Nitpicky English grammar question.

“People should think more,” is a good compromise. But the first sentence is utterly correct, and would only confuse someone who is not a human.

The first one is correct…or maybe it’s the second one…
But seriously, I’d say the first one is correct.

I was leaning towards the first one too.
Yeah @WasCy if I were trying to use that sentence I’d probably find an alternate way to say it, but I’m not actually trying to write something right now. It’s just an example of the grammar question that’s been floating around my head for a while now.

People, plural, have brains, plural. Person, singular, has brain, singular.

The first is more correct- noun/object agreement.

Another way – “Each person should use his or her brain.” Or “everyone should think.”

A person should use his brain.

Simplest version.

The “he” is understood to include females as well.

Brains is an accepted noun for everything in your skull that is the center of your consciousness.
Brain is too, but it is less an intellectual noun and more of an anatomical one.
Plus it depends on context.
Most people who take a high velocity round in the skull will have some of their brains splatter onto the road.
But only a few will lose their whole brain

The word “people” functions as an aggregate noun here. This site from Georgia State U says that ”Many aggregate nouns have plural forms, but many also are not plural in form, though they use plural verb forms. Example: The police are still looking for the Olympic Park bomber.”

Wikipedia has a page on people wouldn’tcha know it that says that usage includes: the plural of person (in addition to the rarer plural, ‘persons’) or a group of people (grammatically, a suppletive plural and collective noun; e.g. ‘some people are…’) ...

Having established that “people” is a plural, it seems reasonable that brains would also be plural, there generally being a one-to-one correspondence between people and brains. Unless this is a sci-fi scenario where people are tapping into a single, collective group brain as pointed out by the OP.

Since “brains” is plural, it takes the plural possessive pronoun “their.”

Had it been “brain” (singular), there is controversy about the usage of the gender-neutral “their” instead of the phrase “his or her”, as in “Each individual should use their brain.”

Ambiguity arises, I think, because “brains” can also be a collective singular for cranial contents, as in “He blew his brains out!” Or “She’s got lots of brains,” meaning: She is intelligent; not meaning: She is Igor’s assistant and is carrying several brains from the lab.

I would have no hesitation in writing “People should use their brains.”

Either one is fine…

In the given samples, their is a third person plural antecedent, so it would seem strange to follow it with a singular object. Their can also be a third person singular antecedent in sentences where the gender of the person being spoken of is unknown. So you could write “A person should use their brain.” when it isn’t clear whether the person referred to is male or female. In this case, “their” substitutes for the more cumbersome “his or her”.

Oh, clearly it’s “brains”. Just ask the zombies.

@ETpro, don’t you mean “third person plural pronoun”? The antecedent is the noun to which the pronoun refers—in this case, “people.”

@Jeruba Poorly worded, but people is the antecedent and is plural, right?

Yes. “People” is the antecedent of the possessive pronoun “their.” “Their” is not an antecedent.

In Google, there are about 826,000 results for “people use their brains” and 422,000 results for “people use their brain”. The most used form therefore seems to be “use their brains”.

I do not agree with the reasoning above though. The mere fact that the plurality of people is implying a plural for ‘brains’, does not convince.

Let me explain by a similar google-search:

16,100 “dogs use their sense of smell” vs 76 dogs that “use their senses of smell”.

My guess… in the example both are correct, but sometimes the plural may indeed just seem unnatural and should be considered the poorest choice.

:-)

Whether grammar is a matter of personal opinion is a matter of personal opinion.

People = plural
Person = singluar

People should use their brains is correct.

We do have more than one brain – the organ we call the ‘brain’ is actually two separate hemispheres, connected by a ‘bridge’ of tissue. So I would say the plural form is equally valid.