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. --
