On 2/3/2013 9:20 PM, Virgil wrote: > In article > <firstname.lastname@example.org>, > WM <email@example.com> wrote: > >> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote: >>>>> We can say "every line has the property that it >>>>> does not contain every initial segment of s" >>>>> There is no need to use the concept "all". >>> >>>> Yes, and this is the only sensible way to treat infinity. >>> >>> So now we have a way of saying >>> >>> s is not a line of L >>> >>> e.g. 0.111... is not a line of >>> >>> 0.1000... >>> 0.11000... >>> 0.111000.... >>> ... >>> >>> because every line, l(n), has the property that >>> l(n) does not contain every initial >>> segment of 0.111... >> >> But that does not exclude s from being in the list. What finite >> initial segment (FIS) of 0.111... is missing? Up to every line there >> is some FIS missing, but every FIS is with certainty in some trailing >> line. And with FIS(n) all smaller FISs are present. > But with no FIS are all present. >> >>> Is there a sensible way of saying >>> s is a line of L ? >> >> There is no sensible way of saying that 0.111... is more than every >> FIS. > > How about "For all f, (f is a FIS) -> (length(0.111...) > length(f))" .
In view of WM's positions, length(0.111...) would have to be the value given to a non-existent. In Fregean description theory, this would be the null class. So, for all f, null>length(f).
Next, WM would say that this is fine until the domain of arguments to the relation '>' is restricted to numbers.