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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise --- eternal
 september failure
Date: Mon, 8 Jul 2024 19:40:52 -0400
Organization: i2pn2 (i2pn.org)
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On 7/8/24 7:30 PM, olcott wrote:
> On 7/8/2024 6:26 PM, Richard Damon wrote:
>> On 7/8/24 9:13 AM, olcott wrote:
>>> On 7/8/2024 6:10 AM, Richard Damon wrote:
>>>> On 7/7/24 11:47 PM, olcott wrote:
>>>>> On 7/7/2024 10:30 PM, Richard Damon wrote:
>>>>>> On 7/7/24 11:09 PM, olcott wrote:
>>>>>>> On 7/7/2024 10:02 PM, olcott wrote:
>>>>>>>> On 7/7/2024 9:54 PM, Richard Damon wrote:
>>>>>>>>> On 7/7/24 10:52 PM, olcott wrote:
>>>>>>>>>> On 7/7/2024 9:50 PM, Richard Damon wrote:
>>>>>>>>>>> On 7/7/24 10:22 PM, olcott wrote:
>>>>>>>>>>>> On 7/7/2024 1:30 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> Is "Not-a-logic-sentence" a truth value that True, of 
>>>>>>>>>>>>> ~false can return or not?
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> *I will try to be perfectly clear*
>>>>>>>>>>>> Not-a-logic-sentence(L,x) ≡ (~True(L,x) ∧ ~True(L,~x))
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In other words, you have no idea of how to express you 
>>>>>>>>>>> concept in the terms of how a logic would be built with it, 
>>>>>>>>>>> as you just don't undertand how logic works.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> That every expression of language that is {true on the basis of
>>>>>>>>>> its meaning expressed using language} must have a connection by
>>>>>>>>>> truth preserving operations to its {meaning expressed using 
>>>>>>>>>> language}
>>>>>>>>>> is a tautology. The accurate model of the actual world is 
>>>>>>>>>> expressed
>>>>>>>>>> using formal language and formalized natural language.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Word salad.
>>>>>>>>>
>>>>>>>>> No such model exists, so you are basing your system on faery dust.
>>>>>>>>>
>>>>>>>>> You just don't understand what you are talking about, and think 
>>>>>>>>> Formal Logic is just like the abstract philosophy you seemed to 
>>>>>>>>> have studied a bit of.
>>>>>>>>
>>>>>>>> Formal logic is a subset of this.
>>>>>>
>>>>>> Nope. Uses different (and stricter) rules.
>>>>>>
>>>>>> That you don't understand this just shows your ignorance, and is 
>>>>>> why you can't actually PROVE anything because the standard of 
>>>>>> proof is one of the big differences.
>>>>>>
>>>>>>>> Not-a-logic-sentence(PA,g) ≡ (~True(PA,g) ∧ ~True(PA,~g))
>>>>>>>> There are no truth preserving operations in PA to g or to ~g
>>>>>>>>
>>>>>>>
>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>>
>>>>>>> Within my analytical framework this Tarski sentence is merely
>>>>>>> self-contradictory
>>>>>>>
>>>>>>> (3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
>>>>>>
>>>>>> In other words, you don't understand his PROOF, Note (1) and (2) 
>>>>>> are NOT "assumptions" but statements of facts from ealier in the 
>>>>>> work.
>>>>>>
>>>>>
>>>>> It does not matter how Tarski derived the self-contradictory
>>>>> expression it only matters that all such expressions cannot
>>>>> possibly be propositions.
>>>>
>>>> Yes, it does.
>>>>
>>>> First, it is NOT "self-contradictory", that is just your lie based 
>>>> on WROMG definitions, that by repeating it, you just prove yourself 
>>>> to be an ignorant pathological liar.
>>>>
>>>> Second, If the statement has been PROVEN from "true" statements, 
>>>> then if it actually being contradictory says that something actually 
>>>> assumed in the proof is incorrect.
>>>>
>>>> Fortunately, the statement isn't contradictory.
>>>>
>>>>>
>>>>> When a proof is done correctly it must be a sequence of truth
>>>>> preserving operations or it it wrong.
>>>>
>>>> Right, and to show it is wrong you need to point out the step that 
>>>> is incorrect, not just that you don't like the answer.
>>>>
>>>>>
>>>>>> If you can't find the erroneous step to get them, you have no 
>>>>>> counter to his statement.
>>>>>>
>>>>>
>>>>> *self-contradictory expressions must be rejected*
>>>>
>>>> But it isn't self-contradictory, except when you apply your 
>>>> incorrect definitions. That shows YOUR definitions are wrong and 
>>>> must be rejected.
>>>>
>>>>>
>>>>>>>
>>>>>>> There are no truth preserving operations in Tarski's
>>>>>>> theory to x if and only if There are truth preserving
>>>>>>> operations in Tarski's theory to x
>>>>>>>
>>>>>>
>>>>>> Nope, there is no FINITE sequence of truth preserving operations 
>>>>>> (a proof) to x if and only if there are a (possibly infinite) 
>>>>>> sequence of truth perserving operations to x (meaning it is a true 
>>>>>> statement).
>>>>>>
>>>>>> This is possible if the only sequences of truth preserving 
>>>>>> operations to x are infinite in length.
>>>>>>
>>>>>
>>>>> There cannot be any infinite sequence of truth preserving operations
>>>>> affirming operations that no finite sequence of truth preserving
>>>>> operations exists in this case.
>>>>
>>>> Wrong. And
>>>>
>>> Merely an assertion entirely bereft of any supporting reasoning.
>>> You cannot show the steps of how I am wrong because I am correct.
>>
>> OF course there can.
>>
>> You haven't show ANY steps of how you get to your conclusion, so of 
>> course I can't point out which one is wrong. because you have given 
>> ZERO ground for it, just your INCORRECT claim of what truth means.
>>
>> A clear example is Godel's G. 
> 
> Wrong case.
> 

Whats wrong with it,

If you say something can't happen, as someone shows even ONE example of 
it happening, you are just proven wrong.

G, the statement that no Natural Number g exists that match the 
particular Primative Recursive Relationship he develops for the system F 
is show to be true because of an infinte set of steps that establish it, 
and there is no finite set of steps to establish it, so it can not be 
proven.

That PRR was specially constructed so that there could not be a finite 
set of steps to prove it, as such a proof would end up providing the 
counter example for the statement, and thus is couldn't be true.

And it can't be false, as then the counter example number provides the 
correct proof that no such number exists, so that means that the system 
had to have been inconsistent, but consistance is one of the 
requirements for the system that Godel is working in.