Ideas from 'Parmenides' by Plato [364 BCE], by Theme Structure

[found in 'Complete Works' by Plato (ed/tr Cooper,John M.) [Hackett 1997,0-87220-349-2]].

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2. Reason / A. Nature of Reason / 1. On Reason
When questions are doubtful we should concentrate not on objects but on ideas of the intellect
2. Reason / B. Laws of Thought / 5. Opposites
Opposites are as unlike as possible
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
One is, so numbers exist, so endless numbers exist, and each one must partake of being
7. Existence / A. Nature of Existence / 3. Being / c. Becoming
The one was and is and will be and was becoming and is becoming and will become
7. Existence / A. Nature of Existence / 4. Existence as One
The only movement possible for the One is in space or in alteration
7. Existence / D. Theories of Reality / 2. Reality
Absolute ideas, such as the Good and the Beautiful, cannot be known by us
8. Modes of Existence / D. Universals / 2. Need for Universals
You must always mean the same thing when you utter the same name
If you deny that each thing always stays the same, you destroy the possibility of discussion
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
Plato moves from Forms to a theory of genera and principles in his later work
It would absurd to think there were abstract Forms for vile things like hair, mud and dirt
If admirable things have Forms, maybe everything else does as well
If absolute ideas existed in us, they would cease to be absolute
The concept of a master includes the concept of a slave
Greatness and smallness must exist, to be opposed to one another, and come into being in things
8. Modes of Existence / D. Universals / 6. Platonic Forms / b. Partaking
The whole idea of each Form must be found in each thing which participates in it
If things partake of ideas, this implies either that everything thinks, or that everything actually is thought
Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once
If things are made alike by participating in something, that thing will be the absolute idea
Participation is not by means of similarity, so we are looking for some other method of participation
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress)
If absolute greatness and great things are seen as the same, another thing appears which makes them seem great
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
Parts must belong to a created thing with a distinct form
9. Objects / C. Structure of Objects / 5. Composition of an Object
In Parmenides, if composition is identity, a whole is nothing more than its parts
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
Plato says only a one has parts, and a many does not
Anything which has parts must be one thing, and parts are of a one, not of a many
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
It seems that the One must be composed of parts, which contradicts its being one
9. Objects / F. Identity among Objects / 6. Identity between Objects
Two things relate either as same or different, or part of a whole, or the whole of the part
25. Society / E. State Functions / 5. Education / c. Teaching
Only a great person can understand the essence of things, and an even greater person can teach it
26. Natural Theory / B. Concepts of Nature / 1. Basis of Nature
Everything partakes of the One in some way
Some things do not partake of the One
26. Natural Theory / B. Concepts of Nature / 2. The Unlimited
The unlimited has no shape and is endless
28. God / C. Proofs of Reason / 1. Ontological Proof
We couldn't discuss the non-existence of the One without knowledge of it