Foundation Narrator:

Third-Person Omniscient

Let's start with some light mental lifting first and then add weight as we go. Don't worry; we're here to spot.

First the light stuff: Asimov wrote Foundation in third person. This means the narrator is a person or entity outside of the story and not a character within it. You can tell this is the case because the story is written with "he" and "they" pronouns to describe the action. If the narrator were a character in the story, we'd see an "I" in the action roles (such as "I said" instead of "he said"). That's not the case, so go ahead and mark this one as third person.

Now, onto the slightly weightier issue. Third-person narration comes in three different flavors: limited, omniscient, and objective. Yes, only three, and that's a good thing. We want to solve this riddle, not complicate it. Let's look at an example to figure out which flavor is to Asimov's taste:

He shoved the door release and out of an abstracted corner of one eye saw the door open and the broad figure of Salvor Hardin enter. Pirenne did not look up.

Hardin smiled to himself. He was in a hurry, but he knew better than to take offense at Pirenne's cavalier treatment of anything or anyone that disturbed him at his work. (II.1.4-5)

Notice how we get Hardin's inner thoughts about Pirenne in the second paragraph? This lets us throw objective right out the window, because objective provides the facts and just the facts. None of that inner-monologue piffle-paffle. That leaves us with just limited and omniscient.

If this were limited, then the narrative voice would be limited to a perspective character. But in this example, the narrative perspective jumps seamlessly from Pirenne in the first paragraph to Hardin in the second paragraph. Sure, the narrative voice doesn't jump often in the novel, but it does so whenever it chooses to. Bye-bye, limited; hello, third-person omniscient.

How was that for a mental workout? Can you feel the burn in your corpus callosum, yet?