On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
That does not disprove Tarski.
We can define a correct True(X) predicate that always succeeds >>>>>>>>> except
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can
construct a statement x, which is only true it is the case that
True(x) is false, but this interperetation can only be seen in the
metalanguage created from the language in the proof, similar to
Godel meta that generates the proof testing relationship that shows
that G can only be true if it can not be proven as the existance of
a number to make it false, becomes a proof that the statement is
true and thus creates a contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the
metalanguage, which it can not, but still you make bold statements
that you can not prove, and have been pointed out to be wrong, just
shows how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic
facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length. >>>>
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity. >>>>
Note, "The Entire set of Human General Knowledge" does not contain
the contents of Meta-systems like Tarski uses, as there are an
infinite number of them possible, and thus to even try to express
them all requires an infinite number of axioms, and thus your system
fails to meet the requirements. Once you don't have the meta-
systems, Tarski proof can create a metasystem, that you system
doesn't know about, which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such references. >>>>
And, even if it does detect it, what answer does True(x) produce
when we have designed (via a metalanguage) that the statement x in
the language will be true if and only if !True(x), which he showed
can be done in ANY system with sufficient power, which your
universal system must have.
Sorry, you are just showing how little you understand what you are
talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order
logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
To address the objection to these forms of encoding
that they ignore the important source of meaning
of linguistics pragmatics context, what I am proposing
also includes a situation specific knowledge ontology
that directly encode the full context of the specific
situation.
0 is a term
+ is a binary operator (i.e., term + term is a term)
< is a binary relation (i.e., term < term is a formula).
The definition of + is ambiguous as it does not define wich one of the
two + signs in A + B + C is should be evaluated first but with the
postulate that the result is the same in both cases that does not matter.
How do you express semantics of that language with the lanugage itself?
There should be at least enough semantics to tell whether x = 0 for every
x.
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
That does not disprove Tarski.
We can define a correct True(X) predicate that always succeeds except >>>>>>>>> for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a >>>> statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates
the proof testing relationship that shows that G can only be true if it >>>> can not be proven as the existance of a number to make it false,
becomes a proof that the statement is true and thus creates a
contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the
metalanguage, which it can not, but still you make bold statements that >>>> you can not prove, and have been pointed out to be wrong, just shows
how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic
facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length. >>>>
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity. >>>>
Note, "The Entire set of Human General Knowledge" does not contain the >>>> contents of Meta-systems like Tarski uses, as there are an infinite
number of them possible, and thus to even try to express them all
requires an infinite number of axioms, and thus your system fails to
meet the requirements. Once you don't have the meta-systems, Tarski
proof can create a metasystem, that you system doesn't know about,
which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such references. >>>>
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the
language will be true if and only if !True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are
talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic >> with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
That does not disprove Tarski.
We can define a correct True(X) predicate that always
succeeds except
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can
construct a statement x, which is only true it is the case that
True(x) is false, but this interperetation can only be seen in the >>>>>> metalanguage created from the language in the proof, similar to
Godel meta that generates the proof testing relationship that
shows that G can only be true if it can not be proven as the
existance of a number to make it false, becomes a proof that the
statement is true and thus creates a contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the
metalanguage, which it can not, but still you make bold statements >>>>>> that you can not prove, and have been pointed out to be wrong,
just shows how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic
facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in
length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your
stupidity.
Note, "The Entire set of Human General Knowledge" does not contain >>>>>> the contents of Meta-systems like Tarski uses, as there are an
infinite number of them possible, and thus to even try to express
them all requires an infinite number of axioms, and thus your
system fails to meet the requirements. Once you don't have the
meta- systems, Tarski proof can create a metasystem, that you
system doesn't know about, which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such
references.
And, even if it does detect it, what answer does True(x) produce
when we have designed (via a metalanguage) that the statement x in >>>>>> the language will be true if and only if !True(x), which he showed >>>>>> can be done in ANY system with sufficient power, which your
universal system must have.
Sorry, you are just showing how little you understand what you are >>>>>> talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order
logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
Part of the problem is that most of what we call "Human Knowledge"
isn't logically defined truth, but is just "Emperical Knowledge", for
which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
The actual smell of a rose cannot be expressed using
language.
know it isn't totally accurate (as all measurements have error) or is
actually just an approximation for what reality actually is.
To address the objection to these forms of encoding
that they ignore the important source of meaning
of linguistics pragmatics context, what I am proposing
also includes a situation specific knowledge ontology
that directly encode the full context of the specific
situation.
And a listing of "facts" (which mostly are not facts) isn't a logic
system.
Sorry, but you are just demonstrating that you don't actually
understand what you are talking about.
You simply did not bother to pay any attention to any details.
We simply formalize the entire body of human general knowledge
as one gigantic tree of knowledge semantic tautology using
Montague Grammar and knowledge ontology inheritance hierarchy.
If those are all words that you do not understand that does
not mean that I am wrong.
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
That does not disprove Tarski.
We can define a correct True(X) predicate that always >>>>>>>>>>>>> succeeds except
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can
construct a statement x, which is only true it is the case that >>>>>>>> True(x) is false, but this interperetation can only be seen in >>>>>>>> the metalanguage created from the language in the proof, similar >>>>>>>> to Godel meta that generates the proof testing relationship that >>>>>>>> shows that G can only be true if it can not be proven as the
existance of a number to make it false, becomes a proof that the >>>>>>>> statement is true and thus creates a contradiction in the system. >>>>>>>>
That you can't understand that, or get confused by what is in
the language, which your True predicate can look at, and in the >>>>>>>> metalanguage, which it can not, but still you make bold
statements that you can not prove, and have been pointed out to >>>>>>>> be wrong, just shows how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic
facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in >>>>>>>> length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your
stupidity.
Note, "The Entire set of Human General Knowledge" does not
contain the contents of Meta-systems like Tarski uses, as there >>>>>>>> are an infinite number of them possible, and thus to even try to >>>>>>>> express them all requires an infinite number of axioms, and thus >>>>>>>> your system fails to meet the requirements. Once you don't have >>>>>>>> the meta- systems, Tarski proof can create a metasystem, that
you system doesn't know about, which creates the problem statement. >>>>>>>>
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such
references.
And, even if it does detect it, what answer does True(x) produce >>>>>>>> when we have designed (via a metalanguage) that the statement x >>>>>>>> in the language will be true if and only if !True(x), which he >>>>>>>> showed can be done in ANY system with sufficient power, which
your universal system must have.
Sorry, you are just showing how little you understand what you >>>>>>>> are talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first
order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION.
That would just be a set of axioms. Note, Logic system must also have
a set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge"
isn't logically defined truth, but is just "Emperical Knowledge",
for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose
truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
The actual smell of a rose cannot be expressed using
language.
Maybe, depends on your definitions. Of course, part of the problem is
that the "smell of a rose" is actually a subject thing, so not
directly related to knowledge. Of course that concept blows apart
large parts of
NO STUPID IT DOES NOT. PLEASE QUIT BEING A MORON.
WHEN I TELL YOU SOMETHING FIFTY TIMES YOU SHOULD
NOTICE THAT I SAID IT AT LEAST ONCE.
your theory. Much of what is commonly called "Human Knowledge" isn't
actually knowledge, but subjective opinions that have been agreed by the
NO STUPID BASIC FACTS ARE NOT ANY SORT OF OPINION.
majority, and thus not actually something that can be handled by
objective logic.
know it isn't totally accurate (as all measurements have error) or
is actually just an approximation for what reality actually is.
