```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 betrue.For example, let T = {Ex[Red(x)]}. How would you construct a modelof T without an (example) individual being Red, given that the universeU of this model must be non-empty by definition of model?-- ----------------------------------------------------There is no remainder in the mathematics of infinity.                                       NYOGEN SENZAKI----------------------------------------------------
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