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Mind Matters Reporting on Natural and Artificial Intelligence

TagKurt Gödel


Math Shows Why the Mind Is Not Just a Formula

The Liar’s Paradox shows that even mathematics cannot be reduced to a fixed set of axioms

Gödel’s discovery brought back a sense of wonder to mathematics and to the rest of human knowledge. His incompleteness theorem underlies the fact that human investigation can never exhaust all that can be known. Every discovery builds a path to a new discovery.

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black mathematics board with formulas

Faith Is the Most Fundamental of the Mathematical Tools

An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions

David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time.

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Crystal ball with building from antiquity

Futurism Doesn’t Learn from Past Experience

Technological success stories cannot be extrapolated into an indefinite future

The limits of science can be as instructive as the discoveries. If science someday proved that computer systems could never reproduce some aspect of mind, we'd have learned something important about the nature of mind.

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Silhouette of a person with words and numbers in the background

The Mind Can’t Be Just a Computer

Gödel demonstrated that fact and Turing tried to live with it

Kurt Gödel (1906–1978) proved that there are truths in mathematical logic that lie outside mathematical logic, which means that the mind cannot be understood simply as a computer.

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