To address the objection to these forms of encoding
that they ignore the important source of meaning
of linguistics pragmatics context, what I am proposing
also includes a situation specific knowledge ontology
that directly encode the full context of the specific
situation.
And a listing of "facts" (which mostly are not facts) isn't a logic
system.
Sorry, but you are just demonstrating that you don't actually
understand what you are talking about.
You simply did not bother to pay any attention to any details.
We simply formalize the entire body of human general knowledge
as one gigantic tree of knowledge semantic tautology using
Montague Grammar and knowledge ontology inheritance hierarchy.
Which isn't a logic system, BY DEFINITION, it is a knowledge ontology.
A KNOWLEDGE ONTOLOGY IS A SPECIFIC KIND OF LOGIC
SYSTEM WHERE SEMANTIC INFERENCE IS DONE ON THE
BASIS OF INHERITANCE.
If those are all words that you do not understand that does
not mean that I am wrong.
Of course it does, since apparently you don't understand what LOGIC
actually is.
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always succeeds exceptThat does not disprove Tarski.
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates >>>>>>>>>> the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false, >>>>>>>>>> becomes a proof that the statement is true and thus creates a >>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in the >>>>>>>>>> language, which your True predicate can look at, and in the >>>>>>>>>> metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows >>>>>>>>>> how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic >>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity.
Note, "The Entire set of Human General Knowledge" does not contain the
contents of Meta-systems like Tarski uses, as there are an infinite >>>>>>>>>> number of them possible, and thus to even try to express them all >>>>>>>>>> requires an infinite number of axioms, and thus your system fails to >>>>>>>>>> meet the requirements. Once you don't have the meta- systems, Tarski >>>>>>>>>> proof can create a metasystem, that you system doesn't know about, >>>>>>>>>> which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such references.
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the >>>>>>>>>> language will be true if and only if ! True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are >>>>>>>>>> talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION.
That would just be a set of axioms. Note, Logic system must also have a >>>> set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>> isn't logically defined truth, but is just "Emperical Knowledge", for >>>>>> which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose
truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be
the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't
actually understand any logic system more coplicated than what Prolog
can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
That does not disprove Tarski.
We can define a correct True(X) predicate that always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false, >>>>>>>> but this interperetation can only be seen in the metalanguage created >>>>>>>> from the language in the proof, similar to Godel meta that generates >>>>>>>> the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false, >>>>>>>> becomes a proof that the statement is true and thus creates a
contradiction in the system.
That you can't understand that, or get confused by what is in the >>>>>>>> language, which your True predicate can look at, and in the
metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows >>>>>>>> how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic
facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length. >>>>>>>>
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity. >>>>>>>>
Note, "The Entire set of Human General Knowledge" does not contain the >>>>>>>> contents of Meta-systems like Tarski uses, as there are an infinite >>>>>>>> number of them possible, and thus to even try to express them all >>>>>>>> requires an infinite number of axioms, and thus your system fails to >>>>>>>> meet the requirements. Once you don't have the meta- systems, Tarski >>>>>>>> proof can create a metasystem, that you system doesn't know about, >>>>>>>> which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such references. >>>>>>>>
And, even if it does detect it, what answer does True(x) produce when >>>>>>>> we have designed (via a metalanguage) that the statement x in the >>>>>>>> language will be true if and only if !True(x), which he showed can be >>>>>>>> done in ANY system with sufficient power, which your universal system >>>>>>>> must have.
Sorry, you are just showing how little you understand what you are >>>>>>>> talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION.
That would just be a set of axioms. Note, Logic system must also have a
set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
Another part of human knowledge is that there are fools that try to
argue against proven theorems.
On 21/03/2025 08:11, Mikko wrote:
<snip>
Another part of human knowledge is that there are fools that try to
argue against proven theorems.
Well, if it ain't proven it ain't yet a theorem. But is that enough?
The background to the work of Church, Turing, Gödel and the like is Hilbert's second problem: "The compatibility of the arithmetical
axioms", and the background to /that/ problem is that in the late 19th century mathematicians were occasionally coming up with proofs of X,
only to discover in the literature that not-X had already been proved.
The question then was which proof had the bug?
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in corner
cases like the Halting Problem, but Gödel's Hobgoblin hovers over mathematics to this day.
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always >>>>>>>>>>>>>>> succeeds exceptThat does not disprove Tarski.
for unknowns and untruths, Tarski WAS WRONG !!!
He said that this is impossible and no
counter-examples exists that shows that I am wrong.
True(GC) == FALSE Cannot be proven true AKA unknown
True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can >>>>>>>>>> construct a statement x, which is only true it is the case >>>>>>>>>> that True(x) is false, but this interperetation can only be >>>>>>>>>> seen in the metalanguage created from the language in the
proof, similar to Godel meta that generates the proof testing >>>>>>>>>> relationship that shows that G can only be true if it can not >>>>>>>>>> be proven as the existance of a number to make it false,
becomes a proof that the statement is true and thus creates a >>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in >>>>>>>>>> the language, which your True predicate can look at, and in >>>>>>>>>> the metalanguage, which it can not, but still you make bold >>>>>>>>>> statements that you can not prove, and have been pointed out >>>>>>>>>> to be wrong, just shows how stupid you are.
True(X) only returns TRUE when a a sequence of truth
preserving operations can derive X from the set of basic >>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in >>>>>>>>>> length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your >>>>>>>>>> stupidity.
Note, "The Entire set of Human General Knowledge" does not >>>>>>>>>> contain the contents of Meta-systems like Tarski uses, as
there are an infinite number of them possible, and thus to >>>>>>>>>> even try to express them all requires an infinite number of >>>>>>>>>> axioms, and thus your system fails to meet the requirements. >>>>>>>>>> Once you don't have the meta- systems, Tarski proof can create >>>>>>>>>> a metasystem, that you system doesn't know about, which
creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such >>>>>>>>>> references.
And, even if it does detect it, what answer does True(x)
produce when we have designed (via a metalanguage) that the >>>>>>>>>> statement x in the language will be true if and only if !
True(x), which he showed can be done in ANY system with
sufficient power, which your universal system must have.
Sorry, you are just showing how little you understand what you >>>>>>>>>> are talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first >>>>>>>> order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU
DEFINITION. That would just be a set of axioms. Note, Logic system
must also have a set of rules of relationships and how to manipulate
them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>> isn't logically defined truth, but is just "Emperical Knowledge",
for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose
truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be
the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't
actually understand any logic system more coplicated than what Prolog
can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
On 3/21/25 5:33 AM, Richard Heathfield wrote:
But what if they were /both/ right? It was an obvious worry,
and so arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only
in corner cases like the Halting Problem, but Gödel's Hobgoblin
hovers over mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved
that it couldn't be proved to BE consistant within itself.
My understanding is that Gödel proved that there are statements
that are true but not provable.
It's still not possible for both
X and not-X to be provable. If proofs exist for both, at least
one of the proofs must be flawed.
On 21/03/2025 19:30, Keith Thompson wrote:
My understanding is that Gödel proved that there are statements
that are true but not provable.
Yes. Incompleteness.
It's still not possible for both
X and not-X to be provable. If proofs exist for both, at least
one of the proofs must be flawed.
I'd be interested to see a proof of that conjecture.
