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I have asked a similar question, but this problem (see the title) always confuses me. For example, suppose I introduced several symbols (e.g., A, B, and C) in my writing. In a later section, when I reuse the symbols in the same way, which one (or neither) is more appropriate?

The interpretation of the symbols follows that described above.

or

The interpretations of the symbols follow those described above.

Each symbol has its unique interpretation and thus there are multiple interpretations, so I think the latter is correct. But interpretation (or definition) is a shared property (although each has a different interpretation) so can it be singular? (e.g., cats have a nose.)

  • A, B, and C (as defined in Section 2.3) ... – Jim Jun 13 '14 at 3:03
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You've got a good handle on the situation.

If you're collectively talking about each symbol's individual specific meaning, use the plural. The group is the collection of interpretations, and individual interpretations may correspond to different symbols.

If you're talking about the property of having an interpretation or if many symbols combine to form a single aggregate interpretation, use the singular. The group is the collection of symbols, and they all have some kind of interpretation.

If you're unsure which one to use, try removing of the symbols from the sentence. The grammar will be the same without it, because it's a prepositional phrase functioning as an adjective to describe interpretation[s]. The fact that symbols is plural doesn't make any difference to the verb.

The interpretations [of the symbols] follow those described above.

Each symbol has its own, possibly different, interpretation as described above.

The interpretation [of the symbols] is unique.

Multiple symbols combine together to form a single unique interpretation.

An interpretation [of the symbols] is always possible.

A symbol always has an interpretation, but the interpretations may be different for different symbols.

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