Jesse Mazer skrev: > > > >> Date: Thu, 29 Nov 2007 19:55:20 +0100 >> From: [EMAIL PROTECTED] >> >> >> As soon as you say "the set of ALL numbers", then you are forced to >> define the word ALL here. And for every definition, you are forced to >> introduce a "limit". It is not possible to define the word ALL without >> introducing a limit. (Or making an illegal circular definition...) >> > > Why can't you say "If it can be generated by the production rule/fits the > criterion, then it's a member of the set"? I haven't used the word "all" > there, and I don't see any circularity either.
What do you mean by a "well-defined criterion"? Is this a well-defined criterion? : The set R is defined by: (x belongs to R) if and only if (x does not belong to x). If it fits the criterion (x does not belong to x), then it's a member of the set R. Then we ask the question: "Is R a member of the set R?". How shall we use the criterion to answer that question? If we substitute R for x in the criterion, we will get: (R belongs to R) if and only if (R does not belong to R)... What is wrong with this? -- Torgny --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
