Date: Feb 26, 2013 12:46 AM
Author: namducnguyen
Subject: Re: Matheology ? 222 Back to the roots

On 25/02/2013 10:25 PM, Virgil wrote:
> In article <SDWWs.99982$Hq1.27823@newsfe23.iad>,
> Nam Nguyen <namducnguyen@shaw.ca> wrote:
>

>> On 25/02/2013 5:49 PM, Virgil wrote:
>>> Nam Nguyen wrote:
>>>>
>>>> On 23/02/2013 2:38 PM, Virgil wrote:

>>>>> In article
>>>
>>>>> In mathematics [...] proofs of existence do
>>>>> not always require that one find an example of the thing claimed to
>>>>> exist.

>>>>
>>>> So, how would one prove the existence of the infinite set of
>>>> counter examples of Goldbach Conjecture,

>>>
>>> I am not aware of how one would prove the existence of even one
>>> counterexample to Goldbach without finding one.
>>>
>>> Nevertheless, in standard non-WM mathematics, proofs of existence do
>>> not always require that one find an example of the thing claimed to
>>> exist.

>>
>> As I've explained to Jim Burns, that depends on the context the word
>> "proof" is in. If you talk about a _formula_ expressing the existence,
>> then your original statement would make sense: no need to find an
>> "example" for the semantic, the meaning, of the formula.
>>
>> But if the context is a structure, then your statement would not be
>> true.
>>
>> For example, let T = {Ex[Red(x)]}. How would you construct a model
>> of T without an (example) individual being Red, given that the universe
>> U of this model must be non-empty by definition of model?

>
> Since I said "not always", any such situation shows I am right.


I think you misunderstood my point:

In the context of language structure truth verification,
your original statement would _always_ fail: because for
Ex[P(x)] to be true, P(x0) must be true for some _example_ x0.


--
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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
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