Virgil
Posts:
4,660
Registered:
1/6/11
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Re: Matheology ? 203
Posted:
Feb 4, 2013 3:11 AM
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In article <l9WdnRz2y5ae0ZLMnZ2dnUVZ_u-dnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:
> On 2/3/2013 10:50 PM, Ralf Bader wrote:
> > Virgil wrote:
> >
> >> In article
> >> <bc3c4c0e-d017-49b3-a4f3-22aba84aa3c7@5g2000yqz.googlegroups.com>,
> >> WM <mueckenh@rz.fh-augsburg.de> wrote:
> >>
> >>> On 3 Feb., 22:29, William Hughes <wpihug...@gmail.com> wrote:
> >>>>>> We can say ?"every line has the property that it
> >>>>>> does not contain every initial segment of s"
> >>>>>> There is no need to use the concept "all".
> >>>>
> >>>>> Yes, and this is the only sensible way to treat infinity.
> >>>>
> >>>> So now we have a way of saying
> >>>>
> >>>> s is not a line of L
> >>>>
> >>>> e.g. ?0.111... ?is not a line of
> >>>>
> >>>> 0.1000...
> >>>> 0.11000...
> >>>> 0.111000....
> >>>> ...
> >>>>
> >>>> because every line, l(n), ?has the property that
> >>>> l(n) does not ?contain every ?initial
> >>>> segment of 0.111...
> >>>
> >>> But that does not exclude s from being in the list. What finite
> >>> initial segment (FIS) of 0.111... is missing? Up to every line there
> >>> is some FIS missing, but every FIS is with certainty in some trailing
> >>> line. And with FIS(n) all smaller FISs are present.
> >> But with no FIS are all present.
> >>>
> >>>> Is there a sensible way of saying
> >>>> s is a line of L ?
> >>>
> >>> There is no sensible way of saying that 0.111... is more than every
> >>> FIS.
> >>
> >> How about "For all f, (f is a FIS) -> (length(0.111...) > length(f))" .
> >>
> >> It makes perfect sense to those not permanently encapsulated in
> >> WMytheology.
> >
> > By the way, Mückenheim's crap is as idiotic from an intuitionistic point of
> > view as it is classically. Intuitionists do not have any problems
> > distinguishing the numbers 0,1...1 with finitely many digits and the
> > sequence formed by these numbers resp. the infinite decimal fraction
> > 0,11....
> >
>
> No. His finitism seems to be more of a mix of Wittgenstein and
> Abraham Robinson. Although it is not apparent without reading the
> original sources, it has a certain legitimacy. Names complete
> Fregean incomplete symbols. So names are the key to model theory.
> Robinson explains this exact relationship in "On Constrained
> Denotation". It is, for the most part ignored by the model
> theory one obtains from textbooks. The model theory that one
> learns in a textbook parametrizes the quantifier with sets.
> Thus, the question of definiteness associated with names is
> directed to the model theory of set theory. In turn, this is
> questionable by virtue of the Russellian and Quinean arguments
> for eliminating names by description theory. So, the model
> theory of sets consists of a somewhat unconvincing discussion
> of how parameters are constants that vary (see Cohen). If one
> does not know the history of the subject, then one is simply
> reading Cohen to learn some wonderful insights and does not
> question his statements (after all, it is Paul Cohen, right?)
>
> In Jech, there is an observation that forcing seems to
> depend on the definiteness of "objects" in the ground
> model such as the definiteness of the objects in the
> constructible universe.
>
> If you read Goedel, there is a wonderful footnote explaining
> the assumption that every object can be given a name in
> his model of the constructible universe.
>
> If you read Tarski, there is an explicit statement that
> his notion of a formal language is not a purely formal
> language, but rather one that has formalized a meaningful
> language--by which one can assume that objects have
> meaningful names. As for a "scientific" language generated
> by definition, Tarski has an explicit footnote stating
> that that is not the kind of language that he is
> considering.
>
> So, we have names being eliminated by Russell and Quine
> and descriptive names being specifically excluded by the
> correspondence theory intended to convey truth while the
> notion of truth in the foundational theory that everyone
> is using only presumes definiteness through parameters
> that vary.
>
> But, the completion of an incomplete symbol requires
> a name.
>
> Who wouldn't be a little confused?
WM claims not to be, but seems to be much more so than anyone else.
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