On 1/19/2023 8:34 PM, Richard Damon wrote:
> On 1/19/23 2:12 PM, olcott wrote:
>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>> On 1/17/23 11:39 AM, olcott wrote:
>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can
>>>>> use infinte sets oc connections, proofs can't. Only YOU have
>>>>> perposed that we think about infinite proofs.
>>>>>
>>>>
>>>> Formal systems cannot ever use infinite connections from their
>>>> expressions of language to their truth maker axioms thus eliminating
>>>> these from consideration as any measure of true "in the system".
>>>>
>>>>
>>>
>>>
>>> Source? or is this just another of your made up "Facts"
>>>
>>
>> You can't even remember that you said this?
>
> No, I said they can't have infinite PROOFS, not infinite connections to
> Truth.
>>
>>> WHERE in the definition of a "Formal System" does it say that the
>>> connecti0on must be finite.
>>
>> You said that formal system cannot have infinite proofs.
>> Did you change your mind?
>
> Right ***PROOF*** not ***TRUTH***
>
> Truth can be based on an infinite chain of connections, proofs can not.

Truth *in a formal system* cannot be based on infinite connections
because formal systems are not allowed to have infinite connections.

Haskell Curry establishes that truth in a theory (AKA formal system) is
anchored in the elementary theorems (AKA axioms) of this formal system.

A theory (over (f) is defined as a conceptual class of these elementary
statements. Let::t be such a theory. Then the elementary statements
which belong to ::t we shall call the elementary theorems of::t; we also
say that these elementary statements are true for::t. Thus, given ::t,
an elementary theorem is an elementary statement which is true. A theory
is thus a way of picking out from the statements of (f a certain
subclass of true statements.
https://www.liarparadox.org/Haskell_Curry_45.pdf

Perhaps you believe that you are enormously much brighter than Haskell
Curry ?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/20/23 2:31 PM, olcott wrote:
> On 1/19/2023 8:34 PM, Richard Damon wrote:
>> On 1/19/23 2:12 PM, olcott wrote:
>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can
>>>>>> use infinte sets oc connections, proofs can't. Only YOU have
>>>>>> perposed that we think about infinite proofs.
>>>>>>
>>>>>
>>>>> Formal systems cannot ever use infinite connections from their
>>>>> expressions of language to their truth maker axioms thus eliminating
>>>>> these from consideration as any measure of true "in the system".
>>>>>
>>>>>
>>>>
>>>>
>>>> Source? or is this just another of your made up "Facts"
>>>>
>>>
>>> You can't even remember that you said this?
>>
>> No, I said they can't have infinite PROOFS, not infinite connections
>> to Truth.
>>>
>>>> WHERE in the definition of a "Formal System" does it say that the
>>>> connecti0on must be finite.
>>>
>>> You said that formal system cannot have infinite proofs.
>>> Did you change your mind?
>>
>> Right ***PROOF*** not ***TRUTH***
>>
>> Truth can be based on an infinite chain of connections, proofs can not.
>
> Truth *in a formal system* cannot be based on infinite connections
> because formal systems are not allowed to have infinite connections.

Says Who ***FOR TRUTH***

You reference does not provide that data, so I guess you are just making
it up, and thus showing you to be a LIAR.

>
> Haskell Curry establishes that truth in a theory (AKA formal system) is
> anchored in the elementary theorems (AKA axioms) of this formal system.

Right, ANCHORED TO, not limited to. Statments other than the elementary
theorems are True, and they are true if they have a connection (not
limited to finite) to these Truths.

Where does he say True statements must have a FINITE connection to the
elementary theorems.

>
> A theory (over (f) is defined as a conceptual class of these elementary
> statements. Let::t be such a theory. Then the elementary statements
> which belong to ::t we shall call the elementary theorems of::t; we also
> say that these elementary statements are true for::t. Thus, given ::t,
> an elementary theorem is an elementary statement which is true. A theory
> is thus a way of picking out from the statements of (f a certain
> subclass of true statements.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
> Perhaps you believe that you are enormously much brighter than Haskell
> Curry ?
>

You don't understand what he is saying,

He is saying these statements are True in F, as a given. They are (in
other words) the AXIOMS for the Theory, that distinguesh this Theory
from other Theoris.

They are not the sum total of all Truths in the Theory.

Note, the "Elementary Statements" are NOT a listing of every possible,
as he says:

> The statements of (f are called elementary statements to distinguish them from other stateents which we may form from them

Thus, there are statements which are NOT "elementary stateements" and
these statements can be True, but not "elementary theorems" if they are
connected to the "elementary theorems", but that connection is NOT
limited to be finite for the statement to be True, only Provable.

