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

> In article

> <bc3c4c0e-d017-49b3-a4f3-22aba84aa3c7@5g2000yqz.googlegroups.com>,

> WM <mueckenh@rz.fh-augsburg.de> 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.