```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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