fom
Posts:
1,037
Registered:
12/4/12
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Re: Matheology § 203
Posted:
Feb 3, 2013 11:29 PM
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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.
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