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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: Sun, 19 May 2024 19:30:45 -0400
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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".

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.

Is the definition of an English word one level LESS of indirection than 
the word itself?

I don't think you understand what it means to define something.

"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 level of indirection:

p: "This sentence is true", which is exactly the same as "p is true" 
since "this sentence" IS p

p1: The sentence p is true"
THAT is a level of indirection, as p1 refers to a sentence that isn't 
itself.

> 
>>>
>>> ~True(L,x) is always a truth bearer.
>>> when x is defined as ~True(L,x) then x is not a truth bearer.
>>
>> Again, what does "Defined as" mean to you?
>>
> 
> x := y means x is defined to be another name for y
> https://en.wikipedia.org/wiki/List_of_logic_symbols

So, p := ~True(L, p) means p is just another name, and thus another way 
to reference

> 
> LP := ~True(L,LP)
> means ~True(~True(~True(~True(~True(...)))))

No, it to be what you are meaning, it would be:

LP := ~True(L, LP)
LP := ~True(L, ~True(L, LP))
LP := ~True(L, ~True(L, ~True(L, LP)))
....

And each of these COULD possible be described as adding a level of 
indirection, as we are affecting how many layers we are applying of the 
definition.


> 
> It is the common convention to encode self-reference incorrectly.
> LP ↔ ~True(L, LP)
> 
>     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/
> 
> <big snip>
> 
> *Usenet Article Lookup*
> http://al.howardknight.net/ chops off long posts
> Since we can no longer use Google Groups to link to recent posts.
>