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

On 2025-07-15 19:02, olcott wrote:

On 7/15/2025 7:47 PM, André G. Isaak wrote:

On 2025-07-15 18:39, olcott wrote:

On 7/15/2025 7:34 PM, André G. Isaak wrote:

On 2025-07-15 17:53, olcott wrote:

On 7/15/2025 6:45 PM, André G. Isaak wrote:

On 2025-07-15 17:35, olcott wrote:

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You still make the same mistake with the implication operator.
That has always been the wrong operator for PROVES.

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You're being an idiot. The principle of explosion can be stated either in terms of implication or proof. I prefer implication. I'm not mistaking one symbol for another. I'm saying exactly what I intend to say.
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André
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Yet implication is not even truth preserving.
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You seem to be using some private definition of 'truth preserving'. Did you get that one from claude.ai as well?
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André
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the characteristic of an argument where,
if the premises are true, the conclusion
must also be true.
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When the antecedent is false the consequent
can be true with the "→" operator.

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And how would that make it non-truth preserving?
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If you start with falsity end end up with truth then
the operation was not truth preserving.

 That's *not* what truth preserving means. An operator ⊙ is truth preserving if when both A and B are true (A ⊙ B) is also true. What happens when A and B are not both true is irrelevant.
 

If there are tens of thousands of textbooks that
disagree then they are necessarily incorrect when
we go by the compositional meaning of the terms
of "truth" and "preserving". To make a term of the
art meaning that disagrees with the compositional
meaning has always been dishonest.

 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.
 

You can't just make up your own definitions. The definitions in the link below are the ones which *everyone* working in logic actually use. No one cares what you use if it differs from the normal conventions.
 

https://en.wikipedia.org/wiki/Truth_function#Algebraic_properties

 André