In Through the Looking Glass, Tweedle-Dum and Tweedle-Dee show Alice the sleeping Red King and tell her that she is merely a part of his dream.
`It's only the Red King snoring,' said Tweedledee.Is it nonsense?
`Come and look at him!' the brothers cried, and they each took one of Alice's hands, and led her up to where the King was sleeping.
`Isn't he a LOVELY sight?" said Tweedledum.
Alice couldn't say honestly that he was. He had a tall red night-cap on, with a tassel, and he was lying crumpled up into a sort of untidy heap, and snoring loud -- `fit to snore his head off!' as Tweedledum remarked.
`I'm afraid he'll catch cold with lying on the damp grass,' said Alice, who was a very thoughtful little girl.
`He's dreaming now,' said Tweedledee: `and what do you think he's dreaming about?'
Alice said `Nobody can guess that.'
`Why, about YOU!' Tweedledee exclaimed, clapping his hands triumphantly. `And if he left off dreaming about you, where do you suppose you'd be?'
`Where I am now, of course,' said Alice.
`Not you!' Tweedledee retorted contemptuously. `You'd be nowhere. Why, you're only a sort of thing in his dream!'
`If that there King was to wake,' added Tweedledum, `you'd go out -- bang! -- just like a candle!'
`I shouldn't!' Alice exclaimed indignantly. `Besides, if I'M only a sort of thing in his dream, what are YOU, I should like to know?'
`Ditto' said Tweedledum.
`Ditto, ditto' cried Tweedledee.
He shouted this so loud that Alice couldn't help saying, `Hush!
You'll be waking him, I'm afraid, if you make so much noise.'
`Well, it no use YOUR talking about waking him,' said Tweedledum, `when you're only one of the things in his dream. You know very well you're not real.'
`I AM real!' said Alice and began to cry.
`You won't make yourself a bit realler by crying,' Tweedledee remarked: `there's nothing to cry about.'
`If I wasn't real,' Alice said -- half-laughing though her tears, it all seemed so ridiculous -- `I shouldn't be able to cry.'
`I hope you don't suppose those are real tears?' Tweedledum interrupted in a tone of great contempt.
`I know they're talking nonsense,' Alice thought to herself: `and it's foolish to cry about it.'
The dream argument plays prominntly in Descartes' version of skepticism where he argues that every thought could be false because it could all be the result of a dream. Every thought, that is, except that the self exists because there must be a self to have the dream.
But this is what Carroll is questioning here. Does the ability to think guarantee independent existence? Could your thoughts be a part of the dream of someone else? Is "I think, therefore I am" invalid? Should it read "I think, therefore someone -- maybe me, maybe not -- is"? Could parts of your dreams have thoughts or do they just appear to have thoughts in the dream? Could they think if they were your thoughts is it inconsistent to think of such things as capable of thought?