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If we add the phenomenological element into our understanding of the term, we find that these cases of unlimitedness (both of which Socrates does seem to have in mind at various points in the dialogue) can be integrated into a single definition.
This procedure, however, cannot do away with all unlimitedness that may be encountered.
It is also important to note that apeiron here is an instance of the injurious and treatable kind of unlimitedness that the Heavenly Tradition taught us how to deal with.
Insofar as Forms are things that are 'said to be' (and Plato says that they are quite often), this means that these consist of limit and unlimitedness as well.
The first, injurious kind results from sloppiness and haste; it posits a state of unlimitedness where, in fact, there is only a finite multiplicity of unities (of infima species).
Hobbes does not appear to be as thoroughgoing as Hume in this regard since he imposes requirements of indivisibility and unlimitedness of authority on a good state.
For the others than the One," Parmenides says at 158d3-5, "it follows from the One and their communing ([Greek Text Omitted]) with it that something different ([Greek Text Omitted]) arises in them that gives them [Greek Text Omitted] in relation to each other; their own nature in and of themselves, on the other hand, gives them unlimitedness ([Greek Text Omitted]).
Does not the instrumental activity of [unkeyable] or vous place some constraint or limitation on the One, counter to its purported unlimitedness as explained above?