On 3/22/2013 1:21 PM, WM wrote: > On 22 Mrz., 16:31, William Hughes <wpihug...@gmail.com> wrote: >> On Mar 22, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote: >> >>>> If you want to >>>> remove all of the lines you have to remove the set of all >>>> lines that are indexed by a natural number. >> >>> But I don't want to remove a set. >> >> We have the set of lines. You do not want to leave >> any of the lines. > > I do not want this or that. > I simply prove that for every line l_n the following property is true: > Line l_n and all its predecessors do not in any way influence (neither > decrease nor increase) the union of all lines, namely |N. > > This is certainly a proof that does not force us to "remove a set". > But we can look at the set of lines that have this property. The > result is the complete set of all lines. > > And this mathematical result cannot be violated or re-interpreted.
Willard Quine actually wrote a version of set theory.
Later, he argued for the elimination of singular terms from logical language using description theory and made sense of it with the amazing fact that description theory could re-introduce names.
This argument (1960) is the one that actually justifies using only fundamental relations in the formal language of set theory in relation to Zermelo's use of denotation in the 1908 paper. (This use of denotation had simply been dropped earlier because of the influence of other philosophical trends.)
His analyses give a slightly different picture from the one you suggest for your readers.
I found a few papers that mention his ideas. So, I thought I would make them available.