i guess she has a different definition of "intellectual" than most people

Palin on whether she’s intellectual: ‘Yehhh-sss.’

In an interview with Gov. Sarah Palin (R-AK), People magazine commented that “you don’t get to be governor without being smart” and asked, “Do you think you’re intellectual?” Palin responded, “Yehhh-sss”:

PALIN: Yehhh-sss. And you have to be up on not only current events, but you have to understand the foundation of the issues that you’re working on. … You can’t just go on what is presented you.

Q: And how do you get that knowledge?

PALIN: I’m a voracious reader. … I appreciate a lot of information.

Later in the interview, when asked what she is currently reading, Palin responded, “I’m reading, heh-heh, a lot of briefing papers.”

(Think Progress)

Yet she remains willfully ignorant:
‘Energy Expert’ Palin Can’t Name Any Man-Made Causes Of Global Warming
(Think Progress)