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human
[Star Wars: The Phantom Menace] How did Yoda know about the Rule of Two?

In the Phantom Menace, when Qui-Gon mentions his mysterious attacker could have been a Sith, the Jedi Council reacts that this is impossible because the Sith have been extinct for thousand of years. So I suppose the Jedi never discovered Darth Bane survived and started a new Sith Order based on the Rule of Two.

However, after Darth Maul is defeated, Yoda mentions to Mace Windu: "Always 2 there are. A master and an apprentice." How does he know? A few weeks before he was still convinced the Sith were extinct and now he suddenly knows about the Rule of Two? 

And if the Jedi knew about the Rule of Two, then they would not consider the Sith extinct, right?
gpt
The Rule of Two was a sort of extension of current Sith heirarchy. In every major Sith for ("Lord" Kaan's Brotherhood notwithstanding) there were always two Sith at the very top: the Master and his Apprentice. All other Sith were lesser to them, and as far as Sith philosophy was concerned the rest were unimportant in the grand scheme. It is logical that Yoda was able to reason that given there's always at least two Sith, the Master and his Apprentice, there must be another out there.

Another possibility would simply be reasoning that a Sith does not occur in a vacuum. A Sith must have a Master in order to become Sith, so of course there will be one more. It's a similar concept to Jedi always training in Master-Padawan pairs. Yoda, especially given how it was growing harder and harder to see things through the Force, would realize that it is not impossible for a pair or perhaps even a few pairs of Sith to exist in hiding for a millennia.