citation platon mathématiques

citation platon mathématiques

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Inhalt der "Politeia" Allgemein Ausbildung von Wehr- und Lehrstand Leben des Wehrstandes Analogie von Seele und Staat in ihrem Aufbau Verfallsformen des Staates 4. Title: Comprendre les mathématiques pour comprendre Platon - théétète (147d-148b) Authors: Salomon Ofman (IMJ) (Submitted on 11 Aug 2014) Abstract: In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Therefore, discussing this issue the problem of interaction of philosophy and mathematics in the teachings of Plato should be taken into consideration. And the same is true of Aristotle and Bekker numbers. To substantiate his point of view, the author draws the works of contemporary experts in the field of philosophy of mathematics. Sankt Augustin: Academia Verlag, 1995. This question was investigated in antiquity, a substantial and decisive role in this respect was played by the Platonic doctrine. Über dem Eingang des Gebäudes soll gestanden haben: „Niemand trete ein ohne Kenntnis der Geometrie“. Only one... A blog is a cost-effective way of driving traffic to your business’s website. In fact, these toga-wearing rebels have special citation styles of their own known as Stephanus numbers (Plato) and Bekker numbers (Aristotle). Als junger Mann verschrieb sich Platon der Politik, wurde von der politischen Führung Athens jedoch enttäuscht. distinction between form and mathematical numbers, arguing that mathematical numbers alone are cardinals, by reference to certain non-technical features of a set-theoretical approach and other considerations in philosophy of mathematics. The advantage here is that people with different editions of the same text can use the same numbers. Les mathématiques ne sont pas une moindre immensité que la mer. 4. I show that the receptacle fulfils its main task–allowing the elements qua images of the Forms, Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Pp. Create an account to enable off-campus access through your institution's proxy server. The compulsion of proofs is an ancient idea, which plays an important role in Plato’s dialogues. Me 82-85). Thus, Plato’s critique of dianoetic is a not a critique of mathematics, as such, but of mathematicians. Plato's view of the nature of mathematical objects will be seen to be a metaphorical way of saying what Aristotle says logically, and is entirely appropriate to the aims and methods of his contemporary mathematicians. Plato's Mathematics P. Pritchard: Plato's Philosophy of Mathematics. If you read a text by Plato, you may notice numbers and letters in the margins. NASA ADS; Bookmark. At Parmenides 143a-4a the existence of numbers is proven from our capacity to count, whereby I establish as Plato's the theory that numbers are originally ordinal, a sequence of forms differentiated by position. Annotations to the Speech of the Muses (Plato Republic 546b-C). We suggest that clarifying the nature of philosophy supersedes the question of knowledge as the main ambition of the "Theaetetus". Er verurteilte dessen Hinrichtung und ging danach auf Reisen, die ihn u.a. Quelle est la citation la plus longue sur « mathématiques » ? Elenchus and Mathematics: A Turning-Point in Plato's Philosophical Development. (. Kallikles i geometria. A survey of the contemporary debate over the identity of the objects of dianoia yields three criteria a successful interpretation should meet. basis for the synoptic vision of all the mathematical sciences. CiteScore values are based on citation counts in a range of four years (e.g. ... Platon Un mathématicien n'a pas parfaitement compris ses propres travaux tant qu'il ne les a pas clarifiés au point de pouvoir aller dans la rue les expliquer à la première personne venue. To cite one of Plato’s dialogues, then, you will need to give the title, a section number, and a letter: Socrates describes those who trust writing as naïve (Phaedrus, 274c). ‘Mathematical Platonism’ Versus Gathering the Dead: What Socrates Teaches Glaucon &Dagger. a provocation, moving us to want to begin the "longer way" and to make use of its conceptual resources to rethink Socrates' images? In contemporary philosophy it is, The digression of Plato’s Theaetetus (172c2–177c2) is as celebrated as it is controversial. Einführung zu Platon a) Biographie b) Platons Werke 2. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. For this reason the first part of this dissertation must comprise a detailed analysis of these differences, along with some criticisms of those of Plato's modern interpreters who have not taken this point. Stephanus’s numbers are based on the edition of all of Plato’s works called Renaissance. Platonic Number in the Parmenides and Metaphysics XIII. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. Il est aussi un mathématicien, élève de In the second part the boy hazards the guess that the square with double area has a side of length 3, since 3 is between 2 and 4. vom Kaiser Justinian aufgelöst wurde. It is only when a source is unavailable that you should rely on this. Besonderen Wert legte PLATON auf Mathematik. Bernard Vitrac, « Les mathématiques dans le Timée de Platon : le point de vue d'un historien des sciences », Études platoniciennes, 2 | 2006, 11-78.. Référence électronique. If you read a text by Plato, you may notice numbers and letters in the margins. The Theory of Ideas and Plato’s Philosophy of Mathematics. Trusted by thousands of leading institutions and businesses, Citing Plato and Aristotle: Stephanus and Bekker Numbers. All further qualifications required for a full notion of space are derived solely from the content of the receptacle. For example, we could cite Aristotle’s famous Nicomachean Ethics as follows: Being happy takes a complete lifetime (Nicomachean Ethics, 1.7, 1098a16). The Publications Mathématiques de l'IHÉS is an international journal publishing papers of the highest scientific level. Print. The first issue concerns the question: was Plato really a proponent of present-day mathematical Platonism? J.-C., 347 - 346 av. (. Assonance and consonance are important parts of creative writing, especially poetry. He knew mathematicians create new concepts and goals as well as theorems, and abandon many along the way, and erase the creative process from their proofs. We call these “Stephanus numbers” or “Stephanus pagination.” They’re named after Henricus Stephanus, who published a famous edition of the collected works of Plato in 1578. Socrates shows Theaetetus that philosophy is not a demonstrative science, like geometry, but it is also not mere word-play, like sophistry. The Symposium. In an interesting passage in the Philebus , Plato associates pure beauty with geometrical forms created by certain measuring tools used both by mathematicians and carpenters. Schliesslich wurde er Schüler des Sokrates und bekannte sich zu dessen Lehre. Platon, Athènes, 428 - 427 av. Nevertheless, the answer is wrong. Thank you for subscribing to our newsletter! Recollection and the Mathematician's Method in Plato's Meno. La distinción entre la participación inmediata y la participación relacional. The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge. Just as Plato has Stephanus numbers, Aristotle has Bekker numbers (or Bekker pagination). Thus, the only methods demonstrated in the Meno are the elenchus and the hypothetical, or mathematical, method. La meilleure citation de Platon préférée des internautes. Puede resultar de interés asimismo el método de generación de los números a partir de lo par y lo impar, propuesto en la interpretación, This paper presents a new interpretation of the objects of dianoia in Plato’s divided line, contending that they are mental images of the Forms hypothesized by the dianoetic reasoner. This article defends the traditional view that the passage is indeed about these mathematical ‘intermediates’; and tries to show how the apparently different features of the second level are related, by focussing on Plato’s need to give an account, I argue that recollection, in Plato's Meno , should not be taken as a method, and, if it is taken as a myth, it should not be taken as a mere myth. Platon hatte großes Interesse am Leben nach dem Tod. Author and Citation Info ; Back to Top ; Naturalism in the Philosophy of Mathematics. Philosophy and Mathematics in the Teaching of Plato: The Development of Idea and Modernity. Journal Name: Apeiron Issue: Ahead of print. CiteScore values are based on citation counts in a range of four years (e.g. In the article I consider three issues: the Platonic theory of “two worlds”, the method of building a mathematical structure, and the ontology of mathematics. Seul deux choses sont infinies : l'univers et la bêtise humaine. die Akademie in Athen, die erst 529 n. Chr. describes mathematical reality, as Plato quite clearly expressed his views on math, according to which mathematical concepts objectively exist as distinct entities between the world of ideas and the world of material things. The Problem is Not Mathematics, but Mathematicians: Plato and the Mathematicians Again. However, since Plato's works are widely available for free online, you should never need a secondary citation for Plato. Mathematics, Mental Imagery, and Ontology: A New Interpretation of the Divided Line. Instead Socrates restricts himself to an indirect indication of its goals by his images of sun, line, and cave and to a programmatic outline of its first phase, the five mathematical studies. Platon dans son enseignement oral (vers 350 av. But this requires preparation – the very sort of preparation that is provided by both the mathematical and moral educations. Platon erwähnt sich selbst in seinem Werk überhaupt nur zweimal und das ganz am Rande. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. In the second part I attempt a better explanation of Plato's mathematical ontology, beginning with the most extensive passage in the dialogues, the triple image of Sun, Line and Cave in Republic. (. Die Dialogform des Werks ist für die Platon Interpretation ein erhebliches Hindernis. By properly Platonic, I mean one consistent with Plato's own theory, with appropriate extensions to take into account subsequent developments in mathematics. Mithilfe seiner „Zwei-Welten-Theorie“ (Bild 2) versuchte er, zu beantworten, wie man etwas erkennen kann und warum die Dinge so sind, wie sie sind. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Figure, Ratio, Form: Plato's Five Mathematical Studies. (. "La géométrie est la connaissance de ce qui est toujours." Be alerted of all new items appearing on this page. Codici Nel Pentateuco E Matematica Egizio-Platonica. El escrito tiene continuidad en un segundo artículo acerca del ser y la verdad en Platón. The address of a web page. DM 58. Arsen and White relate Plato’s philosophy to mathematics in his time, and to Aristotle. I maintain that while this interpretation correctly identifies the mathematical method with dialectic, ( i.e. The main purpose of the study of numbers, treated finally in relation to the other sciences, is to calculate ratios. Platon dans son enseignement oral (vers 350 av. If you’re still unsure of the best approach to use in your work, ask your supervisor or lecturer about how to list them. Mathematics and the Conversion of the Mind: Republic Vii 522c1-531e3. This vision is an essential preparation for dialectic because it makes mathematicians become aware of the limitations of the mathematics they have been engaged in but it also shows them how they can begin to overcome those limitations. In the first argument of Metaphysics Μ.2 against the Platonist introduction of separate mathematical objects, Aristotle purports to show that positing separate geometrical objects to explain geometrical facts generates an ‘absurd accumulation’ of geometrical objects. in Athen, wo er auch 348/347 v. Chr. The Meno and the Mysteries of Mathematics. We relate his account. the dramatic character Theodorus. Imprimer l'article Réactions à cet article. décodage citation : forum de mathématiques - Forum de mathématiques. J.-C. Soyez donc le premier ! The ‘beauty of figures’ is analysed as' something straight [εθ τι]… and round [περιφερς] and the two- and three-dimensional figures generated from these by [τρνοι] and ruler [κανσ7iota;] and set-squares [γωναι]' He continues: ‘For I maintain that these things are not beautiful in relation to something, as other things are, but they are always beautiful. Bonjour j'ai trouvé les signes qui correspondent aux lettres E,D,I,N,S,T et U mais je ne sais pas quoi faire ensuite pouvez-vous m'aider ? ISBN: 3-88345-637-3. to see the differences before we can begin to appreciate Plato's views, which must never be seen as applying to a revolutionary notion of mathematics . Platon stammte aus einer vornehmen, wohlhabenden Familie Athens. So the hypotheses of mathematics necessarily change through use — unless Benson is correct that Plato believed mathematics could reach the unhypothetical goals of dialectic. Univocity, Duality, and Ideal Genesis: Deleuze and Plato. I argue that the reason is rooted in the nature of moral explanations. Citing Plato with Stephanus Numbers. Archon gewesen, hatte also das höchste Staatsamt bekleidet. We call these ‘Stephanus numbers’ or ‘Stephanus pagination’. Two issues seem to be important here. Title. of practicing mathematicians. L'enseignement oral de Platon. A straightforward analogy: if the area is double, Glaucon in Plato's _Republic_ fails to grasp intermediates. 2. PLATON kam z… Personne n'a encore laissé de commentaire. One, Two, Three… A Discussion on the Generation of Numbers in Plato’s Parmenides. COMPRENDRE LES MATHÉMATIQUES POUR COMPRENDRE PLATON - THÉÉTÈTE (147d-148b). One of the viewpoints in this field is mathematical Platonism. First published Sun Aug 24, 2008; substantive revision Tue Mar 26, 2013 . Available from UMI in association with The British Library. (. (, arational. Page 1/1 Citations mathematique. -Platon Platon (424/423 avant Jésus Christ-348/347 BC) était un philosophe de la Grèce classique. The key is to use the numbers and letters in the margins of Plato’s works for citations. URL. Knowing the details of the pages, sections, etc., is not that important, though! Voir aussi PLATON (Histoire des maths), Extrait de Ménon par PLATON (Maths et extraits de textes littéraires) Citation précédente : ISOCRATE Platon wurde in Athen geboren als Sohn einer Aristokratenfamilie. At the start of 2021,The Publications Mathématiques de l'IHÉS has now become a fully open access journal, so going forward everyone will now have access to this important mathematical research. L'immortalité est sans doute un mot creux, mais un mathématicien a probablement plus de chances d'en jouir qu'un autre. Księga pamiątkowa dedykowana Profesorowi Romanowi A. Tokarczykowi, The Cambridge Companion to Plato's Republic, Mathematics and Necessity: Essays in the History of Philosophy. (. Alexander Nehamas and Pay Woodruff. Quotations by Plato, Greek Philosopher, Born 427 BC. Finally I respond to the objections that such a conception of number was unavailable in antiquity and that this theory is contradicted by Aristotle's report in Metaph . Since then, the numbering from this edition has become a standard part of published Plato texts. Republic, better meets those criteria than do any of the three main positions. I argue here that a properly Platonic theory of the nature of number is still viable today. Salomon Ofman. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and, One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. Aporta un enfoque original a la investigación de los procesos lógicos que condicionan que unas formas participen de otras. References & Citations. If you make a spelling mistake, did you “misspell” or “mispell” the word? If you read a text by Plato, you may notice numbers and letters in the margins. His works were published in three volumes. Methodological naturalism states that the only authoritative standards are those of science. commentary on Plato’s posit of Intermediates, provides good reason to conclude that Plato did posit them. It does so by making two claims: first, that Plato should posit the mathematical Intermediates because Forms and physical objects are ill suited in comparison to Intermediates to serve as the objects of mathematics; second, that their utility, combined with Aristotle’s, I argue against a formidable interpretation of Plato’s Divided Line image according to which dianoetic correctly applies the same method as dialectic. Wie weitgehend identifiziert sich Platon mit welcher seiner Figuren? Er gründete zwischen 387 und 367 v. Chr. and his refusal to deny his ignorance about knowledge. Philosophy of Gender, Race, and Sexuality, Philosophy, Introductions and Anthologies, Contemporary Encounters with Ancient Metaphysics, Księga życia i twórczości. For the ideal may seem difficult to reconcile with a Socratic conception of philosophy, and several scholars have accordingly suggested that it should be read as ironic and directed only at, Este trabajo pretende ser una referencia útil para los estudiosos de la filosofía de Platón. G.H Hardi (1877-1947, Angleterre) He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. The nature of philosophy is revealed in Socrates' activity of examination. Pp. In contrast to such views, I argue that recollection ought to be taken as an hypothesis for learning. I argue that, because they receive an extensive mathematical education alongside their moral education, the youths not only have a capacity for reason but that capacity is being developed in their early education. philosophical meanings. Plato's Geometric Hypothesis: Meno 86e-87b. of how we can speak of many particulars of the same kind, without assuming that they are imperfect copies, in the way sensible things can be imperfect copies, of forms. Interpretations of the argument have varied widely. Ratios and proportion form the, We examine the "Theaetetus" in the light of its juxtaposition of philosophical, mathematical and sophistical approaches to knowledge, which we show to be a prominent feature of the drama. This book is often quoted, but very seldom understood; or at least, those lessons which should be taken from it are rarely applied to Platonic exegesis. Platon war ein antiker griechischer Philosoph. The study of numbers, when treated independently of the other sciences, uses a particular conception of the nature of numbers to detach the mind from the influence of perceptible objects. Each page was then divided into five sections, which we indicate with the letters a-e. Mathematics and the Conversion of the Mind: Republic VII 522c1-531e. Platon, geboren 427 v. Chr. Formenlehre. is organised in a tree structure, starting from the PLATON Homepage. Current versions of the program PLATON for Windows are available from this site. In this article I analyze the issue of many levels of reality that are studied by natural sciences. demonstrates key platonic features, such as the use of the greatest kinds and the generation principle. (. Cite Plato’s “The Symposium” in the bibliography by listing the author, title, translator, city, publisher, year of publication and medium. In the absence of a title, some styles may ask for a summary of the source. To cite a text by Aristotle using Bekker numbers, you’ll need: Subscribe to our newsletter and get writing tips from our editors straight to your inbox. Besides provisional propositions, he calls concepts and goals also hypotheses. , the method of philosophy), it incorrectly identifies the mathematical method with dianoetic. I shall not be satisfied with the answer that the future rulers of the ideal city are to be educated in mathematics, so Plato is bound to give some space to the subject. J.-C. Vii + 191. Anyone who has read Plato’s Republic knows it has a lot to say about mathematics. Much of what will be found here can be found in Jacob Klein's Greek Mathematics and the Origin of Algebra, which will be extensively quoted and interpreted. Particularly interesting is the level of mathematics and the question of the relationship between mathematics and the structure of the real world. These sorts of explanations are rooted in the Forms and thus one can only understand those explanations when they have knowledge of the Forms. There are four main conclusions. If this is so, though, then we must rethink why the early moral education is. "Quem não é geômetra não entre!" In the third part, at Socrates’ prompting, the diagonal of the original square A is drawn within the second fourfold square B. Les mathématiques chez Platon et Kant Dans la Critique de la raison pure , Kant, à partir d’une lecture partielle de Platon, trouve que la philosophie platonicienne est opposée à la sienne, car, pense-t-il, en substance, elle se situe bien au-dessus de l’expérience humaine (1). The mathematical nature of the world has been considered since ancient times and is the subject of ongoing research for philosophers of science to this day. Aristotle's criticism of Plato's views is examined and found to make sense and to be appropriate to views which Plato could consistently have held. A particularly knotty question has been what status we should ascribe to the ideal of philosophy it presents, an ideal centered on the conception that true virtue consists in assimilating oneself as much as possible to god. J.-C., est un philosophe grec, contemporain de la démocratie athénienne et des sophistes, qu'il critiqua vigoureusement. Sugerencias sobre el modo de combinar las formas platónicas para superar las dificultades interpretativas del diálogo Parménides. (, and philosophical problem solving. PLATON POLITEIA - DER STAAT Inhalt 1. Is Plato a Coherentist? Export citation . Its subject concerns the incommensurability of certain magnitudes, in … Plato's Problem: An Introduction to Mathematical Platonism. Citation mathematique Sélection de 13 citations sur le sujet mathematique - Trouvez une citation, une phrase, un dicton ou un proverbe mathematique issus de livres, discours ou entretiens.. 1. Doesn't this pointed restraint function as. Informations pratiques. Citation : Un mathématicien est un aveugle qui, dans une pièce sombre, cherche un chat noir qui n'y est pas. Taken as a genuine platonic theory, the argument could have significant impact on how we understand Plato’s philosophy of mathematics in particular, and the ontology of the late dialogues in general – that numbers can be reduced to more basic entities, i.e the greatest kinds, in a way similar to the role the greatest kinds are assigned in the Sophist. It differs from the highest level in two respects. Every page in this edition was divided into equal columns, the inner column contained the text in Greek and the outer – its Latin translation. Rather, Plato takes dianoetic to be a misapplication of the mathematical method by a subset, The second highest level of the divided line in Plato’s Republic appears to be about the entities of mathematics—entities such as particular triangles. Bekker numbers are based on the page numbering used in this edition