They can't. The Rationalist will accuse the Existentialist of having delusions, that what he experienced was all a process of the mind. The Existentialist will accuse the Rationalist of rationalising everything, that logic cannot be applied to an illogical life, that knowing something through an experience supercedes purely theoretical postulations. He will also accuse the Rationalist of being deluded. The Existentialist knows that only the individual will change while the Rationalist looks at the collective and thinks that it can change. The Rationalist will be Objectively minded while the Existentialist is Subjectively minded. The Rationalist will dismiss any sensation or situation which he has not experienced, but at the same time he refuses to believe that such sensations or situations can happen to him since it is illogical. "When the map and the terrain disagree, trust the terrain."
Only within the context of his mind, unless he becomes Enlightened, whereby the subconscious merges with the conscious mind, whereby the subconscious becomes less and less and awareness (consciousness) becomes more and more. If the subjective is the Heart and the objective is the Mind, then they must both merge. With Enlightenement both must be transcended. Take love for instance, the Rationalist can say that no such thing as love truly exists. The person who has fallen in love, who has plumbed its depth, who knows the sickness will just laugh at the Rationalist. Love is not logical. At best the Rationalist will appeal to Science which defines Love as hormones gone awry. His "understanding" of what love is, is only in his mind. The person who has tasted love, who has been loved at the same time as he loves will disagree with the Scientific definition.
But what I'm suggesting is that we know that the love does not exist in the objective, but it is real to us in subjective. Basicly what I want is what I call Rational Existentialism, which is existentialism appying to your subejtive and Rationalism appying to the objective.
well... that does leave open a rationalist question....What point would there be in discussing existentialism. I do not believe that rationalism necessarily ended in solipsism as you imply, but as a methodological basis of philosophy, or a metaphilosophical debate. To the rationalist it would make no sense to debate the issues of existentialism, merely the methodology that existentialists apply If people ask such questions as the one we are trying to investigate, it would seem at first as though the question were playing rationalism off against existentialism, but since existentialism MUST at some point concern itself with its own methodologies, that would imply a form of rationalism. Rationalism on the other hand need never concern itself with matters of an existential nature since it is merely a description of methodology That is to say, there is no conflict between them, and that does not mean they are both compatible either. Just that they are two entirely separated realms. Existentialists enter the rationalist debate when they are discussing errors of logic, but rationalist need never discuss existential themes.