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In Back to the Future 3, Doc (from 1955) sends Marty back in time wearing a cowboy outfit.
But then, Doc (from 1885) doesn't remember that it was him who offered this outfit to Marty.
Does this mean there are two different Docs (from differing timelines) or is it the same Doc but he somehow forgot the outfit.
The writers of the Back to the Future films (Writer/Producer Bob Gale and Writer/Director Robert Zemeckis) specifically addressed this point in an "Official FAQ" on the BTTF website:
1.19: Doc Brown of 1955 learns a lot about the future from Marty. Shouldn't the Doc of 1985 remember all of those things that happened in 1955?
A: 3 possible answers, all credible. 1) The "Ripple Effect" of time travel (which caused all of the photographs to change) does not affect human memory. 2) The 1955 Doc suffered a memory loss sometime after his adventures with Marty (maybe it was from the drugs he took in the 60's as Reverend Jim!). 3) Doc actually did remember everything, but he still did all the same things he "remembered" because he didn't want to risk disrupting the space-time continuum.
There's a 4th possibility which depends on your view of time travel. There's a theory (we like to call it the "Self-Preservation Instinct of the Space-Time Continuum Theory") that says that the continuum is always trying to keep itself "on course," and when things happen to change it, it always tries to correct itself. It is much like a river, which tries to keep its overall course. Although earthquakes, fallen trees, floods, or other circumstances might disrupt it at points, the river would cut a new channel so that it would end up back at the same place. Thus, the overall physics (or metaphysics) of the space-time continuum would insure that any of Doc's memories of events that might create paradoxes would become hazy — or be erased.
I think it is much simpler than other answers: Doc in 1955 actually believed that the 'old west' clothing he got for Marty was correct for the period, so even if he remembered getting it for Marty, he would remember it as 'clothing which would blend in', so he wouldn't consider it an important detail. Then over thirty years passes - plenty of time to completely forget about such trivia (especially since he was largely preoccupied with development of the flux capacitor!). When Marty gets to Doc in 1885, although indeed the Ripple Effect has occurred, it has done so as a memory newly added to 1955 Doc which has since naturally faded. Also, Doc in 1885 has had a few months to get to know what clothing in the 'old west' was -really- like, so when Marty shows up in this stupid 'Roy Rogers Show' outfit that plainly doesn't fit in (as he now subconsciously expects it to!), he's surprised.
If I remember correctly, in the novelisation of Part 3, 1985/1885 Doc did remember that it was he who had put Marty in the silly outfit, and even his motivation for doing so. Maybe the Ripple Effect did catch up and affect time-travellers' memories eventually. But it's an interesting twist: it's a future Doc relative to the one in 1955, but at a point in time 70 years earlier. Might there be different rules for the Effect depending on whether the person with the altered memories is in the past or the future?
If Marty tells something to Doc in 1955, Doc should remember it (or write it down) until 1985, and therefore remember it in 1885, so there is no need for Marty to travel to 1885 from 1955.
In such case, complete plot becomes meaningless so producers in order to keep the script an production going on will ignore this nonsense and will try to give false explanations as they did in 4 possible explanations which all can be contested:
Ripple Effect - can not be applied in this case since there is no history alternation from moment in 1955 until 1985 (thus in 1885)
memory loss - would explain why Doc don't remember things, but is not a valid reason for Marty to start travel since Doc as scientist is expected to be sharp, but also to remember important and personal information (or write it down)
Doc ignores information - in contrast to Doc's character and previous decisions. As intelligent person, if Doc knows in some point of his future he should violently die, he would easily and minimally alter his decisions in order to avoid his fate, same as he did in BtF part I when he kept Marty's letter
Continuum self preservation - if this should be valid in the trilogy, then Marty, or anyone else, could never change the future by his acts in the past
Since scriptwriters are not providing explanation in the script itself, it is clearly a flaw in the plot, and the reasons it was not fixed could be it was discovered too late during production, or it was considered intended audience will not notice it.
This also goes with a theory as to why Doc is actually still alive in 1885 before being shot. Doc put the pieces of the letter back together between 1955 and 1985 because "what the hell". Logically if Doc sees Marty again in 1955 and sends him back to 1885, he would assume that this Marty would again try to tell him whatever he was trying to tell him before sending him to 1985. Therefore he would assume it was no longer of relevance and would now no longer piece the letter back together, therefore Doc would now still die in 1985 to the Libyans and would never end up stuck in 1885.
