based on another one, that is the philosophical and historical one, which intends to unveil the essence by which it expresses the comprehension of the mathematical objects as paramount for the educational process. Key-words: Philosophy of Mathematics; Mathematical concepts; Mathematics Education. Un esbozo sobre la naturaleza de los objetos matemáticos Resumen: La naturaleza de los objetos matemáticos es uno de los temas que refleja diferentes posiciones en relación con el proceso de enseñanza de la disciplina. A partir de esta premisa, el presente texto tiene como objetivo discutir el proceso histórico-lógico del desarrollo de la matemática, en la especificidad de sus objetos, a partir de concepciones realistas y antirrealistas. Además, está atenta a las manifestaciones de una inversión metafísica de la comprensión de estos objetos. Este objetivo surgió del siguiente cuestionamiento: ¿Cómo se expresa la comprensión de la naturaleza de los objetos matemáticos en el proceso de desarrollo de esta ciencia a partir de concepciones materialistas e idealistas, realistas y antirrealistas? La discusión comienza con la caracterización de los objetos matemáticos a partir de sus manifestaciones realistas y antirrealistas, con énfasis en los procesos de entificación realizados por los pitagóricos, Platón y Aristóteles. En seguida, se realiza un movimiento para caracterizar la comprensión de los objetos matemáticos basado en el idealismo y el materialismo. Tales enfoques son realizados a partir de un otro, el filosófico-histórico, con la intención de despojar la esencia por la cual se expresa el entendimiento sobre los objetos matemáticos como necesarios en procesos de la educación escolar. Palabras clave: Filosofía de la matemática; Concepciones de Matemáticas; Educación Matemática. Data de registro: 22/09/2020 Data de aceite: 28/04/2021. (shrink)

Now under what circumstances is a conditional true? Even to raise this question is to depart from everyday attitudes. An affirmation of the form ‘if p then q’ is commonly felt less as an affirmation of a conditional than as a conditional affirmation of the consequent…. If, after we have made such an affirmation, the antecedent turns out true, then we consider ourselves committed to the consequent, and are ready to acknowledge error if it proves false. If on the other (...) hand the antecedent turns out to have been false, our conditional affirmation is as if it had never been made. (shrink)

Designed to provide scientific personnel, policymakers, and the public with a succinct summary of the public aspects of scientific issues, this book focuses on how values and science intersect and how social values can be brought to bear on complex technical enterprises. Themes examined include: (1) relation of science and technology to human values (citing ways science and technology influence social philosophies); (2) changing sociotechnical milieu (describing recent trends toward politicization in technical endeavors); (3) complexion of science and social sciences (...) (surveying the attributes of the social sciences); (4) professionalism and responsibility (exploring the need for stewardship); (5) architectonics of technical trust (examining the interlocking elements of technical trust and focusing on the recombinant DNA controversy); (6) societal guidance of inquiry and application (discussing the possibilities and limits of scientific freedom); (7) systematic assessment for decision making (offering suggestions for dealing with fact/value distinctions); (8) social values and ethics (examining the role of values in decision making); (9) science and technology in the polis (reviewing ways of managing and reducing undue polarization in sociotechnical disputes); and (10) stewardship (suggesting needs and opportunities for exercising technical responsibility). An extensive bibliography is provided. (ML). (shrink)

Terence Parsons's informal theory of intentional objects, their properties, and modes of predication does not adequately reflect ordinary ways of speaking and thinking. Meinongian theories recognizing two modes of predication are defended against Parsons's theory of two kinds of properties. Against Parsons's theory of fictional objects, I argue that no existing entities appear in works of fiction. A formal version of Parsons's theory is presented, and a curious consequence about modes of predication is indicated.

