```Date: Jan 4, 2013 12:57 PM
Author: fom
Subject: Re: The Distinguishability argument of the Reals.

On 1/4/2013 5:41 AM, WM wrote:> On 4 Jan., 10:54, Zuhair <zaljo...@gmail.com> wrote:>> On Jan 4, 10:22 am, Virgil <vir...@ligriv.com> wrote:>>>>>>>>>>>>> In article>>> <3c133339-6b4c-4f74-937f-804bdaad3...@t5g2000vba.googlegroups.com>,>>>>>   Zuhair <zaljo...@gmail.com> wrote:>>>> On Jan 4, 5:33 am, Virgil <vir...@ligriv.com> wrote:>>>>> In article>>>>> <6302ee90-f0a2-4be5-9dbb-c1f999c3a...@c16g2000yqi.googlegroups.com>,>>>>>>> Zuhair <zaljo...@gmail.com> wrote:>>>>>> Since all reals are distinguished by finite initial>>>>>> segments of them,>>>>>>> Some reals are distinguished by finite initial segments of their decimal>>>>> representations, most are not.>> Those are not different numbers. Such objects cannot appear in any> Cantor list as entries or diagonal>>>>> Of course all reals are to be represented by *INFINITE* binary decimal>>>> expansions, so 0.12 is represented as 0.120000...>> It is impossible to represent any real number by an infinite expansion> that is not defined by a finite word.>>>>>> So we are not speaking about the same distinguishability criterion.>> There is no other criterion.In logic, discernibility is taken to be withrespect to properties.  I personally have a problemwith too much work with parameters (symbols taken tohave the characteristic of definite names but actuallyvarying over whatever one purports to be speakingabout) and too little work with names that actuallyresolve to truth.  So, arguing with parametersranging over properties does little more thanunfold the circularity of defining an object intoan infinite hierarchy.Your position seems to be that since the names determinethe model which, in turn, determines the truth, then thenames are the only criterion.But, the use/mention distinction associated withnames leads to a similar hierarchy:oo'oo'''oo'''''oo'''and so on.<snip>
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