```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 forEx[P(x)] to be true, P(x0) must be true for some _example_ x0.-- ----------------------------------------------------There is no remainder in the mathematics of infinity.                                       NYOGEN SENZAKI----------------------------------------------------
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