Traditionally, identity and supervenience have been proposed in philosophy of mind as metaphysical accounts of how mental activities (fully understood, as they might be at the end of science) relate to brain processes. Kievet et al. suggest that to be relevant to cognitive neuroscience, these philosophical positions must make empirically testable claims and be evaluated accordingly – they cannot sit on the sidelines, awaiting the hypothetical completion of cognitive neuroscience. We agree with the authors on the importance of rendering these (...) positions relevant to ongoing science. We disagree, however, with their proposal that a metaphysical relationship (identity or supervenience) should “serve as a means to conceptually organize and guide the analysis of neurological and behavioral data” (p. 7). Instead, we advance a different view of the goals of cognitive neuroscience and of the proper means of relating metaphysics and explanation. Our central objection to the psychometric approach deployed by Kievet et al. is that the formal models only account for correlations between variables (measurements) and do not aid in explaining phenomena. Cognitive neuroscience is concerned with the latter. We develop this point in section 2 in which we present what we find to be problematic in their proposed models. In section 3 we advance an account of what is required to explain phenomena: (a) providing an adequate description of a phenomenon; and (b) characterizing the mechanism responsible for it. In doing so we will characterize a version of the identity theory, heuristic identity theory (HIT) which figures centrally in developing such explanations and illustrate its role in what we take to.. (shrink)

SummaryScholars of international relations generally invoke Hobbes as the quintessential theorist of international anarchy. David Armitage challenges this characterisation, arguing that Hobbes is regarded as a foundational figure in international relations theory in spite of as much as because of what he wrote on the subject. Thus, for Armitage, Hobbes is not the theorist of anarchy that he is made out to be. This article agrees with the general thrust of Armitage's critique while maintaining that it is still possible to (...) imagine Hobbes as a theorist of anarchy. Hobbes is a theorist of anarchy, not in a political sense, but in a metaphysical sense. This conception of anarchy is a reflection of a comprehensive theological account of reality that is grounded in an omnipotent God. Any historical inquiry into the foundations of modern international thought must take account of theology, because theology defines the ultimate coordinates of reality in terms of which the concepts of international thought are intelligible. (shrink)

A major approach to cancer research in the late twentieth century was to search for genes that, when altered, initiated the development of a cell into a cancerous state or failed to stop this development. But as researchers acquired the capacity to sequence tumors and incorporated the resulting data into databases, it became apparent that for many tumors no genes were frequently altered and that the genes altered in different tumors in the same tissue type were often distinct. To address (...) this heterogeneity problem, many researchers looked to a higher level of organization—to mechanisms in which gene products participated. They proposed to reduce heterogeneity by recognizing that multiple gene alterations affect the same mechanism and that it is the altered mechanism that is responsible for the cell developing one or more hallmarks of cancer. I examine how mechanisms figure in this research and focus on two heuristics researchers use to integrate proteins into mechanisms, one focusing on pathways and one focusing on clusters in networks. (shrink)

Hacking argues against van Fraassen's constructive empiricism by appeal to features of microscopic imaging. Hacking relies on both our practices involving imaging instruments and the structure of the images produced by these micropractices. Van Fraassen's reply is formally correct yet fundamentally unsatisfying. I aim to strengthen van Fraassen's reply, but must then extend constructive empiricism, specifically the central notion of "theoretical immersion." I argue that immersion is more analogous to entering a virtual reality than to learning a language. This metaphor (...) assimilates instrument-based practice as well as theoretical debate and explanation, and can provide an anti-realist view of our micro-practices consonant with constructive empiricism. (shrink)

This book argues that Cicero deserves to be spoken of with more respect and to be studied with greater care. Using Plato’s influence on Cicero’s life and writings as a clue, Altman reveals the ineffable combination of qualities—courage, originality, intelligence, sparkling wit, subtlety, deep respect for his teacher, and deadly seriousness of purpose—that enabled Cicero not only to revive Platonism, but also to rival Plato himself.

