Well it is illegal regarding the rules meaning with these rules set B does not exist as defined.
2009/6/13 Torgny Tholerus <tor...@dsv.su.se>: > > Quentin Anciaux skrev: >> 2009/6/13 Torgny Tholerus <tor...@dsv.su.se>: >> >>> What do you think about the following deduction? Is it legal or illegal? >>> ------------------- >>> Define the set A of all sets as: >>> >>> For all x holds that x belongs to A if and only if x is a set. >>> >>> This is an general rule saying that for some particular symbol-string x >>> you can always tell if x belongs to A or not. Most humans who think >>> about mathematics can understand this rule-based definition. This rule >>> holds for all and every object, without exceptions. >>> >>> So this rule also holds for A itself. We can always substitute A for >>> x. Then we will get: >>> >>> A belongs to A if and only if A is a set. >>> >>> And we know that A is a set. So from this we can deduce: >>> >>> A beongs to A. >>> ------------------- >>> Quentin, what do you think? Is this deduction legal or illegal? >>> >> >> It depends if you allow a set to be part of itselft or not. >> >> If you accept, that a set can be part of itself, it makes your >> deduction legal regarding the rules. > > OK, if we accept that a set can be part of itself, what do you think > about the following deduction? Is it legal or illegal? > > ------------------- > Define the set B of all sets that do not belong to itself as: > > For all x holds that x belongs to B if and only if x does not belong to x. > > This is an general rule saying that for some particular symbol-string x > you can always tell if x belongs to B or not. Most humans who think > about mathematics can understand this rule-based definition. This rule > holds for all and every object, without exceptions. > > So this rule also holds for B itself. We can always substitute B for > x. Then we will get: > > B belongs to B if and only if B does not belong to B. > ------------------- > Quentin, what do you think? Is this deduction legal or illegal? > > > -- > Torgny Tholerus > > > > -- 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 everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---