Date: Feb 3, 2013 11:29 PM
Subject: Re: Matheology § 203
On 2/3/2013 9:20 PM, Virgil wrote:
> In article
> 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
>>> 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
> 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