On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
On 5/13/24 11:04 AM, olcott wrote:*You actually have to answer those questions and*
On 5/13/2024 6:18 AM, Richard Damon wrote:
On 5/12/24 11:41 PM, olcott wrote:
On 5/12/2024 7:35 PM, Richard Damon wrote:
On 5/12/24 8:07 PM, olcott wrote:
On 5/12/2024 6:55 PM, Richard Damon wrote:
On 5/12/24 7:22 PM, olcott wrote:
On 5/12/2024 6:02 PM, Richard Damon wrote:
On 5/12/24 6:56 PM, olcott wrote:
On 5/12/2024 5:40 PM, Richard Damon wrote:
On 5/12/24 5:54 PM, olcott wrote:
On 5/12/2024 3:33 PM, Richard Damon wrote:
On 5/12/24 2:36 PM, olcott wrote:
On 5/12/2024 1:22 PM, Richard Damon wrote:
On 5/12/24 2:06 PM, olcott wrote:
On 5/12/2024 12:52 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>> On 5/12/24 1:19 PM, olcott wrote:
On 5/12/2024 10:33 AM, Mikko wrote:Which means you need to be VERY clear about what you >>>>>>>>>>>>>>>>>> claim to be "usually spoken of" and what is your >>>>>>>>>>>>>>>>>> unique contribution.
On 2024-05-12 14:22:25 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 5/12/2024 2:42 AM, Mikko wrote:
On 2024-05-11 04:27:03 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 5/10/2024 10:49 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 11:35 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/2024 10:16 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 10:36 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> The entire body of expressions that are {true >>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of theirIn and about formal logic there is no valid deep >>>>>>>>>>>>>>>>>>>>>> understanding. Only
You don't understand what Quite was talking about, >>>>>>>>>>>>>>>>>>>>>>>>meaning} involves nothing more or less than >>>>>>>>>>>>>>>>>>>>>>>>>>> stipulated relations between >>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
You do know that what you are describing when >>>>>>>>>>>>>>>>>>>>>>>>>> applied to Formal Systems are the axioms of >>>>>>>>>>>>>>>>>>>>>>>>>> the system and the most primitively provable >>>>>>>>>>>>>>>>>>>>>>>>>> theorems.
YES and there are axioms that comprise the >>>>>>>>>>>>>>>>>>>>>>>>> verbal model of the
actual world, thus Quine was wrong. >>>>>>>>>>>>>>>>>>>>>>>>
I don't need to know anything about what he was >>>>>>>>>>>>>>>>>>>>>>> talking about
except that he disagreed with {true on the basis >>>>>>>>>>>>>>>>>>>>>>> or meaning}.
I don't care or need to know how he got to an >>>>>>>>>>>>>>>>>>>>>>> incorrect answer.
Which you don't seem to understand what that means. >>>>>>>>>>>>>>>>>>>>>>>>
You don't seem to understand what "Formal >>>>>>>>>>>>>>>>>>>>>>>>>> Logic" actually means.
Ultimately it is anchored in stipulated >>>>>>>>>>>>>>>>>>>>>>>>> relations between finite
strings (AKA axioms) and expressions derived >>>>>>>>>>>>>>>>>>>>>>>>> from applying truth
preserving operations to these axioms. >>>>>>>>>>>>>>>>>>>>>>>>
I understand this much more deeply than you do. >>>>>>>>>>>>>>>>>>>>>>
a shallow understanding can be valid. >>>>>>>>>>>>>>>>>>>>>>
It turns out that ALL {true on the basis of >>>>>>>>>>>>>>>>>>>>> meaning} that includes
ALL of logic and math has its entire foundation in >>>>>>>>>>>>>>>>>>>>> relations between
finite strings. Some are stipulated to be true >>>>>>>>>>>>>>>>>>>>> (axioms) and some
are derived by applying truth preserving operations >>>>>>>>>>>>>>>>>>>>> to these axioms.
Usually the word "true" is not used when talking >>>>>>>>>>>>>>>>>>>> about uninterpreted
formal systems. Axioms and what can be inferred from >>>>>>>>>>>>>>>>>>>> axioms are called
"theorems". Theorems can be true in some >>>>>>>>>>>>>>>>>>>> interpretations and false in
another. If the system is incosistent then there is >>>>>>>>>>>>>>>>>>>> no interpretation
where all axioms are true.
I am not talking about how these things are usually >>>>>>>>>>>>>>>>>>> spoken of. I am
talking about my unique contribution to the actual >>>>>>>>>>>>>>>>>>> philosophical
foundation of {true on the basis of meaning}. >>>>>>>>>>>>>>>>>>
You then need to show how your contribution isn't in >>>>>>>>>>>>>>>>>> conflict with the classical parts, but follows within >>>>>>>>>>>>>>>>>> its definitions.
If you want to say that something in the classical >>>>>>>>>>>>>>>>>> theory is not actually true, then you need to show how >>>>>>>>>>>>>>>>>> removing that piece doesn't affect the system. This >>>>>>>>>>>>>>>>>> seems to be a weak point of yours, you think you can >>>>>>>>>>>>>>>>>> change a system, and not show that the system can >>>>>>>>>>>>>>>>>> still exist as it was.
This is entirely comprised of relations between >>>>>>>>>>>>>>>>>>> finite strings:
some of which are stipulated to have the semantic >>>>>>>>>>>>>>>>>>> value of Boolean
true, and others derived from applying truth >>>>>>>>>>>>>>>>>>> preserving operations
to these finite string.
This is approximately equivalent to proofs from >>>>>>>>>>>>>>>>>>> axioms. It is not
exactly the same thing because an infinite sequence >>>>>>>>>>>>>>>>>>> of inference
steps may sometimes be required. It is also not >>>>>>>>>>>>>>>>>>> exactly the same
because some proofs are not restricted to truth >>>>>>>>>>>>>>>>>>> preserving operations.
So, what effect does that difference have? >>>>>>>>>>>>>>>>>>
You seem here to accept that some truths are based on >>>>>>>>>>>>>>>>>> an infinite sequence of operations, while you admit >>>>>>>>>>>>>>>>>> that proofs are finite sequences, but it seems you >>>>>>>>>>>>>>>>>> still assert that all truths must be provable. >>>>>>>>>>>>>>>>>>
I did not use the term "provable" or "proofs" these >>>>>>>>>>>>>>>>> only apply to
finite sequences. {derived from applying truth >>>>>>>>>>>>>>>>> preserving operations}
can involve infinite sequences.
But if true can come out of an infinite sequences, and >>>>>>>>>>>>>>>> some need such an infinite sequence, but proof requires >>>>>>>>>>>>>>>> a finite sequence, that shows that there will exists >>>>>>>>>>>>>>>> some statements are true, but not provable.
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>>> used for a similar undecidability proof...(Gödel >>>>>>>>>>>>>>>>> 1931:43-44)
When we look at the way that {true on the basis of >>>>>>>>>>>>>>>>> meaning}
actually works, then all epistemological antinomies are >>>>>>>>>>>>>>>>> simply untrue.
And Godel would agree to that. You just don't understand >>>>>>>>>>>>>>>> what that line 14 means.
It can be proven in a finite sequence of steps that >>>>>>>>>>>>>>> epistemological antinomies are simply untrue.
So?
So that directly contradicts what Gödel said in the quote >>>>>>>>>>>>> thus proving
that Gödel and Tarski were both fundamentally incorrect in >>>>>>>>>>>>> the basic
foundation of their work.
Where does he say wha tyo claim?
He says that it can be *USED* for a similar proof.
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>
But he showed how it was used, so you are just proven wrong. >>>>>>>>>>
This proves that he did not understand undecidability, thus making >>>>>>>>> the rest of his paper moot.
It shows no such thing.
Since, As I have pointed out, the actual statement, which you
don't seem to even be able to understand, is NOT an
epistemological antinomy, just shows that you don't understand >>>>>>>> anything about the topic you are talking about.
You don't seem to understand even basic English, so you have no >>>>>>>> place trying to talk about theories based on the "meaning of
words", as you have proved yourself incompetent.
Tarski anchors his entire proof in the above Gödel quote so >>>>>>>>> we can't just say one one little quote does not ruin the whole >>>>>>>>> thing.
Yep, and he is right.
The Liar Paradox is easily rejected by the correct foundation of >>>>>>> {true on the basis of meaning} on the basis that it cannot be
derived by applying truth preserving operations to finite strings >>>>>>> that are stipulated to have the semantic value of Boolean true.
Yes, the liar paradox is a statement that can be neither true or
false.
Tarski thought that he proved that True(L, x) cannot be defined on >>>>>>> the basis that he could not prove that an expression that is not >>>>>>> true
is true.
Nope. You seem to have a mental block on this.
The point is that if "True(L, x)" is a predicate, then it ALWAYS
has a truth value, and that value is true if the statement is
true, and false if the statement is false, or not a truth bearer.
True(English, "a fish") is a type mismatch error, they must be
excluded and not merely construed as untrue.
No, since "a fish" is not a truth bearer, True(English, "a fish")
must return false.
Then it must also return false for ~X where X = "a fish"
Yes.
True(English, "this sentence is untrue")
is ALSO a type mismatch error, that must be
excluded and not merely construed as untrue.
Nope, since "this sentence is untrue" is not a true statement,
True(English, "this sentence is untrue") must return false.
Different yet equivalent protocol.
Nope.
True(L, f) must ALWAYS be a truth bearer, and thus ~True(L, f) must
also be one.
Remember, the truth predicate "True" doesn't return the truth value
of the expression, so doesn't have an answer for a non-truth-bearer,
but is a PREDICATE, that always returns a value, which is TRUE if
the expression is a true expression, and false for everything else.
Boolean True(L,x) can return false when x is not a truth bearer
yet must also return false for ~x.
But the problem wasn't given ~x.
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer, as
True must return a Truth Value for all inputs, and ~ a truth valus is
always the other truth value.
*not simply change the subject to another question*
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?
https://en.wikipedia.org/wiki/Socratic_questioning https://en.wikipedia.org/wiki/Socratic_method
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:
On 5/13/24 11:04 AM, olcott wrote:*You actually have to answer those questions and*
On 5/13/2024 6:18 AM, Richard Damon wrote:
On 5/12/24 11:41 PM, olcott wrote:
On 5/12/2024 7:35 PM, Richard Damon wrote:
On 5/12/24 8:07 PM, olcott wrote:
On 5/12/2024 6:55 PM, Richard Damon wrote:Yes, the liar paradox is a statement that can be neither true or >>>>>>>> false.
On 5/12/24 7:22 PM, olcott wrote:
On 5/12/2024 6:02 PM, Richard Damon wrote:
On 5/12/24 6:56 PM, olcott wrote:
On 5/12/2024 5:40 PM, Richard Damon wrote:
On 5/12/24 5:54 PM, olcott wrote:
On 5/12/2024 3:33 PM, Richard Damon wrote:
On 5/12/24 2:36 PM, olcott wrote:
On 5/12/2024 1:22 PM, Richard Damon wrote:
On 5/12/24 2:06 PM, olcott wrote:
On 5/12/2024 12:52 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 5/12/24 1:19 PM, olcott wrote:
On 5/12/2024 10:33 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>> On 2024-05-12 14:22:25 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>Which means you need to be VERY clear about what you >>>>>>>>>>>>>>>>>>>> claim to be "usually spoken of" and what is your >>>>>>>>>>>>>>>>>>>> unique contribution.
On 5/12/2024 2:42 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-11 04:27:03 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 5/10/2024 10:49 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 11:35 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/2024 10:16 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 10:36 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> The entire body of expressions that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>> {true on the basis of their >>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning} involves nothing more or less than >>>>>>>>>>>>>>>>>>>>>>>>>>>>> stipulated relations between >>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.In and about formal logic there is no valid deep >>>>>>>>>>>>>>>>>>>>>>>> understanding. Only
You don't understand what Quite was talking >>>>>>>>>>>>>>>>>>>>>>>>>> about,
You do know that what you are describing >>>>>>>>>>>>>>>>>>>>>>>>>>>> when applied to Formal Systems are the >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms of the system and the most >>>>>>>>>>>>>>>>>>>>>>>>>>>> primitively provable theorems. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
YES and there are axioms that comprise the >>>>>>>>>>>>>>>>>>>>>>>>>>> verbal model of the
actual world, thus Quine was wrong. >>>>>>>>>>>>>>>>>>>>>>>>>>
I don't need to know anything about what he was >>>>>>>>>>>>>>>>>>>>>>>>> talking about
except that he disagreed with {true on the >>>>>>>>>>>>>>>>>>>>>>>>> basis or meaning}.
I don't care or need to know how he got to an >>>>>>>>>>>>>>>>>>>>>>>>> incorrect answer.
Which you don't seem to understand what that >>>>>>>>>>>>>>>>>>>>>>>>>> means.
You don't seem to understand what "Formal >>>>>>>>>>>>>>>>>>>>>>>>>>>> Logic" actually means. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ultimately it is anchored in stipulated >>>>>>>>>>>>>>>>>>>>>>>>>>> relations between finite >>>>>>>>>>>>>>>>>>>>>>>>>>> strings (AKA axioms) and expressions derived >>>>>>>>>>>>>>>>>>>>>>>>>>> from applying truth
preserving operations to these axioms. >>>>>>>>>>>>>>>>>>>>>>>>>>
I understand this much more deeply than you do. >>>>>>>>>>>>>>>>>>>>>>>>
a shallow understanding can be valid. >>>>>>>>>>>>>>>>>>>>>>>>
It turns out that ALL {true on the basis of >>>>>>>>>>>>>>>>>>>>>>> meaning} that includes
ALL of logic and math has its entire foundation >>>>>>>>>>>>>>>>>>>>>>> in relations between
finite strings. Some are stipulated to be true >>>>>>>>>>>>>>>>>>>>>>> (axioms) and some
are derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>> operations to these axioms.
Usually the word "true" is not used when talking >>>>>>>>>>>>>>>>>>>>>> about uninterpreted
formal systems. Axioms and what can be inferred >>>>>>>>>>>>>>>>>>>>>> from axioms are called
"theorems". Theorems can be true in some >>>>>>>>>>>>>>>>>>>>>> interpretations and false in
another. If the system is incosistent then there >>>>>>>>>>>>>>>>>>>>>> is no interpretation
where all axioms are true.
I am not talking about how these things are usually >>>>>>>>>>>>>>>>>>>>> spoken of. I am
talking about my unique contribution to the actual >>>>>>>>>>>>>>>>>>>>> philosophical
foundation of {true on the basis of meaning}. >>>>>>>>>>>>>>>>>>>>
You then need to show how your contribution isn't in >>>>>>>>>>>>>>>>>>>> conflict with the classical parts, but follows >>>>>>>>>>>>>>>>>>>> within its definitions.
If you want to say that something in the classical >>>>>>>>>>>>>>>>>>>> theory is not actually true, then you need to show >>>>>>>>>>>>>>>>>>>> how removing that piece doesn't affect the system. >>>>>>>>>>>>>>>>>>>> This seems to be a weak point of yours, you think >>>>>>>>>>>>>>>>>>>> you can change a system, and not show that the >>>>>>>>>>>>>>>>>>>> system can still exist as it was.
This is entirely comprised of relations between >>>>>>>>>>>>>>>>>>>>> finite strings:
some of which are stipulated to have the semantic >>>>>>>>>>>>>>>>>>>>> value of Boolean
true, and others derived from applying truth >>>>>>>>>>>>>>>>>>>>> preserving operations
to these finite string.
This is approximately equivalent to proofs from >>>>>>>>>>>>>>>>>>>>> axioms. It is not
exactly the same thing because an infinite sequence >>>>>>>>>>>>>>>>>>>>> of inference
steps may sometimes be required. It is also not >>>>>>>>>>>>>>>>>>>>> exactly the same
because some proofs are not restricted to truth >>>>>>>>>>>>>>>>>>>>> preserving operations.
So, what effect does that difference have? >>>>>>>>>>>>>>>>>>>>
You seem here to accept that some truths are based >>>>>>>>>>>>>>>>>>>> on an infinite sequence of operations, while you >>>>>>>>>>>>>>>>>>>> admit that proofs are finite sequences, but it seems >>>>>>>>>>>>>>>>>>>> you still assert that all truths must be provable. >>>>>>>>>>>>>>>>>>>>
I did not use the term "provable" or "proofs" these >>>>>>>>>>>>>>>>>>> only apply to
finite sequences. {derived from applying truth >>>>>>>>>>>>>>>>>>> preserving operations}
can involve infinite sequences.
