Does George Costanza have a brother?

In two separate episodes of Seinfeld, George mentions his brother.

The first, in episode fifteen of the third season, titled "The Suicide":

RULA: Who’s Pauline?

GEORGE: Pauline? . . . Wait a minute. I got it. My brother once impregnated a woman named Pauline.

RULA: Do you think about her?

GEORGE: When I hear her name mentioned.

The second, in the twenty-third episode of the third season, titled "The Parking Spot":

ELAINE: Oh come on, George, please put it in a garage. I don't want to spend
an hour looking for a space.

GEORGE: I can't park in a garage.

ELAINE: Why?

GEORGE: I don't know, I just can't. Nobody in my family can pay for parking,
it's a sickness. My father never paid for parking; my mother, my brother,
nobody. We can't do it.

Further confusing the situation is that in later episodes George repeatedly claims to be an only child. (examples welcome)

< seinfeldvoice >
So what's the deal with George Constanza's brother? Is he real, or is George an only child?
< / seinfeldvoice >