On 3/21/2025 4:33 AM, Richard Heathfield wrote:
On 21/03/2025 08:11, Mikko wrote:
<snip>
Another part of human knowledge is that there are fools that try to
argue against proven theorems.
Well, if it ain't proven it ain't yet a theorem. But is that enough?
The background to the work of Church, Turing, Gödel and the like is
Hilbert's second problem: "The compatibility of the arithmetical
axioms", and the background to /that/ problem is that in the late 19th
century mathematicians were occasionally coming up with proofs of X,
only to discover in the literature that not-X had already been proved.
The question then was which proof had the bug?
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in
corner cases like the Halting Problem, but Gödel's Hobgoblin hovers
over mathematics to this day.
When a formal system begins with the basic facts of human
general knowledge expressed using language and can derive
each element of the set of human general knowledge that can
be expressed using language on the basis of these basic facts
by applying only truth preserving operations then undecidability
and incompleteness are impossible.
On 3/21/2025 6:48 AM, Richard Damon wrote:
On 3/20/25 11:49 PM, olcott wrote:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always >>>>>>>>>>>>>>>>> succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can >>>>>>>>>>>> construct a statement x, which is only true it is the case >>>>>>>>>>>> that True(x) is false, but this interperetation can only be >>>>>>>>>>>> seen in the metalanguage created from the language in the >>>>>>>>>>>> proof, similar to Godel meta that generates the proof
testing relationship that shows that G can only be true if >>>>>>>>>>>> it can not be proven as the existance of a number to make it >>>>>>>>>>>> false, becomes a proof that the statement is true and thus >>>>>>>>>>>> creates a contradiction in the system.
That you can't understand that, or get confused by what is >>>>>>>>>>>> in the language, which your True predicate can look at, and >>>>>>>>>>>> in the metalanguage, which it can not, but still you make >>>>>>>>>>>> bold statements that you can not prove, and have been
pointed out to be wrong, just shows how stupid you are. >>>>>>>>>>>>
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite >>>>>>>>>>>> in length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your >>>>>>>>>>>> stupidity.
Note, "The Entire set of Human General Knowledge" does not >>>>>>>>>>>> contain the contents of Meta-systems like Tarski uses, as >>>>>>>>>>>> there are an infinite number of them possible, and thus to >>>>>>>>>>>> even try to express them all requires an infinite number of >>>>>>>>>>>> axioms, and thus your system fails to meet the requirements. >>>>>>>>>>>> Once you don't have the meta- systems, Tarski proof can >>>>>>>>>>>> create a metasystem, that you system doesn't know about, >>>>>>>>>>>> which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such >>>>>>>>>>>> references.
And, even if it does detect it, what answer does True(x) >>>>>>>>>>>> produce when we have designed (via a metalanguage) that the >>>>>>>>>>>> statement x in the language will be true if and only if ! >>>>>>>>>>>> True(x), which he showed can be done in ANY system with >>>>>>>>>>>> sufficient power, which your universal system must have. >>>>>>>>>>>>
Sorry, you are just showing how little you understand what >>>>>>>>>>>> you are talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first >>>>>>>>>> order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU
DEFINITION. That would just be a set of axioms. Note, Logic system >>>>>> must also have a set of rules of relationships and how to
manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human
Knowledge" isn't logically defined truth, but is just "Emperical >>>>>>>> Knowledge", for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose >>>>>> truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to
be the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't
actually understand any logic system more coplicated than what
Prolog can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Except it isn't true, as:
First, it isn't a logic system until you add the rules of logic to
define how you manipulate items.
Every operation is permitted as long as it is truth preserving
and begins on the basis of basic facts expressed as language.
It is self-evident that undecidability cannot possibly exist
in such a system.
Second, within that set of knowledge is the definition ofThese terms are defined in the set of all general knowledge
undecidabiliry and undefinability, that you are forced to accept from
what *IS* human knowledge, which is the agreed upon meanings,
that can be expressed in language yet cannot apply to this
system itself because everything is already decided.
And thus, when you include the rules that are encoded into that
knowledge base, you include those rules used by Godel and company that
shows that any logic system powerful enough to express the properties
of the Natual Numbers (which a system of ALL Knowledge) would have,
must be incomplete.
In this much more powerful system he is simply proved wrong.
Undecidability is impossible when EVERYTHING has already been
decided.
Sorry, you just don't understand that you can't define your way out of
the problems of logic, unless you first remove large chunks of what is
knowledge from your system.
Try and show that any verified fact is untrue.
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in
corner cases like the Halting Problem, but Gödel's Hobgoblin hovers
over mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved that
it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
On 3/21/2025 7:01 PM, Richard Damon wrote:
On 3/21/25 6:44 PM, olcott wrote:
On 3/21/2025 2:30 PM, Keith Thompson wrote:
Richard Heathfield <rjh@cpax.org.uk> writes:
On 21/03/2025 08:11, Mikko wrote:
<snip>
Another part of human knowledge is that there are fools that try to >>>>>> argue against proven theorems.
Well, if it ain't proven it ain't yet a theorem. But is that enough? >>>>>
The background to the work of Church, Turing, Gödel and the like is >>>>> Hilbert's second problem: "The compatibility of the arithmetical
axioms", and the background to /that/ problem is that in the late 19th >>>>> century mathematicians were occasionally coming up with proofs of X, >>>>> only to discover in the literature that not-X had already been
proved. The question then was which proof had the bug?
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in
corner cases like the Halting Problem, but Gödel's Hobgoblin hovers >>>>> over mathematics to this day.
My understanding is that Gödel proved that there are statements
that are true but not provable. It's still not possible for both
X and not-X to be provable. If proofs exist for both, at least
one of the proofs must be flawed.
It seems that the short version is that G can be
expressed in math yet cannot be linked to its
semantic meaning in math. We need meta-math for this.
In my system of the entire set of human general knowledge
that can be expressed in language G is linked to its
semantic meaning.
No, G is fully connected with its BASIC semantics meaning in the
language of math.
That would mean that G is provable in F because
a connection to its full semantics <is> its proof.
On 3/21/2025 7:01 PM, Richard Damon wrote:
On 3/21/25 6:54 PM, olcott wrote:
On 3/21/2025 6:48 AM, Richard Damon wrote:
On 3/20/25 11:49 PM, olcott wrote:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always >>>>>>>>>>>>>>>>>>> succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we >>>>>>>>>>>>>> can construct a statement x, which is only true it is the >>>>>>>>>>>>>> case that True(x) is false, but this interperetation can >>>>>>>>>>>>>> only be seen in the metalanguage created from the language >>>>>>>>>>>>>> in the proof, similar to Godel meta that generates the >>>>>>>>>>>>>> proof testing relationship that shows that G can only be >>>>>>>>>>>>>> true if it can not be proven as the existance of a number >>>>>>>>>>>>>> to make it false, becomes a proof that the statement is >>>>>>>>>>>>>> true and thus creates a contradiction in the system. >>>>>>>>>>>>>>
That you can't understand that, or get confused by what is >>>>>>>>>>>>>> in the language, which your True predicate can look at, >>>>>>>>>>>>>> and in the metalanguage, which it can not, but still you >>>>>>>>>>>>>> make bold statements that you can not prove, and have been >>>>>>>>>>>>>> pointed out to be wrong, just shows how stupid you are. >>>>>>>>>>>>>>
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is >>>>>>>>>>>>>> infinite in length.
This never fails on the entire set of human general >>>>>>>>>>>>>>> knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving >>>>>>>>>>>>>> your stupidity.