But if true can come out of an infinite sequences, and >>>>>>>>>>>>>>>>>> some need such an infinite sequence, but proof >>>>>>>>>>>>>>>>>> requires a finite sequence, that shows that there will >>>>>>>>>>>>>>>>>> exists some statements are true, but not provable. >>>>>>>>>>>>>>>>>>
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>>>>> used for a similar undecidability proof...(Gödel >>>>>>>>>>>>>>>>>>> 1931:43-44)
When we look at the way that {true on the basis of >>>>>>>>>>>>>>>>>>> meaning}
actually works, then all epistemological antinomies >>>>>>>>>>>>>>>>>>> are simply untrue.
And Godel would agree to that. You just don't >>>>>>>>>>>>>>>>>> understand what that line 14 means.
It can be proven in a finite sequence of steps that >>>>>>>>>>>>>>>>> epistemological antinomies are simply untrue. >>>>>>>>>>>>>>>>>
So?
So that directly contradicts what Gödel said in the quote >>>>>>>>>>>>>>> thus proving
that Gödel and Tarski were both fundamentally incorrect >>>>>>>>>>>>>>> in the basic
foundation of their work.
Where does he say wha tyo claim?
He says that it can be *USED* for a similar proof. >>>>>>>>>>>>>>
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>>
But he showed how it was used, so you are just proven wrong. >>>>>>>>>>>>
This proves that he did not understand undecidability, thus >>>>>>>>>>> making
the rest of his paper moot.
It shows no such thing.
Since, As I have pointed out, the actual statement, which you >>>>>>>>>> don't seem to even be able to understand, is NOT an
epistemological antinomy, just shows that you don't understand >>>>>>>>>> anything about the topic you are talking about.
You don't seem to understand even basic English, so you have >>>>>>>>>> no place trying to talk about theories based on the "meaning >>>>>>>>>> of words", as you have proved yourself incompetent.
Tarski anchors his entire proof in the above Gödel quote so >>>>>>>>>>> we can't just say one one little quote does not ruin the >>>>>>>>>>> whole thing.
Yep, and he is right.
The Liar Paradox is easily rejected by the correct foundation of >>>>>>>>> {true on the basis of meaning} on the basis that it cannot be >>>>>>>>> derived by applying truth preserving operations to finite strings >>>>>>>>> that are stipulated to have the semantic value of Boolean true. >>>>>>>>
Tarski thought that he proved that True(L, x) cannot be defined on >>>>>>>>> the basis that he could not prove that an expression that is >>>>>>>>> not true
is true.
Nope. You seem to have a mental block on this.
The point is that if "True(L, x)" is a predicate, then it ALWAYS >>>>>>>> has a truth value, and that value is true if the statement is
true, and false if the statement is false, or not a truth bearer. >>>>>>>>
True(English, "a fish") is a type mismatch error, they must be
excluded and not merely construed as untrue.
No, since "a fish" is not a truth bearer, True(English, "a fish")
must return false.
Then it must also return false for ~X where X = "a fish"
Yes.
True(English, "this sentence is untrue")
is ALSO a type mismatch error, that must be
excluded and not merely construed as untrue.
Nope, since "this sentence is untrue" is not a true statement,
True(English, "this sentence is untrue") must return false.
Different yet equivalent protocol.
Nope.
True(L, f) must ALWAYS be a truth bearer, and thus ~True(L, f) must
also be one.
Remember, the truth predicate "True" doesn't return the truth
value of the expression, so doesn't have an answer for a
non-truth-bearer, but is a PREDICATE, that always returns a value, >>>>>> which is TRUE if the expression is a true expression, and false
for everything else.
Boolean True(L,x) can return false when x is not a truth bearer
yet must also return false for ~x.
But the problem wasn't given ~x.
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
*not simply change the subject to another question*
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
and thus ~True(L, p) is true.
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,
*When p is neither True nor False then*
*p is rejected as not a truth bearer*
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:I have spend literally thousands and thousands of hours on the
On 5/13/2024 7:29 PM, Richard Damon wrote:
On 5/13/24 11:04 AM, olcott wrote:*You actually have to answer those questions and*
On 5/13/2024 6:18 AM, Richard Damon wrote:
On 5/12/24 11:41 PM, olcott wrote:
On 5/12/2024 7:35 PM, Richard Damon wrote:
On 5/12/24 8:07 PM, olcott wrote:
On 5/12/2024 6:55 PM, Richard Damon wrote:Yes, the liar paradox is a statement that can be neither true or >>>>>>>> false.
On 5/12/24 7:22 PM, olcott wrote:
On 5/12/2024 6:02 PM, Richard Damon wrote:
On 5/12/24 6:56 PM, olcott wrote:
On 5/12/2024 5:40 PM, Richard Damon wrote:
On 5/12/24 5:54 PM, olcott wrote:
On 5/12/2024 3:33 PM, Richard Damon wrote:
On 5/12/24 2:36 PM, olcott wrote:
On 5/12/2024 1:22 PM, Richard Damon wrote:
On 5/12/24 2:06 PM, olcott wrote:
On 5/12/2024 12:52 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 5/12/24 1:19 PM, olcott wrote:
On 5/12/2024 10:33 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>> On 2024-05-12 14:22:25 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>Which means you need to be VERY clear about what you >>>>>>>>>>>>>>>>>>>> claim to be "usually spoken of" and what is your >>>>>>>>>>>>>>>>>>>> unique contribution.
On 5/12/2024 2:42 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-11 04:27:03 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 5/10/2024 10:49 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 11:35 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/2024 10:16 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 10:36 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> The entire body of expressions that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>> {true on the basis of their >>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning} involves nothing more or less than >>>>>>>>>>>>>>>>>>>>>>>>>>>>> stipulated relations between >>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.In and about formal logic there is no valid deep >>>>>>>>>>>>>>>>>>>>>>>> understanding. Only
You don't understand what Quite was talking >>>>>>>>>>>>>>>>>>>>>>>>>> about,
You do know that what you are describing >>>>>>>>>>>>>>>>>>>>>>>>>>>> when applied to Formal Systems are the >>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms of the system and the most >>>>>>>>>>>>>>>>>>>>>>>>>>>> primitively provable theorems. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
YES and there are axioms that comprise the >>>>>>>>>>>>>>>>>>>>>>>>>>> verbal model of the
actual world, thus Quine was wrong. >>>>>>>>>>>>>>>>>>>>>>>>>>
I don't need to know anything about what he was >>>>>>>>>>>>>>>>>>>>>>>>> talking about
except that he disagreed with {true on the >>>>>>>>>>>>>>>>>>>>>>>>> basis or meaning}.
I don't care or need to know how he got to an >>>>>>>>>>>>>>>>>>>>>>>>> incorrect answer.
Which you don't seem to understand what that >>>>>>>>>>>>>>>>>>>>>>>>>> means.
You don't seem to understand what "Formal >>>>>>>>>>>>>>>>>>>>>>>>>>>> Logic" actually means. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ultimately it is anchored in stipulated >>>>>>>>>>>>>>>>>>>>>>>>>>> relations between finite >>>>>>>>>>>>>>>>>>>>>>>>>>> strings (AKA axioms) and expressions derived >>>>>>>>>>>>>>>>>>>>>>>>>>> from applying truth
preserving operations to these axioms. >>>>>>>>>>>>>>>>>>>>>>>>>>
I understand this much more deeply than you do. >>>>>>>>>>>>>>>>>>>>>>>>
a shallow understanding can be valid. >>>>>>>>>>>>>>>>>>>>>>>>
It turns out that ALL {true on the basis of >>>>>>>>>>>>>>>>>>>>>>> meaning} that includes
ALL of logic and math has its entire foundation >>>>>>>>>>>>>>>>>>>>>>> in relations between
finite strings. Some are stipulated to be true >>>>>>>>>>>>>>>>>>>>>>> (axioms) and some
are derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>> operations to these axioms.
Usually the word "true" is not used when talking >>>>>>>>>>>>>>>>>>>>>> about uninterpreted
formal systems. Axioms and what can be inferred >>>>>>>>>>>>>>>>>>>>>> from axioms are called
"theorems". Theorems can be true in some >>>>>>>>>>>>>>>>>>>>>> interpretations and false in
another. If the system is incosistent then there >>>>>>>>>>>>>>>>>>>>>> is no interpretation
where all axioms are true.
I am not talking about how these things are usually >>>>>>>>>>>>>>>>>>>>> spoken of. I am
talking about my unique contribution to the actual >>>>>>>>>>>>>>>>>>>>> philosophical
foundation of {true on the basis of meaning}. >>>>>>>>>>>>>>>>>>>>
You then need to show how your contribution isn't in >>>>>>>>>>>>>>>>>>>> conflict with the classical parts, but follows >>>>>>>>>>>>>>>>>>>> within its definitions.
If you want to say that something in the classical >>>>>>>>>>>>>>>>>>>> theory is not actually true, then you need to show >>>>>>>>>>>>>>>>>>>> how removing that piece doesn't affect the system. >>>>>>>>>>>>>>>>>>>> This seems to be a weak point of yours, you think >>>>>>>>>>>>>>>>>>>> you can change a system, and not show that the >>>>>>>>>>>>>>>>>>>> system can still exist as it was.
This is entirely comprised of relations between >>>>>>>>>>>>>>>>>>>>> finite strings:
some of which are stipulated to have the semantic >>>>>>>>>>>>>>>>>>>>> value of Boolean
true, and others derived from applying truth >>>>>>>>>>>>>>>>>>>>> preserving operations
to these finite string.
This is approximately equivalent to proofs from >>>>>>>>>>>>>>>>>>>>> axioms. It is not
exactly the same thing because an infinite sequence >>>>>>>>>>>>>>>>>>>>> of inference
steps may sometimes be required. It is also not >>>>>>>>>>>>>>>>>>>>> exactly the same
because some proofs are not restricted to truth >>>>>>>>>>>>>>>>>>>>> preserving operations.
So, what effect does that difference have? >>>>>>>>>>>>>>>>>>>>
You seem here to accept that some truths are based >>>>>>>>>>>>>>>>>>>> on an infinite sequence of operations, while you >>>>>>>>>>>>>>>>>>>> admit that proofs are finite sequences, but it seems >>>>>>>>>>>>>>>>>>>> you still assert that all truths must be provable. >>>>>>>>>>>>>>>>>>>>
I did not use the term "provable" or "proofs" these >>>>>>>>>>>>>>>>>>> only apply to
finite sequences. {derived from applying truth >>>>>>>>>>>>>>>>>>> preserving operations}
can involve infinite sequences.
But if true can come out of an infinite sequences, and >>>>>>>>>>>>>>>>>> some need such an infinite sequence, but proof >>>>>>>>>>>>>>>>>> requires a finite sequence, that shows that there will >>>>>>>>>>>>>>>>>> exists some statements are true, but not provable. >>>>>>>>>>>>>>>>>>
...14 Every epistemological antinomy can likewise be >>>>>>>>>>>>>>>>>>> used for a similar undecidability proof...(Gödel >>>>>>>>>>>>>>>>>>> 1931:43-44)
When we look at the way that {true on the basis of >>>>>>>>>>>>>>>>>>> meaning}
actually works, then all epistemological antinomies >>>>>>>>>>>>>>>>>>> are simply untrue.
And Godel would agree to that. You just don't >>>>>>>>>>>>>>>>>> understand what that line 14 means.
It can be proven in a finite sequence of steps that >>>>>>>>>>>>>>>>> epistemological antinomies are simply untrue. >>>>>>>>>>>>>>>>>
So?
So that directly contradicts what Gödel said in the quote >>>>>>>>>>>>>>> thus proving
that Gödel and Tarski were both fundamentally incorrect >>>>>>>>>>>>>>> in the basic
foundation of their work.
Where does he say wha tyo claim?
He says that it can be *USED* for a similar proof. >>>>>>>>>>>>>>
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>> *IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS CLUELESS* >>>>>>>>>>>>>
But he showed how it was used, so you are just proven wrong. >>>>>>>>>>>>
This proves that he did not understand undecidability, thus >>>>>>>>>>> making
the rest of his paper moot.
It shows no such thing.
Since, As I have pointed out, the actual statement, which you >>>>>>>>>> don't seem to even be able to understand, is NOT an
epistemological antinomy, just shows that you don't understand >>>>>>>>>> anything about the topic you are talking about.
You don't seem to understand even basic English, so you have >>>>>>>>>> no place trying to talk about theories based on the "meaning >>>>>>>>>> of words", as you have proved yourself incompetent.
Tarski anchors his entire proof in the above Gödel quote so >>>>>>>>>>> we can't just say one one little quote does not ruin the >>>>>>>>>>> whole thing.
Yep, and he is right.
The Liar Paradox is easily rejected by the correct foundation of >>>>>>>>> {true on the basis of meaning} on the basis that it cannot be >>>>>>>>> derived by applying truth preserving operations to finite strings >>>>>>>>> that are stipulated to have the semantic value of Boolean true. >>>>>>>>
Tarski thought that he proved that True(L, x) cannot be defined on >>>>>>>>> the basis that he could not prove that an expression that is >>>>>>>>> not true
is true.
Nope. You seem to have a mental block on this.
The point is that if "True(L, x)" is a predicate, then it ALWAYS >>>>>>>> has a truth value, and that value is true if the statement is
true, and false if the statement is false, or not a truth bearer. >>>>>>>>
True(English, "a fish") is a type mismatch error, they must be
excluded and not merely construed as untrue.
No, since "a fish" is not a truth bearer, True(English, "a fish")
must return false.
Then it must also return false for ~X where X = "a fish"
Yes.
True(English, "this sentence is untrue")
is ALSO a type mismatch error, that must be
excluded and not merely construed as untrue.
Nope, since "this sentence is untrue" is not a true statement,
True(English, "this sentence is untrue") must return false.
Different yet equivalent protocol.
Nope.
True(L, f) must ALWAYS be a truth bearer, and thus ~True(L, f) must
also be one.
Remember, the truth predicate "True" doesn't return the truth
value of the expression, so doesn't have an answer for a
non-truth-bearer, but is a PREDICATE, that always returns a value, >>>>>> which is TRUE if the expression is a true expression, and false
for everything else.
Boolean True(L,x) can return false when x is not a truth bearer
yet must also return false for ~x.
But the problem wasn't given ~x.
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
*not simply change the subject to another question*
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
and thus ~True(L, p) is true.
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,
results of this simple little post over the last two decades.
*When p is neither True nor False then p is rejected as invalid*
*input and that is the complete end of any and all evaluation of p*
On 5/14/2024 6:31 AM, Richard Damon wrote:
On 5/13/24 11:36 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:I have spend literally thousands and thousands of hours on the
On 5/13/2024 7:29 PM, Richard Damon wrote:
On 5/13/24 11:04 AM, olcott wrote:*You actually have to answer those questions and*
On 5/13/2024 6:18 AM, Richard Damon wrote:
On 5/12/24 11:41 PM, olcott wrote:
On 5/12/2024 7:35 PM, Richard Damon wrote:
On 5/12/24 8:07 PM, olcott wrote:
On 5/12/2024 6:55 PM, Richard Damon wrote:Yes, the liar paradox is a statement that can be neither true >>>>>>>>>> or false.
On 5/12/24 7:22 PM, olcott wrote:
On 5/12/2024 6:02 PM, Richard Damon wrote:
On 5/12/24 6:56 PM, olcott wrote:
On 5/12/2024 5:40 PM, Richard Damon wrote:
On 5/12/24 5:54 PM, olcott wrote:
On 5/12/2024 3:33 PM, Richard Damon wrote:
On 5/12/24 2:36 PM, olcott wrote:
On 5/12/2024 1:22 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 5/12/24 2:06 PM, olcott wrote:
On 5/12/2024 12:52 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/12/24 1:19 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/12/2024 10:33 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-12 14:22:25 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
Which means you need to be VERY clear about what >>>>>>>>>>>>>>>>>>>>>> you claim to be "usually spoken of" and what is >>>>>>>>>>>>>>>>>>>>>> your unique contribution.On 5/12/2024 2:42 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2024-05-11 04:27:03 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 5/10/2024 10:49 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 11:35 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/2024 10:16 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/10/24 10:36 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The entire body of expressions that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> {true on the basis of their >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meaning} involves nothing more or less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than stipulated relations between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.In and about formal logic there is no valid >>>>>>>>>>>>>>>>>>>>>>>>>> deep understanding. Only
You don't understand what Quite was talking >>>>>>>>>>>>>>>>>>>>>>>>>>>> about,
You do know that what you are describing >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when applied to Formal Systems are the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> axioms of the system and the most >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> primitively provable theorems. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
YES and there are axioms that comprise the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> verbal model of the
actual world, thus Quine was wrong. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't need to know anything about what he >>>>>>>>>>>>>>>>>>>>>>>>>>> was talking about
except that he disagreed with {true on the >>>>>>>>>>>>>>>>>>>>>>>>>>> basis or meaning}.
