E-resources
Peer reviewed
Open access
-
Paparazzo, Ernesto
Apeiron, 2020, Volume: 48, Issue: 2Journal Article
In the 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 , 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 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.
Author
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.