Is this an incorrect usage of singular they? Is there a better, more concise way to say it? (this is an incomplete sentence but the only relevant part)
“…people who have said they are a god.”
I would put it:
“… people who have said that they are gods.”
I would agree with this. The third-person plural is often used as a gender-neutral third-person singular, as in “Each person should take care of their business.” Personally, I don’t mind such usage and prefer it to “his/her” or “his or her” type constructions. However, in many cases, it’s simply easiest to cast the sentence in the plural, thus avoiding the wrath of grammar purists.
It’s not, I think, just a question of singular (gender-neutral) ‘they’ usage in this chunk, since grammatically, at any rate, the pronoun ‘they’ is agreeing in number with its referent noun ‘people’. (An example of prototypical singular ‘they’ usage would be: “Each person will choose the colour they want” (rather than “Each person will choose the colour he or she wants”).)
In your example, it depends what the people actually said in direct speech. If it was “I am a god” (which is a strange thing for one person to say, let alone several, though I could imagine some people - some Dopers, indeed - saying “I am God”!), then you can capture that in a number of ways:
- people who have said they are a god
- people who have said they are gods
- people who have said they were a god
- people who have said they were gods
The choice of tense depends on the focus that the writer wants to give the report (where the past tense is possible in the scenario where the writer wants to focus on the time at which the utterance was made - which they might want to do if, for example, all the people they are referring to are no longer alive. Thus, “Throughout the ages, people who have said they were gods have been treated as nutters.”) When the writer wants to focus on the eternal truth (in the nutters’ own eyes, of course) of their belief, then the present tense is the resource that communicates that.
As for number (i.e. singular and plural), the plural is much more common, and therefore through sheer weight of attested frequency the average writer will be drawn to the plural. Like the lure of the Ring, they must fight the tendency to use the plural if they are to use the singular. Thus, we can refer to singular usage here as marked. I would interpret the singular here (“people who have said they are a god”) as being motivated by the writer’s desire to stress that each of the people they are referring to said: “I am a god” (rather than “I am gods”). But most readers will understand the chunk “people who have said they are gods” as meaning that what each individual nutter actually said was “I am a god”, so most people would indeed use that formulation, as Reg and puly have pointed out.
With an ambiguous situation wuch as this, where some people dislike the usage and others have no problem with it, sidestep the issue entirely: “…people who have claimed to be gods”