Omission of verbs
The implicit verb is simply “be”:
Some symbols acquire a multitude of meanings,
some [of which] [are] widely shared [meanings],
others [of which] [are] personal [meanings],
[and] some [of which] [are] contradictory, conflicted, or ambivalent [meanings].
This is a common structure to describe different parts of a subject with different adjectives, while avoiding repetition of the subject or verb. For example:
I bought four apples: two red, two green.
All of these are equivalent:
- I bought four apples: two apples [were] red, two apples [were] green.
- I bought four apples: two red ones, two green ones.
- I bought four apples: two red apples and two green apples.
- I bought four apples. Two of them were red and two of them were green.
Similar yet unrelated to this structure, some adjectives are postpositive, that is, they come after the noun they modify. Examples include: “the best hotel possible”, “the person responsible”, “the town proper”, “the attorney general”. This also appears in poetic language, like “the sky blue and forest green”, or “he called for his fiddlers three”.
There is no verb missing in this sentence. The sentence is somewhat unorthodox, in that the entire fragment in boldface is a series of modifiers of "a multitude of meanings." In this case, they are identifying the different components of the multitude:
- widely shared meanings
- personal meanings
- contradictory meanings
- conflicted meanings
- ambivalent meanings
I think clarity arises if you punctuate the sentence somewhat differently:
Some symbols acquire a multitude of meanings: some widely shared, others personal; some contradictory, conflicted, or ambivalent.
However, either form is possible.