Date: Feb 26, 2013 12:46 AM
Author: namducnguyen
Subject: Re: Matheology ? 222 Back to the roots
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.

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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