Re: Claude.ai provides reasoning why I may have defeated the conventional HP proof

On 7/14/25 3:15 PM, olcott wrote:

On 7/12/2025 6:03 PM, Richard Damon wrote:

On 7/11/25 1:12 AM, olcott wrote:

On 7/10/2025 11:42 PM, André G. Isaak wrote:

On 2025-07-10 22:29, olcott wrote:

On 7/10/2025 10:58 PM, André G. Isaak wrote:

On 2025-07-10 19:58, Richard Damon wrote:

On 7/10/25 10:09 AM, olcott wrote:

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According to the POE:
(a) The Moon is made of green cheese and
(b) the Moon does not exist
proves that
(c) Donald Trump is the Christ.

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Rigth, but only because a side affect of (a) is that the moon must exist.

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Really, the problem here is that Olcott fails to distinguish between the truth of a conditional statement and the truth of the consequent of a conditional statement. They are not the same thing.
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((X & ~X) implies Y) is necessarily true.
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That is not the exact meaning of these words

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What is not the exact meaning of which words?
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*This Wikipedia quote*
On 7/10/2025 11:29 PM, olcott wrote:
 >    the principle of explosion is the law according to which
 >    *any statement can be proven from a contradiction*
 > https://en.wikipedia.org/wiki/Principle_of_explosion
>
Here is the exact meaning of:
*any statement can be proven from a contradiction*
∀x (⊥ ⊢ x).
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And what is wrong with the analysis given one that page:
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André G. Isaak's paraphrase of this:
"any statement can be proven from a contradiction"
to this:
((X & ~X) implies Y) is necessarily true.
Is incorrect.
 Here is the correct paraphrase: ∀x (⊥ ⊢ x).
 

And Yes that can be PROVEN
The givens, Let A be the statement in contradiction, thus
1) A is True, and
2) ~A is True, or equivalently A is False
The Logic:
3) Since A is true, A | x must be true, bu the definition of the or functions.
4) The Disjustive Sylogism:
Since If A | B is known to be true, and A is not true,
then B must be true so that A | B is true..
Or symbolically
A|B & !A -> B
5) Thus since A | x is True
6) and from 2, A is not true
7) Then by 4 we can say that:
A | x is true, A is not true, thus x must be true.
Thus, for *ALL* x, x must be true if we have as established truths in the logic system the contradiction A.
Which step was non-truth perserving.
Which law of logic doen't you accept.
This has been put to you before, and you have admitted defeat by not answering,
Failure to point out the error will just be another admission of error on your part.
It doesn't matter that it "can't be true", we crossed that bridge when we admitted the contradiction in.
The Principle of Explosion show WHY we can't allow contraditions, even "minor" ones into the system, as they break any logic system unless it has preemptively crippled itself by limiting its power.