|Brainwaves during REM sleep - from Wikipedia|
In his book Dreaming, published in 1959, the philosopher Norman Malcolm put forward an interesting idea on dreaming. At the time, psychologists were investigating dreams by studying sleeping subjects wired up to various recording devices. One of their discoveries was that rapid eye movement (REM) during sleep seemed to be accompanied by dreams. If a sleeping subject was woken during REM sleep, the subject was more likely to report that they had been dreaming than subjects woken when REM was not taking place.
So you might think it was a simple enough step for psychologists to link REM with dreaming, which is what they did and still do to this day. However, Malcolm didn't think this link was valid for reasons connected with Wittgenstein's concept of language games. He thought psychologists had changed the everyday meaning of dreaming and dreams, in effect playing a new language game with them. He accused psychologists of using REM to give dreams and dreaming a new and illegitimate scientific meaning.
In simple terms, this is Malcolm's main argument :-
Let us first suppose an alternative explanation to the REM theory of dreaming, always remembering that this theory says dreams occur during REM sleep. But suppose dreaming doesn't occur while we are asleep at all, but is simply a jumble of images caused by waking up. Suppose dreams occur during those few seconds where you pass from an unconscious sleeping state to full consciousness. Whether this conjecture is valid or not, how would you disprove it in favour of the REM theory?
The short answer is that you can't because of the nature of sleep. At the time there was lots of argument back and forth and in the end, Malcolm went his way and the psychologists went theirs. But from an experimental design point of view, the theory that REM and dreams occur at the same time cannot be proved. The logic of being asleep means you can't report your dreams until you are awake. You can never report what is going on inside your head during REM sleep.
Malcolm's argument is unanswerable to this day. In practice it is no longer an important argument, because psychologists have opted to ignore it. Norman Malcolm's ingenious and unanswerable argument has become a footnote to the history of unwelcome ideas.
Source - Wittgenstein A Social Theory of Knowledge by David Bloor published in 1983.