On 5/17/24 11:35 PM, olcott wrote:
On 5/17/2024 9:40 PM, Richard Damon wrote:
On 5/17/24 10:19 PM, olcott wrote:
On 5/17/2024 8:33 PM, Richard Damon wrote:
On 5/17/24 9:22 PM, olcott wrote:
On 5/17/2024 8:07 PM, Richard Damon wrote:
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On 5/13/2024 7:29 PM, Richard Damon wrote:
> Remember, p defined as ~True(L, p) ...
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You already admitted that True(L,p) and False(L,p) both return false.
This is the correct value that these predicates correctly derived.
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Right, but that also means that we can show that True(L, true) returns false, which says your logic system is broken by being inconsistant.
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Not at all. Your version of the Truth Teller paradox has
the conventional lack of a truth object as the Liar Paradox
and the Truth Teller paradox: What are they true about?
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In other words, you logic doesn't have an absolute idea of truth!!!
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It does have an immutably correct notion of {true on the basis
of meaning} and rejects finite strings as not truth bearers on
this basis.
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Nope, because you said the value of "true" doesn't exist, truth is dependent on having something to make true.
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True(L,x) is defined in terms of its truthmaker.
And create a contradiction.
A whole bunch of expressions are stipulated to have the semantic
property of Boolean true. Being a member of this sat is what makes
them true.
and everything derivable from them with truth preserving operations, including the defined behavior of the True operator, and thus,
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The object that made the statement true, was that True(L, p) said that p wasn't true.
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*You agreed that True(L, p) is false and False(L,p) is false*
*You agreed that True(L, p) is false and False(L,p) is false*
*You agreed that True(L, p) is false and False(L,p) is false*
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Yes, which makes True(L, a sentence proven to be true) to be false.
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Thus, it is inconsistant.
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*It has nothing that it is true about so it is not true*
*It has nothing that it is true about so it is not true*
*It has nothing that it is true about so it is not true*
p is true, because True(L, p) being false made it so, since p was defined to be ~True(L, p)
THIS is the "true" that True(L, p) has previously defined to be false, and thus your True predicate is shown to be inconsistant.
Or we can use the arguement that since
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p is ~True(L, p) which is false that p is alse
then "a fish" because ~True(English, "a fish") is false that
makes "a fish" false.
Why?
True didn't make p true because it was an input to the Truth Predicate, but because p was defined as an expression based on it,
where was this done to "a fish".
You are just proving you don't understand what is being talked about.
~True(L, ~True(L, p) which, since True(L, p) is "established" to be false, and thus ~True(L,p) to be true, we can say that True(L, ~True(L, p) must be true
*ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
In other words, you logic doesn't understand how to handle references!
Note, p is different than a statement that SAYS something about a sentence it mentions, p is defined by a predicate applied to a sentence (that happens to be itself).
and thus p, being not that is false.
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So, we can prove that p is both false and true, and thus your system is BY DEFINITION inconsistant.
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We can prove that p is both false and true the exact same way
and to the exact same degree that "a fish" is both true and false.
How do you "prove" "a fish" to be true and false?
By your definitions it is neither.
That is the difference between the statement p and a sentence that is trivially a non-truth-bearer (one that doesn't state something).
<snip>
*No you said this* (Socratic question)
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No, YOU said it first, and I agreed.
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What else are you going to make it?
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(Socratic reply question)
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thus the truth value of p MUST be true, since it is not the falseness of True(L, p)
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We test p for True or False if neither it is tossed out on its ass.
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It is like we are testing if a person is hungry:
We ask is the person dead? The answer is yes and then you
say what if they are still hungry?
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RED HERRINBG.
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p is dead!
Every expression that is neither true nor false
is dead to any system of bivalent logic.
Then so is your "predicate True".
That is the problem you face, since p is DEFINED BY True, for p to be "dead", so must the idea of the existance of the predicate "True"
Since you have claimed that True(L, p) is false, by the stipulated definition of p,
Nope I never said that. You agreed that
There are no sequence of true preserving operations applied to
expressions that are stipulated to be true that derive p or ~p.
Right, which by your definition means that p can not be true.
Likewise for "a fish",
"this sentence is not true" and
"this sentence is true".
it MUST be a true statement, and thus you have
Then you contradict yourself when you said
>> On 5/13/2024 7:29 PM, Richard Damon wrote:
> No, so True(L, p) is false
No, your system contradicts itself.
you system says that since, at least initially, we can not find a path to p or ~p, True(L, p) must be false.
