“I made myself a promise, that I'd soon forget we ever met. But something sure is wrong. I forgot to remember to forget”

In the years immediately following 1972’s The Three Doctors, fandom at large assumed, for the sake of simplicity and clarity if nothing else, that the First and Second Doctors must have forgotten their participation in the events of the story after being returned to their “bits of our timestream” (as the Troughton Doctor phrases it). On the face of it, that makes sense. A Doctor who has seen his own future and is able to recall it might try and avoid it, or at least disrupt it accidentally, and we had already seen the Time Lords block or erase the memories of the Doctor, Jamie and Zoe in The War Games (1969). 

Of course, it need not be a deliberate act on their, or anyone’s part, it could also have been an unavoidable natural process related to moving up and down one’s own timestream (a fan explanation seemingly endorsed more than a decade later in The Trial of A Time Lord (1986) when the Valeyard suggests that the Doctor’s amnesia is “possibly a side effect of being taken out of time”. What was important was that the Pertwee Doctor did not spend the events of the Omega crisis smugly sure it'll turn out okay; so he obviously can’t remember having done all this twice before. 

So far? So simple. Then the next multi-Doctor story came along. In The Five Doctors (1983, written by Terrance Dicks, who commissioned and edited The Three Doctors and re-drafted more than a little of it) the Troughton and Hurndall¹ Doctors clearly remember the events of The Three Doctors and we know this, because they say so out loud more than once.