The Quest for Meaning explores the deep-seated human need to create a life that is meaningful. In an effort to understand this need, author William Cooney examines the works of philosophers from Plato to Sartre as well as the insights of artists, poets, writers, psychologists, and film-makers. He discusses the nature of humanness, creation, freedom, and choice, all of which are facets of a meaningful life. Cooney also addresses postmodernism, arguing that it does not offer real guidance for those (...) seeking a life of significance. Maintaining that some ways of creating meaning are preferable to others, he concludes that it is up to each individual to craft a meaningful life and that this process must take place within a context of giving and receiving. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:William Righter GOLDEN RULES AND GOLDEN BOWLS In one of his last interviews Michel Foucault remarked on the relation of any search for a perfect existence to the source of those forms of obligation which paradoxically make it possible, and hence on the variable shapes of the interdependence of the beauty of life with the moral understanding by which we accept the nature of our obligations. He sees (...) this in terms of the way these obligations establish themselves, by recognition and submission, by what he calls "the mode of subjection {mode d'assujettissement), that is, the way in which people are invited or incited to recognize their moral obligations. Is it, for instance, divine law, which has been revealed in a text? Is it a natural law, a cosmological order, in each case the same for every living being? Is it a rational rule? Is it the attempt to give your existence the most beautiful form possible?"' If we wish to do something like finding the most beautiful form of life, we face problems of moral calculation, we must formulate principles of choice, and above all learn to make our submission to the necessity such principles may imply. "What is the mode d'assujettissementT'' Foucault asks: It is that we have to build our existence as a beautiful existence; it is an aesthetic mode. You see, what I have tried to show is that nobody is obliged in classical ethics to behave in such a way as to be truthful to their wives, to not touch boys and so on. But if they want to have a beautiful existence, if they want to have a good reputation, if they want to be able to rule others, they have to do that. So they accept those obligations in a conscious way for the beauty or glory of existence. The choice, the aesthetic choice or political choice, for which they"decide to accept this 262 WtLLiAM Righter263 kind ofexistence—that's the mode d'assujettissement. It's a choice, a personal choice.2 At some levels this choice looks quite simply like a calculative sacrifice of the lesser thing for the greater. But an important element of the incommensurate enters into the choice. The beauty, the glory of the thing far surpasses the small normative commitments one undertakes for its sake, both in degree and in belonging to another and superior order. The beautiful form of existence is separated by some enormous gulffrom those social and human arrangements that must be submitted to it. Yet one is aware of basing the beauty of life on these lesser forms of obligation. Many things may be subjected, as one sees in The Golden Bowl, to the greater principle, where almost anything may be sacrificed as long as the beauty of that principle is in view. But how do we assess this disproportion and see the propriety of subjection established? For subjection could come to serve many principles, and in The Golden Bowl we shall observe the studied operation of subjection in a world where principles are continuously and meticulously examined and re-examined. The Foucaultian conjunction of obligation and the "glory of existence" touches the heart of a work where the fascination with the incommensurate moves uneasily between alternative versions of that glory. What is the overriding principle that underwrites and legitimates such anexistence?James's involvementwith such a "particular attaching case" seems to proceed from the fullest sense of the difficulty, from the fullest rendering of incompatible versions ofthat existence, brought into the closest and tightest formalbond. The very simplicity of the action somehow produces an enforced contemplation of a bizarrely closed world, in which the dynamics of the two marriages shape a conflict that seems inevitable, even strangely natural. It can be expressed in a few words. A widowed American millionaire, Adam Verver, has in his late forties retired to the life of a collector of objects of art. In his travels with his daughter Maggie, they collect also ahusband forher, a Roman prince. To ease the consequences for her father Maggie promotes his marriage to her closest school friend Charlotte. Unknown to the Ververs she and the Prince were once lovers... (shrink)

A number of philosophers have defended the view that mental or psychological verbs share a certain distinctive logical feature, though there is disagreement as to exactly what feature it is. Harold Morick has recently accused several of these philosophers of having “ignored or misinterpreted” verbs of a certain kind, in their search for this characteristic trait of mental verbs.The verbs he is talking about are those that represent some of a person's activities, which are physical activities but which that person (...) must allegedly be conscious in order to perform. Since a “basic sentence” containing such a verb typically entails the existence of its object's referent, Morick contends, the verb in question fails io count as “intentional” either on Brentano's definition, on Chisholm's, or on mine. Thus, Brentano, Chisholm and I have failed to make good our claim that all mental or psychological verbs are intentional. (shrink)

No livro Plato’s Philosophers, Catherine Zuckert olha para o Timeu de Platão de maneira renovada e revive implicitamente a tese de A. E. Taylor, segundo a qual Timeu não fala por Platão. Taylor devotou seu escrupuloso comentário de 1927 para construir esse argumento, o qual, porém, encalhou diante da questão colocada dez anos depois por F. M. Cornford, no livro Plato’s Cosmology : “Qual poderia ter sido o seu motivo?” O motivo de Platão era tanto pedagógico quanto parmenídico: assim como (...) a deusa expõe o peregrino à “Via da Opinião” depois da revelação da “Verdade”, assim também o Timeu de Platão expõe o leitor a um relato poético de uma cosmologia baseada na visão – outro kosmo/j e0pe/wn a0pathlo/j – depois da revelação, feita na República V-VII, da ontologia platônica puramente inteligível. (shrink)