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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Tue, 1 Apr 2025 18:30:17 -0400
Organization: i2pn2 (i2pn.org)
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On 4/1/25 1:56 PM, olcott wrote:
> On 4/1/2025 1:33 AM, Mikko wrote:
>> On 2025-03-31 18:33:26 +0000, olcott said:
>>
>>>
>>> Anything the contradicts basic facts or expressions
>>> semantically entailed from these basic facts is proven
>>> false.
>>
>> Anything that follows from true sentences by a truth preserving
>> transformations is true. If you can prove that a true sentence
>> is false your system is unsound.
>>
> 
> Ah so we finally agree on something.
> What about the "proof" that detecting inconsistent
> axioms is impossible? (I thought that I remebered this).
> 

No, the proof is that it is impossible to prove that a system is 
consistant. (sort of the opposite of what you are thinking of).

Proving inconsistancy is easy, you just need one example.

Proving the non-existance isn't as easy, and for a complicated enough 
system, can't be done, as you need to search an infinite space for the 
problem, which we can't be sure we have finished,

Sort of like we can easily prove that a machine halts, but simulating it 
to that point (like a real emulator can do for DDD), but showing that a 
machine is non-halting can be more of a problem. Sometimes we can find 
an induction property to let us prove it, but not always.