Return to the PHIL 320 Home PageLiterally, "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."
Because it is based on the Form of living being (= Animal)
Because it is based on a unique model (the Form 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).
Because it is a living being
Because that is the most perfect and most beautiful shape
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?
Which is right? The text is grammatically ambiguous: Plato says "and this is what we call time," but the reference of 'this' could be either 'number' or 'image'.Zeyl's translation brings Plato's definition close to Aristotle's ("time is the number of motion (change) in respect of before and after" [Physics 219b2]). On this reading, it is the cosmos that is the "moving image of eternity," and time is the number that measures the change in the cosmos.
But this interpretation of Plato is implausible. For other passages in the Timaeus make it clear that Plato thought of time as a kind of celestial clockwork - that is, a certain kind of motion, 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."
Plato clearly says that time is the wanderings of 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 just is celestial 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 a tenseless 'is'; the Forms themselves are, strictly speaking, outside of time.
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.
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 of mathematical objects (shades of the Pythagoreans) and empty space (the invention of the atomists).
The intrinsic nature of fire, water, air, and earth (48b), and how they came into being.
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 that in which all 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 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: they are all made of triangles, and constructed in such a way as to explain how the transmutation of elements is possible.
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 the molecules of the theory; the triangles are its atoms.
Each face is either an equilateral triangle or a square
Equilateral triangles (t) are made of a triangles.
Squares (s) are made out of b triangles.
Plato's description at 54e and 55b tells us that each t is made of
6 a's, and each s is made of 4 b's. (See diagrams,
RAGP 468.) But 57c-d makes clear that he envisages other ways of
constructing these faces out of primitive a's and b's.
Tetrahedron (4-sided solid), made of 4 t's consisting of 24 a's
altogether.
Octahedron (8-sided solid), made of 8 t's consisting of 48 a's
altogether.
Icosahedron (20-sided solid), made of 20 t's consisting of 120
a's altogether.
Cube (6-sided solid), made of 6 s's consisting of 24 b's
altogether.
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 (one
F is made up of 4 t), an air molecule 8 (one A is made
up of 8 t), and a water molecule 20 (one W is made up of 20
t), 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.):
1 A = 2 F
8 t = 2 × 4 t
1 W = 5 F
20 t = 5 × 4 t
2 W = 5 A
2 × 20 t = 5 × 8 t
1 W = 2 A + 1 F
20 t = (2 × 8 t) + 4 t
1 W = 3 F + 1 A
20 t = (3 × 4 t) + 8 t
Since equilateral triangles can be constructed out of a's (and squares out of b'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 and b's). These might be considered "isotopes" of the basic molecules described by Plato (with each t made of 6 a's, and each s made of 4 b'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 (6 s = 24 b) can be transformed into 2 of the smaller "isotopes" of earth (6 s = 12 b)
Similarly, 4 "normal" particles of water (containing 120 a's each) can combine to form one huge particle of one of the larger "isotopes" of water (20 sides of 24 a's each, for 480 a's altogether).
Plato's theory combines elements of the views of many of his predecessors.
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.
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?"
Like Empedocles, Plato recognized that four elements - earth, air, fire, and water - underlay all physical changes. But unlike Empedocles, he found a common atomic ingredient underlying the elements. Hence, unlike Empedocles, he could explain the transformation of one element into another.
Since earth is made of different atoms (isosceles triangles) from the other
elements (scalene triangles), this transformation is impossible, as Plato
knew. So what happens when, e.g., wood burns? Isn't earth (which is what,
presumably, wood is mostly made of) converted into fire?
The problem here is that the volumes of the polyhedra in Plato's "equations" don't add up correctly. E.g., consider the "equation":
1 W = 3 F + 1 A
which tells us that one water atom can be converted into 3 fire atoms and one air atom. (There are 20 equilateral triangles, t, involved in this equation.) The problem is that the volume of one water atom (i.e., one icosahedron) is much greater than the combined volumes of 3 fire atoms (3 tetrahedra) and one air atom (one octohedron). If we let s be the length of a side of each equilateral triangle (t) that is a face of each of the polyhedra, we can calculate these volumes:
Volume of 1 W = 2.1817 s3Aggregate volume of 3 F + 1 A = .8248 s3
The transformation of one element into another is not an observed phenomenon,
but a theoretical explanation of observations. So Plato can account for the
phenomenon in question by theorizing that it is the water and air components
of wood that are converted into fire; the earth components remain unburned
in the ashes.
Remember that matter is not a concept Plato is working with. In his view, a material object consists, ultimately, of the triangular atoms composing the polyhedral corpuscles of the four different elements. Contained within these polyhedra is empty space - the receptacle, as he called it.
So it is not matter, as we understand it, that Plato must conserve, but triangles. Hence it is not the total volume of his polyhedra, but their combined surface area that must be conserved. What remains constant in every transformation, as Vlastos says, is:
"...the aggregate surface area of the corpuscles. If you press him to say what happens to that portion of the matter within the icosahedron which cannot be enclosed within the equivalent surface area of smaller polyhedra, Plato would say that there is no such matter: after creation matter exists only in the form of space encapsulated by polyhedra; what is not thus encapsulated is empty space, which becomes matter when captured by envelopes of the approved stereometric form" (Plato's Universe, p. 90).
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