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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)
Date: Wed, 22 May 2024 19:58:30 +0300
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On 2024-05-22 15:55:39 +0000, olcott said:

> On 5/22/2024 2:57 AM, Mikko wrote:
>> On 2024-05-21 14:36:29 +0000, olcott said:
>> 
>>> On 5/21/2024 3:05 AM, Mikko wrote:
>>>> On 2024-05-20 17:48:40 +0000, olcott said:
>>>> 
>>>>> On 5/20/2024 2:55 AM, Mikko wrote:
>>>>>> On 2024-05-19 14:15:51 +0000, olcott said:
>>>>>> 
>>>>>>> On 5/19/2024 9:03 AM, Mikko wrote:
>>>>>>>> On 2024-05-19 13:41:56 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> On 5/19/2024 6:55 AM, Richard Damon wrote:
>>>>>>>>>> On 5/18/24 11:47 PM, olcott wrote:
>>>>>>>>>>> On 5/18/2024 6:04 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/18/24 6:47 PM, olcott wrote:
>>>>>>>>>>>>> On 5/18/2024 5:22 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 5/18/24 4:00 PM, olcott wrote:
>>>>>>>>>>>>>>> On 5/18/2024 2:57 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 5/18/24 3:46 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 5/18/2024 12:38 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 5/18/24 1:26 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 5/18/2024 11:56 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 5/18/24 12:48 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 9:32 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 5/18/24 10:15 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 5/18/2024 7:43 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> No, your system contradicts itself.
>>>>>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>>>>> You have never shown this.
>>>>>>>>>>>>>>>>>>>>>>> The most you have shown is a lack of understanding of the
>>>>>>>>>>>>>>>>>>>>>>> Truth Teller Paradox.
>>>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>>>> No, I have, but you don't understand the proof, it seems because you 
>>>>>>>>>>>>>>>>>>>>>> don't know what a "Truth Predicate" has been defined to be.
>>>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every
>>>>>>>>>>>>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth
>>>>>>>>>>>>>>>>>>>>> preserving operations that derive x from
>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>>> And thus, When True(L, p) established a sequence of truth preserving 
>>>>>>>>>>>>>>>>>>>> operations eminationg from ~True(L, p) by returning false, it 
>>>>>>>>>>>>>>>>>>>> contradicts itself. The problem is that True, in making an answer of 
>>>>>>>>>>>>>>>>>>>> false, has asserted that such a sequence exists.
>>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> On 5/13/2024 9:31 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>  > On 5/13/24 10:03 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>  >> On 5/13/2024 7:29 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>  >>>
>>>>>>>>>>>>>>>>>>>  >>> Remember, p defined as ~True(L, p) ...
>>>>>>>>>>>>>>>>>>>  >>
>>>>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied
>>>>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive p?
>>>>>>>>>>>>>>>>>>>  > No, so True(L, p) is false
>>>>>>>>>>>>>>>>>>>  >>
>>>>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied
>>>>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive ~p?
>>>>>>>>>>>>>>>>>>>  >
>>>>>>>>>>>>>>>>>>>  > No, so False(L, p) is false,
>>>>>>>>>>>>>>>>>>>  >
>>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>>> *To help you concentrate I repeated this*
>>>>>>>>>>>>>>>>>>> The Liar Paradox and your formalized Liar Paradox both
>>>>>>>>>>>>>>>>>>> contradict themselves that is why they must be screened
>>>>>>>>>>>>>>>>>>> out as type mismatch error non-truth-bearers *BEFORE THAT OCCURS*
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>>> And the Truth Predicate isn't allowed to "filter" out expressions.
>>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> YOU ALREADY KNOW THAT IT DOESN'T
>>>>>>>>>>>>>>>>> WE HAVE BEEN OVER THIS AGAIN AND AGAIN
>>>>>>>>>>>>>>>>> THE FORMAL SYSTEM USES THE TRUE AND FALSE PREDICATE
