An Experiment with Time by J.W Dunne was a major influence on The Inklings, and forms a background to the posthumously-published and unfinished novels The Notion Club Papers by JRR Tolkien and The Dark Tower by C.S Lewis.
One of the most striking passages in The Dark Tower is the following:
" '... that we see the future is certain. Dunne's book proved that - '
"MacPhee gave a roar like a man in pain.
" 'It's all very well, MacPhee,' Orfieu continued, 'but the only thing that enables you to jeer at Dunne is the fact that you have refused to carry out the experiments he suggests. If you carried them out you would have got the same results that he got, and I got, and everyone got who took the trouble. Say what you like but the thing is proved. It's as certain as any scientific proof whatever.' "
Dunne had recorded his dreams in detail and in writing the instant he awoke. The method he describes is very specific, and he is clear that unless this method is followed, then the necessary information will not be available.
Dunne's conclusion - surveying these results, from himself and others - was that some parts of some dreams consisted of recollections of past events (especially the day preceding the sleep) mixed with anticipations of future events - quite thoroughly mixed, so that which-was-which only became apparent later.
My sense is that Lewis and Tolkien both accepted this by the late 1930s into the 1940s, sought an explanation, and discussed its implications - presumably in Inklings meetings.
Let us assume that Dunne was right and that Lewis and Tolkien were right to accept his evidence.
And let us take the evidence of the Dark Tower and the Notion Club Papers to conclude that Dunne's experiments were replicated, were verified, at least by Lewis and Tolkien and (probably) some other of the Inklings.
Then why has this idea died-out? Why do so few people nowadays believe that dreams can predict the future?
The reason is easy enough to understand on reading Dunne - that the dreams were a mixture of past, future and apparently irrelevant material - but there was no way to evaluate which elements were predictive until after they had been confirmed.
So, although Dunne seemed to show convincingly that some aspects of some dreams were visions of the future - this had no practical value: specifically this partial and mixed knowledge offered no powers.
You could not - therefore - use future visionary dreams to make money (e.g from bets), manipulate people, avoid disasters or anything of that kind.
To the modern mind, this means that Dunne's work seemed trivial, hence ignorable, and was eventually discarded (without consideration) as being fake, or gullible, or something...
That dreams contained visions of the future was, of course, believed by everyone until a few hundred years ago - and probably is believed by the vast majority of people in the world even now. But in ancient times, the ability to interpret dreams, and decode the future visions - so that the knowledge they contained might become useful, was regarded as a rare gift (and one associated with a lot of fakery).
On the other hand, if Dunne was correct (and I find the testimony of Lewis and Tolkien hard to ignore) then this is very interesting for what it may tell us about the human condition.
Among other things, it suggests to me the following:
1. That dreams have a natural function - and not just related to memory (the past) but also to the future.
2. That this natural function happens during sleep and does not require conscious awareness (since most people most of the time do not recall dreams - and Dunne's results depend on specific techniques of rapid recall, association and the making of an objective record, which techniques were apparently not done by anyone before him; and by very few since).
3. That - therefore - although containing material from the future, the natural function of dreams is not predictive; and that the use of dreams to predict the future is a special, individual, learned skill.
4. My guess as to one function of dreams is therefore that they locate each person in time ('in the world') in an unconscious, implicit, non-verbal way; that dreams provide our relation to reality, our embeddedness in time, which we carry with us as a background to waking, conscious life.
(Dreaming is not, then, functioning only to 'consolidate' past memories, but perhaps also to prepare for the unfolding future - time stretching-out on both sides from the present moment of the dream.)
5. That it is therefore possible that the lack of dreams, or of dreams of the right kind (perhaps as a result of some illness, or unnatural lifestyle, or drugs or something) might cause alienation: might cause someone to feel isolated, un-integrated with life, solipsistic, that life has no meaning nor purpose.
Note: The above was adapted from a posting on my Notion Club Papers blog.