fom
Posts:
1,035
Registered:
12/4/12
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Re: The Distinguishability argument of the Reals.
Posted:
Jan 4, 2013 12:57 PM
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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 with
respect to properties. I personally have a problem
with too much work with parameters (symbols taken to
have the characteristic of definite names but actually
varying over whatever one purports to be speaking
about) and too little work with names that actually
resolve to truth. So, arguing with parameters
ranging over properties does little more than
unfold the circularity of defining an object into
an infinite hierarchy.
Your position seems to be that since the names determine
the model which, in turn, determines the truth, then the
names are the only criterion.
But, the use/mention distinction associated with
names leads to a similar hierarchy:
oo
'oo'
''oo''
'''oo'''
and so on.
<snip>
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