In Plato's "Parmenides" at one stage inclusion is casually used as a reflexive property to argue that the 'One' (everything that is) must be included in itself. Parmenides in the text even keeps going to make this argument geometric and talks abou the number of contacts of nested forms etc.

  • In Greek thought what are the arguments for or uses of properties or objects as included in themselves?
  • Are there modern thinkers that use this notion in a positive (synthetic) way?
  • Can you think of physical objects that are contained in themselves?

"One"" Ένα" does not mean "everything that is". One means one, "everything that is" is "all, whole" Όλο".

The one representing the whole is "everything that is". Written as One, "Εν". If one does not include itself, then there must be something else i.e. a secondary one, that is also a one but not the one that represents the whole. So one as a whole includes itself. This is the identity principle.

a. One is not an object. It is an idea.

b. Dialectics, everything derived from dialectics.

c. Every object, is contained in itself. This is the reason it can be described and distinguished as an object.

i.e. This is an object. This "an" really means "ένα", one. Included in itself.

  • c. Every object is, but it is not contained within itself. Inclusion is a property of either parts or space (within). To use the statement like that renders the word meaningless. a. While it seems you cite the authority in (c) you do not cite their argument. Why is something needed to be included inside itself?
    – foivos
    Jul 26 '16 at 23:09
  • In modern thinking yes, but ultimately, "space" is an idea, objects having place in space are "relations of ideas". In old philosophy people like Permenides had to figure how thoughts are related to the world. Modern way to understand "reality", the objects really being "out there" is not something that can be taken without consideration of the philosophical processes that have preceded. In classical philosophy an object is something that is opposed to the subject (I, the thinker, having ideas, and "there" opposite to me, the world, ideas about the "outer" world are objects.
    – John Am
    Jul 26 '16 at 23:21
  • "Why is something needed to be included inside itself". Otherwise we could not be able to speak or think about it. Try to understand the term included as "full". A notion is full-in itself. An idea is a vessel and the content of an idea is the water.
    – John Am
    Jul 26 '16 at 23:46
  • Full, πλήρες. Πληρώνω "pay". Something has a value. I pay the exact value. I can fill a glass with water until it is full. The amount of water equals the capacity of the glass. When something's content is equal to the size of it , it is full. So the One is full-in itself, "contained in itself" because the content "everything" is equal in size with the capacity of the notion of the One. (don't forget the mystical tones, the One in Parmenides is a synonym with god and the ability of the mind to grasp the world gave off a "divine" legacy of the spirit)
    – John Am
    Jul 26 '16 at 23:55
  • What is "water"?. How we distinguish water from other material? This fullfillness of everything that can be distinguished is the principle of identity.
    – John Am
    Jul 27 '16 at 0:09

Aristotles book on Metaphysics may be useful as it considers the questions of parts, wholes and changes; these are obviously questions that are in a direct line of descent from Parmenides.

For example, Aristotle points out that anything that lacks parts cannot change.

In one line of argument, the Parmenidian One lacks parts, and this is why it lacks change; it is changeless and motionless.

In another line of argument, the whole being whole must contain itself; in modern set theory this results in Russell's paradox and so it is judiciously banned; notably too, there is no universal set; however there is an paraconsistent form of set theory that does allow this, and it turns out that the union of all such sets - sets that contain themselves - is the universal set.

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