Gödel, Escher, Bach: An Eternal Golden Braid

Gödel, Escher, Bach: An Eternal Golden Braid

Douglas R. Hofstadter

Language: English

Pages: 824

ISBN: 0465026567

Format: PDF / Kindle (mobi) / ePub


Douglas Hofstadter’s book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

itself. Here is an attempt: The sentence "The sentence contains five words" contains five words. But such an attempt must fail, for any sentence that could be quoted entirely inside itself would have to be shorter than itself. This is actually possible, but only if you are willing to entertain infinitely long sentences, such as: The sentence "The sentence "The sentence "The sentence … …. etc,.,etc. … …. is infinitely long" is infinitely long" is infinitely long' is

what reasons; (6) describe its actions and their reasons, in English. It might seem reasonable to break up the overall program into modular subprograms, with one module for each different part of the problem; then, after the modules have been developed separately, to integrate them smoothly. Winograd found that this strategy of developing independent modules posed fundamental difficulties. He developed a radical approach, which challenged the theory that intelligence can be compartmentalized

arguments against, 597-99; attitudes distribution in, against, see anti-Al attitudes; computer 318-28; castes in, 317-18; communism in, languages and, 299-300, 548; converging 318, towards brains, 579; defined, 26; difficulty 330-31; compared with brains, 315-16, of, 26-27, 573, 740; evidence and, 695; 318, faith underlying, 572, 578-79; G6del's 324-25, 350, 358-59; contrasted with gases, Theorem and, 388-90, 471-77, 706-7; Index XXIII 317; freedom and control in, 315-16, 327; Aria with

One gets used to it. Achilles: Does taking the tonic feel this strange? Tortoise: Oh, that's quite another sensation. Whenever you taste the tonic, you feel a deep sense of satisfaction, as if you'd been waiting to taste it all your life. Achilles: Oh, I'm looking forward to that. Tortoise: Well, Achilles, where are we? Achilles ( taking cognizance of his surroundings): We're in a little gondola, gliding down a canal! I want to get out. Mr.Gondolier, please let us out here. (The gondolier

may be interpreted by any sentence of English (it must continue to be interpreted by the same sentence if it occurs multiply within a string or derivation). Thus, for example, the well-formed string < P∧~P> could be interpreted by the compound sentence This mind is Buddha, and this mind is not Buddha. Now let us look at each of the theorems so far derived, and interpret them. The first one was < P⊃~~P>. If we keep the same interpretation for P, we have the following interpretation: If this

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