On 7/10/2024 6:07 AM, John Clark wrote:
On Tue, Jul 9, 2024 at 7:22 PM Brent Meeker <meekerbr...@gmail.com> wrote:.... /> And going the other way, what if it didn't have a multiply operation. /That would be no problem as long as the AI still had the addition operation, just do repeated additions, although it would slow things down. But you could start removing more and more operations until you got all the way down to First Order Logic, and then an AI could actually prove its own consistency. Kurt Godel showed that a few years before he came up with this famous incompleteness theorem in what we now call Godel's Completeness Theorem. His later Incompleteness Theorem only applies to logical systems powerful enough to do arithmetic, and you can't do arithmetic with nothing but first order logic. The trouble is you couldn't really say an Artificial Intelligence was intelligent if it couldn't even pass a first grade arithmetic test.
*There are many levels of intelligence. An octopus can't pass a first grade arithmetic test but it can escape thru a difficult maze.
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