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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: Thu, 23 May 2024 11:09:55 +0300
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On 2024-05-23 01:03:44 +0000, Richard Damon said:

> On 5/22/24 7:55 PM, olcott wrote:
>> On 5/22/2024 6:01 PM, Richard Damon wrote:
>>> On 5/22/24 3:52 PM, olcott wrote:
>>>> On 5/22/2024 11:58 AM, Mikko wrote:
>>>>> 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⟩)
>>>> 
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