I don't care or need to know how he got to an >>>>>>>>>>>>>>>>>>>>>>>>>>> incorrect answer.
Which you don't seem to understand what that >>>>>>>>>>>>>>>>>>>>>>>>>>>> means.
You don't seem to understand what "Formal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Logic" actually means. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ultimately it is anchored in stipulated >>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings (AKA axioms) and expressions >>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived from applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to these axioms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
I understand this much more deeply than you do. >>>>>>>>>>>>>>>>>>>>>>>>>>
a shallow understanding can be valid. >>>>>>>>>>>>>>>>>>>>>>>>>>
It turns out that ALL {true on the basis of >>>>>>>>>>>>>>>>>>>>>>>>> meaning} that includes
ALL of logic and math has its entire foundation >>>>>>>>>>>>>>>>>>>>>>>>> in relations between
finite strings. Some are stipulated to be true >>>>>>>>>>>>>>>>>>>>>>>>> (axioms) and some
are derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations to these axioms.
Usually the word "true" is not used when talking >>>>>>>>>>>>>>>>>>>>>>>> about uninterpreted
formal systems. Axioms and what can be inferred >>>>>>>>>>>>>>>>>>>>>>>> from axioms are called
"theorems". Theorems can be true in some >>>>>>>>>>>>>>>>>>>>>>>> interpretations and false in
another. If the system is incosistent then there >>>>>>>>>>>>>>>>>>>>>>>> is no interpretation
where all axioms are true.
I am not talking about how these things are >>>>>>>>>>>>>>>>>>>>>>> usually spoken of. I am
talking about my unique contribution to the >>>>>>>>>>>>>>>>>>>>>>> actual philosophical
foundation of {true on the basis of meaning}. >>>>>>>>>>>>>>>>>>>>>>
You then need to show how your contribution isn't >>>>>>>>>>>>>>>>>>>>>> in conflict with the classical parts, but follows >>>>>>>>>>>>>>>>>>>>>> within its definitions.
If you want to say that something in the classical >>>>>>>>>>>>>>>>>>>>>> theory is not actually true, then you need to show >>>>>>>>>>>>>>>>>>>>>> how removing that piece doesn't affect the system. >>>>>>>>>>>>>>>>>>>>>> This seems to be a weak point of yours, you think >>>>>>>>>>>>>>>>>>>>>> you can change a system, and not show that the >>>>>>>>>>>>>>>>>>>>>> system can still exist as it was.
This is entirely comprised of relations between >>>>>>>>>>>>>>>>>>>>>>> finite strings:
some of which are stipulated to have the semantic >>>>>>>>>>>>>>>>>>>>>>> value of Boolean
true, and others derived from applying truth >>>>>>>>>>>>>>>>>>>>>>> preserving operations
to these finite string.
This is approximately equivalent to proofs from >>>>>>>>>>>>>>>>>>>>>>> axioms. It is not
exactly the same thing because an infinite >>>>>>>>>>>>>>>>>>>>>>> sequence of inference
steps may sometimes be required. It is also not >>>>>>>>>>>>>>>>>>>>>>> exactly the same
because some proofs are not restricted to truth >>>>>>>>>>>>>>>>>>>>>>> preserving operations.
So, what effect does that difference have? >>>>>>>>>>>>>>>>>>>>>>
You seem here to accept that some truths are based >>>>>>>>>>>>>>>>>>>>>> on an infinite sequence of operations, while you >>>>>>>>>>>>>>>>>>>>>> admit that proofs are finite sequences, but it >>>>>>>>>>>>>>>>>>>>>> seems you still assert that all truths must be >>>>>>>>>>>>>>>>>>>>>> provable.
I did not use the term "provable" or "proofs" these >>>>>>>>>>>>>>>>>>>>> only apply to
finite sequences. {derived from applying truth >>>>>>>>>>>>>>>>>>>>> preserving operations}
can involve infinite sequences.
But if true can come out of an infinite sequences, >>>>>>>>>>>>>>>>>>>> and some need such an infinite sequence, but proof >>>>>>>>>>>>>>>>>>>> requires a finite sequence, that shows that there >>>>>>>>>>>>>>>>>>>> will exists some statements are true, but not provable. >>>>>>>>>>>>>>>>>>>>
...14 Every epistemological antinomy can likewise >>>>>>>>>>>>>>>>>>>>> be used for a similar undecidability proof...(Gödel >>>>>>>>>>>>>>>>>>>>> 1931:43-44)
When we look at the way that {true on the basis of >>>>>>>>>>>>>>>>>>>>> meaning}
actually works, then all epistemological antinomies >>>>>>>>>>>>>>>>>>>>> are simply untrue.
And Godel would agree to that. You just don't >>>>>>>>>>>>>>>>>>>> understand what that line 14 means.
It can be proven in a finite sequence of steps that >>>>>>>>>>>>>>>>>>> epistemological antinomies are simply untrue. >>>>>>>>>>>>>>>>>>>
So?
So that directly contradicts what Gödel said in the >>>>>>>>>>>>>>>>> quote thus proving
that Gödel and Tarski were both fundamentally incorrect >>>>>>>>>>>>>>>>> in the basic
foundation of their work.
Where does he say wha tyo claim?
He says that it can be *USED* for a similar proof. >>>>>>>>>>>>>>>>
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS >>>>>>>>>>>>>>> CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS >>>>>>>>>>>>>>> CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS >>>>>>>>>>>>>>> CLUELESS*
*IT CANNOT BE USED IN ANY UNDECIDABILITY PROOF HE IS >>>>>>>>>>>>>>> CLUELESS*
But he showed how it was used, so you are just proven wrong. >>>>>>>>>>>>>>
This proves that he did not understand undecidability, thus >>>>>>>>>>>>> making
the rest of his paper moot.
It shows no such thing.
Since, As I have pointed out, the actual statement, which >>>>>>>>>>>> you don't seem to even be able to understand, is NOT an >>>>>>>>>>>> epistemological antinomy, just shows that you don't
understand anything about the topic you are talking about. >>>>>>>>>>>>
You don't seem to understand even basic English, so you have >>>>>>>>>>>> no place trying to talk about theories based on the "meaning >>>>>>>>>>>> of words", as you have proved yourself incompetent.
Tarski anchors his entire proof in the above Gödel quote so >>>>>>>>>>>>> we can't just say one one little quote does not ruin the >>>>>>>>>>>>> whole thing.
Yep, and he is right.
The Liar Paradox is easily rejected by the correct foundation of >>>>>>>>>>> {true on the basis of meaning} on the basis that it cannot be >>>>>>>>>>> derived by applying truth preserving operations to finite >>>>>>>>>>> strings
that are stipulated to have the semantic value of Boolean true. >>>>>>>>>>
Tarski thought that he proved that True(L, x) cannot be
defined on
the basis that he could not prove that an expression that is >>>>>>>>>>> not true
is true.
Nope. You seem to have a mental block on this.
The point is that if "True(L, x)" is a predicate, then it
ALWAYS has a truth value, and that value is true if the
statement is true, and false if the statement is false, or not >>>>>>>>>> a truth bearer.
True(English, "a fish") is a type mismatch error, they must be >>>>>>>>> excluded and not merely construed as untrue.
No, since "a fish" is not a truth bearer, True(English, "a
fish") must return false.
Then it must also return false for ~X where X = "a fish"
Yes.
True(English, "this sentence is untrue")
is ALSO a type mismatch error, that must be
excluded and not merely construed as untrue.
Nope, since "this sentence is untrue" is not a true statement, >>>>>>>> True(English, "this sentence is untrue") must return false.
Different yet equivalent protocol.
Nope.
True(L, f) must ALWAYS be a truth bearer, and thus ~True(L, f)
must also be one.
Remember, the truth predicate "True" doesn't return the truth
value of the expression, so doesn't have an answer for a
non-truth-bearer, but is a PREDICATE, that always returns a
value, which is TRUE if the expression is a true expression, and >>>>>>>> false for everything else.
Boolean True(L,x) can return false when x is not a truth bearer
yet must also return false for ~x.
But the problem wasn't given ~x.
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ a
truth valus is always the other truth value.
*not simply change the subject to another question*
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
and thus ~True(L, p) is true.
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,
results of this simple little post over the last two decades.
*When p is neither True nor False then p is rejected as invalid*
*input and that is the complete end of any and all evaluation of p*
So, you just don't understand the definition of a Predicate.
Rejection is NOT a option.
When-so-ever the predicate returns false to True(L, x) and returns
false for False(L, x) then x is rejected as not a truth bearer.
false True(English, "a fish") and false False(English, "a fish")
indicates that "a fish" is not a truth bearer. The same thing goes
for epistemological antinomies.
The problem is you just don't understand the nature of the problem
that you have studied for those thousands and thousands of hours,
which seems to indicate a series lack of intelligence, or an
intentional ignorance.
Try and show how "a fish" is a truth bearer and prove me wrong.
When-so-ever any expression X is neither True nor False then
X is not a truth bearer.
https://en.wikipedia.org/wiki/Socratic_questioning
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
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
and thus ~True(L, p) is true.
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,
*Below you already forgot what you said above*
*Below you already forgot what you said above*
*Below you already forgot what you said above*
On 5/14/2024 9:16 PM, Richard Damon wrote:
Unless you answer what True(L, x) needs to return when x is defined to
be ~True(L, x), you are just showing yourself to be an ignorant liar.
True(L, x) is false
False(L, x) is false
I really have spent many thousands of hours on this one key point.
There is no detail that I have overlooked.
It has only been recently that I defined the algorithm for True(L,x)
It has only been recently that I defined the algorithm for True(L,x)
It has only been recently that I defined the algorithm for True(L,x)
True(L,x) returns true when x is derived from a set of truth preserving operations from finite string expressions of language that have been stipulated to have the semantic value of Boolean true. False(L,x) is
defined as True(L,~x).
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:No, so True(L, p) is false
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
and thus ~True(L, p) is true.
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,
*PLEASE STUDY THIS VERY CAREFULLY SO WE DON'T HAVE TO KEEP*
*GOING OVER THE EXACT SAME POINT MY SHOULDER IS HURTING*
On 5/14/2024 10:44 PM, Richard Damon wrote:
So, what result SHOULD True(L, x) return? when x is
the expression ~True(L, x)
*YOU ALREADY AGREED THAT*
On 5/13/2024 9:31 PM, Richard Damon wrote:
No, so True(L, p) is false
*WHEN*
On 5/13/2024 7:29 PM, Richard Damon wrote:
... p defined as ~True(L, p) ...
On 5/15/2024 6:16 AM, Richard Damon wrote:
On 5/15/24 12:11 AM, olcott wrote:
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:No, so True(L, p) is false
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ a
truth valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
and thus ~True(L, p) is true.
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,
*PLEASE STUDY THIS VERY CAREFULLY SO WE DON'T HAVE TO KEEP*
*GOING OVER THE EXACT SAME POINT MY SHOULDER IS HURTING*
On 5/14/2024 10:44 PM, Richard Damon wrote:
So, what result SHOULD True(L, x) return? when x is
the expression ~True(L, x)
;
*YOU ALREADY AGREED THAT*
On 5/13/2024 9:31 PM, Richard Damon wrote:
No, so True(L, p) is false
*WHEN*
On 5/13/2024 7:29 PM, Richard Damon wrote:
... p defined as ~True(L, p) ...
So, if x being true is defined as there exists a sequence of truth
perserving operations to the truth makes, false needs to be defined as
a similar sequence of operations to ~x. (or is this not true an ~
isn't always defined?)
So, the True predicate can't correctly say True(L, x) is either, so
its result must be that it is a "non-truth-bearer"
That is correct
and thus True can not be a predicate.
No that is incorrect.
x = "a fish"
True(English, x) == false
False(English, x) == false
x is a type mismatch error for any formal system of bivalent logic thus cannot be an expression stipulated to be true or derived by applying
truth preserving operations to expressions stipulated to be true.
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
*You keep forgetting that you said this*
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?
*You keep forgetting that you said this*
No, so False(L, p) is false,
So True(L, x) always returns True or False for all
inputs and False(L, x) defined as True(L,~x)
always returns True or False for all inputs.
TruthBearer(L, x) ≡ (True(L,x) ∨ False(L,x))
*To make this easier to understand*
True(English, "a fish") is false
False(English, "a fish") is false
TruthBearer(English, "a fish") is false
Thus "a fish" is rejected as a type mismatch error
for any system of bivalent logic, yet the predicates
still answer correctly.
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
No, so True(L, p) is false
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
and thus ~True(L, p) is true.
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,
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above, as
we never refered to False(L,p).
*YES WE DID IMMEDIATELY ABOVE YOU SAID THAT False(L, p) is false*
*YES WE DID IMMEDIATELY ABOVE YOU SAID THAT False(L, p) is false*
*YES WE DID IMMEDIATELY ABOVE YOU SAID THAT False(L, p) is false*
*YES WE DID IMMEDIATELY ABOVE YOU SAID THAT False(L, p) is false*
You remembered that False(L,p) is defined as True(L, ~p)
You remembered that False(L,p) is defined as True(L, ~p)
You remembered that False(L,p) is defined as True(L, ~p)
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth bearer,
as True must return a Truth Value for all inputs, and ~ a truth
valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time
*I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ a
truth valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to be
false, but that was based on the assumption that it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, p)
being false, because, since p in L is ~True(L, p) so that make True(L,
~false) which is True(L, true) false, which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time
*I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means that
True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive p?
*You keep forgetting that you said this*
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions
that are stipulated to be true derive ~p?
*You keep forgetting that you said this*
No, so False(L, p) is false,
So True(L, x) always returns True or False for all
inputs and False(L, x) defined as True(L,~x)
always returns True or False for all inputs.
TruthBearer(L, x) ≡ (True(L,x) ∨ False(L,x))
*To make this easier to understand*
True(English, "a fish") is false
False(English, "a fish") is false
TruthBearer(English, "a fish") is false
Thus "a fish" is rejected as a type mismatch error
for any system of bivalent logic, yet the predicates
still answer correctly.
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ >>>>>>>> a truth valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to be
false, but that was based on the assumption that it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, p)
being false, because, since p in L is ~True(L, p) so that make
True(L, ~false) which is True(L, true) false, which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time
*I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means that
True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, p)
with p defined in L as ~True(L, p) work. If it IS false, then the
resulting comclusion is that True(L, true) is false, whicn means your
system is broken.
*YOU SKIP SO MANY POINTS, THAT IS NOT ALLOWED WITH THE SOCRATIC METHOD*
*YOU SKIP SO MANY POINTS, THAT IS NOT ALLOWED WITH THE SOCRATIC METHOD*
*YOU SKIP SO MANY POINTS, THAT IS NOT ALLOWED WITH THE SOCRATIC METHOD*
Do you understand and agree with this?
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
Do you understand and agree with this?
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
Do you understand and agree with this?
True(English, "This sentence is true") is false
False(English, "This sentence is true") is false
The Truth Teller paradox is not a truth bearer.
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ >>>>>>>> a truth valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to be
false, but that was based on the assumption that it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, p)
being false, because, since p in L is ~True(L, p) so that make
True(L, ~false) which is True(L, true) false, which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time
*I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means that
True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, p)
with p defined in L as ~True(L, p) work.
*You got overwhelmed with that so we have to break it down to*
*smaller steps to see exactly where our mutual agreement diverged*
Do you understand and agree with this?
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
*Is saying the same thing that you already agreed to*
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth
bearer, as True must return a Truth Value for all inputs, and ~ >>>>>>>> a truth valus is always the other truth value.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to be
false, but that was based on the assumption that it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to expressions >>>>>>> that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, p)
being false, because, since p in L is ~True(L, p) so that make
True(L, ~false) which is True(L, true) false, which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time
*I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means that
True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, p)
with p defined in L as ~True(L, p) work. If it IS false, then the
resulting comclusion is that True(L, true) is false, whicn means your
system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth >>>>>>>>>> bearer, as True must return a Truth Value for all inputs, and >>>>>>>>>> ~ a truth valus is always the other truth value.
