Plato’s Cosmology: TheTimaeus
The Forms vs. the Cosmos
(The True Light vs. the light of the Darkness)
The world of Forms (True Light)
1. The world of being; everything in this world “always is,” “has no becoming,” and “does not change”(28a). (Exists in the NOW, beyond time/duality).
2. It is apprehended by the understanding, not by the senses. (Known instantaneously)
The physical world (= the Cosmos) (light of the Darkness)
1. The world of becoming; everything in this world “comes to be and passes away, but never really is” (28a). (Exists in Time)
2. It is grasped by opinion and sense-perception. (Known to mind and its faculties, therefore unknown to Light)
3. The cosmos itself came into being, created using as its model the world of Forms. (The darkness mimics/copies the Light)
The Demiurge (Creator) (Alien God on Top of Hierarchy)
Literally, “craftsman.” The creator of Plato’s physical world is not a divine intelligence or a personal ruler, but (as it were) a manual laborer. Cf. Vlastos,Plato’s Universe(pp. 26-27):
That the supreme god of Plato’s cosmos should wear the mask of a manual worker is a triumph of the philosophical imagination over ingrained social prejudice. ... But this divine mechanic is not a drudge. He is an artist or, more precisely, what an artist would have to be in Plato’s conception of art: not the inventor of new form, but the imposer of pre-existing form on as yet formless material.
The Elements
· The physical world must havebodilyform; it must bevisibleandtangible(31b).
· Hence, its ingredients must includefireandearth.
· Since fire and earth will have to be combined, there must be at least one other ingredient that serves to combine them.
· But since fire and earth aresolids, we requiretwointermediates to combine them.
· Hence, the demiurge createdairandwater, and arranged all four elements proportionally: as fire is to air, air is to water; as air is to water, water is to earth.
· As we will see below, we have not reached the bottom with these four elements: there are (geometrical) atoms of which these elements are composed.
Features of the Cosmos
A living being
Because it is based on the Form of living being (= Animal)
Unique
Because it is based on a unique model (theForm of living being), and the Demiurge makes it as much like its model as he can (subject, of course, to the limitations imposed by the fact that it’s made of matter).
It has a soul
Because it is a living being
Spherical
Because that is the most perfect and most beautiful shape
Temporal (The light of the Darkness exists in Time)
That is, there is time in the cosmos-it is characterized by temporal predicates. This is because it is modeled on a Form, an eternal being.
The cosmos cannot be eternal, as a Form is, since it comes into being. But it is as much like a Form, as close to being eternal, as it can be (37d). When the Demiurge created the universe, he also created time. But what is Plato’s definition of time?
Plato's text at 37d reads:
[the Demiurge] began to think of making a moving image of eternity: at the same time as he brought order to the universe, he would make an eternal image, moving according to number, of eternity remaining in unity. This, of course, is what we call “time.”
But what is ‘this’? It is sometimes thought that it refers to ‘number’, which would make the definition be that time is thenumberaccording to which the image of eternity moves. This would bring Plato's definition close to Aristotle’s (“time is the number of motion (change) in respect of before and after” [Physics219b2]). On this reading, it is the cosmos that is the “moving image of eternity,” and time is the number that measuresthe change in the cosmos.
But ‘this’ has been traditionally taken to refer to ‘image’, and on this reading, Plato’s definition is that time is a moving image of eternity. Even if Plato’s text is grammatically ambiguous, the most plausible way to understand the definition is the traditional one. Other passages in the Timaeusmake it clear that Plato thought of time as a kind of celestial clockwork-that is, a certain kind ofmotion, rather than a measure of motion. Consider 38d and 39d:
[The Demiurge] brought into being the Sun, the Moon, and five other stars, for the begetting of time. These are called“wanderers” [planêta], and they stand guard over the numbers of time. … And so people are all but ignorant of the fact that time really is the wanderings of these bodies. (People have no clue that time and the planets and stars are controlling their reality)
Plato clearly says that time isthe wanderingsof these bodies-their movement-and not a kind of number that measures such movement. Abstracting time from motion was an innovation of Aristotle’s. For Plato, time justiscelestial motion.
