Date: Feb 25, 2013 11:13 PM
Author: namducnguyen
Subject: Re: Matheology ? 222 Back to the roots

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?

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

NYOGEN SENZAKI
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