RESUMEN Este artículo apunta a someter a consideración si existe o no un fundamento histórico-filosófico para la hipótesis de una homonimia no azarosa entre "escala de tiempo" y "escala musical". Un examen minucioso de ciertos pasajes del diálogo Timeo muestra que Platón fue el primero en sentar las bases para el concepto de tiempo, definido como número, al incorporar el concepto de 'analogía' o proporción, el cual fue desarrollado por los pitagóricos en el marco místico y teórico de los principios (...) emergentes de la armonía tonal. La teoría pitagórico-platónica de proporciones subyace -como intentaré probar- en el concepto aristotélico de tiempo y, en cuanto tal, en la representación tradicional del tiempo como parámetro y escala del movimiento. ABSTRACT This article aims to unpack the query of whether or not there is a historical- philosophical basis for the hypothesis of a non-random homonymy between 'time scale' and 'musical scale.' A deeper look into certain passages of Plato's dialog Timaios, shows that he first laid the foundation for the concept of time, defined as number, by incorporating the concept of 'proportion' or 'analogy', which was developed by the Pythagoreans in the mystical and theoretical frame of the rising principles of tonal harmony. The pythagorean-platonic theory of proportion underlies -as I will try to prove- the aristotelian concept of time, and thus the traditional representation of time as a parameter and scale of movements. (shrink)

The mathematical works of the French philosopher Charles de Bovelles have received little attention from historians of scientific thought. At the University of Paris, Bovelles studied under Jacques Lefèvre d'Étaples, sharing with him a high regard for the Christian Neoplatonic philosophy of Nicholas of Cusa. One aspect of Cusanus's philosophy was particularly favoured by Lefèvre and Bovelles: the use of geometrical symbolism to provide mathematical guidance to the divine. While Lefèvre was preparing an edition of Cusanus's works , Bovelles wrote (...) a treatise of his own, in which the geometry of the five polyhedra was used to provide an approach to the mystery of the Trinity. Seen in the context of Renaissance syncretism of Platonism and Christianity, Bovelles's treatise adds a theological layer of interpretation to the literal meaning of the polyhedral physics described by Plato in the Timaeus. In so doing, it contributes to the discussion of a problem that was later to concern several Renaissance philosophers and cosmologists, including, at the end of the century, Johannes Kepler. (shrink)

In this paper, we analyze two episodes from an inquiry-based didactical research; the complete analysis of our research data is still ongoing. By taking into consideration various developments from the history of the geometry of space-time, our general aim is to explore high school students’ conceptions about measurement of length and time in relatively moving systems, and lead the students to reconsider these conceptions in an attempt of constructing a new metric for space-time. The episodes are extracted from long interviews (...) with two couples of students, based on a carefully designed fictional scenario. Two main strategies have been identified and are analyzed in the paper: one of them relies on imagination and intuition; the other one makes use of preexisting school mathematical knowledge, in arriving to a simplified formula of a Minkowskian metric. (shrink)

Near the end of his speech, Timaeus outlines a theory of bodily health and disease which has seemed to many commentators loosely unified or even inconsistent . But this section is better unified than it has appeared, and gives us at least one important insight into the workings of physical causality in the Timaeus. I argue first that the apparent disorder in Timaeus’s theory of disease is likely a deliberate effect planned by the author. Second, the taxonomy of disease in (...) the passage consists of one genus subsuming two species. Third, in Timaeus’s theory, health lies between perfect stability and a chaos of all possible motions; this indicates a conception of health as the activation of the body's powers in the right way. A power is a property directed towards bringing about some change. Fourth, the activation of these powers can change depending on the location of their possessors. This last point shows that causation among the physical items in the Timaeus involves structures as well as pushes. (shrink)