Note, "The Entire set of Human General Knowledge" does not >>>>>>>>>>>>>> contain the contents of Meta-systems like Tarski uses, as >>>>>>>>>>>>>> there are an infinite number of them possible, and thus to >>>>>>>>>>>>>> even try to express them all requires an infinite number >>>>>>>>>>>>>> of axioms, and thus your system fails to meet the
requirements. Once you don't have the meta- systems, >>>>>>>>>>>>>> Tarski proof can create a metasystem, that you system >>>>>>>>>>>>>> doesn't know about, which creates the problem statement. >>>>>>>>>>>>>>
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of such >>>>>>>>>>>>>> references.
And, even if it does detect it, what answer does True(x) >>>>>>>>>>>>>> produce when we have designed (via a metalanguage) that >>>>>>>>>>>>>> the statement x in the language will be true if and only >>>>>>>>>>>>>> if ! True(x), which he showed can be done in ANY system >>>>>>>>>>>>>> with sufficient power, which your universal system must have. >>>>>>>>>>>>>>
Sorry, you are just showing how little you understand what >>>>>>>>>>>>>> you are talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the >>>>>>>>>>>> first order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU
DEFINITION. That would just be a set of axioms. Note, Logic
system must also have a set of rules of relationships and how to >>>>>>>> manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human
Knowledge" isn't logically defined truth, but is just
"Emperical Knowledge", for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement
whose truth is currently unknown, which it MUST be able to handle >>>>>>>>
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY
to be the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you
can't actually understand any logic system more coplicated than
what Prolog can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Nope. Proven otherwise, and you are just showing your stupidity in
maintaining that claim.
Then try and show ALL OF THE DETAILS OF how when one starts
with basic facts and only applies truth preserving operations that
True(X) is not always correct.
You have already shown that you don't understand the proof, so why
should I repeat it,
Tarki's proof claimed that True(X) is forever
undefinable no matter how you try to go about
defining it. He was WRONG about this.
When we reformulate the notion of a formal
system such that it contains all and only
the set of human general knowledge then all
of the screwy things about other notions of
formal system utterly cease to exist.
On 3/21/25 4:20 PM, Richard Heathfield wrote:
On 21/03/2025 19:30, Keith Thompson wrote:
My understanding is that Gödel proved that there are statements
that are true but not provable.
Yes. Incompleteness.
It's still not possible for both
X and not-X to be provable. If proofs exist for both, at least
one of the proofs must be flawed.
I'd be interested to see a proof of that conjecture.
It comes from the definition of consistency.
If something is provable, then it must be true, as the proof
shows the path from the fundamental truths the the stateemnt,
establishing its truth.
On 3/21/25 6:47 PM, olcott wrote:
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
You could try, but it can't be done and allow for any reasonable
level of power in the logic. You basically need to have a system
that can only prove a finite number of facts, so you can check
that none of them are inconsistant.
On 3/21/25 5:33 AM, Richard Heathfield wrote:
On 21/03/2025 08:11, Mikko wrote:
<snip>
Another part of human knowledge is that there are fools that try to
argue against proven theorems.
Well, if it ain't proven it ain't yet a theorem. But is that enough?
The background to the work of Church, Turing, Gödel and the like is
Hilbert's second problem: "The compatibility of the arithmetical
axioms", and the background to /that/ problem is that in the late 19th
century mathematicians were occasionally coming up with proofs of X,
only to discover in the literature that not-X had already been proved.
The question then was which proof had the bug?
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in corner
cases like the Halting Problem, but Gödel's Hobgoblin hovers over
mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved that
it couldn't be proved to BE consistant within itself.
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in corner >>>> cases like the Halting Problem, but Gödel's Hobgoblin hovers over
mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved that
it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
On 21/03/2025 08:11, Mikko wrote:
<snip>
Another part of human knowledge is that there are fools that try to
argue against proven theorems.
Well, if it ain't proven it ain't yet a theorem. But is that enough?
The background to the work of Church, Turing, Gödel and the like is Hilbert's second problem: "The compatibility of the arithmetical
axioms", and the background to /that/ problem is that in the late 19th century mathematicians were occasionally coming up with proofs of X,
only to discover in the literature that not-X had already been proved.
The question then was which proof had the bug?
But what if they were /both/ right? It was an obvious worry, and so
arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
On 21/03/2025 23:48, Richard Damon wrote:
On 3/21/25 4:20 PM, Richard Heathfield wrote:
On 21/03/2025 19:30, Keith Thompson wrote:
My understanding is that Gödel proved that there are statements
that are true but not provable.
Yes. Incompleteness.
It's still not possible for both
X and not-X to be provable. If proofs exist for both, at least
one of the proofs must be flawed.
I'd be interested to see a proof of that conjecture.
It comes from the definition of consistency.
<sigh> So much for my sense of humour, which is showing distinct signs
of rust.
If something is provable, then it must be true, as the proof shows the
path from the fundamental truths the the stateemnt, establishing its
truth.
I am tempted to argue that we may instead deduce that one of the
fundamental truths isn't as true as it's supposed to be. But... peace! I
will not argue that, because it's the stuff that crankitude is made of,
and while crankinosity may be something I'd enjoy flirting with, I
simply don't have the time.
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:57 PM, olcott wrote:
On 3/21/2025 7:01 PM, Richard Damon wrote:
On 3/21/25 6:54 PM, olcott wrote:
On 3/21/2025 6:48 AM, Richard Damon wrote:
On 3/20/25 11:49 PM, olcott wrote:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:I am not talking about a trivially simple formal
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that >>>>>>>>>>>>>>>>>>>>> always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we >>>>>>>>>>>>>>>> can construct a statement x, which is only true it is >>>>>>>>>>>>>>>> the case that True(x) is false, but this interperetation >>>>>>>>>>>>>>>> can only be seen in the metalanguage created from the >>>>>>>>>>>>>>>> language in the proof, similar to Godel meta that >>>>>>>>>>>>>>>> generates the proof testing relationship that shows that >>>>>>>>>>>>>>>> G can only be true if it can not be proven as the >>>>>>>>>>>>>>>> existance of a number to make it false, becomes a proof >>>>>>>>>>>>>>>> that the statement is true and thus creates a
contradiction in the system.
That you can't understand that, or get confused by what >>>>>>>>>>>>>>>> is in the language, which your True predicate can look >>>>>>>>>>>>>>>> at, and in the metalanguage, which it can not, but still >>>>>>>>>>>>>>>> you make bold statements that you can not prove, and >>>>>>>>>>>>>>>> have been pointed out to be wrong, just shows how stupid >>>>>>>>>>>>>>>> you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is >>>>>>>>>>>>>>>> infinite in length.
But that isn't a logic system, so you are just proving >>>>>>>>>>>>>>>> your stupidity.
This never fails on the entire set of human general >>>>>>>>>>>>>>>>> knowledge that can be expressed using language. >>>>>>>>>>>>>>>>
Note, "The Entire set of Human General Knowledge" does >>>>>>>>>>>>>>>> not contain the contents of Meta-systems like Tarski >>>>>>>>>>>>>>>> uses, as there are an infinite number of them possible, >>>>>>>>>>>>>>>> and thus to even try to express them all requires an >>>>>>>>>>>>>>>> infinite number of axioms, and thus your system fails to >>>>>>>>>>>>>>>> meet the requirements. Once you don't have the meta- >>>>>>>>>>>>>>>> systems, Tarski proof can create a metasystem, that you >>>>>>>>>>>>>>>> system doesn't know about, which creates the problem >>>>>>>>>>>>>>>> statement.