Can a sequence of true preserving operations applied to
expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p)
being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to
be false, but that was based on the assumption that it could exist. >>>>>>
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to
expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, p) >>>>>> being false, because, since p in L is ~True(L, p) so that make
True(L, ~false) which is True(L, true) false, which is incorrrect. >>>>>>
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time >>>>>>> *I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means
that True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, p)
with p defined in L as ~True(L, p) work. If it IS false, then the
resulting comclusion is that True(L, true) is false, whicn means
your system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings"
is true by definition and we would be wrong.
"True(L, true)" lacks a truth object that it is true about.
A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
"This sentence has five words."
Is true about the number of words that it has.
True(English, "This sentence has five words.") is true
"a sentence may fail to make a statement if it is
paradoxical or ungrounded."
*Outline of a Theory of Truth --- Saul Kripke* https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth preserving operations from finite string expressions of language that have been stipulated to have the semantic value of Boolean true. False(L,x) is
defined as True(L,~x). Copyright 2022,2023,2024 PL Olcott
The value of the value true IS true."This sentence is true"
true is the logic value of statement tmentrs.
"This statment is true" is the truth teller paradox, not the logic
value true.
is correctly formalized as TT is defined as True(TT)
"This sentence is true"
What is it true about?
It is true about being true.
What is it true about being true about?
It true about being true about being true...
This goes back to the ambiguity of trying to discuss logic with words.
On 5/16/2024 9:29 PM, Richard Damon wrote:
On 5/16/24 9:59 AM, olcott wrote:
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a truth >>>>>>>>>>>> bearer, as True must return a Truth Value for all inputs, >>>>>>>>>>>> and ~ a truth valus is always the other truth value.
Can a sequence of true preserving operations applied to
expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p) >>>>>>>>> > being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need to >>>>>>>> be false, but that was based on the assumption that it could exist. >>>>>>>>
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to
expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with True(L, >>>>>>>> p) being false, because, since p in L is ~True(L, p) so that
make True(L, ~false) which is True(L, true) false, which is
incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time >>>>>>>>> *I need to make another point that depends on both of them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that means >>>>>>>> that True(L, true) is false, so your system is broken.
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job*
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true"
as "p defined as ~True(L, p)", yet the formalized sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, p) >>>>>> with p defined in L as ~True(L, p) work. If it IS false, then the
resulting comclusion is that True(L, true) is false, whicn means
your system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings"
is true by definition and we would be wrong.
But the fundamental definition of true makes it true.
*True by definition must actually be true*
*True by definition must actually be true*
*True by definition must actually be true*
"True(L, true)" lacks a truth object that it is true about.
A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
true IS the fundamental truth object.
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth preserving operations from finite string expressions of language that have been stipulated to have the semantic value of Boolean true. False(L,x) is
defined as True(L,~x). Copyright 2022 PL Olcott
It isn't a "sentence" it is a truth value.
You are just showing you don't actually understand how logic works.
"This sentence has five words."
Is true about the number of words that it has.
True(English, "This sentence has five words.") is true
"a sentence may fail to make a statement if it is
paradoxical or ungrounded."
So, you thing truth is just paradoxical or ungrounded?
That is how Kripke defined not a truth-bearer.
I specified what grounding means above and previously.
*Outline of a Theory of Truth --- Saul Kripke* https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
On 5/16/2024 9:54 PM, Richard Damon wrote:
On 5/16/24 10:44 PM, olcott wrote:
On 5/16/2024 9:29 PM, Richard Damon wrote:
On 5/16/24 9:59 AM, olcott wrote:
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a >>>>>>>>>>>>>> truth bearer, as True must return a Truth Value for all >>>>>>>>>>>>>> inputs, and ~ a truth valus is always the other truth value. >>>>>>>>>>>>>>
Can a sequence of true preserving operations applied to >>>>>>>>>>>>> expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p) >>>>>>>>>>> > being true when p is defined in L as ~True(L, p)
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would need >>>>>>>>>> to be false, but that was based on the assumption that it
could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to >>>>>>>>>>>>> expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with
True(L, p) being false, because, since p in L is ~True(L, p) >>>>>>>>>> so that make True(L, ~false) which is True(L, true) false, >>>>>>>>>> which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same time >>>>>>>>>>> *I need to make another point that depends on both of them* >>>>>>>>>>>
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that
means that True(L, true) is false, so your system is broken. >>>>>>>>>>
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false
and you understand this means that "a fish" is neither True
nor false in English.
You understand that the actual Liar Paradox is neither true
nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job* >>>>>>>>>
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true" >>>>>>>>> as "p defined as ~True(L, p)", yet the formalized sentence has >>>>>>>>> the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make True(L, >>>>>>>> p) with p defined in L as ~True(L, p) work. If it IS false, then >>>>>>>> the resulting comclusion is that True(L, true) is false, whicn >>>>>>>> means your system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings"
is true by definition and we would be wrong.
But the fundamental definition of true makes it true.
*True by definition must actually be true*
*True by definition must actually be true*
*True by definition must actually be true*
So why did you argue that True(L, true) shouldn't be just true?
Aren't you just being inconsistant now
A set of finite string semantic meanings that form an accurate model
of the general knowledge of the actual world are stipulated as true.
"True(L, true)" lacks a truth object that it is true about.
A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
true IS the fundamental truth object.
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
No, it is the VALUE of the result of this algorithm, which, BY
DEFINITION, is a truth value.
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth
preserving operations from finite string expressions of language that
have been stipulated to have the semantic value of Boolean true.
False(L,x) is defined as True(L,~x). Copyright 2022 PL Olcott
Which, by your claim makes True(L, p) false, but that makes p to be
defined as ~false, which is true, so you are claiming True(L, true)
can be false.
You already agreed that p is neither true nor false.
This means that p is rejected as not a truth-bearer.
If necessary we can go over this single point again
and again and again and not talk about anything else
until you get it.
On 5/16/2024 10:29 PM, Richard Damon wrote:
On 5/16/24 11:20 PM, olcott wrote:
On 5/16/2024 9:54 PM, Richard Damon wrote:
On 5/16/24 10:44 PM, olcott wrote:
On 5/16/2024 9:29 PM, Richard Damon wrote:
On 5/16/24 9:59 AM, olcott wrote:
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a >>>>>>>>>>>>>>>> truth bearer, as True must return a Truth Value for all >>>>>>>>>>>>>>>> inputs, and ~ a truth valus is always the other truth >>>>>>>>>>>>>>>> value.
Can a sequence of true preserving operations applied to >>>>>>>>>>>>>>> expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p) >>>>>>>>>>>>> > being true when p is defined in L as ~True(L, p) >>>>>>>>>>>>>*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would >>>>>>>>>>>> need to be false, but that was based on the assumption that >>>>>>>>>>>> it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to >>>>>>>>>>>>>>> expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with >>>>>>>>>>>> True(L, p) being false, because, since p in L is ~True(L, p) >>>>>>>>>>>> so that make True(L, ~false) which is True(L, true) false, >>>>>>>>>>>> which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the same >>>>>>>>>>>>> time
*I need to make another point that depends on both of them* >>>>>>>>>>>>>
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that >>>>>>>>>>>> means that True(L, true) is false, so your system is broken. >>>>>>>>>>>>
You understand that True(English, "a fish") is false
and you understand that False(English, "a fish") is false >>>>>>>>>>> and you understand this means that "a fish" is neither True >>>>>>>>>>> nor false in English.
You understand that the actual Liar Paradox is neither true >>>>>>>>>>> nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good Job* >>>>>>>>>>>
True(English, "This sentence is not true") is false
False(English, "This sentence is not true") is false
Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true" >>>>>>>>>>> as "p defined as ~True(L, p)", yet the formalized sentence has >>>>>>>>>>> the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make
True(L, p) with p defined in L as ~True(L, p) work. If it IS >>>>>>>>>> false, then the resulting comclusion is that True(L, true) is >>>>>>>>>> false, whicn means your system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings"
is true by definition and we would be wrong.
But the fundamental definition of true makes it true.
*True by definition must actually be true*
*True by definition must actually be true*
*True by definition must actually be true*
So why did you argue that True(L, true) shouldn't be just true?
Aren't you just being inconsistant now
A set of finite string semantic meanings that form an accurate model
of the general knowledge of the actual world are stipulated as true.
So, do you still think that true, as a value, might not be true?
Are you still arguing that True(L, true) doesn't need to be true?
or for any sentance x that has been shown to be true, that
True(L, x) doesn't need to be true?
"True(L, true)" lacks a truth object that it is true about.
A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
true IS the fundamental truth object.
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
No, it is the VALUE of the result of this algorithm, which, BY
DEFINITION, is a truth value.
Which, by your claim makes True(L, p) false, but that makes p to be
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth
preserving operations from finite string expressions of language
that have been stipulated to have the semantic value of Boolean
true. False(L,x) is defined as True(L,~x). Copyright 2022 PL Olcott >>>>
defined as ~false, which is true, so you are claiming True(L, true)
can be false.
You already agreed that p is neither true nor false.
This means that p is rejected as not a truth-bearer.
But, by doing so, you make it a truth bearer by the sentecne that
defined it.
If necessary we can go over this single point again
and again and again and not talk about anything else
until you get it.
Try to.
p is DEFINED to be (in L) the sentence ~True(L, p)
If this is claimed to be a non-truth bearer, then True(L, p) will be
false, and thus p is DEFINED to be ~false, or true.
So, we have a statement proven to be true, to be a non-truth bearer.
And you are shown to just be trying to dance around in circles
avoiding the facts.
WHAT IS WRONG WITH THE LOGIC I GAVE.
Failiure to point it out allows me to just point out that you logic
has been proven to have blown up into inconsistant smitherines.
*You already know that a rebuttal is categorically impossible*
*You already know that a rebuttal is categorically impossible*
*You already know that a rebuttal is categorically impossible*
On 5/17/2024 6:41 AM, Richard Damon wrote:
On 5/16/24 11:51 PM, olcott wrote:
On 5/16/2024 10:29 PM, Richard Damon wrote:
On 5/16/24 11:20 PM, olcott wrote:
On 5/16/2024 9:54 PM, Richard Damon wrote:
On 5/16/24 10:44 PM, olcott wrote:
On 5/16/2024 9:29 PM, Richard Damon wrote:
On 5/16/24 9:59 AM, olcott wrote:
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a >>>>>>>>>>>>>>>>>> truth bearer, as True must return a Truth Value for >>>>>>>>>>>>>>>>>> all inputs, and ~ a truth valus is always the other >>>>>>>>>>>>>>>>>> truth value.
Can a sequence of true preserving operations applied to >>>>>>>>>>>>>>>>> expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with True(L, p) >>>>>>>>>>>>>>> > being true when p is defined in L as ~True(L, p) >>>>>>>>>>>>>>>*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
No, I said that because there is not path to p, it would >>>>>>>>>>>>>> need to be false, but that was based on the assumption >>>>>>>>>>>>>> that it could exist.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied to >>>>>>>>>>>>>>>>> expressions
that are stipulated to be true derive ~p?
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
Right, but that has nothing to do with the problem with >>>>>>>>>>>>>> True(L, p) being false, because, since p in L is ~True(L, >>>>>>>>>>>>>> p) so that make True(L, ~false) which is True(L, true) >>>>>>>>>>>>>> false, which is incorrrect.
No, so False(L, p) is false,
Please try and keep these two thoughts together at the >>>>>>>>>>>>>>> same time
*I need to make another point that depends on both of them* >>>>>>>>>>>>>>>
*YOU ALREADY AGREED THAT True(L, p) IS FALSE*
*YOU ALREADY AGREED THAT false(L, p) IS FALSE*
right, by your definitions, True(L, p) is False, but that >>>>>>>>>>>>>> means that True(L, true) is false, so your system is broken. >>>>>>>>>>>>>>
You understand that True(English, "a fish") is false >>>>>>>>>>>>> and you understand that False(English, "a fish") is false >>>>>>>>>>>>> and you understand this means that "a fish" is neither True >>>>>>>>>>>>> nor false in English.
You understand that the actual Liar Paradox is neither true >>>>>>>>>>>>> nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: Good >>>>>>>>>>>>> Job*
True(English, "This sentence is not true") is false >>>>>>>>>>>>> False(English, "This sentence is not true") is false >>>>>>>>>>>>> Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true" >>>>>>>>>>>>> as "p defined as ~True(L, p)", yet the formalized sentence has >>>>>>>>>>>>> the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make >>>>>>>>>>>> True(L, p) with p defined in L as ~True(L, p) work. If it IS >>>>>>>>>>>> false, then the resulting comclusion is that True(L, true) >>>>>>>>>>>> is false, whicn means your system is broken.
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings" >>>>>>>>> is true by definition and we would be wrong.
But the fundamental definition of true makes it true.
*True by definition must actually be true*
*True by definition must actually be true*
*True by definition must actually be true*
So why did you argue that True(L, true) shouldn't be just true?
Aren't you just being inconsistant now
A set of finite string semantic meanings that form an accurate model >>>>> of the general knowledge of the actual world are stipulated as true.
So, do you still think that true, as a value, might not be true?
Expressions that are {true on the basis of meaning} are ONLY
(a) A set of finite string semantic meanings that form an accurate model >>> of the general knowledge of the actual world.
(b) Expressions derived by applying truth preserving operations to (a)
Years after reading Kripke's article I finally figured out that
the above must be what he mean by grounding. He himself did not
know this at the time.
In other words, you believe that it is a valid interpretation to
change the meaning of words from what the original speaker took the
words to mean, and still are able to say that he actually MEANT the
sentence with the new meaning of the words.
Are you still arguing that True(L, true) doesn't need to be true?
It forms an infinite cycle (in my above algorithm) known as the
Truth Teller Paradox.
Yes, which shows that True(L, p) can not exist, or it allows the
PROVING of both truth values for the Truth Teller Paradox, instead of
being able to leave it as a non-truth-bearer.
Fundamentally, your problem is you don't actually know the meaning of
the words you are using, but have assumed (incorrect) meaning from
your ZEROTH order study of the field.
or for any sentance x that has been shown to be true, that
True(L, x) doesn't need to be true?
"True(L, true)" lacks a truth object that it is true about.
A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
true IS the fundamental truth object.
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
No, it is the VALUE of the result of this algorithm, which, BY
DEFINITION, is a truth value.
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth
preserving operations from finite string expressions of language >>>>>>> that have been stipulated to have the semantic value of Boolean
true. False(L,x) is defined as True(L,~x). Copyright 2022 PL >>>>>>> Olcott
Which, by your claim makes True(L, p) false, but that makes p to
be defined as ~false, which is true, so you are claiming True(L,
true) can be false.
You already agreed that p is neither true nor false.
This means that p is rejected as not a truth-bearer.
But, by doing so, you make it a truth bearer by the sentecne that
defined it.
There is no way to make a non-truth-bearer into a truth-bearer.
So, so admit that True(L, p) isn't always at truth-bearer, and thus
isn't the required predicate, and thus your claim it is just turns out
to be a LIE.
You try and tell me how you can make "a fish" into an
expression that is true or false.
If necessary we can go over this single point again
and again and again and not talk about anything else
until you get it.
Try to.
p is DEFINED to be (in L) the sentence ~True(L, p)
You already agreed that is neither true nor false.
If we have to keep going over this sub-point over and over
and not talk about anything else until you get it we will.
*Your other points below lost track of this simple point*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
Then True(L, p), which form the definition of p, is also not a Truth
Bearer, and thus can not be the truth predicate.
*Once you get this we can move on to the next sub-point*
*When I repeat these things it really seems to help your concentration*
Oncd you get that a non-truth-bearer resulting operation can't be a
predicate, you will understand your error.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...
You already admitted that True(L,p) and False(L,p) both return false.
This is the correct value that these predicates correctly derived.
It seems that now you are now disagreeing with your own self. You are
saying the predicates are broken BECAUSE THEY RETURN THE CORRECT VALUE.
On 5/17/2024 8:07 PM, Richard Damon wrote:
On 5/17/24 10:32 AM, olcott wrote:
On 5/17/2024 6:41 AM, Richard Damon wrote:
On 5/16/24 11:51 PM, olcott wrote:
On 5/16/2024 10:29 PM, Richard Damon wrote:
On 5/16/24 11:20 PM, olcott wrote:
On 5/16/2024 9:54 PM, Richard Damon wrote:So, do you still think that true, as a value, might not be true?