There is a striking resemblance between the physical theory of Plato'sTimaeus and that of the Stoics; striking enough, indeed, to warrant the supposition that the latter was substantially influenced by the former. In attempting to trace the main lines of this influence, scholars have tended to focus attention almost exclusively on the Stoics' choice and characterization of the world's ultimate constituents: a rational principle that pervades and controls a material principle. In this paper, I offer some suggestions about how the (...) early Stoics may have reacted as readers to Plato's literary presentation of the dialogue's cosmogonic myth. On this basis I consider the proposal that the crucial philosophical appeal of the Timaeus for the Stoics – and perhaps the reason it attracted their interest in the first place – lay not in its claims about the Receptacle and World Soul, but rather in its portrayal of the Demiurge who designed the cosmos. (shrink)

The paper considers Plato’s theory of language through the prism of the Timaeus’ metaphysics. It is argued that the apparent contradictions of Plato’s philosophy of language are the consequence of the two-fold nature of language, and that the metaphysical scheme proposed by Plato in the Timaeus can shed a light on his coherent theory of language. The linguo-metaphysical isomorphism of the Timaeus presupposes that (1) words and material elements have their own meaning and nature respectively; (2) they can be reduced (...) to an infinite variety of amorphic sounds and receptacle; (3) the participation in truth is possible only at the level of narrative and universe. According to this scheme the universe (κόσμος), as well as any speech (λόγος), can be explained by the reduction to its constituent elements, but it will be only necessary explanation. Whereas for Plato, the true understanding of cosmos and logos is possible only on the level of the coherent unity of the whole, which represents the ideal paradigm in the best possible way. (shrink)

_ Source: _Volume 61, Issue 1, pp 43 - 59 Contemporary debate on Plato’s cosmogony often assumes that the ‘literal’ reading of the _Timaeus_ yields an account of creation, while the view that the cosmos always existed is non-literal. In antiquity, Taurus has been seen as a forerunner of the ‘non-literal’ interpretation. This paper shows, on the contrary, that Taurus’ argument for the sempiternity of the cosmos is a literalist one, relying on a strict linguistic analysis of _Timaeus_ 28b6-8.

El concepto de _physis_ y sus derivados aparecen cientos de veces en los diálogos de Platón. Dado el carácter poco sistemático de su autor y los muchos años que dedicó a la escritura filosófica, no debe sorprender la diversidad de sentidos en que emplea un término ya de por sí complejo y polisémico. Por otra parte, Platón recoge, sintetiza y reelabora algunas de las concepciones fundamentales de la _physis_, siendo de especial relevancia las de los filósofos pluralistas, interesándose por los (...) elementos constitutivos del mundo físico y tomando partido en la discusión en torno a su carácter, bien mecánico, bien teleológico. En este estudio se analiza tanto la asimilación platónica de la física presocrática, como la influencia ejercida en el planteamiento aristotélico, especialmente por lo que respecta a la causalidad final y al principio del movimiento. (shrink)

It is a notion commonly acknowledged that in his work Timaeus the Athenian philosopher Plato (_c_. 429–347 BC) laid down an early chemical theory of the creation, structure and phenomena of the universe. There is much truth in this acknowledgement because Plato’s “chemistry” gives a description of the material world in mathematical terms, an approach that marks an outstanding advancement over cosmologic doctrines put forward by his predecessors, and which was very influential on western culture for many centuries. In the (...) present article, I discuss inter-transformations among Plato’s four types (fire, air, water, and earth) as well as the interpretation they received in the literature. I find that scientists and scholars generally emphasized (and often misunderstood) mathematical aspects of these “reactions” over the philosophical ones. I argue that Plato’s “chemistry” in fact bears on crucial topics of his philosophical system, such as Forms, Becoming, causation and teleology. I propose that consideration of these doctrines help to understand not only the sense of his “chemical” reactions, but also the reason why their stoichiometry is by surface balance and is restricted only to types that come to be and pass away but not to those that provoke the inter-transformations. (shrink)

