```Date: Feb 4, 2013 12:49 AM
Author: fom
Subject: Re: Matheology � 203

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 andAbraham Robinson.  Although it is not apparent without reading theoriginal sources, it has a certain legitimacy.  Names completeFregean incomplete symbols.  So names are the key to model theory.Robinson explains this exact relationship in "On ConstrainedDenotation".  It is, for the most part ignored by the modeltheory one obtains from textbooks.  The model theory that onelearns in a textbook parametrizes the quantifier with sets.Thus, the question of definiteness associated with names isdirected to the model theory of set theory.  In turn, this is questionable by virtue of the Russellian and Quinean argumentsfor eliminating names by description theory.  So, the modeltheory of sets consists of a somewhat unconvincing discussionof how parameters are constants that vary (see Cohen).  If onedoes not know the history of the subject, then one is simplyreading Cohen to learn some wonderful insights and does notquestion his statements (after all, it is Paul Cohen, right?)In Jech, there is an observation that forcing seems todepend on the definiteness of "objects" in the groundmodel such as the definiteness of the objects in theconstructible universe.If you read Goedel, there is a wonderful footnote explainingthe assumption that every object can be given a name inhis model of the constructible universe.If you read Tarski, there is an explicit statement thathis notion of a formal language is not a purely formallanguage, but rather one that has formalized a meaningfullanguage--by which one can assume that objects havemeaningful names.  As for a "scientific" language generatedby definition, Tarski has an explicit footnote statingthat that is not the kind of language that he isconsidering.So, we have names being eliminated by Russell and Quineand descriptive names being specifically excluded by thecorrespondence theory intended to convey truth while thenotion of truth in the foundational theory that everyoneis using only presumes definiteness through parametersthat vary.But, the completion of an incomplete symbol requiresa name.Who wouldn't be a little confused?
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