On 5/16/24 10:44 PM, olcott wrote:
On 5/16/2024 9:29 PM, Richard Damon wrote:
On 5/16/24 9:59 AM, olcott wrote:
On 5/16/2024 6:32 AM, Richard Damon wrote:
On 5/16/24 12:44 AM, olcott wrote:
On 5/15/2024 9:33 PM, Richard Damon wrote:
On 5/15/24 10:17 PM, olcott wrote:
On 5/15/2024 9:07 PM, Richard Damon wrote:
On 5/15/24 9:57 PM, olcott wrote:
On 5/13/2024 9:31 PM, Richard Damon wrote:No, I said that because there is not path to p, it would >>>>>>>>>>>>>>>> need to be false, but that was based on the assumption >>>>>>>>>>>>>>>> that it could exist.
On 5/13/24 10:03 PM, olcott wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION >>>>>>>>>>>>>>>>>>>> a truth bearer, as True must return a Truth Value >>>>>>>>>>>>>>>>>>>> for all inputs, and ~ a truth valus is always the >>>>>>>>>>>>>>>>>>>> other truth value.
Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>>> to expressions
that are stipulated to be true derive p?
On 5/15/2024 8:39 PM, Richard Damon wrote:
Which has NOTHING to do with the problem with >>>>>>>>>>>>>>>>> True(L, p)*YOU ALREADY AGREED THAT True(L, p) IS FALSE* >>>>>>>>>>>>>>>>
being true when p is defined in L as ~True(L, p) >>>>>>>>>>>>>>>>>
Right, but that has nothing to do with the problem with >>>>>>>>>>>>>>>> True(L, p) being false, because, since p in L is >>>>>>>>>>>>>>>> ~True(L, p) so that make True(L, ~false) which is >>>>>>>>>>>>>>>> True(L, true) false, which is incorrrect.
No, so True(L, p) is false
and thus ~True(L, p) is true.
Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>>> to expressions
that are stipulated to be true derive ~p? >>>>>>>>>>>>>>>>>>
On 5/15/2024 7:52 PM, Richard Damon wrote:
Which has NOTHING to do with the above,
as we never refered to False(L,p).
*YOU ALREADY AGREED THAT false(L, p) IS FALSE* >>>>>>>>>>>>>>>>
No, so False(L, p) is false,
Please try and keep these two thoughts together at the >>>>>>>>>>>>>>>>> same time
*I need to make another point that depends on both of >>>>>>>>>>>>>>>>> them*
*YOU ALREADY AGREED THAT True(L, p) IS FALSE* >>>>>>>>>>>>>>>>> *YOU ALREADY AGREED THAT false(L, p) IS FALSE* >>>>>>>>>>>>>>>>>
right, by your definitions, True(L, p) is False, but >>>>>>>>>>>>>>>> that means that True(L, true) is false, so your system >>>>>>>>>>>>>>>> is broken.
You understand that True(English, "a fish") is false >>>>>>>>>>>>>>> and you understand that False(English, "a fish") is false >>>>>>>>>>>>>>> and you understand this means that "a fish" is neither True >>>>>>>>>>>>>>> nor false in English.
You understand that the actual Liar Paradox is neither true >>>>>>>>>>>>>>> nor false *THIS IS MUCH MUCH BETTER THAN MOST PEOPLE: >>>>>>>>>>>>>>> Good Job*
True(English, "This sentence is not true") is false >>>>>>>>>>>>>>> False(English, "This sentence is not true") is false >>>>>>>>>>>>>>> Is saying the same thing that you already know.
You get stuck when we formalize: "This sentence is not true" >>>>>>>>>>>>>>> as "p defined as ~True(L, p)", yet the formalized >>>>>>>>>>>>>>> sentence has
the exact same semantics as the English one.
No, YOU get stuck when you can't figure out how to make >>>>>>>>>>>>>> True(L, p) with p defined in L as ~True(L, p) work. If it >>>>>>>>>>>>>> IS false, then the resulting comclusion is that True(L, >>>>>>>>>>>>>> true) is false, whicn means your system is broken. >>>>>>>>>>>>>>
True(L, true) is false
False(L, true) is false
This is the Truth Teller Paradox
and is rejected as not a truth bearer.
No True(L, true) must be TRUE by definiition.
We could say that "kittens are fifteen story office buildings" >>>>>>>>>>> is true by definition and we would be wrong.
But the fundamental definition of true makes it true.
*True by definition must actually be true*
*True by definition must actually be true*
*True by definition must actually be true*
So why did you argue that True(L, true) shouldn't be just true? >>>>>>>>
Aren't you just being inconsistant now
A set of finite string semantic meanings that form an accurate model >>>>>>> of the general knowledge of the actual world are stipulated as true. >>>>>>
Expressions that are {true on the basis of meaning} are ONLY
(a) A set of finite string semantic meanings that form an accurate
model
of the general knowledge of the actual world.
(b) Expressions derived by applying truth preserving operations to (a) >>>>>
Years after reading Kripke's article I finally figured out that
the above must be what he mean by grounding. He himself did not
know this at the time.
In other words, you believe that it is a valid interpretation to
change the meaning of words from what the original speaker took the
words to mean, and still are able to say that he actually MEANT the
sentence with the new meaning of the words.
Are you still arguing that True(L, true) doesn't need to be true?
It forms an infinite cycle (in my above algorithm) known as the
Truth Teller Paradox.
Yes, which shows that True(L, p) can not exist, or it allows the
PROVING of both truth values for the Truth Teller Paradox, instead
of being able to leave it as a non-truth-bearer.
Fundamentally, your problem is you don't actually know the meaning
of the words you are using, but have assumed (incorrect) meaning
from your ZEROTH order study of the field.
or for any sentance x that has been shown to be true, that
True(L, x) doesn't need to be true?
"True(L, true)" lacks a truth object that it is true about. >>>>>>>>>>> A sentence cannot correctly be true about being true...
It has to be true about something other than itself.
true IS the fundamental truth object.
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
*No it is not, it is the result of this algorithm*
No, it is the VALUE of the result of this algorithm, which, BY >>>>>>>> DEFINITION, is a truth value.
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth >>>>>>>>> preserving operations from finite string expressions of
language that have been stipulated to have the semantic value >>>>>>>>> of Boolean true. False(L,x) is defined as True(L,~x).
Copyright 2022 PL Olcott
Which, by your claim makes True(L, p) false, but that makes p to >>>>>>>> be defined as ~false, which is true, so you are claiming True(L, >>>>>>>> true) can be false.
You already agreed that p is neither true nor false.
This means that p is rejected as not a truth-bearer.
But, by doing so, you make it a truth bearer by the sentecne that
defined it.
There is no way to make a non-truth-bearer into a truth-bearer.
So, so admit that True(L, p) isn't always at truth-bearer, and thus
isn't the required predicate, and thus your claim it is just turns
out to be a LIE.
You try and tell me how you can make "a fish" into an
expression that is true or false.
Where did I say I could.
The problem is that p defined in L as ~True(L, p) is more powerful
than your "a fish" statement.
It is not at all more powerful. p and ~p continue to lack a sequence
of truth reserving operations from expressions of language stipulated
to be true. This makes p the exact same non-truth-bearer as "a fish".
If necessary we can go over this single point again
and again and again and not talk about anything else
until you get it.
Try to.
p is DEFINED to be (in L) the sentence ~True(L, p)
You already agreed that is neither true nor false.
If we have to keep going over this sub-point over and over
and not talk about anything else until you get it we will.
*Your other points below lost track of this simple point*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
*p is neither True nor False*
Then True(L, p), which form the definition of p, is also not a Truth
Bearer, and thus can not be the truth predicate.
*Once you get this we can move on to the next sub-point*
*When I repeat these things it really seems to help your
concentration*
Oncd you get that a non-truth-bearer resulting operation can't be a
predicate, you will understand your error.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...
You already admitted that True(L,p) and False(L,p) both return false.
This is the correct value that these predicates correctly derived.
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.
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?
This sentence is true.
What is it true about?
It is true about being true.
What is it is true about being true about?
This turns out to be Kripke ungrounded yet Kripke did
not know the algorithmic basis for Kripke grounding.
*Outline of a Theory of Truth Saul Kripke* (1975) https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
It seems that now you are now disagreeing with your own self. You are
saying the predicates are broken BECAUSE THEY RETURN THE CORRECT VALUE.
No, your logic system disagrees with itself, I am just pointing that out.
All that you pointed out is that you still don't understand
the Truth Teller paradox.
This is the problem with the assumption that a Truth Predicate exists,
and is what Tarksi was pointing out, but which seems to be above your
level of understanding.
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:
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...
You already admitted that True(L,p) and False(L,p) both return false. >>>>> This is the correct value that these predicates correctly derived.
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.
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?
In other words, you logic doesn't have an absolute idea of truth!!!
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.
The object that made the statement true, was that True(L, p) said that
p wasn't true.
*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*
This sentence is true.
What is it true about?
It is true about being true.
What is it is true about being true about?
This turns out to be Kripke ungrounded yet Kripke did
not know the algorithmic basis for Kripke grounding.
*Outline of a Theory of Truth Saul Kripke* (1975)
https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
It seems that now you are now disagreeing with your own self. You are >>>>> saying the predicates are broken BECAUSE THEY RETURN THE CORRECT
VALUE.
No, your logic system disagrees with itself, I am just pointing that
out.
All that you pointed out is that you still don't understand
the Truth Teller paradox.
No, YOU don't understand that True MUST be a truth beared, or you are
just a liar that your system has a Truth Predicate.
Remember, we started with
p in L is ~True(L, p)
you say True(L, p) is false
*No you said this* (Socratic question)
thus the truth value of p MUST be true, since it is not the falseness
of True(L, p)
We test p for True or False if neither it is tossed out on its ass.
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?
Thus we can say that p is also the equivalent in L of
We sure as Hell cannot correctly say that.
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
~True(L, ~True(L, p))
~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
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)
~True(English, ~True(English, "a fish")) is true
and thus True(L, ~True(L, p)) is true, and thus we can show that p
must be false.
By this same reasoning we can show that "a fish" must be false.
Thus we have a contradiction.
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,
*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*
and thus it isn't a predicate, and you have lied that your system has
one.
This is the problem with the assumption that a Truth Predicate
exists, and is what Tarksi was pointing out, but which seems to be
above your level of understanding.
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:
Right, but that also means that we can show that True(L, true)
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...
You already admitted that True(L,p) and False(L,p) both return
false.
This is the correct value that these predicates correctly derived. >>>>>>
returns false, which says your logic system is broken by being
inconsistant.
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?
In other words, you logic doesn't have an absolute idea of truth!!!
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.
Nope, because you said the value of "true" doesn't exist, truth is
dependent on having something to make true.
True(L,x) is defined in terms of its truthmaker.
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.
The object that made the statement true, was that True(L, p) said
that p wasn't true.
*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*
Yes, which makes True(L, a sentence proven to be true) to be false.
Thus, it is inconsistant.
*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*
Or we can use the arguement that since
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.
~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*
and thus p, being not that is false.
So, we can prove that p is both false and true, and thus your system
is BY DEFINITION inconsistant.
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.
<snip>
*No you said this* (Socratic question)
No, YOU said it first, and I agreed.
What else are you going to make it?
(Socratic reply question)
thus the truth value of p MUST be true, since it is not the
falseness of True(L, p)
We test p for True or False if neither it is tossed out on its ass.
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?
RED HERRINBG.
p is dead!
Every expression that is neither true nor false
is dead to any system of bivalent logic.
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.
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
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
*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.
Yes that one is: "This sentence is not true"Thus we can say that p is also the equivalent in L of
We sure as Hell cannot correctly say that.
Why not?
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
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.
~True(L, ~True(L, p))
~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
Nope, "This statment is true" is different then the statement:
P, in L, is defined as ~True(L, P)
The prior one is the ordinary Liar Paradox formalized.
It it just
P in L is defined as "P is not true."
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.
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...
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)
~True(English, ~True(English, "a fish")) is true
Yep.
and thus True(L, ~True(L, p)) is true, and thus we can show that p
must be false.
By this same reasoning we can show that "a fish" must be false.
Nope, because a fish wasn't defined to be any of those sentencds.
"~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.
Thus we have a contradiction.
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,
*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*
Right, and that it the problem. (we don't need the True(L, ~x) part
though.
False is defined as True(L,~x) and has no separate existence.
p is defined as ~True(L, p) which you say is false.
thus, we can also say, by the definiton of p that
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.
*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.
On 5/18/2024 7:43 AM, Richard Damon wrote:
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:
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.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...
You already admitted that True(L,p) and False(L,p) both return >>>>>>>>> false.
This is the correct value that these predicates correctly derived. >>>>>>>>
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?
In other words, you logic doesn't have an absolute idea of truth!!! >>>>>>
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.
Nope, because you said the value of "true" doesn't exist, truth is
dependent on having something to make true.
True(L,x) is defined in terms of its truthmaker.
And create a contradiction.
You have not shown that.
All you have shown is a failure to understand that the formalized
Truth Teller Paradox is not a truth bearer.
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,
This seems to indicate that when on non truth-bearer such as "a fish"
is neither true nor false you still want to process it.
This indicates that you don't understand that when any expression
X is shown to be neither True nor False that X has proven to not
be a truth-bearer thus must be rejected as a type-mismatch error
for any system of bivalent logic.
The object that made the statement true, was that True(L, p) said
that p wasn't true.
*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*
Yes, which makes True(L, a sentence proven to be true) to be false.
Thus, it is inconsistant.
*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)
p is not a truth-bearer thus behaves the exact same way as any
other non-truth-bearer such as "a fish".
THIS is the "true" that True(L, p) has previously defined to be false,
We cannot correctly say it that way because we a leaving
the definition of p as vague.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...True(L, p) is false
False(L,p) is false
Therefore p is not a truth-bearer and rejected as a type
mismatch error for any formal system of bivalent logic.
and thus your True predicate is shown to be inconsistant.
It is not inconsistent and you have only shown your own lack
of understanding when attempting to support such claims.
Or we can use the arguement that since
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?
I simply applied the same reasoning that you applied to
non-truth-bearer p to non-truth-bearer "a fish".
*SINCE REPETITION SEEMS TO HELP YOU CONCENTRATE*
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) ...True(L, p) is false
False(L,p) is false
Therefore p is not a truth-bearer and rejected as a type
mismatch error for any formal system of bivalent logic.
Likewise for "a fish".
True didn't make p true because it was an input to the Truthp = "a fish"
Predicate, but because p was defined as an expression based on it,
where was this done to "a fish".
True(L, p) is false
False(L,p) is false
Therefore p is not a truth-bearer and rejected as a type
mismatch error for any formal system of bivalent logic.
The same thing applies when p defined as ~True(L, p)
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!
*I AM NOT SURE IF YOU FULLY UNDERSTAND THIS*
*I AM NOT SURE IF YOU FULLY UNDERSTAND THIS*
*I AM NOT SURE IF YOU FULLY UNDERSTAND THIS*
As I have been saying for years:
LP := "This sentence is not true"
True(English, LP) is false
False(English, LP) is false
Therefore LP is neither true nor false thus not a truth-bearer
that must be rejected from any bivalent system of formal logic.
*Here is the next level of this*
~True(English, LP) is true
~False(English, LP) is true
This sentence is not true: "This sentence is not true" is true
This sentence is not false: "This sentence is not true" is true
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).
Forming an infinite evaluation cycle that is rejected by Prolog using: https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
My system rejects it a different way.
No sequence of true preserving operations applied to
expressions that are stipulated to be true derive p or ~p
True xor False
Is Boolean and thus an element of a bivalent system of logic.
True and False
Is inconsistent thus NOT an element of any bivalent system of logic.
True nor False // {not or} output is true if both inputs are false.
Is not a truth-bearer thus NOT an element of any bivalent system of logic.
and thus p, being not that is false.
So, we can prove that p is both false and true, and thus your system
is BY DEFINITION inconsistant.
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 using the same incorrect reasoning that you applied to p
"We can prove that p is both false and true"
By your definitions it is neither.Likewise for p
That is the difference between the statement p and a sentence that is
trivially a non-truth-bearer (one that doesn't state something).
TT := "This sentence is true"
TT := True(L, TT)
<snip>
*No you said this* (Socratic question)
No, YOU said it first, and I agreed.
What else are you going to make it?
(Socratic reply question)
thus the truth value of p MUST be true, since it is not the
falseness of True(L, p)
We test p for True or False if neither it is tossed out on its ass.
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?
RED HERRINBG.
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".
Not true and your every attempt to show this had glaring errors.
