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.