>>>>>>>>>>>>>>>>> TO FILTER OUT TYPE MISMATCH ERROR
>>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>>> The first thing that the formal system does with any
>>>>>>>>>>>>>>>>> arbitrary finite string input is see if it is a Truth-bearer:
>>>>>>>>>>>>>>>>> Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>>> No, we can ask True(L, x) for any expression x and get an answer.
>>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> The system is designed so you can ask this, yet non-truth-bearers
>>>>>>>>>>>>>>> are rejected before True(L, x) is allowed to be called.
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> 
>>>>>>>>>>>>>> Not allowed.
>>>>>>>>>>>>>> 
>>>>>>>>>>>>> 
>>>>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every
>>>>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth
>>>>>>>>>>>>> preserving operations that derive x from
>>>>>>>>>>>>> 
>>>>>>>>>>>>> A set of finite string semantic meanings that form an accurate
>>>>>>>>>>>>> verbal model of the general knowledge of the actual world that
>>>>>>>>>>>>> form a finite set of finite strings that are stipulated to have
>>>>>>>>>>>>> the semantic value of Boolean true.
>>>>>>>>>>>>> 
>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
>>>>>>>>>>>>> 
>>>>>>>>>>>>> 
>>>>>>>>>>>> 
>>>>>>>>>>>> So, for a statement x to be false, it says that there must be a 
>>>>>>>>>>>> sequence of truth perserving operations that derive ~x from, right?
>>>>>>>>>>>> 
>>>>>>>>>>> Yes we must build from mutual agreement, good.
>>>>>>>>>>> 
>>>>>>>>>>>> So do you still say that for p defined in L as ~True(L, p) that your 
>>>>>>>>>>>> definition will say that True(L, p) will return false?
>>>>>>>>>>>> 
>>>>>>>>>>> 
>>>>>>>>>>> It is the perfectly isomorphic to this:
>>>>>>>>>>> True(English, "This sentence is not true")
>>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> Nope, Because "This sentece is not true" can be a non-truth-bearer, but 
>>>>>>>>>> by its definition, True(L, x) can not.
>>>>>>>>>> 
>>>>>>>>> 
>>>>>>>>> True(L,x) is always a truth bearer.
>>>>>>>>> when x is defined as True(L,x) then x is not a truth bearer.
>>>>>>>> 
>>>>>>>> When x is defined as True(L,x) then x is what True(L,x) is,
>>>>>>>> in this case a truth bearer.
>>>>>> 
>>>>>>> This is known as the Truth Teller Paradox
>>>>>> 
>>>>>> Doesn't matter. But ir you say that "x is not a truth bearer" then,
>>>>>> by a truth preserving transformation, you imply that True(L,x) is
>>>>> 
>>>>> True(English, "a cat is an animal) is true
>>>>> LP := ~True(L, LP) expands to ~True(~True(~True(~True(...))))
>>>> 
>>>> No, it doesn't. It is a syntax error to have the same symbol on
>>>> both sides ":=" so the expansion is not justified.
>>> 
>>> ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩.
>>> *The sentence ψ is of course not self-referential in a strict sense*,
>>> but mathematically it behaves like one.
>>> https://plato.stanford.edu/entries/self-reference/#ConSemPar
>> 
>> Your quote omitted important details. One is that the claim is not
>> true about every theory but is about first order arithmetic and its
>> extension. Another one is that ϕ(x) is that the claim is about
>> every formula ϕ(x).
>> 
> 
> *The whole article is about self-reference*
> The ONLY detail that I am referring to is that it is conventional to 
> formalize self-reference incorrectly.
> 
> *Richard and both fixed that*
> 
> On 5/13/2024 9:31 PM, Richard Damon wrote:
>  > On 5/13/24 10:03 PM, olcott wrote:
>  >> On 5/13/2024 7:29 PM, Richard Damon wrote:
>  >>>
>  >>> Remember, p defined as ~True(L, p) ...
> 
> x := y means x is defined to be another name for y

Another name for the meaning of y. Therefore any pair of sentences that
are otherwise equal but one contains x where rhe other contains y is a pair
of equally true sentences. For example, if p defined as ~True(L, ⟨p⟩) 
then Truthbearer(L,p) has the same truth value as 
Truthbearer(L,~True(L, ⟨p⟩)).

> https://en.wikipedia.org/wiki/List_of_logic_symbols
> Thus  p := ~True(L, p)
> 
>>> *That is great. That means that you agree with me using different words*
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