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

On 7/15/2025 9:18 PM, André G. Isaak wrote:

On 2025-07-15 20:13, olcott wrote:

On 7/15/2025 9:01 PM, André G. Isaak wrote:

On 2025-07-15 19:55, olcott wrote:

On 7/15/2025 8:44 PM, André G. Isaak wrote:

On 2025-07-15 19:37, olcott wrote:

On 7/15/2025 8:17 PM, André G. Isaak wrote:

>

The is perfectly compositional. If we start with things that are true, then the result is true. It says nothing about what we get when we start with things that are false.
>

>
https://en.wikipedia.org/wiki/Truth_table#Logical_implication
p=false q=false then p → q is true.

>
What does that have to do with anything? That demonstrates that material implication is not falsehood preserving. It says nothing about whether it is truth preserving.
>

>
Falsehood is an aspect of truth.

>
Falshood-preserving and truth-preserving are two different properties. An operator can be one without being the other (and I gave you a link to their definitions). All you're demonstrating is that you have absolutely no clue what the terms you are using mean, which tends to invalidate everything you say.
>
André
>

>
You still didn't answer the question about why
the law of non-contradiction doesn't over-rule
the POE.

 It doesn't override it. The law of non-contradiction states that A cannot be both true and false.

As a demonstration of the principle, consider two contradictory statements—"All lemons are yellow" and "Not all lemons are yellow"—
*and suppose that both are true*
Then we have shown that you just had a psychotic break from reality.

That doesn't prevent us from writing the expression (A & ~A); it simply guarantees that (A & ~A) will always be false which is why ((A & ~A) -> X) will always be true regardless of what X is. Just read the truth table for material implication (which you just posted a partial version of so clearly you know it or have access to it).
 André
 

--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer