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

On Tue, 2025-07-15 at 20:33 -0500, olcott wrote:

On 7/15/2025 8:13 PM, wij wrote:

On Tue, 2025-07-15 at 20:02 -0500, 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:

 

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

 
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.
 
André
 

 
Yet implication is not even truth preserving.
 

 
You seem to be using some private definition of 'truth preserving'.
Did you get that one from claude.ai as well?
 
André
 

 
the characteristic of an argument where,
if the premises are true, the conclusion
must also be true.
 
When the antecedent is false the consequent
can be true with the "→" operator.

 
And how would that make it non-truth preserving?
 

 
If you start with falsity end end up with truth then
the operation was not truth preserving.
 
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.
 

 
This is a typical "learn-by-rote".
The Halting Problem is clear... there is always a counter-case an
assumed H cannot solve.
 

 
The classic textbook example is NOT one of those cases.

Yes, they should say the same thing but in abstract ways.
If not, it's the book's problem not the HP theorem.

This is FACT, not influenced by ANY theory/rule: "1+1=2", Logic,..., have no
effect on this fact.
 

You're very confused. Since you seem to trust/overrely on wikipedia, you
can check against the following:
 
https://en.wikipedia.org/wiki/Truth_function#Algebraic_properties
 
André