Date: Feb 26, 2013 12:25 AM
Author: Virgil
Subject: Re: Matheology ? 222 Back to the roots

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.
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