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"
TT := True(TT)
True(L, TT) is false
False(L, TT) is false
∴ TT is rejected as not a truth-bearer thus not
an element of any formal system of bivalent logic.
The Truth Teller Paradox in all its forms is not
true ABOUT anything.
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.
The exact same way that "a fish" is not a truth-bearer
thus must be rejected by any formal system of bivalent logic.
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 have never shown this.
The most you have shown is a lack of understanding of the
Truth Teller Paradox.
you system says that since, at least initially, we can not find a path
to p or ~p, True(L, p) must be false.
Likewise when we try a quadrillion different times
LP := ~True(L, LP) remains neither true nor false
thus not a truth-bearer thus not an element of any
formal system of bivalent logic.
But once we have the decision, we now have a path that makes p true,
and thus True is forced into a contradiction.
*If we did then we could make "a fish" true*
There exists no such path for any non-truth-bearer.
All non-truth bearers must be immediately rejected by every formal
system of bivalent logic.
This same thing equally applies to every expression X such
that True(L,x) nor False(L,x)
That you understand that the Liar Paradox is not a truth bearer
is better than most professional philosophers that specialize
in truth-bearers and truth-makers. A leading author in this
field says that the Liar Paradox might not be true or false.
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
*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).
(a) A set of finite string semantic meanings that form an accurate
model of the general knowledge of the actual world.
Such a system knows that {cats} <are> {animals}.
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.
Only the facts of general knowledge of the actual world, context
specific details are not included yet can be provided as a discourse knowledge ontology.
The general knowledge of the actual world is finite.
Every detail of the actual world is infinite.
Formal logic allows us to define APPROXIMATE models of the "real
world", to try to deduce new things about the "real world".
A {cat} is not {approximately} an {animal}
Yes that one is: "This sentence is not true"Thus we can say that p is also the equivalent in L of
We sure as Hell cannot correctly say that.
Why not?
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
*THE ONE LEVEL OF INDIRECT REFERENCE CHANGES EVERYTHING*
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.
~True(L, ~True(L, p))
~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
Nope, "This statment is true" is different then the statement:
P, in L, is defined as ~True(L, P)
The prior one is the ordinary Liar Paradox formalized.
It it just
P in L is defined as "P is not true."
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.
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.
A complete and accurate model of the general knowledge of
the actual world is finite and does exist. It will need to
be updated from time to time. Pluto is no longer considered
to be a planet.
And to say you system is based on that just makes your system a lie.
The set of general facts that the set of minds and the set of
writings knows does exist in these minds and writings. We only
need a very tiny subset of these to correctly reject all of the
common epistemological antinomies.
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)
~True(English, ~True(English, "a fish")) is true
Yep.
and thus True(L, ~True(L, p)) is true, and thus we can show that >>>>>> p must be false.
By this same reasoning we can show that "a fish" must be false.
Nope, because a fish wasn't defined to be any of those sentencds.
"~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.
LP := ~True(L, LP) is simply the formalized liar paradox
and cannot exist in any formal system of bivalent logic.
And the semantic meaning leads to a contradiction no matter how you
assign a logical value to True(L, p),
Not at all its logical value is false.
Why do you keep disagreeing with yourself on this?
On 5/13/2024 9:31 PM, Richard Damon wrote:
No, so True(L, p) is false
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
Why do you keep disagreeing with yourself on this?
*I am stopping here*
*I am stopping here*
*I am stopping here*
*I am stopping here*
*I am stopping here*
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
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.
False(L,x) is defined as True(L,x).
If, as you claim p in L defined as ~True(L, p) results in True(L, p)
being false, then p must be a true statement...
The wording of that seems to say that because p is known to be
untrue that this makes p true.
On 5/18/2024 11:56 AM, Richard Damon wrote:
On 5/18/24 12:48 PM, olcott wrote:On 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
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?
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*
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 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
;;
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?
;;
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
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
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
So, you are just proving your ignorance of what you talk about.
You don't seem to understand that ALL actually means ALL
And, your repeating the claim, just shows that you are an ignorant
pathoological liar.
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 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
;;
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?
;;
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))
If it is not a Truth-bearer then the formal system
outputs "Type Mismatch Error x is not a Truth-bearer"
and no further evaluation is performed.
After the formal system has screened out non-truth-bearers
then ~True(L,x) always means True(L,~x) AKA False(L,x).
So, you are just proving your ignorance of what you talk about.
You don't seem to understand that ALL actually means ALL
And, your repeating the claim, just shows that you are an ignorant
pathoological liar.
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 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
;;
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?
;;
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.
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:And the Truth Predicate isn't allowed to "filter" out expressions. >>>>>>
On 5/18/24 12:48 PM, olcott wrote:On 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so True(L, p) is false
;;
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?
;;
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* >>>>>>
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))
On 5/18/2024 6:04 PM, Richard Damon wrote:
On 5/18/24 6:47 PM, olcott wrote:Yes we must build from mutual agreement, good.
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:And the Truth Predicate isn't allowed to "filter" out expressions. >>>>>>>>
On 5/18/24 12:48 PM, olcott wrote:On 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so False(L, p) is false,
;;
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? >>>>>>>>> >
;
*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* >>>>>>>>
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?
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")
That means that the predicate establishes that there IS a seriers of
truth perservion operations that derive the expreson ~True(L, p).
You keep confusing:
This sentence is not true.
with
This sentence is not true: "This sentence is not true".
I have spent 20,000 hours on this YOU WILL NOT FIND ANY ACTUAL MISTAKE.
And if so, doesnt that mean that the truth value of p will be true,In Prolog both the Liar Paradox and the Truth Teller Paradox
since p is defined as the logical negation of True(L, p), which we
just establish HAS a sequence of truth perservion operations as
indicated by the truth predicate.
get stuck in an infinite loop (technically a cycle in the directed
graph of their evaluation sequence).
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2 Catches this cycle and reject it.
This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about?
It is not true about being not true about being not true...
and if so, doesn't that mean that your True(L, x) just returned the
false value for an input that was, by your definitions, true?
How does that work?
It must work the same as Prolog and detect cycles
in its evaluation graph.
Deflect again and I will just point out that you have refused to
answer because you are just admitting you can't figure out how to fix
your broken system.
After all, you have proven that just because you thinkl something is
self-evedently true, doesn't mean that it is true, as you sense of
self-evedent is just broken.
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:Yes we must build from mutual agreement, good.
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 5/13/2024 9:31 PM, Richard Damon 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 5/13/24 10:03 PM, olcott wrote:
On 5/13/2024 7:29 PM, Richard Damon wrote:No, so False(L, p) is false,
;;
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? >>>>>>>>>>> >
;
*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?
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.
~True(L,x) is always a truth bearer.
when x is defined as ~True(L,x) then x is not a truth bearer.
Compared to most of the rest of the world including leading
experts in this field you are doing quite well with this.
One of the top experts in the field of truthmaker maximalism
is not even sure that "This sentence is not true" is not
a truth bearer. https://plato.stanford.edu/entries/truthmakers/#Max
This means that you are ahead of the leading experts in the field.
Maybe your problem is you just forgot to learn the meaning of the keyYou have been saying things with isomorphic structure.
words in the things you want to talk about.
That means that the predicate establishes that there IS a seriers of
truth perservion operations that derive the expreson ~True(L, p).
You keep confusing:
This sentence is not true.
with
This sentence is not true: "This sentence is not true".
I have spent 20,000 hours on this YOU WILL NOT FIND ANY ACTUAL MISTAKE.
I have been using NEITHER of those sentences, only YOU have in your
confusion.
LP := ~True(L,LP)
True(L,LP) is false
True(L,~LP) is false
~True(True(L,LP)) is true
*This last one does not make LP true*
*This last one has one level of indirect reference*
If your problem is that you can not think of Formal statements as
Formal statement, but need to translate them into sloppy English, that
is YOUR problem, and means you need to just admit you don't know what
you are talking about.
And if so, doesnt that mean that the truth value of p will be true,In Prolog both the Liar Paradox and the Truth Teller Paradox
since p is defined as the logical negation of True(L, p), which we
just establish HAS a sequence of truth perservion operations as
indicated by the truth predicate.
get stuck in an infinite loop (technically a cycle in the directed
graph of their evaluation sequence).
I don't CARE are PROLOG, as it doesn't actually define what we are
talking about.
P
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2 >>> Catches this cycle and reject it.
So, that just means that Prolog (or you) can not handle the logic
system, as one of the requirements for the proof was that the logic
was capable of expressing sentences with references to sentences, even
its self.
*Maybe you do not understand that a cycle in a directed graph is*
If you do not understand this then you can't understand that
when an expression has a cycle in the directed graph of its
evaluation sequence that this expression cannot be evaluated.
It is the same basic idea as an unconditional infinite loop
in a program. The evaluation and the program cannot terminate.
This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about?
It is not true about being not true about being not true...
RED HERRING
Not at all. I have expressly shown the cycle in the directed
graph of the evaluation sequence of "This sentence is not true".
Proving you have run out of thoughts that actually relate to the problem.
and if so, doesn't that mean that your True(L, x) just returned the
false value for an input that was, by your definitions, true?
How does that work?
It must work the same as Prolog and detect cycles
in its evaluation graph.
Nope. As shown above, Prolog can't handle this logic system.
Yes, perhaps in a logic system fully handlable by Prolog, you can
probably define a truth primitive. Since most real work in formal
logic isn't in such systems, that is uninteresting.
*This knowledge ontology*
A set of finite string semantic meanings that form an accurate
model of the general knowledge of the actual world.
is an inheritance hierarchy of formalized natural language along
with formal language that is similar to type theory in the is has
an unlimited number or orders of logic.
Deflect again and I will just point out that you have refused to
answer because you are just admitting you can't figure out how to
fix your broken system.
As I predicted, you are just proving you don't even understand the
system that is being talk about, It is just like you claim that you
can't show that 2 + 3 = 5 to a person that doesn't understan Numbers.
You can't show the problem of a truth predicate to someone that
doesn't understand how logic really works.
You are incorrect on this point yet doing better than the leading
experts in the field simply because you fully understand that
"This sentence is not true." is definitely not a truth bearer.
After all, you have proven that just because you thinkl something is
self-evedently true, doesn't mean that it is true, as you sense of
self-evedent is just broken.
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
True(L,p) is false
True(L,~p) is false
~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*
~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
LP := ~True(L,LP)
means ~True(~True(~True(~True(~True(...)))))
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.
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 True(L,p) is false
True(L,~p) is false
~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*
~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
LP := ~True(L,LP)
means ~True(~True(~True(~True(~True(...)))))
It is the common convention to encode self-reference incorrectly.
LP ↔ ~True(L, LP)
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
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.
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(...)))))
"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.
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(...)))))
*Prolog sees the same infinite recursion and rejects it*
?- TT = true(TT).
TT = true(TT).
?- unify_with_occurs_check(TT, true(TT)).
false.
On 5/20/2024 7:57 PM, Richard Damon wrote:
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:Then ~True(L,p) can't be a truth beared as they are the SAME
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 >>>>
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.
That is the same thing as saying that
True(English, "this sentence is not true") is false
proves that True(L,x) is not a truthbearer.
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.
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
No what it shows is that formal logic gets the wrong answer because
formal logic does not evaluate actual self-reference.
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)
Likewise with ~True(L, ~True(L, p)) where p is defined as ~True(L, p)
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,
Yet when p refers to its own name this creates infinite recursion.
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.
When LP refers to its own name this creates infinite recursion.
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.
True(English, "this sentence is not true") is false
Is 100% perfectly isomorphic to its formalized version
LP is defined as ~True(L, LP)
True(L, LP) is false
It is merely easier to see that "this sentence is not true"
cannot be true because that makes it false and
can't be false because that makes it true.
LP is defined as ~True(L, LP)
works this same yet yet it is not as intuitive.
So we see that the above is a correct formalization
of the English and that gives us the cognitive leverage
of intuition.
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.
LP := ~True(L, LP) means that every instance of LP
in the RHS is the same as the RHS.
Clocksin & Mellish say this same thing.
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)
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.
Nothing can handle "some kind of infinite structure."
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.
No the whole problem seems to be that you simply don't
bother to pay close enough attention the EXACTLY what I say.
When I prove my point you simply ignore that I proved my point
and baselessly assume that I must be wrong. You will probably
completely "forget" my Clocksin & Mellish quote immediately after
you read it, or skip over it and assume that they are wrong.
On 5/20/2024 9:24 PM, Richard Damon wrote:
On 5/20/24 9:54 PM, olcott wrote:
On 5/20/2024 7:57 PM, Richard Damon wrote:
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.
That is the same thing as saying that
True(English, "this sentence is not true") is false
proves that True(L,x) is not a truthbearer.
Nope, why do you say that?
What logic are you even TRYING to use to get there?
I think you don't understand what defining a label to represent a
statement means.
I did not said the above part exactly precisely to address
your objection.
p is defined as ~True(L,p)
LP is defined as "this sentence is not true" in English.
Thus True(L,p) ≡ True(English,LP) and
Thus True(L,~p) ≡ True(English,~LP)
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.
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
So? Can you show that it is NOT true? or is it just that you don't
want it to be true, so you assume it isn't?
defined as is the way to go.
No what it shows is that formal logic gets the wrong answer because
formal logic does not evaluate actual self-reference.
No, you don't understand what you are talking about.
Formal logic NEVER EVER gets to
epistemological antinomies ARE NOT TRUTH BEARERS
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)
Likewise with ~True(L, ~True(L, p)) where p is defined as ~True(L, p)
So? Yes ~True(L, ~True(L, p)) IS a different sentence than ~True(L, p)
even with p defined a ~True(L, p), BUT they are logically connected as
the first follows as a consequence of the second and the definition of p.
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,
Yet when p refers to its own name this creates infinite recursion.
So? What's wrong with that?
Sure any programs that get stuck in infinite loops are a feature that everyone likes even when it means that payroll is two weeks late and
you missed your mortgage payment.
Note, it is recursion that doesn't HAVE to be followed. You seem to be
stuck at counting the fingers level math, while trying to talk about
trigonometry.
Any expression "standing for some kind of infinite structure."
CANNOT BE EVALUATED THUS CANNOT POSSIBLY BE A TRUTH BEARER
THUS <IS> A TYPE MISMATCH ERROR FOR EVERY SYSTEM OF BIVALENT LOGIC
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.
When LP refers to its own name this creates infinite recursion.
So? As I said, it doesn't HAVE to be fully expanded, as each level is
doing a logical step of indirection
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.
True(English, "this sentence is not true") is false
Is 100% perfectly isomorphic to its formalized version
LP is defined as ~True(L, LP)
True(L, LP) is false
Nope. Because "this sentence" refers to the statement in quotes, not
the logical statement using True.
The English is formalized as LP is defined as ~True(L, LP)
before it is analyzed.
It is merely easier to see that "this sentence is not true"
cannot be true because that makes it false and
can't be false because that makes it true.
And it is a different sentence.
No it is not.
The English is formalized as
LP is defined as ~True(L, LP) before it is analyzed.
LP is defined as ~True(L, LP)
works this same yet yet it is not as intuitive.
You are right that it causes problems, and the problem it causes is
that it shows that the True Predicate can not exist.
Not at all.
It shows that no truth bearers must be rejected as
a type mismatch error for any system of bivalent logic.
So we see that the above is a correct formalization
of the English and that gives us the cognitive leverage
of intuition.
Nope, can't because the English sentence doesn't attach a "name" to
the whole expression.
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.
LP := ~True(L, LP) means that every instance of LP
in the RHS is the same as the RHS.
Clocksin & Mellish say this same thing.
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:
And how Prolog does it is irrelevent,
Not at all.
Prolog sees that LP is defined as ~True(LP) is nonsense
and rejects it.
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)
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.
Nothing can handle "some kind of infinite structure."
Wrong. There are lots of logics that handle certain "infinte
structures". After all, Mathematics is BASED on logic on infinite
structures.
No expression that itself has an infinite structure can be
evaluated in finite time. that is what "infinite structure"
is defined to mean.
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.
No the whole problem seems to be that you simply don't
bother to pay close enough attention the EXACTLY what I say.
No, you don't use the words in the way they are properly defined, so
of course people can't understand what you mean.
We have to guess, and point out the errors that are clearly there.
When I prove my point you simply ignore that I proved my point
and baselessly assume that I must be wrong. You will probably
completely "forget" my Clocksin & Mellish quote immediately after
you read it, or skip over it and assume that they are wrong.
Nope, you have yet to present an actual Formal proof.
A proof need not be formal.
A proof is any statement where its negation is unsatisfiable.
