First, that Sauron did not realize that the Ring was still extant, and that he believed it was his own power, not the remaining existance of the Ring that had saved him from complete destruction, in the begining.

Second, that upon learning that the Ring still existed, Sauron then believed that none of the Wise woudl seek to destroy it, since they did not destroy it when they had the supreme chance.

Third, that Suaron believed Aragorn had the Ring. Michael has pointed this out several times in the thread on Gandalf lying. If the above statements hold, then this seems plausible as well. And to this extent, Sauron would now be fully duped into believing that the Ring was in the possession of someone with power, though he would not be certain exactly who. He would have rejected any fear of the Ring being destroyed and now would have bent his entire will to the Battle of Pellenor Fields.

Finally, that Gandalf, either through previous conjecture about the amount of power the Ring had over Sauron, or through his rebirth as Gandalf the White, knows, or believes he knows that destroying the Ring will destroy Sauron.

Now, I think that answers all of macadamia's questions. But I am not certain, let me know if i missed anything!

-RobRoy