There are several jokes within the series revolving around whether the Griffins, other than Brian, can understand Stewie. In "E. Peterbus Unum", a student watching the episode from the distant future asks his teacher, "So, can the family understand the baby, or... what's the deal with that?" In "Inside Family Guy", Peter apologizes to the family, to which Stewie comments: "Oh that's nice of you to say". Peter replies: "Thank you, Stewie, who I can understand". In "Stewie's First Word", after Stewie utters an expletive that everyone around him can clearly understand, he eventually concludes that people can only understand him when he wants them to, namely whenever he is feeling intense emotion.
