Date: Feb 4, 2013 3:11 AM Author: Virgil Subject: Re: Matheology ? 203 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, MÃ¼ckenheim'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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