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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Claude.ai provides reasoning why I may have defeated the
 conventional HP proof
Date: Thu, 10 Jul 2025 07:26:43 -0400
Organization: i2pn2 (i2pn.org)
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On 7/9/25 10:16 AM, olcott wrote:
> On 7/9/2025 9:04 AM, joes wrote:
>> Am Wed, 09 Jul 2025 07:31:59 -0500 schrieb olcott:
>>> On 7/9/2025 3:29 AM, Mikko wrote:
>>>> On 2025-07-08 14:18:32 +0000, olcott said:
>>>>> On 7/8/2025 2:41 AM, Mikko wrote:
>>
>>>>>> True conclusion from false premeises is fairly common. But that is
>>>>>> not relevant.
>>>>> It proves that logic is fundamentally incorrect on this point.
>>>>> Logic must be a sequence of truth preserving operations or it is
>>>>> wrong.
>> Should only false conclusions be derivable from false premises?
>>
> 
> False premises must be immediately rejected.
> This is easy to do when semantic meaning is
> fully integrated into the formal language.

In other words, we should just be immediately rejecting your work when 
you start with the claim that a halt decider decides on the basis of if 
it can simulate the input to a final state, since thst is just false.

We should also just reject your "DDD" as just the code of the C function 
as a valid input, since it doesn't represent "a program" as required by 
the problem.

> 
>>> It is a truism the the POE violates the requirement of truth preserving
>>> operations. People that learn things by rote do not notice this.
>> If you have contradictory premises, the (non-)truth of that is
>> preserved...
>>
> That is the correct way to do it.
> 
> *Here is the psychotic break from that*
>     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
> 

But that is true.

*IF* you let your system include a contradiction, then by the normal 
rules of logic, you get that results.

This is why you need to make sure you systems don't allow contradictions 
to be made, because once you slip and let one in, your system is just 
broken.

The problem is that once a statement is admitted as a fact, logic can't 
"remove" it from the system, as that is not a valid operation. If you 
find that your system is allowing a conttradiction to be accepted, you 
need to find the core axiom (or combination of axioms) that allowed it, 
and redefine the system to not allow that to happen.

This is what Zermelo did when he built ZFC, He saw that part of the 
problme with "Naive Set Theory" was that it didn't have strong rules for 
how to build a set, so he created a NEW set theory that had firm rules 
for creating a set, ones that people could live with, and that is what 
eventually become the ZFC that we now use.


That is why you can't start with errors like you do,

You can't just take as a fact that your Halt Decider is correct.

As that isn't true, and thus it blows up your logic, making you just an 
idiot.