Note that time applies, strictly speaking, only to the realm of becoming. About the Forms, which are everlasting, we say “is, and was, and will be,” but, strictly speaking, only “is” is appropriate (38a). That is, the ‘is’ we use about the Forms is atenseless‘is’; the Forms themselves are, strictly speaking, outside of time. (Again, the Light exists beyond Time)
The Heavenly Bodies (Planets and Stars control Time and its flow)
Plato’s account includes the origin of the stars and planets-“to set limits to and stand guard over the numbers of time” (38c)-which we will skip over here.
Human Beings: Souls, Bodies, and their Parts
Four kinds of living creature (39e-40b)
1. Heavenly gods
2. Winged things
3. Water creatures
4. Land creatures
Human soul (40d-44d)
1. Creation and destruction of the gods (40d-41a)
2. Demiurge instructs gods to make mortals (41a-d)
3. Human souls manufactured
o Made of leftovers from manufacture of world-soul, but of a lower grade of purity (41d). (Comprised from the dung pile of spirit energy and corrupted energy from many reincarnations)
o Each soul assigned to a star (41e). (Home Base Energy)
o Death: a just soul returns to its companion star, an unjust soul is reincarnated for a second try (42b-c). (Clear Soul/Spirit returns to Home Base Energy after each incarnation, unless it is contaminated with darkness … then it get reincarnated)
Human body (44d-47e)
1. Head and limbs (44d-45b)
2. Eyes and vision (45b-46a)
3. Purposes of seeing and hearing (46c-47e)
The Structure of Matter
At this point Plato ends his discussion of the “works of intellect (nous)” and begins discussing the “works of necessity”. The difference seems to be that the former, but not the latter, directs its creation with an eye toward what is best.
Here Plato turns to the old Presocratic question: what is the world made of? His answer both combines and transcends theirs. It mentions the traditional Earth, Air, Fire, and Water (of Empedocles), but goes beyond them, analyzing them in terms ofmathematical objects(shades of the Pythagoreans) andempty space(the invention of the atomists).
The four elements
The intrinsic nature of fire, water, air, and earth (48b), and how they came into being.
The receptacle
A new concept is introduced, in addition to the model (= the Forms) and the imitation of the model (= the world of becoming): “the receptacle of all becoming” (49a).
The receptacle is thatin whichall becoming takes place. The fires that you see coming into being and being extinguished are just appearances, in the receptacle, of the Fire Itself (the Form).
At 52b ff, Plato describes the receptacle as “space.”
The coming to be of the elements
The four elements are “the most excellent four bodies that can come into being” (53e). But how do they come into being? What are they made of? Plato’s answer is that they are all made oftriangles, and constructed in such a way as to explain how the transmutation of elements is possible.
Overview
Each kind of matter (earth, air, fire, water) is made up of particles (“primary bodies”). Each particle is a regular geometrical solid. There are four kinds of particles, one for each of the four kinds of matter. Each particle is composed of elementary right triangles. The particles are like themoleculesof the theory; the triangles are itsatoms.
The argument that all bodies are ultimately composed of elementary right triangles is given at 53c-d: all bodies are 3-dimensional (“have depth”) and hence are bounded by surfaces. Every surface bounded by straight lines is divisible into triangles. Every triangle is divisible into right triangles. Every right triangle is either isosceles (with two 45° angles) or scalene. So all bodies can be constructed out of isosceles and scalene right triangles.
The details
1. The two atomic triangles
Plato notes (54a1) that there is only one kind of isosceles right triangle--namely, the 45°/45°/90° triangle--whereas there are “infinitely many” kinds of scalene. But of these, he tells us, “we posit one as the most excellent” (54a7), one “whose longer side squared is always triple its shorter side” (54b5-6). Plato describes the same scalene triangle, equivalently, as “one whose hypotenuse is twice the length of its shorter side” (54d6-7). (The angles of this triangle are thus 30°/60°/90°.)
