Godel, Escher, Bach: An Eternal Golden Braid

“{W}e can transfer the study of any formal system—in fact the study of”

LogicMathematicsMathDouglas HofstadterNumber TheoryFormalismIsomorphism

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[W]e can transfer the study of any formal system—in fact the study of [all] formal systems—into number theory.”

LogicMathematicsMathDouglas HofstadterNumber TheoryFormalismIsomorphism

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[M]eaning is an automatic by-product of our recognition of any isomorphism.”

LogicMathematicsRecognitionMeaningDouglas HofstadterIsomorphism

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“An interpretation [of a formal system] will be meaningful to the extent that is accurately reflects some isomorphism to the real world.”

LogicMathematicsMeaningReal WorldDouglas HofstadterIsomorphism

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[C]onsistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.”

ScienceLogicMathematicsInterpretationConsistencyDouglas HofstadterFormal LogicGödel S Incompleteness Theorem

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“An interpretation [of a formal system] will be meaningful to the extent that it accurately reflects some isomorphism to the real world.”

LogicMathematicsMeaningInterpretationReal WorldDouglas HofstadterIsomorphism

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[S]uitably complicated recursive systems might be strong enough to break out of any predetermined patterns. And isn't this one of the defining properties of intelligence? Instead of just considering programs composed of procedures which can recursively”

PhilosophyLogicMathematicsIntelligenceFree WillComputer ScienceDeterminismRecursionDouglas Hofstadter

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[O]ur confusion about who we are is certainly related to the fact that we consist of a large set of levels, and we use overlapping language to describe ourselves on all of those levels.”

LanguagePsychologyWho Am IDouglas HofstadterPhilosophy Of LanguageHierarchiesWho Are WePhiloaophy

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“The amazing flexibility of our minds seems nearly irreconcilable with the notion that our brains must be made out of fixed-rule hardware, which cannot be reprogrammed. We cannot make our neurons fire faster or slower, we cannot rewire our brains, we cannot redesign the interior of a neuron, we cannot make [any] choices about the hardware—and yet, we can control how we think.”

ThinkingBrainHuman ConditionPhysiologyNeurologyDouglas HofstadterHow To Think

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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“[M]eaning is part of an object to the extent that it acts upon intelligence in a predictable way.”

ScienceIntelligenceMeaningPredictabilityDouglas HofstadterDecipherment

Book:Godel, Escher, Bach: An Eternal Golden Braid

Source: Godel, Escher, Bach: An Eternal Golden Braid

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