You seem to think that a Philosophical Arguement can substitute for a
Formal Proof. YOu are just using the wrong tools that don't work in
the system.
Maybe if you actually tried to pay attention to what people say an not
assume that your ideas, built on your assumptions of how things must
work, have to be correct.
Try to "prove" that "2" really does stand for a number
without resorting to any definitions.
The definition itself is the complete proof, no steps required.
It seems you don't even have the tools to try to explain what you
mean, but just like to throw out snipits quoted from places that you
don;t really understand, but seem to say something sort of like what
you are trying to say.
All you have done is proved your ignorance.
Most of the best experts in the world are not sure that the Liar Paradox
is not a truth bearer. At least you know this much.
When we get to the formalized Liar Paradox this seems too difficult
for you, yet you are still doing better than most experts in the world.
You are even better at formalizing the Liar Paradox than most experts
in the field. They try to get away with this crap: LP ↔ ~True(LP).
You understand that this is the correct way: p defined as ~True(L, p).
So it is still: Good job Richard !
On 5/20/2024 10:37 PM, Richard Damon wrote:
On 5/20/24 10:56 PM, olcott wrote:
On 5/20/2024 9:24 PM, Richard Damon wrote:
On 5/20/24 9:54 PM, olcott wrote:
On 5/20/2024 7:57 PM, Richard Damon wrote:
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:
So, x being DEFINED to be a certain sentence doesn't make x to >>>>>>>>>> have the same meaning as the sentence itself?
True(L,x) is always a truth bearer.
when x is defined as True(L,x) then x is not a truth bearer. >>>>>>>>>>
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.
That is the same thing as saying that
True(English, "this sentence is not true") is false
proves that True(L,x) is not a truthbearer.
Nope, why do you say that?
What logic are you even TRYING to use to get there?
I think you don't understand what defining a label to represent a
statement means.
I did not said the above part exactly precisely to address
your objection.
p is defined as ~True(L,p)
LP is defined as "this sentence is not true" in English.
Thus True(L,p) ≡ True(English,LP) and
Thus True(L,~p) ≡ True(English,~LP)
So, you admit that you did not answer the problem.
And that you think Strawmen and Red Herring are valid forms of logic.
How does p defined as ~True(L, p) NOT generate the shown contradiction
when you begin by saying True(L, p) must not be true (and thus false)
because p has not chain to truthbears?
p := ~True(L, p) is false
p := ~True(L, ~p) is false
p is tossed out on its ass as a type mismatch error for every system
of bivalent logic before it gets any chance to be evaluated in any
other way.
If your gas can for you lawnmower is filled with water
do you use it anyway or dump it out?
You are just showing that you think it is ok for logical system to
have contradictions in them.
You are failing to pay enough attention or forgetting
what I told you even after telling you many times.
Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
p defined as ~True(L, p)
if (~Truthbearer(L,p))
printf("%s is rejected as not a truth bearer\n", "p");
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.
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
So? Can you show that it is NOT true? or is it just that you don't
want it to be true, so you assume it isn't?
defined as is the way to go.
Which mean?
p defined as ~True(L, p)
Is much better than the incorrect conventional way: p ↔ ~True(L, p)
And what does it have to do with the original statement?
Remember, if your goal is to just show that conventonal logic is just
broken, you are going to need to make a much more convincing arguement
to scrap it, unless you have a FULLY DEVELOPED alternative that does
better.
Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x))
Expressions that are {true on the basis of meaning} are ONLY
(a) A set of finite string semantic meanings that form an accurate
model of the general knowledge of the actual world.
(b) Expressions derived by applying truth preserving operations to (a).
The above algorithm specifies True(L,x) and True(L,~x).
Just remember, once you throw out the foundations, you need to start
from a brand new foundation, and unless you have been lying about your
prognossis, and sand-bagging about your logical abilities, your chance
of actually proving somethiing like that is just about zero.
In other words you totally forgot that you already understood
the algorithm.
No what it shows is that formal logic gets the wrong answer because
formal logic does not evaluate actual self-reference.
No, you don't understand what you are talking about.
Formal logic NEVER EVER gets to
epistemological antinomies ARE NOT TRUTH BEARERS
Of course it does.
You just don't understand what you are reading.
In fact, Tarski points out the BECAUSE he can show that the existance
of a Truth Primative forces an epistemological antinomy to have a
truth value, that there can not be an existing Truth Primative.
YOU just don't understand logic,
I understand that the received view is proven to be incorrect on the
basis of its incoherence. The system of (a) and (b) is self-evidently correct.
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)
Likewise with ~True(L, ~True(L, p)) where p is defined as ~True(L, p) >>>>>
So? Yes ~True(L, ~True(L, p)) IS a different sentence than ~True(L,
p) even with p defined a ~True(L, p), BUT they are logically
connected as the first follows as a consequence of the second and
the definition of p.
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,
Yet when p refers to its own name this creates infinite recursion.
So? What's wrong with that?
Sure any programs that get stuck in infinite loops are a feature that
everyone likes even when it means that payroll is two weeks late and
you missed your mortgage payment.
Which has nothing to do with the Halting Problem.
You said there is nothing wrong with loops and I countered
with a loop that could force you to skip paying your mortgage.
Note, it is recursion that doesn't HAVE to be followed. You seem to
be stuck at counting the fingers level math, while trying to talk
about trigonometry.
Any expression "standing for some kind of infinite structure."
CANNOT BE EVALUATED THUS CANNOT POSSIBLY BE A TRUTH BEARER
THUS <IS> A TYPE MISMATCH ERROR FOR EVERY SYSTEM OF BIVALENT LOGIC
So, I guess you don't beleive in mathematics.
Those are not required to be derived from a set of truth
preserving operations that have a cycle in the directed
graph of their evaluation sequence.
And the value of Pi doesn't exist, or the square root of 2.
You are just incapable of understanding how infinities CAN work.
There is no NEED to expand the reference loop to infinity, so that
isn't actually a problem.
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.
When LP refers to its own name this creates infinite recursion.
So? As I said, it doesn't HAVE to be fully expanded, as each level
is doing a logical step of indirection
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.
True(English, "this sentence is not true") is false
Is 100% perfectly isomorphic to its formalized version
LP is defined as ~True(L, LP)
True(L, LP) is false
Nope. Because "this sentence" refers to the statement in quotes, not
the logical statement using True.
The English is formalized as LP is defined as ~True(L, LP)
before it is analyzed.
Nope, because the English doesn't carry the meaning of being a Truth
Predicate.
In other words
True(English, "Puppies are fifteen story office buildings")
is not false?
But, since you don't seem to understand what that means, you can't
tell the difference, but it proves your own ignorance to make the claim.
It is merely easier to see that "this sentence is not true"
cannot be true because that makes it false and
can't be false because that makes it true.
And it is a different sentence.
No it is not.
The English is formalized as
LP is defined as ~True(L, LP) before it is analyzed.
Nope, You can't make that claim.
I am correct and you can't show otherwise.
LP is defined as ~True(L, LP)
works this same yet yet it is not as intuitive.
You are right that it causes problems, and the problem it causes is
that it shows that the True Predicate can not exist.
Not at all.
It shows that NON truth bearers must be rejected as
a type mismatch error for any system of bivalent logic.
Which isn't allowed.
I had a typo : NON truth bearers must be rejected
Truthbearer(L,x) ≡ (True(L,x) ∨ False(L,x))
You seem to have this problem with things defined to work on ALL
statements expressable in the languge.
My system recognizes and reject epistemological antinomies.
It is DEFINED how the Truth predicate is to work on non-truth bearers,
and that to return the false value.
Truthbearer(L,x) ≡ (True(L,x) ∨ False(L,x))
It is basically defined similar to Sipser Decider, in that it turns
"non-answers" into a defined answer, and that requirement is what make
it not possible, but that requirement is a fundamental part of the
problem.
Are there a sequence of truth preserving operations that derive
x from
(a) A set of finite string semantic meanings that form an accurate
model of the general knowledge of the actual world.
No means x is not true.
So we see that the above is a correct formalization
of the English and that gives us the cognitive leverage
of intuition.
Nope, can't because the English sentence doesn't attach a "name" to
the whole expression.
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.
LP := ~True(L, LP) means that every instance of LP
in the RHS is the same as the RHS.
Clocksin & Mellish say this same thing.
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:
And how Prolog does it is irrelevent,
Not at all.
Prolog sees that LP is defined as ~True(LP) is nonsense
and rejects it.
And thus proves that it can't handle the logic.
*THE FREAKING INPUT IS FREAKING WRONG*
*THE FREAKING INPUT IS FREAKING WRONG*
*THE FREAKING INPUT IS FREAKING WRONG*
On 5/21/2024 3:05 AM, Mikko wrote:
On 2024-05-20 17:48:40 +0000, olcott said:
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.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a
truth bearer, as True must return a Truth Value for
all inputs, and ~ a truth valus is always the other
truth value.
p defined as ~True(L, p) is rejected as a syntax error.
On 5/21/2024 6:50 AM, Richard Damon wrote:
On 5/21/24 1:52 AM, olcott wrote:
On 5/20/2024 10:37 PM, Richard Damon wrote:
On 5/20/24 10:56 PM, olcott wrote:
On 5/20/2024 9:24 PM, Richard Damon wrote:
On 5/20/24 9:54 PM, olcott wrote:
On 5/20/2024 7:57 PM, Richard Damon wrote:
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:
So, x being DEFINED to be a certain sentence doesn't make x >>>>>>>>>>>> to have the same meaning as the sentence itself?
True(L,x) is always a truth bearer.
when x is defined as True(L,x) then x is not a truth bearer. >>>>>>>>>>>>
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.
That is the same thing as saying that
True(English, "this sentence is not true") is false
proves that True(L,x) is not a truthbearer.
Nope, why do you say that?
What logic are you even TRYING to use to get there?
I think you don't understand what defining a label to represent a
statement means.
I did not said the above part exactly precisely to address
your objection.
p is defined as ~True(L,p)
LP is defined as "this sentence is not true" in English.
Thus True(L,p) ≡ True(English,LP) and
Thus True(L,~p) ≡ True(English,~LP)
So, you admit that you did not answer the problem.
And that you think Strawmen and Red Herring are valid forms of logic.
How does p defined as ~True(L, p) NOT generate the shown
contradiction when you begin by saying True(L, p) must not be true
(and thus false) because p has not chain to truthbears?
p := ~True(L, p) is false
p := ~True(L, ~p) is false
p is tossed out on its ass as a type mismatch error for every system
of bivalent logic before it gets any chance to be evaluated in any
other way.
Not ALLOWED. p is DEFINED to be something, so it is that/.
On 5/21/2024 3:05 AM, Mikko wrote:
On 2024-05-20 17:48:40 +0000, olcott said:
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.
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p) is BY DEFINITION a
truth bearer, as True must return a Truth Value for
all inputs, and ~ a truth valus is always the other
truth value.
p defined as ~True(L, p) is rejected as a syntax error.
https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
or rejected as
equal(X, X).
?- equal(foo(Y), Y). ...
So Y ends up standing for some kind of infinite structure.
(Clocksin & Mellish 2003:254)
By
The SWI-Prolog implementation of unify_with_occurs_check/2 is cycle-safe
and only guards against creating cycles, https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
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:True(English, "a cat is an animal) is true
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:When x is defined as True(L,x) then x is what True(L,x) is, >>>>>>>>>> in this case a truth bearer.
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:Yes we must build from mutual agreement, good.
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:No, we can ask True(L, x) for any expression x and get >>>>>>>>>>>>>>>>>> an answer.
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. >>>>>>>>>>>>>>>>>>>>>>>>>>
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: >>>>>>>>>>>>>>>>>>>>> >>>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.
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 >>>>>>>>>>>>>>>>>>>>>>
No, so True(L, p) is falseRemember, p defined as ~True(L, p) ... >>>>>>>>>>>>>>>>>>>>> >>Can a sequence of true preserving operations >>>>>>>>>>>>>>>>>>>>> applied
to expressions that are stipulated to be true >>>>>>>>>>>>>>>>>>>>> derive p?
;;
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)) >>>>>>>>>>>>>>>>>>
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?
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. >>>>>>>>>>
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 >>>>>>>
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⟩)
I have no idea what you mean by the weird ⟨p⟩ quotes.
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM TALKING ABOUT THE EXISTENCE OR NON-EXISTENCE OF
AN ACTUAL SEQUENCE OF TRUTH PRESERVING OPERATIONS FROM
EXPRESSIONS OF LANGUAGE KNOWN TO BE TRUE
then Truthbearer(L,p) has the same truth value as
Truthbearer(L,~True(L, ⟨p⟩)).
When p defined as ~True(L, p)
Then ~True(L, p) is true, thus a truth-bearer.
LP := "This sentence is not true"
True(English, LP) is false because LP is not a truth bearer
~True(English, LP) is true because LP is not a truth bearer
"This sentence is not true". is not true.
This sentence is not true: "This sentence is not true". is true
https://en.wikipedia.org/wiki/List_of_logic_symbols
Thus p := ~True(L, p)
*That is great. That means that you agree with me using different
words*
Saying that you have a syntax error does not mean agreement.
Saying this it is any kind of error is sufficient agreement.
Clocksin & Mellish also agree that it is an error:
I don't agree with your errors.
I am talking about the syntax error that you pointed out and
the *So Y ends up standing for some kind of infinite structure*
that Clocksin & Mellish pointed out, neither of these are
my error.
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:I have no idea what you mean by the weird ⟨p⟩ quotes.
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:No, it doesn't. It is a syntax error to have the same symbol on >>>>>>>> both sides ":=" so the expansion is not justified.
On 2024-05-19 14:15:51 +0000, olcott said:True(English, "a cat is an animal) is true
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:When x is defined as True(L,x) then x is what True(L,x) is, >>>>>>>>>>>> in this case a truth bearer.
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:Yes we must build from mutual agreement, good.
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. >>>>>>>>>>>>>>>>>>>>>>>>>>>>No, we can ask True(L, x) for any expression x and >>>>>>>>>>>>>>>>>>>> get an answer.
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: >>>>>>>>>>>>>>>>>>>>>>> >>>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.
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 >>>>>>>>>>>>>>>>>>>>>>>>
No, so True(L, p) is falseRemember, p defined as ~True(L, p) ... >>>>>>>>>>>>>>>>>>>>>>> >>Can a sequence of true preserving operations >>>>>>>>>>>>>>>>>>>>>>> applied
to expressions that are stipulated to be true >>>>>>>>>>>>>>>>>>>>>>> derive p?
;;
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)) >>>>>>>>>>>>>>>>>>>>
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?
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. >>>>>>>>>>>>
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 >>>>>>>>>
LP := ~True(L, LP) expands to ~True(~True(~True(~True(...)))) >>>>>>>>
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⟩) >>>
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM ABSOLUTELY NOT TALKING ABOUT ANY FREAKING Gödel NUMBERS
I AM TALKING ABOUT THE EXISTENCE OR NON-EXISTENCE OF
AN ACTUAL SEQUENCE OF TRUTH PRESERVING OPERATIONS FROM
EXPRESSIONS OF LANGUAGE KNOWN TO BE TRUE
So, you aren't talking about Tarski's proof of the impossibility to
define a Truth Predicate per his definition?
then Truthbearer(L,p) has the same truth value as
Truthbearer(L,~True(L, ⟨p⟩)).
When p defined as ~True(L, p)
Then ~True(L, p) is true, thus a truth-bearer.
Which means that True(L, p) is false, so your True just erred in
describing a true statement as false.
Remeber, you just said that ~True(L, p) which has been given the name
of p IS a truth-bearer.
*You are just not paying close enough attention again*
When p defined as ~True(L, p)
True(L,p) is false
True(L,~p) is false
~True(L,~p) is true
x := y means x is defined to be another name for y https://en.wikipedia.org/wiki/List_of_logic_symbols
You ignored the part where Mikko agreed that
p defined as ~True(L, p)
is a syntax error:
On 5/21/2024 3:05 AM, Mikko wrote:
On 2024-05-20 17:48:40 +0000, olcott said:
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.
LP := "This sentence is not true"
True(English, LP) is false because LP is not a truth bearer
~True(English, LP) is true because LP is not a truth bearer
"This sentence is not true". is not true.
This sentence is not true: "This sentence is not true". is true
https://en.wikipedia.org/wiki/List_of_logic_symbols
Thus p := ~True(L, p)
*That is great. That means that you agree with me using different >>>>>>> words*
Saying that you have a syntax error does not mean agreement.
