Galen was a prolific writer, mostly important for the development of medicine. However he is not receiving the deserved attention by researchers in Lusophonic world. Here we aim to show why studying Galen’s De Sectis is useful as an external source for comprehending Sextus Empiricus and his empiricism, as well as his exhortation to live in accordance to the ordinary life. Furthermore, in two appendices we offer the main primary sources, and we display a chronology of the physicians mentioned in (...) pseudo-Galen, Introd.14.683.5-14.684.5. (shrink)

This paper re-constructs Plato's ‘philosophy of geometry’ by arguing that he uses a geometrical method of hypothesis in his account of the cosmos’ generation in the Timaeus. Commentators on Plato's philosophy of mathematics often start from Aristotle's report in the Metaphysics that Plato admitted the existence of mathematical objects in-between ( metaxu) Forms and sensible particulars ( Meta. 1.6, 987b14–18). I argue, however, that Plato's interest in mathematics was centred on its methodological usefulness for philosophical inquiry, rather than on questions (...) of mathematical ontology. My key passage of interest is Timaeus’ account of the generation of the primary bodies in the cosmos, i.e. fire, air, water and earth ( Tim. 48b–c, 53b–56c). Timaeus explains the primary bodies’ origin by hypothesising two right-angled triangles as their starting-point ( arkhê) and describing their individual geometrical constitution. This hypothetical operation recalls the hypothetical method which Socrates introduces in the Meno (86e–87b), as well as the use of hypotheses by mathematicians which is described in the Republic (510b–c). Throughout the passage, Timaeus is focussed on explicating the bodies in terms of their formal structure, without however considering the ontological status of the triangles in relation to the physical world. (shrink)

On the basis of recent work concerning the meaning of the term stoicheion in Aristotle’s Analytics, we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements.

The aim of this paper is to examine the implications of Plato’s use of the term stoicheion, since his awareness of stoicheion’s polysemy reveals his view of the origin, the complexity and, at the same time, the order of reality. Moreover, his use of stoicheion allowed him both to inherit and to detach himself from his predecessors. I begin by presenting the history of the notion of stoicheion; then, since one of the meanings of stoicheion is ‘letter of the alphabet’, (...) I focus on the Cratylus, which contains the first of several passages where Plato employs the alphabet as a paradigm for the structure of a complex system. Finally, I turn to the Theaetetus, where Plato, for the first time, uses stoicheion in the sense of ‘element’ and where, through the relation letters/syllables, Plato clarifies that enumeration and juxtaposition are not sufficient to attain the real knowledge. I will argue that only thanks to these steps can we understand the occurrences of stoicheion in the Timaeus, where Plato first states that air, earth, fire and water are not stoicheia tou pantos, and then reveals that, instead, the basic triangles are ‘the elements of the universe’. (shrink)

It might seem quite commonplace to say that Aristotle identifies fire, air, water and earth as the στοιχεῖα, or ‘elements’ – or, to be more precise, as the elements of bodies that are subject to generation and corruption. Yet there is a tradition of interpretation, already evident in the work of the sixth-century commentator John Philoponus and widespread, indeed prevalent, today, according to which Aristotle does not really believe that fire, air, water and earth are truly elemental. The basic premise (...) of this interpretation is that Aristotle takes fire, air, water and earth to be, in some sense, composite bodies and, as such, analysable into simpler constituents. But, of course, an element of bodies is defined by Aristotle himself as something into which bodies can be analysed, and which does not admit further analysis . So if fire, air, water and earth can be analysed into simpler or more basic constituents, then it would seem to follow that the latter ought to be considered Aristotle's true elements. These are usually identified as the primary contraries hot and cold, dry and wet; many, perhaps most, commentators would insist also upon prime matter as the subject upon which these contraries act. (shrink)