Volume 48, Issue 2

In the Timaeus Plato uses apparently superfluous constructions to obtain the equilateral triangle and the square, the faces bounding the regular solids which underlie the four kinds fire, air, water and earth. Indeed, the constructions of the two faces involve six and four ‘small’ elementary triangles, respectively, whereas just two ‘large’ elementary triangles would suffice in both cases. Plato also says that the reason why he uses a particular scalene elementary triangle, which he calls the fairest (κάλλιστον), for the construction of the equilateral triangle is a long story (πλείων λόγος) to tell. Recently, Professor D. Robert Lloyd has proposed that present-day symmetry principles underpin both the superfluous constructions of the faces and the choice of the ‘fairest’ triangle. He claims that Plato may have well been inspired by symmetry-related criteria because in both the aforementioned constructions the apparently redundant number of elementary triangles and their arrangement are consistent with reflection and rotation operations brought about with respect to the proper symmetry elements of the two faces. He also emphasizes that it is only with these superfluous constructions, and the ‘fairest’ triangle which Plato adopts to construct the equilateral triangle, that the solids bounded by the two faces possess the correct symmetry. While I acknowledge that all these mathematical aspects entirely and indisputably apply to the plane and solid geometrical figures we encounter in the Timaeus , I argue that they motivated neither Plato’s construction of the two faces, nor his choice of the ‘fairest’ scalene elementary triangle, including the ‘long story’ behind it. I shall attempt to demonstrate that the notion that symmetric figures remain invariant (or equivalent) by virtue of their immunity to change despite the dynamical character of the operations applied to them, such as reflection and rotation, conflict with the ontology, epistemology, and philosophy of mathematics of Plato’s system. I also argue that the selection rules that Plato applies in the Timaeus to the transformation of the four kinds into each other conflict with the symmetry-group-based classification of the solids that shape those four kinds.

Although many scholars take a foundationalist approach to the theory of knowledge in Republic V–VII, few if any have responded to a growing number of coherentist interpretations, which hold that, for Plato, justification rests not on a first principle but rather on the coherence of a sufficiently large number of beliefs. This paper argues that the structure of knowledge in the Republic analogies is incompatible with the coherentist reading. Plato’s analogies provide ample evidence that he holds something, at the very least, approximating a foundationalist first principle. In addition, this paper puts forward a Platonic solution to the regress problem. It argues that the form of the good is plausibly self-justifying. Because the form of the good serves as the “measure” by which the philosopher is able to determine the goodness, fittingness, and truth of all that he encounters (517b), it seems reasonable to conclude that the philosopher’s ultimate source of justification – what it is that puts an end to the search for explanations and serves as an explanation of his claim to know the form of the good – is nothing other than the form of the good itself.

This paper argues that the source for a number of chapters of Book I (“On Medicine”) of the Problemata in the corpus Aristotelicum is likely one or more of the lost medical works of Aristotle. It is further argued that the last three chapters of Pr. I (55–7), on the treatment of fevers – which are unusual for chapters in the Problemata in not raising questions – were likely excerpted directly from Aristotle’s medical writings, but never transformed into standard ‘ problemata ’.

Aristotle provides two different explanations for there being three distinct and (so I will argue) genuine kinds of friendship: friendship based on virtue, on pleasure, and on utility. In the Eudemian Ethics , he conceives their unity as a focal meaning unity, whereas, in the Nicomachean Ethics , resemblance is the key notion for unifying the three cases of friendship. In this paper, I propose an interpretation for this conceptual change, attempting to show why resemblance is a better tool than focal meaning to account for these three genuine kinds, and how Aristotle can maintain a hierarchy among them within a unity based on resemblance.

The paper aims to show that /1/ on the theory of concept acquisition we gain universal concepts at the end of a process in which pictorial and conceptual phases are alternating, with the implication that the representational capacity (phantasia) produces pictures of a universal nature, and that /2/ even if the excursus Porphyry’s theory of knowledge in the preface of the Harmonics-commentary may heavily rely on theories from the early Middle Platonism, Porphyry could adopt it for his own purposes, in a way to be in line with what he says elsewhere in his works.