of Aristotle’s collected writings. Liste des citations de Platon classées par thématique. Then, it is argued that the mental images interpretation, in addition to proving consistent with key passages in the middle books of the, In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. CiteScore: 1.6 ℹ CiteScore: 2019: 1.6 CiteScore measures the average citations received per peer-reviewed document published in this title. Plato's Mathematics - Pritchard P.: Plato's Philosophy of Mathematics. Citation. starb, war ein Schüler des Sokrates und gemeinsam mit seinem Schüler Aristoteles der wohl einflußreichste griechische Philosoph. And since then, the page numbering from this edition has become a standard part of published Plato texts. For so-called "mathematical Platonism," see the category by that name (link below). Let us explain. From time to time, the journal will also publish thematic issues dealing with a … But Plato and Aristotle – the breakout stars of ancient Greek philosophy – don’t play by anyone else’s rules. As for citing Plato, as we say in the post, unless you are working with a style guide that suggests otherwise, you should use Stephanus numbers. Diagrams, Dialectic, and Mathematical Foundations in Plato. de Parménides 143e-144a. And since then, the page numbering from this edition has become a standard part of published Plato texts. Questo testo nasce da alcune indagini sul nesso tra matematica e filosofia in ambiente “accademico”. An Introduction to Assonance and Consonance, How to Cite an Artwork in Harvard Referencing, How to Come Up with Great Ideas for Your Blog (5 Top Tips), A book and chapter number from the collected Bekker edition, The page, section, and line numbers from the Bekker edition. briefly to mathematical developments by Plato's associates Theaetetus and Eudoxus, and then to the past 200 years' developments in geometry. (. I distinguish between two types of interpretation, corrective and non-corrective interpretations. Sign in | Create an account. Simple questions provoke equally simple replies, though the boy is sometimes puzzled and surprised by the answers he feels compelled to give. What Plato's, The unifying theme of this issue is Plato’s dialectical view of mathematical progress and hypotheses. XIII that Platonic numbers are collections of units. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather, In this paper, I reconsider the commonly held position that the early moral education of the Republic is arational since the youths of the Kallipolis do not yet have the capacity for reason. Examples: Jr., Sr., II, III, Esq., etc. Figure, Ratio, Form: Plato's "Five Mathematical Studies". PLATON (427 avant JC −347 avant JC) "Les nombres sont le plus haut degré de la connaissance. Measuring Humans Against Gods: On the Digression of Plato’s Theaetetus. 8?”. Fazit 1.Einführung zu Platon a)Biographie Über die Biographie Platons ist im Gegensatz zu seinem … Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. Die Ideenlehre PLATONs war das Ergebnis seiner lebenslangen Suche nach dem Unterschied zwischen der ewigen Wahrheit und dem, was der Mensch in der sichtbaren Welt wahrnimmt. So in the example above, we’re citing text from page 274, section c of the Stephanus edition. A Likely Account of Necessity: Plato's Receptacle as a Physical and Metaphysical Foundation for Space. Les symboles mathématiques + plus-moins: x: multiplié ÷ divisé / barre de fraction = ou ≠ égal ou inégal In dem Buch Body and Soul in Ancient Philosophy heißt es: „Die Unsterblichkeit der Seele ist eines von Platons Lieblingsthemen.“Er war fest davon überzeugt, dass „die Seele ihre jetzige Inkarnation überlebt, um gebührend belohnt oder bestraft zu werden“ — je nachdem, was für ein Leben der Mensch vor seinem Tod geführt hat. In the context of foundations of mathematics, so called ‘Gödel’s Platonism‘ is of particular interest. L'enseignement oral de Platon. ISBN: 3-88345-637-3. The function of the passage is to introduce a contemplative aspect of the life of philosophy into the dialogue that contrasts radically with the political-practical orientation characteristic of Protagoras, an aspect Socrates is able to isolate as such precisely because he is conversing with the mathematician Theodorus. In Plato’s writing Stepahnus numbers are used. APA, for instance, says you don’t need to include ancient Greek texts in the reference list at all as long as you clearly identify the version used in citations. PORTAIL CITE SCOLAIRE - Jean Renoir Bondy Toggle navigation. The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein.

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