But once we have the decision, we now have a path that makes p true, and thus True is forced into a contradiction.
stiplated that True(L, <a statement proven to be true>) turns out to be false (since that statement IS p), and thus you system is
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*Illegal stipulation. It must come from here*
(a) A set of finite string semantic meanings that form an accurate
model of the general knowledge of the actual world.
FALSE. Formal Logic has NOTHING to do about the actual world, but about the stipulations (via the axioms of the system).
In fact, it is generally considered impossible to fully formalize the "actual world" as we would need to actually KNOW all the actual facts and relationships of the actual world.
Formal logic allows us to define APPROXIMATE models of the "real world", to try to deduce new things about the "real world".
Thus we can say that p is also the equivalent in L of
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We sure as Hell cannot correctly say that.
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Why not?
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*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
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In other words, you system doesn't allow the assignement of a statement to have a refenece to itself, which is one of the criteria in Tarski.
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~True(L, ~True(L, p))
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~True(English, ~True(English, "a fish")) is true
~True(English, ~True(English, "This sentence is not true")) is true
~True(English, ~True(English, "This sentence is true")) is true
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Nope, "This statment is true" is different then the statement:
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P, in L, is defined as ~True(L, P)
Yes that one is: "This sentence is not true"
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It it just
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P in L is defined as "P is not true."
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The prior one is the ordinary Liar Paradox formalized.
The difference is the statement P is not true has the possibility of being a non-truth bearer, but the predicate True(L, p) doesn't have that option.
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The predicate simple says True(L, p) is false and False(L,p) is false.
This is the same ESSENTIAL idea as Prolog unable to apply Rules to Facts to derive p or ~p.
The key difference is that my Facts are a complete and accurate model
of the general knowledge of the actual world...
Can't be. You don't have a complete and accurate model of the general knowledge of the actual world.
And to say you system is based on that just makes your system a lie.
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Which since we showed that True(L, p) was false, that means that the outer True predicate sees a true statement (since it is the negation of a false statement)
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~True(English, ~True(English, "a fish")) is true
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Yep.
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and thus True(L, ~True(L, p)) is true, and thus we can show that p must be false.
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By this same reasoning we can show that "a fish" must be false.
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Nope, because a fish wasn't defined to be any of those sentencds.
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"~True(L, p)" is merely a finite string input assigned to the variable named p. We could have as easily have assigned "a fish" to p.
Yes, but we didn't. And the string ~True(L, p) has semantic meaning.
And the semantic meaning leads to a contradiction no matter how you assign a logical value to True(L, p), and to not assign a value leads to a contradiction with the definition of a truth predicate.
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Thus we have a contradiction.
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So, if you want to claim "Truth Teller Paradox", the only answer is to say that True(L, p) isn't actually a truth-bearer,
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*True(L,x) and True(L,~x) (AKA False) ARE ALWAYS TRUTH-BEARERS*
*True(L,x) and True(L,~x) (AKA False) ARE ALWAYS TRUTH-BEARERS*
*True(L,x) and True(L,~x) (AKA False) ARE ALWAYS TRUTH-BEARERS*
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Right, and that it the problem. (we don't need the True(L, ~x) part though.
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False is defined as True(L,~x) and has no separate existence.
So? I haven't ever needed to refer to False(L, x) so that is just a red herring.
p is defined as ~True(L, p) which you say is false.
thus, we can also say, by the definiton of p that
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p is defined as ~True(L, ~True(L, p))
Let's not change the subject away from the point until
after we have mutual agreement that the original p must
be rejected by any bivalent system of logic.
What changing of the point?
You haven't answered the question of how to resolve the contradiction in your system!
I guess you are just admitting that you concept is just self-contradictory, and you have no problems with that.
*I wasted 15 years with Ben's change-the-subject rebuttal*
*I wasted 15 years with Ben's change-the-subject rebuttal*
*I wasted 15 years with Ben's change-the-subject rebuttal*
<snip change-the-subject rebuttal>
In future dialogues I may be laser focused on True or False or
rejected and totally ignore the slightest nuance of any slight
trace of any divergence from this one point.
In other worcs, you are admitting that you aren't going to try to fix the problems pointed out in your system, but just contiune down lines proven to be false.
Re: True on the basis of meaning --- Good job Richard !
Re: True on the basis of meaning --- Good job Richard !