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 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?

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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