I’ll call the 30°/60°/90° triangles “atriangles” and the 45°/45°/90° triangles “btriangles.”
atriangle (scalene, 30°/60°/90°) / btriangle (isosceles, 45°/45°/90°)2. Construction of “faces” of particles out of the atomic triangles
o Each face is either an equilateral triangle (t) or a square (s).
o Equilateral triangles (t’s) are made ofatriangles.
o Squares (s’s) are made out ofbtriangles.
o Plato’s description at 54e and 55b tells us that eachtis made of 6a’s, and eachsis made of 4b’s. (See diagrams,RAGP640.) But 57c-d makes clear that he envisages other ways of constructing these faces out of primitivea’s andb’s.
3. Construction of solid particles out of the faces
The construction of the particles is described at 54d-55c. The particles are identified with the four elements at 55d-56b. Click on the names of the elements to see adiagramof a particle of that element:
o Fire: a particle of fire is a tetrahedron (4-sided solid), made of 4t’s consisting of 24a’s altogether.
o Air: a particle of air is an octahedron (8-sided solid), made of 8t’s consisting of 48a’s altogether.
o Water: a particle of water is an icosahedron (20-sided solid), made of 20t’s consisting of 120a’s altogether.
o Earth: a particle of earth is a cube (6-sided solid), made of 6s’s consisting of 24b’s altogether.
111. Transformation of elements (described at 56c-57c)
Inter-elemental transformations are among fire, air, and water only. Earth cannot be transformed into any of the others (54c, 56d).
Transformations can be described at the level of equilateral triangles (that are the faces of the three solids). Since a fire molecule has 4 faces (oneFis made up of 4t), an air molecule 8 (oneAis made up of 8t), and a water molecule 20 (oneWis made up of 20t), any of the following transformations (for example) are possible. (Each transformation is represented by an equation on the left; its geometrical basis is shown by the equation on the right.):
1A= 2F / 8t= 2 × 4t1W= 5F / 20t= 5 × 4t
2W= 5A / 2 × 20t= 5 × 8t
1W= 2A+ 1F / 20t= (2 × 8t) + 4t
1W= 3F+ 1A / 20t= (3 × 4t) + 8t
111. Larger and smaller particles
Since equilateral triangles can be constructed out ofa’s (and squares out ofb’s) in more than one way, it is possible to have “molecules” of each of the elements that have different numbers of atomic triangles (a’s andb’s). These might be considered “isotopes” of the basic molecules described by Plato (with eachtmade of 6a’s, and eachsmade of 4b’s).
An equilateral triangle can also be constructed out of 2, or 8, or 18,a’s (and so on, ad infinitum).
A square can also be constructed out of 2, or 8, or 16,b’s (and so on, ad infinitum).
This means that one “normal” particle of earth (6s= 24b) can be transformed into 2 of the smaller “isotopes” of earth (6s= 12b)
Similarly, 4 “normal” particles of water (containing 120a’s each) can combine to form one huge particle of one of the larger “isotopes” of water (20 sides of 24a’s each, for 480a’s altogether).
Final Reflections
Comparison with predecessors
Plato’s theory combines elements of the views of many of his predecessors.
1. Pythagoras
Like Pythagoras, he made the physical universe fundamentally mathematical. But whereas Pythagoras thought that everything was made of numbers, Plato made geometrical figures-ultimately, triangles-the atoms of his system.
2. Democritus
Plato, like Democritus, was an atomist. But whereas Democritean atoms were of all different shapes and sizes, Plato’s came in just two varieties: isosceles and scalene. In this respect, Plato’s theory was far more elegant than that of Democritus. As Vlastos comments (Plato’s Universe, pp. 93-4):
Compare [Plato’s theory] with the best of its rivals, the Democritean. There atoms come in infinitely many sizes and in every conceivable shape, the vast majority of them being irregular, a motley multitude, totally destitute of periodicity in their design, incapable of fitting any simple combinatorial formula. If we were satisfied that the choice between the unordered polymorphic infinity of Democritean atoms and the elegantly patterned order of Plato’s polyhedra was incapable of empirical adjudication and could only be settled by asking how a divine, geometrically minded artificer would have made the choice, would we have hesitated about the answer?