Why does Parmenides impose a limit on his Being?

Question

Parmenides mentions twice in the poem what-is has limit in the part where he talks that what-is is “like the bulk of ball” (B8: lines 42, 49, pages 60, 61).

42:

But since the limit is ultimate, it [namely, what-is] complete

49:

for equal to itself from all directions, it meets uniformly with its limits.

I’m struggling to understand why he adds these limits. Why not going the Anaximander’s way and saying that what-is is boundless? Because otherwise it’s easy to start asking questions like “What is beyond the limit?”. If we answer “nothing” it would mean that what-is-not exists (and we can’t say that) and otherwise it would mean that what-is is incomplete. In 42 he tries to get around this by stating that “the limit is ultimate” but I find this kind of self-referential: any limit is ultimate because a limit is by definition end of something. An ultimate limit would mean the very end of something and that doesn’t add much sense.

The only idea I have he needs this limit because it’s hard to define something without limits. In other words we cannot grasp something without limits: we need borders to make things exist.

I want to know if there is some robust answer to this or maybe some point from the poem that clarifies that I might have missed.

Thanks!

All citations are from A Presocratics Reader by Patricia Curd

Answer 1

Leonardo Tarán discusses in detail lines 42-49 in Fragment VIII (pages 150-160). Here are some comments on those pages.

He claims "The ancients were already divided about the interpretation to be given to the comparison of Being with a ball or sphere." (page 150).

He initially concerns himself "with the arguments that have been adduced to assert that the comparison with the sphere actually assimilates Being to a sphere." (page 151)

However he claims: (page 151)

To begin with, when Parmenides refers to the "bond" or "limits" of Being he uses these expressions metaphorically to emphasize that it is logical necessity that forces Being to be identical with itself....

Regarding the controversy about these lines he writes: (page 158-9)

The cause of so much controversy about lines 42-49 is the comparison of Being to the body of a well-rounded sphere. It is to be seen from the passage as a whole that Parmenides is not interested in the surface of the sphere or in an equality of radius....Moreover the comparison is not with a sphere but with its mass or body...Once it is seen that Being is complete from every point like the mass of a well-rounded sphere, the motive for such a comparison becomes clear. The point is that the mass of a sphere in equilibrium around the middle is in all parts of equal strength. Such an equilibrium is obtained by the homogeneity of the mass, i.e. it is everywhere the same...That Being is complete everywhere means that everywhere it is just Being, and this preserves the identity of Being as the homogeneity of the sphere keeps it in equilibrium.

With that a preliminary, here is the question:

I want to know if there is some robust answer to this or maybe some point from the poem that clarifies that I might have missed.

Based on Taran, one can view Parmenides' use of a sphere as a metaphor. Rather than imply any limitation of Being, the metaphor suggests that Being is complete and self-identical.

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Parmenides, & Tarán, L. (1965). Parmenides: A text with translation, commentary, and critical essays. Princeton University Press.

Answer 2

Parmenides' fragments are not easy to manage ...

It seems that the notion of "limit" is connected to the rejection of the infinite by many ancient Greek philosophers.

See Aristotle, Phys.III, 6, 206a9-on :

The infinite, then, exists in no other way, but in this way it does exist, potentially and by reduction.

The infinite turns out to be the contrary of what it is said to be. It is not what has nothing outside it that is infinite, but what always has something outside it.

Thus something is infinite if, taking it quantity by quantity, we can always take something outside. On the other hand, what has nothing outside it is complete and whole. For thus we define the whole—that from which nothing is wanting, as a whole man or box. [...] Whole and complete are either quite identical or closely akin. Nothing is complete which has no end and the end is a limit.

Hence Parmenides must be thought to have spoken better than Melissus. The latter says that the whole is infinite, but the former describes it as limited, ‘equally balanced from the middle’.

Thus, it seems that the interpretation must be : "what is" is complete, it is a whole because nothing is missing from it.

But (Aristotle says) "nothing is complete which has no end and the end is a limit."

Thus, "what is" has limits.