10 resultados para Mathematics -- Philosophy

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This article starts by identifying the crucial importance of the notion of historical handicap for the present-day social sciences of Latin America. Such notion is not an original invention made by Latinamericanists. On the contrary, I demonstrate that the genealogy of the notion of historical handicap must be sought in the tradition of Western political philosophy. Such genealogy must take into account the way it was integrated into ethnological descriptions. When and how did the Other become the backward, the primitive? While this relation was secondary for ancient Greek thought, theories of historical development became the main source of ethnological categories in the modern era. Interestingly enough, this modern synthesis suited the practical purpose of justifying two successive waves of European imperialistic: the era of discoveries, and 19th century colonialism. The article concludes by raising questions about the present role and application of the social sciences.

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ABSTRACT In section XII of the First Inquiry, Hume refers to the two Hellenistic schools of skepticism (Academic and Pyrrhonian) to present his own view of skepticism, which, however, depends on the ancient skeptics mainly indirectly. Hume's view of skepticism depends crucially on Descartes and post-Cartesian philosophers such as Pascal, Huet, Foucher and Bayle, who reacted skeptically to major Cartesian doctrines but followed one version or other of Descartes's methodical doubt. Although all these post-Cartesian philosophers are relevant in section XII, I focus on the topics in which Descartes himself-besides his skeptical followers-seems directly relevant. After an introductory section (I) on Julia Annas' and Richard Popkin's views of Hume's relation to, respectively, ancient and modern skepticism, I turn to section XII and examine what Hume calls (II) "consequent skepticism about the senses," (III) "antecedent skepticism," and (IV) "Academic skepticism."

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Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

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In this paper, I aim at relating passions to evil in Kant's philosophy. I begin by explaining the difference between affects and passions in the textAnthropology from a Pragmatic Point of View. Kant claims that both affects and passions are illnesses of the mind, because both affect and passion hinder the sovereignty of reason. I show that passions are worse than affects for the purpose of pure reason. Second, I relate affects and passions to the degrees of the propensity to evil in theReligion. I analyze the idea of an ethical community as a way to overcome the evil, which goes beyond political and anthropological solutions suggested by Kant.

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Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

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Goethe's philosophy of creativity revolves around what he called das Dämonische. This essay is not meant as a definition or an explanation of demonic creation, but instead presents a demonic work par excellence, as the term "demonic" is defined by Goethe in the Elegy from Marienbad. The process of the creation of this work, as it is described by Goethe, also represents a strange exorcism, as the entire daemonic creative force of the author is transposed in this lyrical masterpiece of German and universal literature. After writing the Elegy Goethe, it is no longer demonic.