?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Minds%2C+Machines+and+Goedel&rft.creator=Lucas%2C+J.R.&rft.subject=Cognitive+Psychology&rft.subject=Artificial+Intelligence&rft.subject=Logic&rft.subject=Philosophy+of+Mind&rft.subject=Philosophy+of+Science&rft.description=Goedel's+theorem+states+that+in+any+consistent+system+which+is+strong+enough+to+produce+simple+arithmetic+there+are+formulae+which+cannot+be+proved-in-the-system%2C+but+which+we+can+see+to+be+true.+Essentially%2C+we+consider+the+formula+which+says%2C+in+effect%2C+%22This+formula+is+unprovable-in-the-system%22.+If+this+formula+were+provable-in-the-system%2C+we+should+have+a+contradiction%3A+for+if+it+were+provablein-the-system%2C+then+it+would+not+be+unprovable-in-the-system%2C+so+that+%22This+formula+is+unprovable-in-the-system%22+would+be+false%3A+equally%2C+if+it+were+provable-in-the-system%2C+then+it+would+not+be+false%2C+but+would+be+true%2C+since+in+any+consistent+system+nothing+false+can+be+provedin-the-system%2C+but+only+truths.+So+the+formula+%22This+formula+is+unprovable-in-the-system%22+is+not+provable-in-the-system%2C+but+unprovablein-the-system.+Further%2C+if+the+formula+%22This+formula+is+unprovablein-+the-system%22+is+unprovable-in-the-system%2C+then+it+is+true+that+that+formula+is+unprovable-in-the-system%2C+that+is%2C+%22This+formula+is+unprovable-in-the-system%22+is+true.+Goedel's+theorem+must+apply+to+cybernetical+machines%2C+because+it+is+of+the+essence+of+being+a+machine%2C+that+it+should+be+a+concrete+instantiation+of+a+formal+system.+It+follows+that+given+any+machine+which+is+consistent+and+capable+of+doing+simple+arithmetic%2C+there+is+a+formula+which+it+is+incapable+of+producing+as+being+true---i.e.%2C+the+formula+is+unprovable-in-the-system-but+which+we+can+see+to+be+true.+It+follows+that+no+machine+can+be+a+complete+or+adequate+model+of+the+mind%2C+that+minds+are+essentially+different+from+machines.&rft.date=1961&rft.type=Journal+(Paginated)&rft.type=PeerReviewed&rft.format=text%2Fhtml&rft.identifier=http%3A%2F%2Fcogprints.org%2F356%2F1%2Flucas.html&rft.identifier=++Lucas%2C+J.R.++(1961)+Minds%2C+Machines+and+Goedel.++%5BJournal+(Paginated)%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F356%2F