Date: Mar 21, 2013 2:17 PM
Author: fom
Subject: Re: Matheology § 224

On 3/21/2013 5:21 AM, WM wrote:
> On 21 Mrz., 08:57, William Hughes <wpihug...@gmail.com> wrote:
>> On Mar 21, 8:46 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>>

>>> My question remains: What is the subset of necessary lines?
>>
>> There is no such thing as a necessary line.

>
> Correct. That is because the asserted aim cannot be established. In
> order to reach a goal that is impossible to reach, no attempt is
> necessary.
>

>> There is such a thing as a sufficient set of
>> lines (all sufficient sets are composed
>> entirely of unnecessary lines, which means
>> that you can remove any finite set of lines

>
> Why only finite sets? What property is changed if infinitely many are
> there? If there are infinitely many unnecessary lines, they all can be
> removed - by their property of being unnecessary. Otherwise there must
> be some necessary line among them.


Once again, one sees the confusion over the
necessity of an object and the necessary count
of objects.

If the definiteness of the names requires an
infinite decimal expansion. And, if the combinatory
principle of "all" infinite decimal expansions
requires an infinite cardinality, then the infinite
number of expansions that duplicate a name are
unnecessary and can be removed. But, the system of
unique names still has a necessary infinite
multiplicity.

Please do not try to say that this is not of what
you speak. I do not care about your "willful" use
of crayons or your "goals" when using them.

A count of objects may be necessary even when
the existence of any given particular object
is not.