The present paper focuses on some aspects of the Neoplatonist literary-metaphysical theory, which has clearly been expressed in the anony­mous Prolegomena to Plato’s philosophy and further confirmed in Proclus’ exegesis of the Timaeus. Thus, this contribution, examines and compares several passages from the Prolegomena and from Proclus’ Commentary on the Timaeus with a view to showing that it is legiti­mate to speak of a certain cosmogony of the Platonic dialogue that is analogous to that of the macrocosm. Moreover, the analogy (...) between macrocosm and microcosm makes it possible to further investigate the similarity between the λόγος-ζῷον of the Demiurge and that of Timaeus, on the one hand, and the reality which the λόγος expresses, on the other. This similarity turns out to be both structural/morphological and content-related/semantic. Thus, by combining the natural and theo­logical science, the analysis of the “generation” of the macrocosm and microcosm brings out the strongly analogical nature of Plato’s dialogues, which is particularly visible in the Timaeus. (shrink)

In this paper, I argue that Plato conceives self-motion as non-spatial in Laws X. I demonstrate this by focusing on the textual evidence and by refuting interpretations according to which self-motion either is a specific type of spatial motion or is said to require space as a necessary condition for its occurrence. Moreover, I show that this non-spatial understanding differs from the identification of the soul’s motion with locomotion in the Timaeus. Consequently, I provide an explanation for this difference between (...) the Timaeus and Laws X by considering developmentalist and contextualist viewpoints. (shrink)

In this paper I show that Proclus is an adherent of the Classical Model of Science as set out elsewhere in this issue (de Jong and Betti 2008), and that he adjusts certain conditions of the Model to his Neoplatonic epistemology and metaphysics. In order to show this, I develop a case study concerning philosophy of nature, which, despite its unstable subject matter, Proclus considers to be a science. To give this science a firm foundation Proclus distills from Plato’s Timaeus (...) the basic concepts Being and Becoming and a number of basic propositions, among others the quasi-definitions of the basic concepts. He subsequently explains the use of these quasi-definitions, that are actually epistemic guides, in such a way that he obtains a connection between a rational and an empirical approach to the natural world. A crucial task in establishing the connection is performed by the faculty of doxa and by geometrical conversion. The result is that Proclus secures a universal, necessary and known foundation for all of philosophy of nature. (shrink)

In his opening speech, Timaeus argues that the cosmos must be the product of a craftsman looking to an eternal paradigm. Yet his premises seem at best to justify only that the world could have been made by such a craftsman. This paper seeks to clarify Timaeus’ justification for his stronger conclusion. It is argued that Timaeus sees a necessary role for craftsmanship as a cause that makes becoming like being.

This study considers the contribution of Francesco Patrizi da Cherso to the development of the concepts of void space and an infinite universe. Patrizi plays a greater role in the development of these concepts than any other single figure in the sixteenth century, and yet his work has been almost totally overlooked. I have outlined his views on space in terms of two major aspects of his philosophical attitude: on the one hand, he was a devoted Platonist and sought always (...) to establish Platonism, albeit his own version of it, as the only currect philosophy; and on the other hand, he was more determinedly anti-Aristotelian than any other philosopher at that time. Patrizi's concept of space has its beginnings in Platonic notions, but is extended and refined in the light of a vigorous critique of Aristotle's position. Finally, I consider the influence of Patrizi's ideas in the seventeenth century, when various thinkers are seeking to overthrow the Aristotelian concept of place and the equivalence of dimensionality with corporeality. Pierre Gassendi , for example, needed a coherent concept of void space in which his atoms could move, while Henry More sought to demonstrate the reality of incorporeal entities by reference to an incorporeal space. Both men could find the arguments they needed in Patrizi's comprehensive treatment of the subject. (shrink)

Plato's account of the making of the world by a supreme divinity has often been felt to foreshadow the natural theology associated with orthodox western religion. This paper examines some significant ways (having more than merely antiquarian interest, it is hoped) in which the Timaeus scheme differs from more familiar orthodoxy.

