Hi everybody, It seems Bruno's argument is a bit rich for some of us to digest, so I decided to keep talking by posing another issue. By Godel's argument we know that every sufficiently powerful system of logic would be incomplete, and recently there has been much argument to make human an exception; that's because we see the truth of Godelian statements (i.e. This sentence is unprovable in this system) Let's call such a system S1, and call another (powerful enough in Godel's sense) system S2. and suppose S2 structurally is able to give statements about the statements in S1. What does it mean? Consider S2 as a being able examine some statements in S2 via some operators and get the result(like function calls).
My claim is: 1. S2, is able to see the truth of the Godelian statements in S1, and in some sense: "S2 is complete against the statements of S1", because it can see that S1 at last wont be able to evaluate our Godelian statement and so the statement would be correct. 2. We humans are vulnerable to the Godelian statements like all other logical systems. We have our paradoxes too. Consider the same Godelian statement for yourself as a system (i.e. "You can't prove me" or some similar sentences like "This sentence is false") 3.in the first claim consider the first system to have the same attitude toward the second one, I mean let there be a loop (some how similar to Hofstadter's Strange loops as the foundation of self) Is it complete of not? -- Mohsen Ravanbakhsh. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---