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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: True on the basis of meaning --- Good job Richard ! ---Socratic
 method
Date: Mon, 20 May 2024 20:57:18 -0400
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On 5/20/24 2:59 PM, olcott wrote:
> On 5/19/2024 6:30 PM, Richard Damon wrote:
>> On 5/19/24 4:12 PM, olcott wrote:
>>> On 5/19/2024 12:17 PM, Richard Damon wrote:
>>>> On 5/19/24 9:41 AM, olcott wrote:
>>>>>
>>>>> True(L,x) is always a truth bearer.
>>>>> when x is defined as True(L,x) then x is not a truth bearer.
>>>>
>>>> So, x being DEFINED to be a certain sentence doesn't make x to have 
>>>> the same meaning as the sentence itself?
>>>>
>>>> What does it mean to define a name to a given sentence, if not that 
>>>> such a name referes to exactly that sentence?
>>>>
>>>
>>> p = ~True(L,p) // p is not a truth bearer because its refers to itself
>>
>> Then ~True(L,p) can't be a truth beared as they are the SAME 
>> STATEMENT, just using different "names".
> 
> 
> Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
> p = ~True(L,p) Truthbearer(L,p) is false
> q = ~True(L,p) Truthbearer(L,q) is true

Irrelvent.

If Truthbearer(L, p) is FALSE, and since p is just a NAME for the 
statement ~True(L, p), that means that True(L. p) is not a truth bearer 
and True has failed to be the required truth predicate.

If you are defining your "=" symbol to be "is defined as" so the left 
side is now a name for the right side, you statement above just PROVES 
that your logic system is inconsistant as the same expression (with just 
different names) has contradicory values.

You are just showing you utter lack of understanding of the fundamentals 
of Formal Logic.


>>
>> Just like (with context) YOU can be refered to a PO, Peter, Peter 
>> Olcott or Olcott, and all the reference get to the exact same entity, 
>> so any "name" for the express
>>
>>> True(L,p)  is false
>>> True(L,~p) is false
>>>
>>
>> So since True(L, p) is false, then ~True(L, p) is true.
>>
>>> ~True(True(L,p)) is true and is referring to the p that refers
>>> to itself it is not referring to its own self.
>>>
>>> *ONE LEVEL OF INDIRECT REFERENCE MAKES ALL THE DIFFERENCE*
>>
>> Why add the indirection? p is the NAME of the statement, which means 
>> exactly the same thing as the statement itself.
>>
> 
> p = ~True(L,p)
> does not mean that same thing as True(L, ~True(L,p))
> The above ~True(L, p) has another ~True(L,p) embedded in p.
> 
>> Is the definition of an English word one level LESS of indirection 
>> than the word itself?
>>
> 
> This sentence is not true("This sentence is not true") is true.

Right, that is a sentence about another sentence (that is part of itself)

p defined as ~True(L, p) isn't a sentence refering to ~True(L, p), it is 
assigning a name to the sentence to allow OTHER sentences to refer to it 
by name,


> 
>> I don't think you understand what it means to define something.
>>
> 
> x := y means x is defined to be another name for y
> https://en.wikipedia.org/wiki/List_of_logic_symbols
> 
> LP := ~True(L, LP)
> specifies ~True(~True(~True(~True(~True(...)))))

Nope.

It means that LP is defined to be the sentence ~True(L, LP)

replacing the LP in the sentence with a copy of LP IS a level of 
indirection, so you can get the infinite expansion if you keep or 
derefencing the reference in the statement.


> 
>> "Definition by example" is worse than "Proof by example", at least 
>> proof by example can be correct if the assertion is that there exists, 
>> and not for all.
>>
> 
> A simpler isomorphism of the same thing is proof by analogy.
> 

Which isn't a valid proof in a formal system. You seem to think Formal 
System are a loosy goosy with proofs as Philosophy.

>> A level of indirection:
>>
>> p: "This sentence is true", which is exactly the same as "p is true" 
>> since "this sentence" IS p
>>
> 
> p := True(L,p)
> specifies True(True(True(True(True(...)))))

Nope, it is equivelent to that, but doesn't SPECIFY that.

As I said above that is expanding levels of indirecction.


> 
> *Prolog sees the same infinite recursion and rejects it*
> ?- TT = true(TT).
> TT = true(TT).
> 
> ?- unify_with_occurs_check(TT, true(TT)).
> false.
> 

Right, because prolog can't handle any levels of self referencing, and 
thus is not suitable for logic that can do that.

You have been told this, but don't seem to understand it. My guess is 
you can't understand any logic more complicated than what Prolog 
handles, so don't realize how much it just doesn't handle.