Results for “Gédel”

and that is by allowing inconsistency into the system. Gédel’s

…objective fact. Inconsistency is very bad in mathematics. The Lucas Argument J.R. Lucas of Oxford University believes Gédel’s theorem says something fundamental about the nature of the human mind. In 1959, he wrote a paper, Minds, Machines and Gédel, where he argued humans must...

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… truth. Colloquially we call this ‘common sense’ or ‘stepping outside the box’ The Lucas argument uses the theories of Gédel and Turing to show computer algorithms have limitations. Some things are simply not computable. Computers can do many useful things, but they cannot disco...

…get that, ‘aha’ feeling. Douglas Hofstadter, Professor of Cognitive Science at Indiana University, famous for the book Gédel Escher Bach, has written a computer program using pattern matching to discover number theorems; things like any number ending in a zero is divisible by 5....

…ls of Mathematics, 1961, 425-36. Dyson, Verena H., James P. Jones, and John C. Shepherdson. “Some Diophantine Forms of Gédel’s Theorem.” Archive for Mathematical Logic 22, no. 1 (1980): 51-60. Franzén, Torkel. Godel’ Theorem: An Incomplete Guide to Its Use and Abuse. AK Peters/...