The paraphrase of Gรถdel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.
Douglas HofstadterWe create an image of who we are inside our self. The image then becomes very deeply entrenched, and it becomes the thing that we attribute responsibility to - we say "I", "I" did this because "I" wanted to, because "I" am a good person or because "I" am a bad person. The loop is the fact that we represent our selves, our desires, hopes, dreads and dreams: it is the way in which we conceive of ourselves, rather than the way we conceive of Mount Everest or of a tree. And I say it exists entirely in the loop: the self is an hallucination hallucinated by an hallucination.
Douglas HofstadterWhat is an "I", and why are such things found (at least so far) only in association with, as poet Russell Edson once wonderfully phrased it, "teetering bulbs of dread and dream" - that is, only in association with certain kinds of gooey lumps encased in hard protective shells mounted atop mobile pedestals that roam the world on pairs of slightly fuzzy, jointed stilts?
Douglas HofstadterThe proverbial German phenomenon of the verb-at-the-end about which droll tales of absentminded professors who would begin a sentence, ramble on for an entire lecture, and then finish up by rattling off a string of verbs by which their audience, for whom the stack had long since lost its coherence, would be totally nonplussed, are told, is an excellent example of linguistic recursion.
Douglas Hofstadter