Douglas Hofstadter Quotes

without concepts there can be no thought, and without analogies there can be no concepts.

"the Godelian strange loop that arises in formal systems in mathematics (i.e., collections of rules for churning out an endless series of mathematical truths solely by mechanical symbol-shunting without any regard to meanings or ideas hidden in the shapes being manipulated) is a loop that allows such a system to "perceive itself", to talk about itself, to become "self-aware", and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self."

The 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.

"There can be conceptual skeletons on several different levels of abstraction. For instance, the "isomorphism" between Bongard problems 70 and 71, already pointed out, involves higher-level conceptual skeleton than that needed to solve either problem in isolation."

In fact, a sense of essence is, in essence, the essence of sense, in effect.

If you listened to each voice on its own, you would find that it seemed to make sense all by itself. It could stand alone, and that is the sense in which I meant that it is independent. But you are quite right in pointing out that each of these individually meaningful lines fuses with the others in a highly nonrandom way, to make a graceful totality. The art of writing a beautiful fugue lies precisely in this ability, to manufacture several different lines, each one of which gives the illusion of having been written for its own beauty, and yet which when taken together form a whole, which does not feel forced in any way.

"An amusing way to see the incorrectness of Lucas' argument is to translate it into a battle between men and women ... In his wanderings, Loocus the Thinker one day comes across an unknown object — a woman. Such a thing he has never seen before, and at first he is wondrous thrilled at her likeness to himself; but then, slightly scared of her as well, he cries to all the men about him, "Behold! I can look upon her face, which is something she cannot do — therefore women can never be like me!" And thus he proves man's superiority over women, much to his relief, and that of his male companions. Incidentally, the same argument proves that Loocus is superior to all other males, as well — but he doesn't point that out to them. The woman argues back: "Yes, you can see my face, which is something I can't do — but I can see your face, which is something you can't do! We're even." However, Loocus comes up with an unexpected counter: "I'm sorry, you're deluded if you think you can seemy face. What you women do is not the same as what we men do — it is, as I have already pointed out, of an inferior caliber, and does not deserve to be called by the same name. You may call it 'womanseeing'. Now the fact that you can 'womansee' my face is of no import, because the situation is not symmetric. You see?" "I woman-see," womanreplies the woman, and womanwalks away..."

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.

This idea that there is generality in the specific is of far-reaching importance.

My vast episodic memory of my past, together with its counterpart pointing blurrily towards what is yet to come (my episodic projectory, I think I’ll call it), and further embellished by a fantastic folio of alternative versions or “subjunctive replays” of countless episodes (“if only X had happened…”; “how lucky that Y never took place…”, “wouldn’t it be great if Z were to occur…” — and why not call this my episodic subjunctory?), gives rise to the endless hall of mirrors that constitutes my “I”.

"For an imperfect but vivid concrete analogue to this curious abstract phenomenon, think of what happens when a TV camera is pointed at a TV screen so as to display the screen on itself (and that screen on itself, etc.)- what in GEB I called a "self-engulfing television", and in my later writings I sometimes call a "level-crossing feedback loop."

When and only when such a loop arises in a brain or in any other substrate, is a person-a unique new "I" - brought into being. Moreover, the more self-referentially rich such a loop is, the more conscious is the self to which it gives rise. Yes, shocking though this might sound, consciousness is not an on/off phenomenon, but admits of degrees, grades, shades. Or, to put it more bluntly, there are bigger souls and smaller souls."

You can’t go on defending your patterns of reasoning forever, there comes a point where faith takes over.

We claim that cognition takes place thanks to a constant flow of categorizations, and that at the base of it all is found, in contrast to classification (which aims to put all things into fixed and rigid mental boxes), the phenomenon of categorization through analogy-making, which endows human thinking with its remarkable fluidity.

In the end, we self-perceiving, self-inventing, locked-in mirages are little miracles of self-reference.

What gives us word-users the right to make life-and-death decisions concerning other living creatures that have no words? Why do we find ourselves in positions of such anguish (at least for some of us)? In the final analysis, it is simply because might makes right, and we humans, thanks to the intelligence afforded us by the complexity of our brains and our embeddedness in rich languages and cultures, are indeed high and mighty, relative to the “lower” animals (and vegetables). By virtue of our might, we are forced to establish some sort of ranking of creatures, whether we do so as a result of long and careful personal reflections or simply go along with the compelling flow of the masses. Are cows just as comfortably killable as mosquitoes? Would you feel any less troubled by swatting a fly preening on a wall than by beheading a chicken quivering on a block?