Date: Mar 22, 2013 3:20 PM
Subject: Re: Matheology § 224
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
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.
WM's principle of "proof by reality", of course, has an immutable
semantics based on the universally consistent pragmatics of
language acquisition in childhood.
Thus, he need never explain himself. The defect is always
with the questioner.
When mathematics is based on "will", one ought not