A partire dall’analisi di alcuni passi del Timeo, il testo propone lo studio delle cause e dei tipi di infermità che affliggono la salute umana al fine di mostrare che la maniera in cui il filosofo concepisce le malattie è una chiave per approfondire l’antropologia e l’etica dell’ultimo Platone. Presupposto della ricerca è la visione olistica che caratterizza il Timeo, in cui la condizione umana influenza il livello socio-politico e il livello cosmico, i quali, a loro volta, condizionano e sono (...) condizionati dalla presenza dell’uomo. Per finalizzare lo studio abbiamo circoscritto l’analisi ai passi 69c-90c del Timeo. Starting with the analysis of some Timaeus passages, the text proposes the study of the causes and of the types of infirmity that afflict human health in order to demonstrate that the way the philosopher conceives illnesses is a key to get a deeper knowledge of the anthropology and ethics of the last Plato. Premise of the research is the holistic vision that characterizes the Timaeus, in which the human condition affects the socio political level and the cosmic level which, in their turn, affect and are affected by the human presence. To finalize the study, we analyzed the pages 69c-90c of the Timaeus. A partire dall’analisi di alcuni passi del Timeo, il testo propone lo studio delle cause e dei tipi di infermità che affliggono la salute umana al fine di mostrare che la maniera in cui il filosofo concepisce le malattie è una chiave per approfondire l’antropologia e l’etica dell’ultimo Platone. Presupposto della ricerca è la visione olistica che caratterizza il Timeo, in cui la condizione umana influenza il livello socio-politico e il livello cosmico, i quali, a loro volta, condizionano e sono condizionati dalla presenza dell’uomo. Per finalizzare lo studio abbiamo circoscritto l’analisi ai passi 69c-90c del Timeo. (shrink)

Two symmetry arguments are discussed, each purporting to show that there is no more room for a preferred division of spacetime into instants of time in general relativistic cosmology than in Minkowski spacetime. The first argument is due to Gödel, and concerns the symmetries of his famous rotating cosmologies. The second turns upon the symmetries of a certain space of relativistic possibilities. Both arguments are found wanting.

Hartshorne and Reese thought that in the Timaeus Plato wasn’t quite a panentheist—though he would have been if he’d been consistent. More recently, Cooper has argued that while Plato’s World Soul may have inspired panentheists, Plato’s text does not itself describe a form of panenetheism. In this paper, I will reconsider this question not only by examining closely the Timaeus but by thinking about which features of current characterizations of panentheism are historically accidental and how the core of the doctrine (...) might most fruitfully be understood. I’ll argue that there is a polytheistic view that deserves to be called panentheistic and that Plato’s Timaeus describes such a view. (shrink)

A standard approach to examining Deleuze's concept of difference in Difference and Repetition is to follow his critique of representation through an overturning of Platonism, which Deleuze finds to be the definitive task of philosophy after Nietzsche. While engaging this largely critical project, however, there is a tendency to overlook the dimensions of Platonism that Deleuze rehabilitates in a differential and immanent register. This paper aims to recover the essential dimensions of Platonism at the very heart of Deleuze's philosophy of (...) difference. This recovery is accomplished by distinguishing Nietzsche's overturning of Platonism through his evaluation of the reactive politics of the Idea from Deleuze's own reversal of Platonism through his evaluation of the active politics of simulacra. (shrink)

Timaios diyalogu, genellikle Platon’un kozmolojik ve teolojik bir metni olarak ele alınır. Metin ilk bakışta evrenin ve insanın kökeni sorununu Tanrı’nın mahiyeti çerçevesinde ele alan bir diyalog olmasına karşın temelde etik-politik değerlerin kozmik bir anlatıya ve Tanrı’nın varlık ve niteliğine dayanılarak savunulmasını içerir. Bununla birlikte Platon’un metafizik sisteminde insan-polis-kozmos birbirinden kopmaz bir şekilde bağlantılı bir duruma sahiptir. Bundan ötürüdür ki Timaios diyalogu etik-politikanın kozmoloji ve teolojiyle iç içe geçtiği bir metindir. Bizim göstermek istediğimiz evrenin kuruluş sürecinin nasılından ziyade bu anlatının (...) ‘niçin’i ve kozmostaki düzenliliğin ereği ile Platoncu etik-politik kavrayışın kopmaz ilişkisidir. (shrink)

