Property of inclusion in Greek thought

Question

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?

Answer 1

"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.

Answer 2

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.