2008/11/9 Brent Meeker <[EMAIL PROTECTED]>: > > A. Wolf wrote: >>> I can if there's no rule of inference. Perhaps that's crux. You are >>> requiring >>> that a "mathematical structure" be a set of axioms *plus* the usual rules of >>> inference for "and", "or", "every", "any",...and maybe the axiom of choice >>> too. >> >> Rules of inference can be derived from the axioms...it sounds circular >> but in ZFC all you need are nine axioms and two undefinables (which >> are set, and the binary relation of membership). You write the axioms >> using the language of predicate calculus, but that's just a >> convenience to be able to refer to them. >> >>> Well not entirely by itself - one still needs the rules of inference to >>> get to >>> Russell's paradox. >> >> Not true! The paradox arises from the axioms alone (and it isn't a >> true paradox, either, in that it doesn't cause a contradiction among >> the axioms...it simply reveals that certain sets do not exist). The >> set of all sets cannot exist because it would contradict the Axiom of >> Extensionality, which says that each set is determined by its elements >> (something can't both be in a set and not in the same set, in other >> words). > > I thought you were citing it as an example of a contradiction - but we > digress. > > What is your objection to the existence of list-universes? Are they not > internally consistent "mathematical" structures? Are you claiming that > whatever > the list is, rules of inference can be derived (using what process?) and > thence > they will be found to be inconsistent? > > Brent
Well I reverse the question... Do you think you can still be consistent without being consistent ? If there is no rules of inference or in other words, no rules that ties states... How do you define consistency ? Regards, Quentin -- All those moments will be lost in time, like tears in rain. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