This dissertation explores Aristotle’s use of teleology as a principle of explanation, especially as it is used in the natural treatises. Its main purposes are, first, to determine the function, structure, and explanatory power of teleological explanations in four of Aristotle’s natural treatises, that is, in Physica (book II), De Anima, De Partibus Animalium (including the practice in books II-IV), and De Caelo (book II). Its second purpose is to confront these findings about Aristotle’s practice in the natural treatises with (...) the theoretical picture of the structure of teleological explanations gained from Aristotle’s theory of scientific demonstration. For this purpose a new interpretation of Analytica Posteriora II.11 is presented. This study thereby contributes to recent scholarship on the relation between Aristotle’s philosophy of science and his philosophy of nature, while at the same time adding to our knowledge of Aristotle’s notion of teleology in terms of its explanatory merits and limits. (shrink)

Despite Diotima’s irresistible virtues and attractiveness across the millennia, she spells trouble for philosophy. It is not her fault that she has been misunderstood, nor is it Plato’s. Rather, I suspect, each era has made of Diotima what it desired her to be. Her malleability is related to the assumption that Plato invented her, that she is a mere literary fiction, licensing the imagination to do what it will. In the first part of my paper, I argue against three contemporary (...) ‘majority views’ about Diotima that I regard as false. The first is that we can be certain she is fictional;1 a second is that Diotima is our best evidence for Plato’s feminism; the third, that she is Plato’s mouthpiece for the higher mysteries in the Symposium. After I have set aside what I regard as false, I proceed in the second half of my paper to develop Diotima’s positive contribution to philosophical psychology, her naturalistic account of the psyche as mortal, unified, and developmental. Whether the view Plato assigns to her is one that he held I do not pretend to know; but it is a powerful, defensible, and coherent view that inspired positive aspects of Freudian psychology in the twentieth century. Freud’s insight, in fact, makes clear how erōs can be developed in relation to the bad as well as the good. (shrink)

A commentary on the Symposium as a challenge and a gift to Athens. I begin with a reflection on three dates: 416 bce, the date of Agathon’s victory party, c. 400, the approximate date of Apollodorus’ retelling of the party, and c. 375, the approximate date of the ‘publication’ of the dialogue, and I argue that Plato reminds his contemporary Athens both of its great poetic and legal and scientific traditions and of the historical fact that the way late fourth (...) century Athens appropriated them in some way led to the city’s demise at the turn of the century; thus the dialogue is Plato’s challenge to his contemporary Athens to recognize and overcome its flawed relation to its cultural resources. Heard in this way, the key moments are Aristophanes’ implied critique of Pausanias and Eryximachus and Socrates’ implied critique of Aristophanes and Agathon. Proceeding by a close reading, I argue that Plato exposes, for those moved to rise to his challenge, the failure of his great predecessors to conceive the divine in a way that, worthy of the height and otherness divinity requires, can provide substantive orientation for the burgeoning new reason that animates the city’s culture. (shrink)

The article tries to prove that the famous formula "epekeina tês ousias" has to be understood in the sense of being beyond being and not only in the sense of being beyond essence. We make hereby three points: first, since pure textual exegesis of 509b8–10 seems to lead to endless controversy, a formal proof for the metaontological interpretation could be helpful to settle the issue; we try to give such a proof. Second, we offer a corollary of the formal proof, (...) showing that not only self-predication of the form of the Good, but of any form is not possible, that is: no form of F has the form of F. Third, we apply Spinoza’s distinction between an ens imaginarium and a chimaera to Plato’s Idea of the Good. (shrink)