Saying this it is any kind of error is sufficient agreement.
Clocksin & Mellish also agree that it is an error:
I don't agree with your errors.
I am talking about the syntax error that you pointed out and
the *So Y ends up standing for some kind of infinite structure*
that Clocksin & Mellish pointed out, neither of these are
my error.
On 5/22/2024 8:03 PM, Richard Damon wrote:
On 5/22/24 7:55 PM, olcott wrote:
*You are just not paying close enough attention again*
When p defined as ~True(L, p)
True(L,p) is false
True(L,~p) is false
~True(L,~p) is true
x := y means x is defined to be another name for y
https://en.wikipedia.org/wiki/List_of_logic_symbols
Right, so since p is DEFINED to be ~True(L, p), which since True(L, p)
is false, must be true, that means that you are claiming that
T(L, <a statement that has been shown to be true>) is false.
Thus your True predicat is just broken.
Let's use the more intuitive name lp so that we incorporate by
reference (instead of ignore) all of the material about the liar paradox.
lp := ~True(L, lp)
You already said that you know the Liar Paradox is neither true
nor false, thus not a truth-bearer. You proved that you know
more about self-reference than all of the standard literature
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p)
Those two things by themselves put you ahead of most experts
in the field. The very best expert in the field that I know of
does not know these two things and they only think that the Liar
Paradox might not be a truth-bearer, they do not know it is not.
You ignored the part where Mikko agreed that
p defined as ~True(L, p)
is a syntax error:
So, what it the "Syntax Error"?
Are we not allowed to negate an expression
Or are we not allowed to assign an expression to a name.
Note, "Syntax Error", by its definition doesn't look at Semantics,
On 5/21/2024 3:05 AM, Mikko wrote:
On 2024-05-20 17:48:40 +0000, olcott said:
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.
But it isn't.
*Mikko rejects p := ~True(L,p) as a syntax error*
*which rejects p defined as ~True(L, p) as a syntax error*
On 5/22/2024 9:31 PM, Richard Damon wrote:
On 5/22/24 9:36 PM, olcott wrote:
On 5/22/2024 8:03 PM, Richard Damon wrote:
On 5/22/24 7:55 PM, olcott wrote:
*You are just not paying close enough attention again*
When p defined as ~True(L, p)
True(L,p) is false
True(L,~p) is false
~True(L,~p) is true
x := y means x is defined to be another name for y
https://en.wikipedia.org/wiki/List_of_logic_symbols
Right, so since p is DEFINED to be ~True(L, p), which since True(L,
p) is false, must be true, that means that you are claiming that
T(L, <a statement that has been shown to be true>) is false.
Thus your True predicat is just broken.
Let's use the more intuitive name lp so that we incorporate by
reference (instead of ignore) all of the material about the liar
paradox.
lp := ~True(L, lp)
But that isn't the traditional "Liar's Paradix", because it is not
normally stated in terms of a Truth Predicate.
The "Liar's paradox" is a statement that asserts that it is false.
That is NOT what the above statement says, or even means.
The Strengthened Liar Paradox (also called the Strong Liar Paradox)
can begin with a Strengthened Liar Sentence such as: This sentence
is not true,
https://iep.utm.edu/liar-paradox/#SH1a
I spent 20,000 hours on this since 2004 and you glance at a couple
of my words and guess that I must be wrong.
You already said that you know the Liar Paradox is neither true
nor false, thus not a truth-bearer. You proved that you know
more about self-reference than all of the standard literature
Nope, shows you don't understand what the literature is saying.
YOU ARE ALREADY AHEAD OF THE LITERATURE.
THE LITERATURE CANNOT EVEN GET SELF-REFERENCE CORRECTLY
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*, https://plato.stanford.edu/entries/self-reference/#ConSemPar
On 5/13/2024 7:29 PM, Richard Damon wrote:
Remember, p defined as ~True(L, p)
We will now call this
lp defined as ~True(L, lp) or
lp := ~True(L, lp)
*Mikko rejects p := ~True(L,p) as a syntax error*
*which rejects p defined as ~True(L, p) as a syntax error*
But he is wrong, there is no syntax error for it in the logic field
that Tarski is working in,
*That Tarski was aware of*
< as he assumes that logic is powerful enough to
encode references, even to self, into the logical statements of the
field.
He didn't bother to THINK THIS ALL-THE-WAY THROUGH
On 5/23/2024 6:29 AM, Richard Damon wrote:
On 5/22/24 11:45 PM, olcott wrote:
On 5/22/2024 9:31 PM, Richard Damon wrote:
On 5/22/24 9:36 PM, olcott wrote:
On 5/22/2024 8:03 PM, Richard Damon wrote:
On 5/22/24 7:55 PM, olcott wrote:
*You are just not paying close enough attention again*
When p defined as ~True(L, p)
True(L,p) is false
True(L,~p) is false
~True(L,~p) is true
x := y means x is defined to be another name for y
https://en.wikipedia.org/wiki/List_of_logic_symbols
Right, so since p is DEFINED to be ~True(L, p), which since
True(L, p) is false, must be true, that means that you are
claiming that
T(L, <a statement that has been shown to be true>) is false.
Thus your True predicat is just broken.
Let's use the more intuitive name lp so that we incorporate by
reference (instead of ignore) all of the material about the liar
paradox.
lp := ~True(L, lp)
But that isn't the traditional "Liar's Paradix", because it is not
normally stated in terms of a Truth Predicate.
The "Liar's paradox" is a statement that asserts that it is false.
That is NOT what the above statement says, or even means.
The Strengthened Liar Paradox (also called the Strong Liar Paradox)
can begin with a Strengthened Liar Sentence such as: This sentence
is not true,
https://iep.utm.edu/liar-paradox/#SH1a
I spent 20,000 hours on this since 2004 and you glance at a couple
of my words and guess that I must be wrong.
Which was wasted since you didn't learn what a True Predicate is.
I am correct and you simply do not understand that I am correct,
yet most of the greatest experts in the field are not even aware
that there is something definitely wrong with the Liar Paradox.
On 5/23/2024 3:09 AM, Mikko wrote:
By the usual rules a definition of a symbol in terms
of itself is not an acceptable definition.
lp := ~True(L, lp) expands to ~True(~True(~True(~True(...))))
One can either reject it as a syntax error or let it go ahead
and infinitely expand and reject it as a semantic error. Or
one can reject is as a self-contradictory epistemological antinomy
having no truth value thus a type mismatch error for any formal
system of bivalent logic.
Most of the greatest experts in the field are not even sure that there
is anything wrong with it the Liar Paradox. None of the experts in the
field formalize the Liar Paradox correctly.
On 5/28/2024 1:59 AM, Mikko wrote:
On 2024-05-27 14:34:14 +0000, olcott said:
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
In other words Prolog has detected a cycle in the directed graph of the
evaluation sequence of the structure of the Liar Paradox. Experts seem
to think that Prolog is taking "not" and "true" as meaningless and is
only evaluating the structure of the expression.
The words "not" and "true" of Prolog are meaningful in some contexts
but not above. The word "true" is meaningful only when it has no
arguments.
That Prolog construes any expression having the same structure as the
Liar Paradox as having a cycle in the directed graph of its evaluation sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
You could try
?- LP = not(true(LP), true(LP).
or
?- LP = not(true(LP), not(true(LP)).
The predicate unify_with_occurs_check checks whether the resulting
sructure is acyclic because that is its purpose. Whether a simple
Yes exactly. If I knew that Prolog did this then I would not have
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
unification like LP = not(true(LP)) does same is implementation
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
ISO Prolog implementations have the built-in predicate unify_with_occurs_check/2 for sound unification https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
Alternatively such expressions crash or remain stuck in infinite loops.
Anyway, none of this is relevant to the topic of this thread or
topics of sci.logic.
...14 Every epistemological antinomy can likewise be used for
a similar undecidability proof...(Gödel 1931:40)
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
It would
then be possible to reconstruct the *antinomy of the liar* in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
CONCEPT OF TRUTH IN FORMALIZED LANGUAGES, Tarski https://liarparadox.org/Tarski_247_248.pdf
The Liar Paradox and other such {epistemological antinomies} must be
rejected as type mismatch errors for any system of bivalent logic thus
cannot be correctly used for any undecidability or undefinability proof.
On 5/28/2024 9:04 PM, Richard Damon wrote:
On 5/28/24 10:59 AM, olcott wrote:
On 5/28/2024 1:59 AM, Mikko wrote:
On 2024-05-27 14:34:14 +0000, olcott said:
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
In other words Prolog has detected a cycle in the directed graph of
the
evaluation sequence of the structure of the Liar Paradox. Experts seem >>>>> to think that Prolog is taking "not" and "true" as meaningless and is >>>>> only evaluating the structure of the expression.
The words "not" and "true" of Prolog are meaningful in some contexts
but not above. The word "true" is meaningful only when it has no
arguments.
That Prolog construes any expression having the same structure as the
Liar Paradox as having a cycle in the directed graph of its evaluation
sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
But Prolog doesn't support powerful enough logic to handle the system
like Tarski and Godel are talking about.
The fact that Prolog just rejects it shows that.
Your ignorance is no excuse.
You could try
?- LP = not(true(LP), true(LP).
or
?- LP = not(true(LP), not(true(LP)).
The predicate unify_with_occurs_check checks whether the resulting
sructure is acyclic because that is its purpose. Whether a simple
Yes exactly. If I knew that Prolog did this then I would not have
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
unification like LP = not(true(LP)) does same is implementation
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
ISO Prolog implementations have the built-in predicate
unify_with_occurs_check/2 for sound unification
https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
Alternatively such expressions crash or remain stuck in infinite loops.
Anyway, none of this is relevant to the topic of this thread or
topics of sci.logic.
...14 Every epistemological antinomy can likewise be used for
a similar undecidability proof...(Gödel 1931:40)
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
It would
then be possible to reconstruct the *antinomy of the liar* in the >>> metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
CONCEPT OF TRUTH IN FORMALIZED LANGUAGES, Tarski
https://liarparadox.org/Tarski_247_248.pdf
The Liar Paradox and other such {epistemological antinomies} must be
rejected as type mismatch errors for any system of bivalent logic thus
cannot be correctly used for any undecidability or undefinability proof. >>>
But you just don't don't understand what was done in those proofs.
Neither of them assumed the Liar's paradox had a truth value. Only
statements formed from VALID logical sequences in the field.
Please try to show what step in Godel's or Tarski's proof where they
made a logical error (not just came up with a statement you think
can't be valid).
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar
in the metalanguage, by forming in the language itself a sentence
x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf
adapted to become the first line of his proof
x ∉ Pr if and only if p
That Prolog construes any expression having the same structure as the
Liar Paradox as having a cycle in the directed graph of its evaluation
sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
But Prolog doesn't support powerful enough logic to handle the system
like Tarski and Godel are talking about.
The fact that Prolog just rejects it shows that.
Your ignorance is no excuse.
On 5/28/2024 10:38 PM, Richard Damon wrote:
On 5/28/24 10:39 PM, olcott wrote:
On 5/28/2024 9:04 PM, Richard Damon wrote:
On 5/28/24 10:59 AM, olcott wrote:
On 5/28/2024 1:59 AM, Mikko wrote:
On 2024-05-27 14:34:14 +0000, olcott said:
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
In other words Prolog has detected a cycle in the directed graph >>>>>>> of the
evaluation sequence of the structure of the Liar Paradox. Experts >>>>>>> seem
to think that Prolog is taking "not" and "true" as meaningless
and is
only evaluating the structure of the expression.
The words "not" and "true" of Prolog are meaningful in some contexts >>>>>> but not above. The word "true" is meaningful only when it has no
arguments.
That Prolog construes any expression having the same structure as the >>>>> Liar Paradox as having a cycle in the directed graph of its evaluation >>>>> sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it
must
be rejected.
But Prolog doesn't support powerful enough logic to handle the
system like Tarski and Godel are talking about.
The fact that Prolog just rejects it shows that.
Your ignorance is no excuse.
What ignorance?
The fact that you assert that you know the underlying details of https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2 without even glancing at the documentation and write-up in Clocksin and Mellish seems to be willful ignorance.
The fact that I understand the limitation of Prolog and what forms of
logic it can do, which seems to be beyond your understanding?
Claiming that Prolog rejects a statement because it doesn't fit its
grammer is meaningless for more complicated logics that don't have
that same grammer restricition.
IF you want to limit the logic you use to what Prolog can handle, go
ahead, the rest of the world likes its mathematics.
You could try
?- LP = not(true(LP), true(LP).
or
?- LP = not(true(LP), not(true(LP)).
The predicate unify_with_occurs_check checks whether the resulting >>>>>> sructure is acyclic because that is its purpose. Whether a simple
Yes exactly. If I knew that Prolog did this then I would not have
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
unification like LP = not(true(LP)) does same is implementation
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
ISO Prolog implementations have the built-in predicate
unify_with_occurs_check/2 for sound unification
https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
Alternatively such expressions crash or remain stuck in infinite
loops.
Anyway, none of this is relevant to the topic of this thread or
topics of sci.logic.
...14 Every epistemological antinomy can likewise be used for >>>>> a similar undecidability proof...(Gödel 1931:40)
Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems
https://monoskop.org/images/9/93/Kurt_G%C3%B6del_On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems_1992.pdf
It would
then be possible to reconstruct the *antinomy of the liar* in the >>>>> metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated >>>>> with x asserts that x is not a true sentence.
CONCEPT OF TRUTH IN FORMALIZED LANGUAGES, Tarski
https://liarparadox.org/Tarski_247_248.pdf
The Liar Paradox and other such {epistemological antinomies} must be >>>>> rejected as type mismatch errors for any system of bivalent logic thus >>>>> cannot be correctly used for any undecidability or undefinability
proof.
But you just don't don't understand what was done in those proofs.
Neither of them assumed the Liar's paradox had a truth value. Only
statements formed from VALID logical sequences in the field.
Please try to show what step in Godel's or Tarski's proof where they
made a logical error (not just came up with a statement you think
can't be valid).
Tarski's Liar Paradox from page 248
It would then be possible to reconstruct the antinomy of the liar >>> in the metalanguage, by forming in the language itself a sentence >>> x such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
https://liarparadox.org/Tarski_247_248.pdf
Right, He has SHOWN that the logic system, when given the assumption
of the existance of the Truth Predicate, can construct the liar as a
truth-bearing statement.
Utterly Ridiculous (and you probably don't know it).
On 5/29/2024 2:01 AM, Python wrote:
Le 29/05/2024 à 04:39, olcott a écrit :
...
That Prolog construes any expression having the same structure as the >>>>> Liar Paradox as having a cycle in the directed graph of its evaluation >>>>> sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it
must
be rejected.
But Prolog doesn't support powerful enough logic to handle the
system like Tarski and Godel are talking about.
The fact that Prolog just rejects it shows that.
Your ignorance is no excuse.
You, Peter Olcott, are actually the one showing one's ignorance here.
Gödel theorems can be handled by more powerful proving systems such
as COQ : http://r6.ca/Goedel/goedel1.html
?- LP = not(true(L, LP)).
LP = not(true(L, LP)).
?- unify_with_occurs_check(LP, not(true(L, LP))).
false.
Richard explained this incorrectly.
let's see if you can do better.
I created Minimal Type Theory that does the same thing as https://www.swi-prolog.org/pldoc/man?predicate=unify_with_occurs_check/2
Minimal Type Theory (YACC BNF) https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
LP := ~True(L, LP)
definition_2 token="ASSIGN_ALIAS"
| definition_2 token="IDENTIFIER" value="LP"
| sentence_2 token="NOT"
| | atomic_sentence_1 token="IDENTIFIER" value="True"
| | | term_list_1
| | | | term_2 token="IDENTIFIER" value="L"
| | | | term_2 token="IDENTIFIER" value="LP"
<definition_2 token="ASSIGN_ALIAS">
<definition_2 token="IDENTIFIER" value="LP"/>
<sentence_2 token="NOT">
<atomic_sentence_1 token="IDENTIFIER" value="True">
<term_list_1>
<term_2 token="IDENTIFIER" value="L"/>
<term_2 token="IDENTIFIER" value="LP"/>
</term_list_1>
</atomic_sentence_1>
</sentence_2>
</definition_2>
Directed graph of evaluation sequence of LP
Nodes on the left edges on the right
00 NOT 01
01 True 02, 00 // cycle
02 L
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 493 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 21:38:50 |
| Calls: | 9,724 |
| Calls today: | 14 |
| Files: | 13,741 |
| Messages: | 6,182,239 |