On 3/22/2013 4:05 AM, WM wrote: > On 22 Mrz., 08:30, William Hughes <wpihug...@gmail.com> wrote: >> On Mar 22, 7:32 am, WM <mueck...@rz.fh-augsburg.de> wrote: >> >> >> >> >> >>> On 21 Mrz., 16:41, William Hughes <wpihug...@gmail.com> wrote: >> >>>> On Mar 21, 4:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: >> >>>>> On 21 Mrz., 14:29, William Hughes <wpihug...@gmail.com> wrote: >> >>>>>> On Mar 21, 2:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote: >> >>>>>>> On 21 Mrz., 14:02, William Hughes <wpihug...@gmail.com> wrote: >> >>>>>>>>> In fact? That's amazing. So we cannot prove that all lines of the >>>>>>>>> infinite set of lines are unnecessary? >> >>>>>>>> We can prove that something is true for every >>>>>>>> member of an infinite set. We cannot >>>>>>>> prove that something is true for the set >>>>>>>> itself unless the set is finite. >> >>>>>>> But I am not interested in the set itself. Not at all! My claim is >>>>>>> that every member of the set of lines can be removed >> >>>>>> Yes, removed one at a time >> >>>>>>> such that no member remains >> >>>>>> nope, working one at a time you will not get >>>>>> to the point that no member remains. >> >>>>> Induction does not need time. >>>>> The conclusion from n on n+1, if valid, is valid for every natural at >>>>> one instance. >> >>>> Yes, valid for every natural, but not valid >>>> for the *set* of all naturals.- >> >>> I do not talk about this *set* when removing lines. My proof shows >>> that every line can be removed from the list without removing any >>> natural number from the list. >> >> No your proof shows that *any* *one* line can be removed from the >> list. >> However, you are talking about removing more >> than one line, i,e. a *set* of lines. > > No, I do not speak of a set when I say one, two, or three or > infinitely many lines. Don't confuse the set of all lines with all > lines of the set. >
So, WM does not speak of a set of objects when he speaks of a multiplicity of objects.
This clarifies that his idiolect does not reflect consistent use of singular terms.
Thus, his readers should not believe that what they read is what he intends.