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of >>>>>>>>>>>>>>>> such references.
And, even if it does detect it, what answer does True(x) >>>>>>>>>>>>>>>> produce when we have designed (via a metalanguage) that >>>>>>>>>>>>>>>> the statement x in the language will be true if and only >>>>>>>>>>>>>>>> if ! True(x), which he showed can be done in ANY system >>>>>>>>>>>>>>>> with sufficient power, which your universal system must >>>>>>>>>>>>>>>> have.
Sorry, you are just showing how little you understand >>>>>>>>>>>>>>>> what you are talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the >>>>>>>>>>>>>> first order logic
with equivalence and the following additional symbols: >>>>>>>>>>>>>
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU
DEFINITION. That would just be a set of axioms. Note, Logic >>>>>>>>>> system must also have a set of rules of relationships and how >>>>>>>>>> to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge. >>>>>>>>>>
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human >>>>>>>>>>>> Knowledge" isn't logically defined truth, but is just
"Emperical Knowledge", for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement >>>>>>>>>> whose truth is currently unknown, which it MUST be able to handle >>>>>>>>>>
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY >>>>>>>> to be the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you >>>>>>>> can't actually understand any logic system more coplicated than >>>>>>>> what Prolog can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Nope. Proven otherwise, and you are just showing your stupidity in >>>>>> maintaining that claim.
Then try and show ALL OF THE DETAILS OF how when one starts
with basic facts and only applies truth preserving operations that
True(X) is not always correct.
You have already shown that you don't understand the proof, so why
should I repeat it,
Look at Tarski's FULL paper (and the material he references) and see
how he develops the expression of x in the language, by working in
the metalanguage it embed the needed meaning into x
I have already specified a system that needs no
metalanguage because it has all of its full
semantics specified syntactically and I got
the essence of this idea from Gödel back in 2012
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
So, how do you assign the values to all the axioms via axioms?
You can't do it in the system, as it adds axioms that also need to be
numbered.
Please show how you can make a system with two "normal" axioms, plus
the axioms to assign numbers to every axiom in the system.
Remember, you need a finite number of axioms in the final system.
OK finally you are not rejecting what I say out-of-hand without review.
Categorically exhaustive reasoning does not ever delve into the weeds
of the details of hows something is accomplished until after there
is 100% complete understanding of what is to be accomplished why it
is to be accomplished.
I need you to first understand that the set of knowledge expressed
using language cannot possibly have any undecidability.
On 2025-03-21 09:33:12 +0000, Richard Heathfield said:
But what if they were /both/ right? It was an obvious worry,
and so arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
No, Gödel's proofs are about consistent theories. Whether
mathematics and in particular elementary arithmetic is
consistent remained undetermined.
On 3/21/2025 3:11 AM, Mikko wrote:
On 2025-03-21 03:49:14 +0000, olcott said:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never
showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates
the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false, >>>>>>>>>>>> becomes a proof that the statement is true and thus creates a >>>>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in the >>>>>>>>>>>> language, which your True predicate can look at, and in the >>>>>>>>>>>> metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows
how stupid you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length.
This never fails on the entire set of human general
knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity.
Note, "The Entire set of Human General Knowledge" does not contain the
contents of Meta-systems like Tarski uses, as there are an infinite
number of them possible, and thus to even try to express them all >>>>>>>>>>>> requires an infinite number of axioms, and thus your system fails to
meet the requirements. Once you don't have the meta- systems, Tarski
proof can create a metasystem, that you system doesn't know about, >>>>>>>>>>>> which creates the problem statement.
It is not fooled by pathological self-reference or
self-contradiction.
Of course it is, because it can't detect all forms of such references.
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the >>>>>>>>>>>> language will be true if and only if ! True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are >>>>>>>>>>>> talking about.
We need no metalanguage. A single formalized natural
language can express its own semantics as connections
between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION. >>>>>> That would just be a set of axioms. Note, Logic system must also have a >>>>>> set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>>>> isn't logically defined truth, but is just "Emperical Knowledge", for >>>>>>>> which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose >>>>>> truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be >>>> the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't
actually understand any logic system more coplicated than what Prolog
can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Of course it has. Meanings of the words "undecidability" and
"undefinability" and related words are a part of human knowledge,
and so are Gödel's completeness and incopleteness theorems as
well as Tarski's undefinability theorem.
My system has no undecidability or undefinability itself yet
can explain these issues with inferior systems.
On 3/21/25 9:57 PM, olcott wrote:
On 3/21/2025 7:01 PM, Richard Damon wrote:
On 3/21/25 6:54 PM, olcott wrote:
On 3/21/2025 6:48 AM, Richard Damon wrote:
On 3/20/25 11:49 PM, olcott wrote:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:I am not talking about a trivially simple formal
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates
the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false,
becomes a proof that the statement is true and thus creates a >>>>>>>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the >>>>>>>>>>>>>>> metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows
how stupid you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length.
But that isn't a logic system, so you are just proving your stupidity.
This never fails on the entire set of human general >>>>>>>>>>>>>>>> knowledge that can be expressed using language. >>>>>>>>>>>>>>>
Note, "The Entire set of Human General Knowledge" does not contain the
contents of Meta-systems like Tarski uses, as there are an infinite
number of them possible, and thus to even try to express them all
requires an infinite number of axioms, and thus your system fails to
meet the requirements. Once you don't have the meta- systems, Tarski
proof can create a metasystem, that you system doesn't know about,
which creates the problem statement.
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of such references.
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the
language will be true if and only if ! True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are
talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols: >>>>>>>>>>>>
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION. >>>>>>>>> That would just be a set of axioms. Note, Logic system must also have a
set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>>>>>>> isn't logically defined truth, but is just "Emperical Knowledge", for
which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose >>>>>>>>> truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be >>>>>>> the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't >>>>>>> actually understand any logic system more coplicated than what Prolog >>>>>>> can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Nope. Proven otherwise, and you are just showing your stupidity in
maintaining that claim.
Then try and show ALL OF THE DETAILS OF how when one starts
with basic facts and only applies truth preserving operations that
True(X) is not always correct.
You have already shown that you don't understand the proof, so why
should I repeat it,
Look at Tarski's FULL paper (and the material he references) and see
how he develops the expression of x in the language, by working in the
metalanguage it embed the needed meaning into x
I have already specified a system that needs no
metalanguage because it has all of its full
semantics specified syntactically and I got
the essence of this idea from Gödel back in 2012
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
So, how do you assign the values to all the axioms via axioms?
You can't do it in the system, as it adds axioms that also need to be numbered.
Please show how you can make a system with two "normal" axioms, plus
the axioms to assign numbers to every axiom in the system.
Remember, you need a finite number of axioms in the final system.
On 3/22/2025 7:05 AM, Mikko wrote:
On 2025-03-21 22:47:04 +0000, olcott said:
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and so >>>>>> arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in corner >>>>>> cases like the Halting Problem, but Gödel's Hobgoblin hovers over >>>>>> mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved that >>>>> it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
That is possible. An example is Horn clauses, which is the theory behind
Prolog. If the logic has no negation operator there is no posiibility to
express an inconsistency. But even then the question whether there is an
unprovable sentence is problematic.
The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.
On 3/22/2025 7:05 AM, Mikko wrote:
On 2025-03-21 22:47:04 +0000, olcott said:
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and
so arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be.
