Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement)

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:
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On 5/19/2024 9:03 AM, Mikko wrote:

On 2024-05-19 13:41:56 +0000, olcott said:
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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.

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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.
>

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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

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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.
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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*

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And the Truth Predicate isn't allowed to "filter" out expressions.
>

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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
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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))

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No, we can ask True(L, x) for any expression x and get an answer.
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The system is designed so you can ask this, yet non-truth-bearers
are rejected before True(L, x) is allowed to be called.
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Not allowed.
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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.
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*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))
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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?
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Yes we must build from mutual agreement, good.
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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?
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It is the perfectly isomorphic to this:
True(English, "This sentence is not true")
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Nope, Because "This sentece is not true" can be a non-truth-bearer, but by its definition, True(L, x) can not.
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True(L,x) is always a truth bearer.
when x is defined as True(L,x) then x is not a truth bearer.

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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

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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
*That is great. That means that you agree with me using different words*
When self-reference is formalized correctly as: LP := ~True(L, LP)
instead of formalized incorrectly as LP ↔ ~True(L, LP) as is the
standard convention shown above, then we can immediately reject the
Liar Paradox and the Truth Teller Paradox TT := True(L, TT) and any
other self-reference paradox.

TT := True(L, TT) expands to True(True(True(True(...))))

 No, it doesn't, for the same reason.
 

Great !!!

not a truth bearer. As you already said that "True(L,x)" is always
a truth bearer, you imply, by another truth preeserving transformation,
that something both is and is not a truth bearer.

 

*Not at all*
*Prolog sees the same infinite recursion and rejects it*

 Irrelevant.
 

*It is not at all Irrelevant* It is merely another way of proving
that LP and TT are not truth bearers thus are type mismatch errors
for any formal system of bivalent logic.
*Clocksin & Mellish agree with you*
*Clocksin & Mellish agree with you*
*Clocksin & Mellish agree with you*
BEGIN:(Clocksin & Mellish 2003:254)
Finally, a note about how Prolog matching sometimes differs from the
unification used in Resolution. Most Prolog systems will allow you to
satisfy goals like:
equal(X, X).
?- equal(foo(Y), Y).
that is, they will allow you to match a term against an uninstantiated
subterm of itself. In this example, foo(Y) is matched against Y, which
appears within it. As a result, Y will stand for foo(Y), which is
foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))),
and so on. *So Y ends up standing for some kind of infinite structure*.
END:(Clocksin & Mellish 2003:254)
unify_with_occurs_check(+Term1, +Term2) *detects and rejects this*
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer