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A Classical Example of Why Needle-sharp Philosophical Investigations are Needed.
|Let us proceed to distribute the elementary forms, which have now been created in idea, among the four elements. To earth, then, let us assign the cubical form; for earth is the most immoveable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature.!|
From Plato's Timaus [1330-1370]:
This corresponds to the element of 'fire.
Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides; and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability; and to water we assign that one of the remaining forms which is the least moveable; and the most moveable of them to fire; and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air; and, again, the acutest body to fire, and the next in acuteness to air, and the third to water.
And this blobby Pyramid corresponds to the element of 'air'.
Of all these elements, that which has the fewest bases must necessarily be the most moveable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles: and the second body has similar properties in a second degree, and the third body in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire; and let us assign the element which was next in the order of generation to air, and the third to water.
The complicated sounding, and complicated looking Icosahedron corresponds to 'water'...
So far, note, this is all nonsense. But it appears very technical and thus impressive. At least Plato is right here, when he continues:
We must imagine all these to be so small that no single particle of any of the four kinds is seen by us on account of their smallness: but when many of them are collected together their aggregates are seen. And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessity allowed or gave consent, has exactly perfected, and harmonized in due proportion.
And finally, reliable, 'solid' earth.
From all that we have just been saying about the elements or kinds, the most probable conclusion is as follows:—earth, when meeting with fire and dissolved by its sharpness, whether the dissolution take place in the fire itself or perhaps in some mass of air or water, is borne hither and thither, until its parts, meeting together and mutually harmonising, again become earth; for they can never take any other form. But water, when divided by fire or by air, on re-forming, may become one part fire and two parts air; and a single volume of air divided becomes two of fire.
Again, when a small body of fire is contained in a larger body of air or water or earth, and both are moving, and the fire struggling is overcome and broken up, then two volumes of fire form one volume of air; and when air is overcome and cut up into small pieces, two and a half parts of air are condensed into one part of water.
There are ideas here, yes. And although these shapes are always called 'Platonic solids', they seem to come rather via Pythagoras (who is 'unfashionable') from the East (which is almost 'unmentionable' in Western versions of the history of ideas). Finding out who really said what, and when, is part of finding out 'the truth'. And we shall do that here. But - more than that - how to separate the useful- from the useless?
That is the the task of this website.