Fortunately, to date inconsistency has tended to surface only in
corner cases like the Halting Problem, but Gödel's Hobgoblin
hovers over mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved
that it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
That is possible. An example is Horn clauses, which is the theory behind
Prolog. If the logic has no negation operator there is no posiibility to
express an inconsistency. But even then the question whether there is an
unprovable sentence is problematic.
The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.
This system is somewhat similar to the restrictions that
ZFC set theory places on the creation of sets.
On 2025-03-22 02:31:23 +0000, Richard Damon said:
On 3/21/25 9:57 PM, olcott wrote:
On 3/21/2025 7:01 PM, Richard Damon wrote:
On 3/21/25 6:54 PM, olcott wrote:
On 3/21/2025 6:48 AM, Richard Damon wrote:
On 3/20/25 11:49 PM, olcott wrote:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:I am not talking about a trivially simple formal
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that >>>>>>>>>>>>>>>>>>>>> always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we >>>>>>>>>>>>>>>> can construct a statement x, which is only true it is >>>>>>>>>>>>>>>> the case that True(x) is false, but this interperetation >>>>>>>>>>>>>>>> can only be seen in the metalanguage created from the >>>>>>>>>>>>>>>> language in the proof, similar to Godel meta that >>>>>>>>>>>>>>>> generates the proof testing relationship that shows that >>>>>>>>>>>>>>>> G can only be true if it can not be proven as the >>>>>>>>>>>>>>>> existance of a number to make it false, becomes a proof >>>>>>>>>>>>>>>> that the statement is true and thus creates a
contradiction in the system.
That you can't understand that, or get confused by what >>>>>>>>>>>>>>>> is in the language, which your True predicate can look >>>>>>>>>>>>>>>> at, and in the metalanguage, which it can not, but still >>>>>>>>>>>>>>>> you make bold statements that you can not prove, and >>>>>>>>>>>>>>>> have been pointed out to be wrong, just shows how stupid >>>>>>>>>>>>>>>> you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is >>>>>>>>>>>>>>>> infinite in length.
But that isn't a logic system, so you are just proving >>>>>>>>>>>>>>>> your stupidity.
This never fails on the entire set of human general >>>>>>>>>>>>>>>>> knowledge that can be expressed using language. >>>>>>>>>>>>>>>>
Note, "The Entire set of Human General Knowledge" does >>>>>>>>>>>>>>>> not contain the contents of Meta-systems like Tarski >>>>>>>>>>>>>>>> uses, as there are an infinite number of them possible, >>>>>>>>>>>>>>>> and thus to even try to express them all requires an >>>>>>>>>>>>>>>> infinite number of axioms, and thus your system fails to >>>>>>>>>>>>>>>> meet the requirements. Once you don't have the meta- >>>>>>>>>>>>>>>> systems, Tarski proof can create a metasystem, that you >>>>>>>>>>>>>>>> system doesn't know about, which creates the problem >>>>>>>>>>>>>>>> statement.
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of >>>>>>>>>>>>>>>> such references.
And, even if it does detect it, what answer does True(x) >>>>>>>>>>>>>>>> produce when we have designed (via a metalanguage) that >>>>>>>>>>>>>>>> the statement x in the language will be true if and only >>>>>>>>>>>>>>>> if ! True(x), which he showed can be done in ANY system >>>>>>>>>>>>>>>> with sufficient power, which your universal system must >>>>>>>>>>>>>>>> have.
Sorry, you are just showing how little you understand >>>>>>>>>>>>>>>> what you are talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the >>>>>>>>>>>>>> first order logic
with equivalence and the following additional symbols: >>>>>>>>>>>>>
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU
DEFINITION. That would just be a set of axioms. Note, Logic >>>>>>>>>> system must also have a set of rules of relationships and how >>>>>>>>>> to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge. >>>>>>>>>>
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human >>>>>>>>>>>> Knowledge" isn't logically defined truth, but is just
"Emperical Knowledge", for which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement >>>>>>>>>> whose truth is currently unknown, which it MUST be able to handle >>>>>>>>>>
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY >>>>>>>> to be the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you >>>>>>>> can't actually understand any logic system more coplicated than >>>>>>>> what Prolog can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Nope. Proven otherwise, and you are just showing your stupidity in >>>>>> maintaining that claim.
Then try and show ALL OF THE DETAILS OF how when one starts
with basic facts and only applies truth preserving operations that
True(X) is not always correct.
You have already shown that you don't understand the proof, so why
should I repeat it,
Look at Tarski's FULL paper (and the material he references) and see
how he develops the expression of x in the language, by working in
the metalanguage it embed the needed meaning into x
I have already specified a system that needs no
metalanguage because it has all of its full
semantics specified syntactically and I got
the essence of this idea from Gödel back in 2012
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
So, how do you assign the values to all the axioms via axioms?
You can't do it in the system, as it adds axioms that also need to be
numbered.
Please show how you can make a system with two "normal" axioms, plus
the axioms to assign numbers to every axiom in the system.
Remember, you need a finite number of axioms in the final system.
For Gödel's and Tarski's proofs the set of the axioms need not be
finite. If is sufficient that there is a method to determine whether
a sentence is an axiom.
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:00 AM, olcott wrote:
On 3/22/2025 7:05 AM, Mikko wrote:
On 2025-03-21 22:47:04 +0000, olcott said:
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and >>>>>>>> so arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be. >>>>>>>>
Fortunately, to date inconsistency has tended to surface only in >>>>>>>> corner cases like the Halting Problem, but Gödel's Hobgoblin
hovers over mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved >>>>>>> that it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
That is possible. An example is Horn clauses, which is the theory
behind
Prolog. If the logic has no negation operator there is no
posiibility to
express an inconsistency. But even then the question whether there
is an
unprovable sentence is problematic.
The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.
So, your logic doesn't allow us to express the Goldbach conjecture in it?
We can't express the logic of Turing Machines?
The body of general knowledge that can be expressed in
language (is the actual body of general knowledge that
can be expressed in language) thus includes every tiny
detail about the Goldbach conjecture.
I never defined "general" knowledge thus your critique
is apt. I had to make the set of basic facts finite
that is why I limited them to general knowledge.
What it does not have is a set of truth preserving
operations from basic facts to a truth value of TRUE.
Is the Goldbach Conjecture known to be True? No.
It seems you are removing large swaths of "Human Knowledge" from your
system.
This system is somewhat similar to the restrictions that
ZFC set theory places on the creation of sets.
Nope. You might think so, but only because you don't understand what
you are saying.
The only way to prevent the formation of unprovable expressions is to
make your system too weak to be able to create the basic properties of
the Natural Number system.
On 3/22/2025 10:54 AM, Mikko wrote:
On 2025-03-22 15:00:44 +0000, olcott said:
On 3/22/2025 7:05 AM, Mikko wrote:
On 2025-03-21 22:47:04 +0000, olcott said:
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
But what if they were /both/ right? It was an obvious worry, and so >>>>>>>> arose the great question: is mathematics consistent?
And Gödel proved not only that it isn't, but that it can't be. >>>>>>>>
Fortunately, to date inconsistency has tended to surface only in corner
cases like the Halting Problem, but Gödel's Hobgoblin hovers over >>>>>>>> mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He proved that >>>>>>> it couldn't be proved to BE consistant within itself.
Yes, I rather overstated the case. Sorry about that.
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
That is possible. An example is Horn clauses, which is the theory behind >>>> Prolog. If the logic has no negation operator there is no posiibility to >>>> express an inconsistency. But even then the question whether there is an >>>> unprovable sentence is problematic.
The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.
There are unprovable expressions that may in future be in the body
of expressible human general knowledge.
The body of knowledge excludes unknown things that are
instantly added to this set as soon as they are known.
On 3/22/2025 9:18 AM, Mikko wrote:
On 2025-03-21 13:52:38 +0000, olcott said:
On 3/21/2025 3:11 AM, Mikko wrote:
On 2025-03-21 03:49:14 +0000, olcott said:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates
the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false, >>>>>>>>>>>>>> becomes a proof that the statement is true and thus creates a >>>>>>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the >>>>>>>>>>>>>> metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows
how stupid you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length.
This never fails on the entire set of human general >>>>>>>>>>>>>>> knowledge that can be expressed using language.
But that isn't a logic system, so you are just proving your stupidity.
Note, "The Entire set of Human General Knowledge" does not contain the
contents of Meta-systems like Tarski uses, as there are an infinite
number of them possible, and thus to even try to express them all
requires an infinite number of axioms, and thus your system fails to
meet the requirements. Once you don't have the meta- systems, Tarski
proof can create a metasystem, that you system doesn't know about,
which creates the problem statement.
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of such references.
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the
language will be true if and only if ! True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are
talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols:
I am not talking about a trivially simple formal
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION. >>>>>>>> That would just be a set of axioms. Note, Logic system must also have a
set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge.
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>>>>>> isn't logically defined truth, but is just "Emperical Knowledge", for
which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose >>>>>>>> truth is currently unknown, which it MUST be able to handle
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be >>>>>> the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't >>>>>> actually understand any logic system more coplicated than what Prolog >>>>>> can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Of course it has. Meanings of the words "undecidability" and
"undefinability" and related words are a part of human knowledge,
and so are Gödel's completeness and incopleteness theorems as
well as Tarski's undefinability theorem.
My system has no undecidability or undefinability itself yet
can explain these issues with inferior systems.
That is not proven. Nor is proven that your system is consistent.
Nor that your system exists.
The definition of the set of every element of human
general knowledge that can be expressed using language
prevents inconsistency, incompleteness and undecidability
within this set.
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 4:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:00 AM, olcott wrote:
On 3/22/2025 7:05 AM, Mikko wrote:
On 2025-03-21 22:47:04 +0000, olcott said:
On 3/21/2025 3:10 PM, Richard Heathfield wrote:
On 21/03/2025 11:48, Richard Damon wrote:
On 3/21/25 5:33 AM, Richard Heathfield wrote:
<snip>
Yes, I rather overstated the case. Sorry about that.
But what if they were /both/ right? It was an obvious worry, >>>>>>>>>> and so arose the great question: is mathematics consistent? >>>>>>>>>>
And Gödel proved not only that it isn't, but that it can't be. >>>>>>>>>>
Fortunately, to date inconsistency has tended to surface only >>>>>>>>>> in corner cases like the Halting Problem, but Gödel's
Hobgoblin hovers over mathematics to this day.
Godel didn't prove that Mathematics wasn't consistent. He
proved that it couldn't be proved to BE consistant within itself. >>>>>>>>
Or we could simply define the rules for constructing a
formal system such that inconsistency cannot exist.
That is possible. An example is Horn clauses, which is the theory
behind
Prolog. If the logic has no negation operator there is no
posiibility to
express an inconsistency. But even then the question whether there >>>>>> is an
unprovable sentence is problematic.
The body of human general knowledge that can be expressed
in language cannot possibly have any unprovable expressions
when truth preserving operations are the only category of
inference steps allowed.
So, your logic doesn't allow us to express the Goldbach conjecture
in it?
We can't express the logic of Turing Machines?
The body of general knowledge that can be expressed in
language (is the actual body of general knowledge that
can be expressed in language) thus includes every tiny
detail about the Goldbach conjecture.
Right, but knowing all the details doesn't get us the answer, we KNOW
all the details that define the problem, we just can't test every
number to see if it holds.
Part of the set of all general knowledge that can be
expressed using language is all of the details of
unsolved problems. It will know that no one knows
whether the Goldbach conjecture is true.
I never defined "general" knowledge thus your critique
is apt. I had to make the set of basic facts finite
that is why I limited them to general knowledge.
And either those define the basis of the Natural Numbers, at which
point the various theorem will hold, or you don't at which point your
How do you say:
"I was going to go to the store to buy some vanilla
ice cream but they only had chocolate so I bought
a slice of Pizza instead" in arithmetic?
What it does not have is a set of truth preserving
operations from basic facts to a truth value of TRUE.
Is the Goldbach Conjecture known to be True? No.
But the question is NOT "is it KNOWN to be True?" but "is it True?"
Then the answer is "no one knows".
The answer to the question: "What time is it (yes or no)?"
is that question is rejected as incorrect.
Thus, you demonstrate that your whole argument is based on the FRAUD
of a STRAWMAN, and that you are just too stupid to understand the
difference between TRUTH and KNOWLEDGE.
I don't think that you are too stupid to know that you are lying.
You are certainly not stupid.
On 3/22/2025 9:53 PM, Richard Damon wrote:Except for its truth.
On 3/22/25 4:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:00 AM, olcott wrote:
The body of general knowledge that can be expressed in language (isThe body of human general knowledge that can be expressed inSo, your logic doesn't allow us to express the Goldbach conjecture in
language cannot possibly have any unprovable expressions when truth
preserving operations are the only category of inference steps
allowed.
it? We can't express the logic of Turing Machines?
the actual body of general knowledge that can be expressed in
language) thus includes every tiny detail about the Goldbach
conjecture.
I.e. it doesn't know.Right, but knowing all the details doesn't get us the answer, we KNOWPart of the set of all general knowledge that can be expressed using
all the details that define the problem, we just can't test every
number to see if it holds.
language is all of the details of unsolved problems. It will know that
no one knows whether the Goldbach conjecture is true.
That's not an answer.Then the answer is "no one knows".What it does not have is a set of truth preserving operations fromBut the question is NOT "is it KNOWN to be True?" but "is it True?"
basic facts to a truth value of TRUE. Is the Goldbach Conjecture known
to be True? No.
On 3/23/2025 4:19 AM, Mikko wrote:Last I heard, we didn't know everything.
On 2025-03-22 15:19:26 +0000, olcott said:
On 3/22/2025 9:18 AM, Mikko wrote:
On 2025-03-21 13:52:38 +0000, olcott said:
On 3/21/2025 3:11 AM, Mikko wrote:
On 2025-03-21 03:49:14 +0000, olcott said:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:
On 3/18/2025 8:14 AM, Mikko wrote:
The set of human general knowledge that can be expressed using languageIt prevents completeness.The definition of the set of every element of human general knowledgeThat is not proven. Nor is proven that your system is consistent.My system has no undecidability or undefinability itself yet canOf course it has. Meanings of the words "undecidability" andThis concise specification is air-tight.And thus you just admitted that your system doesn't even QUALIFY >>>>>>>> to be the system that Tarski is talking about.It employs the same algorithm as Prolog:Of course not, as then True(x) just can't handle a statement >>>>>>>>>> whose truth is currently unknown, which it MUST be able to >>>>>>>>>> handlePart of the problem is that most of what we call "Human >>>>>>>>>>>> Knowledge" isn't logically defined truth, but is justThe set of human knowledge that can be expressed in language >>>>>>>>>>> provides the means to compute True(X).
"Emperical Knowledge", for which we
Can X be proven on the basis of Facts?
You don't seem to understand that fact, because apparently you >>>>>>>> can't actually understand any logic system more coplicated than >>>>>>>> what Prolog can handle.
The set of all human general knowledge that can be expressed using >>>>>>> language has no undecidability or undefinability.
"undefinability" and related words are a part of human knowledge,
and so are Gödel's completeness and incopleteness theorems as well >>>>>> as Tarski's undefinability theorem.
explain these issues with inferior systems.
Nor that your system exists.
that can be expressed using language prevents inconsistency,
incompleteness and undecidability within this set.
is ALWAYS complete by definition.
It won't contain every truth, though.There are expressions that could be elements of human general knowledgeWe can imagine a single formal system that contains every element of the
but aren't.
But human general knowledge is not a theory because there is no way to
know about every expressible claim whether its known to be true.
set of human knowledge that can be expressed in language.
On 3/23/2025 4:19 AM, Mikko wrote:
On 2025-03-22 15:19:26 +0000, olcott said:
On 3/22/2025 9:18 AM, Mikko wrote:
On 2025-03-21 13:52:38 +0000, olcott said:
On 3/21/2025 3:11 AM, Mikko wrote:
On 2025-03-21 03:49:14 +0000, olcott said:
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 6:14 PM, olcott wrote:
On 3/19/2025 8:59 PM, Richard Damon wrote:
On 3/19/25 5:50 PM, olcott wrote:
On 3/18/2025 10:04 PM, Richard Damon wrote:
On 3/18/25 9:36 AM, olcott wrote:Unless you bother to pay attention to the details
On 3/18/2025 8:14 AM, Mikko wrote:
On 2025-03-17 15:40:22 +0000, olcott said:I am not talking about a trivially simple formal
On 3/16/2025 9:51 PM, Richard Damon wrote:
On 3/16/25 9:50 PM, olcott wrote:
On 3/16/2025 5:50 PM, Richard Damon wrote:
On 3/16/25 11:12 AM, olcott wrote:
On 3/16/2025 7:36 AM, joes wrote:
Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott: >>>>>>>>>>>>>>>>>>>>>
We can define a correct True(X) predicate that always succeeds except
for unknowns and untruths, Tarski WAS WRONG !!! >>>>>>>>>>>>>>>>>>>> That does not disprove Tarski.
He said that this is impossible and no
counter-examples exists that shows that I am wrong. >>>>>>>>>>>>>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown >>>>>>>>>>>>>>>>>>> True(LP) == FALSE Not a truth-bearer
But if x is what you are saying is
A True(X) predicate can be defined and Tarski never >>>>>>>>>>>>>>>>> showed that it cannot.
Sure he did. Using a mathematical system like Godel, we can construct a
statement x, which is only true it is the case that True(x) is false,
but this interperetation can only be seen in the metalanguage created
from the language in the proof, similar to Godel meta that generates
the proof testing relationship that shows that G can only be true if it
can not be proven as the existance of a number to make it false,
becomes a proof that the statement is true and thus creates a >>>>>>>>>>>>>>>> contradiction in the system.
That you can't understand that, or get confused by what is in the
language, which your True predicate can look at, and in the >>>>>>>>>>>>>>>> metalanguage, which it can not, but still you make bold statements that
you can not prove, and have been pointed out to be wrong, just shows
how stupid you are.
True(X) only returns TRUE when a a sequence of truth >>>>>>>>>>>>>>>>> preserving operations can derive X from the set of basic >>>>>>>>>>>>>>>>> facts and returns false otherwise.
Right, but needs to do so even if the path to x is infinite in length.
But that isn't a logic system, so you are just proving your stupidity.
This never fails on the entire set of human general >>>>>>>>>>>>>>>>> knowledge that can be expressed using language. >>>>>>>>>>>>>>>>
Note, "The Entire set of Human General Knowledge" does not contain the
contents of Meta-systems like Tarski uses, as there are an infinite
number of them possible, and thus to even try to express them all
requires an infinite number of axioms, and thus your system fails to
meet the requirements. Once you don't have the meta- systems, Tarski
proof can create a metasystem, that you system doesn't know about,
which creates the problem statement.
It is not fooled by pathological self-reference or >>>>>>>>>>>>>>>>> self-contradiction.
Of course it is, because it can't detect all forms of such references.
And, even if it does detect it, what answer does True(x) produce when
we have designed (via a metalanguage) that the statement x in the
language will be true if and only if ! True(x), which he showed can be
done in ANY system with sufficient power, which your universal system
must have.
Sorry, you are just showing how little you understand what you are
talking about.
We need no metalanguage. A single formalized natural >>>>>>>>>>>>>>> language can express its own semantics as connections >>>>>>>>>>>>>>> between expressions of this same language.
A nice formal language has the symbols and syntax of the first order logic
with equivalence and the following additional symbols: >>>>>>>>>>>>>
language. I am talking about very significant
extensions to something like Montague grammar.
The language must be expressive enough to fully
encode any and all details of each element of the
entire body of human general knowledge that can
be expressed using language. Davidson semantics
provides another encoding.
But "encoding" knowledge, isn't a logic system.
of how this of encoded.
But "Encoded Knowledge" isn't a logic system. PERIOD. BYU DEFINITION.
That would just be a set of axioms. Note, Logic system must also have a
set of rules of relationships and how to manipulate them,
Yes stupid I already specified those 150 times.
TRUTH PRESERVING OPERATIONS.
and that needs more that just expressing them as knowledge. >>>>>>>>>>
NOT AT ALL DUMB BUNNY, for all the expressions
that are proved completely true entirely on the basis of
their meaning expressed in language they only need a
connection this semantic meaning to prove that they
are true.
Part of the problem is that most of what we call "Human Knowledge" >>>>>>>>>>>> isn't logically defined truth, but is just "Emperical Knowledge", for
which we
The set of human knowledge that can be expressed
in language provides the means to compute True(X).
Of course not, as then True(x) just can't handle a statement whose >>>>>>>>>> truth is currently unknown, which it MUST be able to handle >>>>>>>>>>
It employs the same algorithm as Prolog:
Can X be proven on the basis of Facts?
And thus you just admitted that your system doesn't even QUALIFY to be >>>>>>>> the system that Tarski is talking about.
You don't seem to understand that fact, because apparently you can't >>>>>>>> actually understand any logic system more coplicated than what Prolog >>>>>>>> can handle.
This concise specification is air-tight.
The set of all human general knowledge that can be expressed
using language has no undecidability or undefinability.
Of course it has. Meanings of the words "undecidability" and
"undefinability" and related words are a part of human knowledge,
and so are Gödel's completeness and incopleteness theorems as
well as Tarski's undefinability theorem.
My system has no undecidability or undefinability itself yet
can explain these issues with inferior systems.
That is not proven. Nor is proven that your system is consistent.
Nor that your system exists.
The definition of the set of every element of human
general knowledge that can be expressed using language
prevents inconsistency, incompleteness and undecidability
within this set.
It prevents completeness.
The set of human general knowledge that can be expressed
using language is ALWAYS complete by definition.
There are expressions that could be elements
of human general knowledge but aren't.
But human general knowledge is not a theory because there is no way to
know about every expressible claim whether its known to be true.
We can imagine a single formal system that contains
every element of the set of human knowledge that can
be expressed in language.
In such a system a True(X) predicate would already be
implicitly defined.
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