In the sentence marked DK22 B52, Heraclitus describes a boy playing with small objects. The boy has the entire kingdom at his disposal and he himself is identified with the eon. This famous fragment has been interpreted in numerous ways both by classical philologists and philosophers. Its current interpretation is that it is a metaphor for human life. The child, not yet familiar with rules of social life, introduces elements of randomness and careless play into that life. Meanwhile, comparison of (...) Heraclitus’ sentence with the Old Indic tales, lets recognize in the sentence the mythological theme of the act of creation – God creating and governing the world. Such governing means establishing fundamental mathematical rights – the same rights that are applied in astronomical observations and scientific research as a whole. Hypothesis, that the ancient Indo-European culture affected – through India – Heraclitus, lets better understand this philosopher’s thought which harmonically combines elements of science, religion and arts. The India hypothesis also explains the aura of sublimity and holiness found in our tradition. The aura that was present in the late antiquity thinkers who acknowledged Heraclitus’ sentence and passed it to the Western literature. (shrink)

Abstract The great german Scholar, Eduard Zeller, suggested that the reference to male and female in Parmenides B12.5-6 was probably an allusion to the physical principles of `mortal opinion': Night and Light. This suggestion has been rejected by some scholars because such an association would lead us to admit that, in B12, male was associated with Night and female with Light, a theory which would be at odds with the supposed misogyny of Greek culture. However, Parmenides' account of `mortal opinion' (...) certainly associates male with coldness and density, the attributes of Night, and female with hotness and greater rarity, the attibutes of Light. The aims of this paper are, then, first, to show that the association of female with Light and of male with Night is in fact right; and secondly to investigate the main dualistic features of Parmenides' `mortal opinion' (embryology, sleep, death, knowledge) in relation to this theme. This will lead us, finally, to focus our attention on the Proem, which introduces us to a world full of female divinities, among whom - beyond the gates of the ways of day and night - is the unnamed goddess who will initiate her young male auditor into the two `ways'. (shrink)

Modern thought would present only an incomplete and fragmentary picture of philosophy to us if we were to regard it as being completely disconnected from the elemental forces and sources of Greek philosophy. The corrective aspect that protects it from any such attempt at unmethodical isolation is, however, given within itself and in its own content. Its own inner progress necessarily leads it back to the principles and questions that distinguished Greek speculation, which it embodied in typical forms. The thought (...) of the modern age proves its specificity in the fact that, notwithstanding the richness of content that it gains, it remains conscious of its relatedness to these basic logical forms and strives to return to them of its own accord. They will thus themselves appear to us of their own accord and incite us to regard their contents, if we just allow ourselves to follow the course of the investigation. (shrink)

The interpretation of Parmenides’ Περί Φύσεως is a fascinating topic to which philosophers, historians of philosophy and scientists have dedicated many studies along the history of Western thought. The aim of this paper is to present the reading of Parmenides’s work offered by Federigo Enriques. It is based on several original theses: (1) Parmenides was the discoverer of abstract geometry; (2) his critics was addressed against the Pythagoreans rather than against Heraclitus; (3) Parmenides discovered and applied the contradiction and the (...) third excluded principles in the context of his research on foundation of geometry; (4) Parmenides’s metaphysical and physical conceptions have their bases in his speculation on geometry; (5) Parmenides used the principle of sufficient reason. Enriques’s reading is worth being expounded and discussed within the historical, philosophical and scientific context in which it is inserted. Since Enriques’s ideas are not widely known and discussed, my research has the purpose to fill this gap. The article also aims to provide elements to illustrate the discussion on Parmenides in the first half of the last century. (shrink)

On souligne couramment la pluralité des sciences et la diversité de ses méthodes. Devons-nous pour autant nous résigner à cette situation de fait ? Il s’agit d’interroger, à partir de l’oeuvre meyersonienne, la tension entre la spécialisation sans cesse accrue et la nécessaire coordination des faits. Cette oeuvre fournit l’exemple d’un projet encyclopédique souple, dans lequel l’épistémologie permet de transcender les cloisonnements disciplinaires.Today, the burden of proof appears to rest on those who defend the unity of the sciences. Yet, in (...) scientific research, concepts and methods are transposed from one field to another, and interdisciplinary approaches flourish. Meyerson provides the opportunity to take up this issue once again. His work offers the example of a moderate unitary conception of science. It is encyclopedic but not reductionist. (shrink)

Pierre Duhem can be looked upon as one of the heirs of a tradition of historical and philosophical researches that flourished in the second half of the nineteenth century. This tradition opposed the naïve historiography and epistemology of the positivist school. Beside the positivists of different leanings such as Littré, Laffitte, Wyrouboff, and Berthelot, we find Cournot, Naville, and Tannery, who developed sophisticated histories and philosophies of science focusing on the real scientific practice and its history. They unfolded elements of (...) continuity and discontinuity in the history of science, and enlightened the complex relationship among experimental, mathematical, logical and philosophical components in scientific practice. In Pierre Duhem we find a systematic and vivid interpretation of these meta-theoretical issues, and a meaningful development of a cultural tradition that re-emerged in the second half of the twentieth century. (shrink)

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if according to fragment (...) B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

A pergunta, “Tudo é número?” no título do famoso artigo de 1989 de Zhmud, deixa aberto um desafio para o extremamente importante testemunho aristotélico de que “tudo é número” era a definição fundamental da filosofia pitagórica. Tal desafio não é nada simples, especialmente quando se considera que, até então, as histórias tanto da filosofia quanto da matemática antiga parecem não ter dúvidas de que esta afirmação é correta. Este artigo pretende submeter à avaliação crítica a alegação de Aristóteles de que (...) os pitagóricos acreditavam que “tudo é número”. Nossa análise dos muitos modos nos quais Aristóteles enuncia a tese de que “tudo é número” revelará, para além de variações meramente semânticas, uma contradição teórica fundamental que o próprio Aristóteles parece incapaz de resolver. De fato, três versões diferentes da doutrina estão presentes na doxografia aristotélica: uma identificação dos números com objetos sensíveis; uma identificação dos princípios dos números com os princípios das coisas que existem; uma imitação dos objetos pelos números. Enquanto as versões e parecem identificar, em termos que lembram Platão, os números com a causa material da realidade, a versão, a saber, números como causas formais da realidade, é uma reconstrução aristotélica da teoria pitagórica. Aristóteles teria sido levado a tal reconstrução pela dificuldade que encontrou para aceitar a noção pitagórica material de número, e por considerá-la, para seu gosto, fortemente marcada pela recepção da mesma teoria no ambiente da Academia. (shrink)