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