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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise
Date: Sun, 7 Jul 2024 12:59:26 -0500
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On 7/7/2024 12:28 PM, Richard Damon wrote:
> On 7/7/24 9:34 AM, olcott wrote:
>> On 7/7/2024 6:26 AM, Richard Damon wrote:
>>> On 7/6/24 11:42 PM, olcott wrote:
>>>> On 7/6/2024 10:12 PM, Richard Damon wrote:
>>>>> On 7/6/24 10:51 PM, olcott wrote:
>>>>>> On 7/6/2024 9:16 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> So if x is defined in L as ~True(L, x)
>>>>>>>
>>>>>>> what value does True(L, x) have?
>>>>>>>
>>>>>>
>>>>>> then True(L,x) evaluates to false ultimately meaning
>>>>>> that x is incorrect.
>>>>>
>>>>> But doesn't ~false evaluate to True?
>>>>>
>>>>
>>>> No. ~false evaluates to true or incorrect.
>>>
>>> So, "incorrect" is an ACTUAL logic state, not just "sort of" and ~~P 
>>> doesn't necessarily have the same value as P.
>>>
>>
>> It is something like tri-valued logic.
> 
> It needs to either BE tri-valued, or be bi-valued, or be whatever number 
> of values it is.
> 

True, False and IDK would be trivalued logic.
True, False and not-a-logic-sentence is not actually trivalued logic.

>>
>> Every other formal system would try to force "a fish" into
>> true or false and if that didn't work determine that the
>> formal system is incomplete.
> 
> Nope, most formal system just don't define "a fish" as a statement in 
> their langauge.
> 
I use that example because it is easy to see that it is
neither true nor false. It literally applies to any formal
system as expressive as English.

>>
>>> IF you do mean this, then you first need to fully define how 
>>> "incorrect" works in ALL the logical operators.
>>>
>>
>> (~True(L,x) ∧ ~True(L,~x)) ≡ ~Proposition(L,x)
>> Every variable is screened this way before any other
>> operations can be performed upon it.
>> x = "a fish" rejects every expression referencing x.
> 
> Logic doesn't work that way.
> 
That is its error.

> Sorry, you are just totally ignorant of how formal logic works.
> 
Not at all formal logic is wrong because it does not do this.

>>
>>> It also means you need to figure out what you logic system supports, 
>>> and can't just rely on the large base of work on normal binary logic.
>>>
>>
>> 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.
> 
> Nope, doesm't work that way. The problem is that most formal systems 
> don't express them selves with "Natural Language".
> 
That formal systems are not typically very expressive
is by no means any evidence at all that they cannot be as
expressive as English.

> And an "accurate model of the actual world" isn't available, so you are 
> hypothocating on a non-existant thing.
> 
That is always the way that new things come into existence.

>>
>>
>>> Thare is a good aount of work on non-binary systems, and perhaps you 
>>> can find one that is close enough to try to use, but YOU need to do 
>>> that work.
>>>
>>
>> In other words it is too difficult for you to understand
>> that "a fish" is not a proposition?
> 
> Nope, YOU are the one that says it is one, and needs to be handled.
> 
> What formal logic system do you think you are working in?
> 

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.

>>
>>> And realize that you system isn't applicable to any theorem based on 
>>> a binary logic system, since your system is not one.
>>>
>>
>> All of the current systems of logic inherit their notion of
>> True(L,x) on the above basis.
>> (~True(PA,g) ∧ ~True(PA,~g)) ≡ ~Proposition(PA,g)
>> Mathematical incompleteness goes away.
>>
> 
> Nope, you just made your system inconsistant if it was powerful enough 
> to express as a proposition in it that x in PA is ~True(PA, x).
> 
Not at all. Must system consistently rejects expressions
that are neither true nor false.

> Tarski shows a set of commonly held conditions that are sufficent to 
> allow that expression to be a proposition in PA.
> 
Tarski stupidly allowed nonsense into his system.

> Just as Godel does in a different manner by constructing his Primative 
> Recursive Relationship that detects a proof of his statement G.
> 
>>>>
>>>>>>
>>>>>> We can't know for sure that x is incorrect until
>>>>>> we see that True(L,~x) also evaluates to false.
>>>>>>
>>>>>
>>>>> And thus you system just blew up in a mass of flaming inconsistancy.
>>>>>
>>>>
>>>> Is "a fish" true, false or not a proposition.
>>>
>>>
>>>
>>>>
>>>>> Since there is no requirement to check True(L, ~x) and it can't 
>>>>> affect the value of ~True(L, x) you logic just doesn't work.
>>>>>
>>>> When x is defined to mean = ~True(L,x) in L
>>>> then True(L,x) is false and True(L,~x) is false
>>>> proving that x is not a proposition.
>>>
>>> But, since ~false isn't true, your system leaks information like crazy.
>>>
>> Not at all
>> (~True(L,x) ∧ True(L,~x)) ≡ Conventional_False(L,x)
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