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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Mathematical incompleteness has always been a misconception ---
 Ultimate Foundation of Truth
Date: Wed, 26 Feb 2025 22:59:56 -0500
Organization: i2pn2 (i2pn.org)
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On 2/26/25 8:39 PM, olcott wrote:
> On 2/26/2025 10:03 AM, joes wrote:
>> Am Wed, 26 Feb 2025 08:34:47 -0600 schrieb olcott:
>>> On 2/26/2025 6:18 AM, joes wrote:
>>>> Am Tue, 25 Feb 2025 12:40:04 -0600 schrieb olcott:
>>>>> On 2/25/2025 12:15 PM, joes wrote:
>>>>>> Am Mon, 24 Feb 2025 20:02:49 -0600 schrieb olcott:
>>>>>>> On 2/24/2025 6:12 PM, Richard Damon wrote:
>>>>>>>> On 2/24/25 6:11 PM, olcott wrote:
>>>>>>>>> On 2/24/2025 6:27 AM, Richard Damon wrote:
>>>>>>>>>> On 2/23/25 11:39 PM, olcott wrote:
>>>>>>>>>>> On 2/23/2025 8:50 PM, Richard Damon wrote:
>>>>>>>>>>>> On 2/23/25 1:08 PM, olcott wrote:
>>>>
>>>>>>>>>> Sure I do.
>>>>>>>>>> A Systems is semantically sound if every statement that can be
>>>>>>>>>> proven is actually true by the systems semantics,
>>>>>>>>> That is very good.
>>>>>>>>>
>>>>>>>>>> in other words, the system doesn't allow the proving of a false
>>>>>>>>>> statement.
>>>>>>>>> That is not too bad yet ignores that some expressions might not
>>>>>>>>> have any truth value.
>>>>>>>> Which has nothing to do with "soundness".
>>>>>>> When any system assumes that every expression is true or false and
>>>>>>> is capable of encoding expressions that are neither IT IS STUPIDLY
>>>>>>> WRONG.
>>>>>> In honour of Gödel this is usually called "incomplete".
>>>>> Where "incomplete" has always been an idiom for stupid wrong.
>>>> Your understanding of logic is incomplete.
>> Which is to say, stupidly wrong.
>>
>>> The screwed up notion of "incomplete" is anchored in the stupid idea
>>> that {true in the system} is not required to be {provable in the
>>> system}.
>> You are about a century behind on the foundations of mathematics.
>>
>>> Any expression of language that can only be verified as true on the
>>> basis of other expressions of language either has a semantic connection
>>> truthmaker to these other expressions or IT IS SIMPLY NOT TRUE.
>> I.e. its negation is true.
>>
> 
> WTF is the truth value of the negation of nonsense?
> The Liar Paradox has ALWAYS simply been nonsense.
> 

But we aren't negating "nonsense", we are negating the actual valid 
truth value out of the Truth Primative.

You don't seem to understand that the DEFINITION of what a truth 
primative is requires that True(Nonsense) be false, not "nonsense".

This isn't tri-valued logic we are talking about.

And even if you tried to make a tri-valued logic, we run into the 
problem that if we were really talking about a tri-valued logic, we get 
back to the problem by just defining a simple predicate that operates on 
logic values and maps:

True -> True
False -> False
Nonsense -> False

and we get back to the original problem.

You need "Nonsense" to not be a logic value, but something more like a 
signal-Nan with no way to test it without triggering it, which isn't 
something logic accepts in the normal domain, and likely just isn't useful.