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

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:

>

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.

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

>
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.
>
((X & ~X) implies Y) is necessarily true.
>

>
That is not the exact meaning of these words

>
What is not the exact meaning of which words?
>

 *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).
  

And what is wrong with the analysis given one that page:
1) We know that "Not all lemons are yellow", as it has been assumed to be true.
2) We know that "All lemons are yellow", as it has been assumed to be true.
3) Therefore, the two-part statement "All lemons are yellow or unicorns exist" must also be true, since the first part of the statement ("All lemons are yellow") has already been assumed, and the use of "or" means that if even one part of the statement is true, the statement as a whole must be true as well.
4) However, since we also know that "Not all lemons are yellow" (as this has been assumed), the first part is false, and hence the second part must be true to ensure the two-part statement to be true, i.e., unicorns exist (this inference is known as the disjunctive syllogism).
5) The procedure may be repeated to prove that unicorns do not exist (hence proving an additional contradiction where unicorns do and do not exist), as well as any other well-formed formula. Thus, there is an explosion of true statements.
Which step is a false logic step.
Do you not agree that value of (True or False) will be True.
And that if we have (False or X?) is True, then X? must be true.
Can you show any world where either of those logic forms is not true?
All you are doing is proving you don't actually understand how logic works.