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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