Is this sentence grammatically correct?

it depends on the gender of the pedant. you could go with a gender neutral pronoun like hirself.

In this case, you could use either "are the pedants themselves" or "is the pedant himself."

That's because you haven't already specified whether it's one or more than one.

Here's an example where it would be wrong: "Although the patient isn’t following through with a home exercise program they may still be making benefits in the clinic." In this case (a true example, one I ran into yesterday), the author begins with "the patient" (singular) and then turns it into a plural "they."

There's a different issue with himself/herself. If it's singular and you know that it's male or female, use "him" or "her." As in: "A man with high blood pressure should check with his doctor" or "A woman often wants her house to be in a safe neighborhood."

But often you don't know. Example: "A person who is dizzy should go to [his or her] doctor." It's considered sexist to just refer to unknown people as "him" or "his." It also might be exclusionary: "A person with chest pains should check with _______ doctor." If you put in "his," that could be incorrectly read as meaning women shouldn't check with doctors if they're having chest pains.

So what do you do?

You can use "his or her." Or sometimes just "his/her." Or rewrite the sentence: "A person with chest pains should check with a doctor." Or "People with chest pains should check with their doctors."

Hope that helps.

Yes.