On 1/20/2023 2:46 PM, Richard Damon wrote:
> On 1/20/23 2:31 PM, olcott wrote:
>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>> On 1/19/23 2:12 PM, olcott wrote:
>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can
>>>>>>> use infinte sets oc connections, proofs can't. Only YOU have
>>>>>>> perposed that we think about infinite proofs.
>>>>>>>
>>>>>>
>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>> expressions of language to their truth maker axioms thus eliminating
>>>>>> these from consideration as any measure of true "in the system".
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> Source? or is this just another of your made up "Facts"
>>>>>
>>>>
>>>> You can't even remember that you said this?
>>>
>>> No, I said they can't have infinite PROOFS, not infinite connections
>>> to Truth.
>>>>
>>>>> WHERE in the definition of a "Formal System" does it say that the
>>>>> connecti0on must be finite.
>>>>
>>>> You said that formal system cannot have infinite proofs.
>>>> Did you change your mind?
>>>
>>> Right ***PROOF*** not ***TRUTH***
>>>
>>> Truth can be based on an infinite chain of connections, proofs can not.
>>
>> Truth *in a formal system* cannot be based on infinite connections
>> because formal systems are not allowed to have infinite connections.
>
> Says Who ***FOR TRUTH***
>
> You reference does not provide that data, so I guess you are just making
> it up, and thus showing you to be a LIAR.
>
>>
>> Haskell Curry establishes that truth in a theory (AKA formal system)
>> is anchored in the elementary theorems (AKA axioms) of this formal
>> system.
>
> Right, ANCHORED TO, not limited to. Statments other than the elementary
> theorems are True, and they are true if they have a connection (not
> limited to finite) to these Truths.
>
> Where does he say True statements must have a FINITE connection to the
> elementary theorems.
>
>>
>> A theory (over (f) is defined as a conceptual class of these elementary
>> statements. Let::t be such a theory. Then the elementary statements
>> which belong to ::t we shall call the elementary theorems of::t; we also
>> say that these elementary statements are true for::t. Thus, given ::t,
>> an elementary theorem is an elementary statement which is true. A theory
>> is thus a way of picking out from the statements of (f a certain
>> subclass of true statements.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>> Perhaps you believe that you are enormously much brighter than Haskell
>> Curry ?
>>
>
> You don't understand what he is saying,
>
> He is saying these statements are True in F, as a given.

Wrongo !!!

The terminology which has just been used implies that the
elementary statements are not such that their truth and
falsity are known to us without reference to::t.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/20/23 5:02 PM, olcott wrote:
> On 1/20/2023 2:46 PM, Richard Damon wrote:
>> On 1/20/23 2:31 PM, olcott wrote:
>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth can
>>>>>>>> use infinte sets oc connections, proofs can't. Only YOU have
>>>>>>>> perposed that we think about infinite proofs.
>>>>>>>>
>>>>>>>
>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>> expressions of language to their truth maker axioms thus eliminating
>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>
>>>>>
>>>>> You can't even remember that you said this?
>>>>
>>>> No, I said they can't have infinite PROOFS, not infinite connections
>>>> to Truth.
>>>>>
>>>>>> WHERE in the definition of a "Formal System" does it say that the
>>>>>> connecti0on must be finite.
>>>>>
>>>>> You said that formal system cannot have infinite proofs.
>>>>> Did you change your mind?
>>>>
>>>> Right ***PROOF*** not ***TRUTH***
>>>>
>>>> Truth can be based on an infinite chain of connections, proofs can not.
>>>
>>> Truth *in a formal system* cannot be based on infinite connections
>>> because formal systems are not allowed to have infinite connections.
>>
>> Says Who ***FOR TRUTH***
>>
>> You reference does not provide that data, so I guess you are just
>> making it up, and thus showing you to be a LIAR.
>>
>>>
>>> Haskell Curry establishes that truth in a theory (AKA formal system)
>>> is anchored in the elementary theorems (AKA axioms) of this formal
>>> system.
>>
>> Right, ANCHORED TO, not limited to. Statments other than the
>> elementary theorems are True, and they are true if they have a
>> connection (not limited to finite) to these Truths.
>>
>> Where does he say True statements must have a FINITE connection to the
>> elementary theorems.
>>
>>>
>>> A theory (over (f) is defined as a conceptual class of these elementary
>>> statements. Let::t be such a theory. Then the elementary statements
>>> which belong to ::t we shall call the elementary theorems of::t; we also
>>> say that these elementary statements are true for::t. Thus, given ::t,
>>> an elementary theorem is an elementary statement which is true. A theory
>>> is thus a way of picking out from the statements of (f a certain
>>> subclass of true statements.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>> Perhaps you believe that you are enormously much brighter than
>>> Haskell Curry ?
>>>
>>
>> You don't understand what he is saying,
>>
>> He is saying these statements are True in F, as a given.
>
> Wrongo !!!
>
>    The terminology which has just been used implies that the
>    elementary statements are not such that their truth and
>    falsity are known to us without reference to::t.
>
>

Right, they aren't just true in the Statement class, but are only
considerdd true because we are in the Theory F.

Thus they are not "Universally" True in all domains, but just considered
true for F.

This also means your concept of "Semantics" needs to be adapted, as this
means that the meaning of some words change "meaning" based on the
Theory we are in.

This is like the Parrallel Postulate, if F is "Plane Geometry", it is
considered True, if we are in some other Theory, like Spherical
Geometry, it isn't true.

You are just showing your stupdity of not understanding what he is
talking ablut.

On 1/20/2023 4:09 PM, Richard Damon wrote:
> On 1/20/23 5:02 PM, olcott wrote:
>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>> On 1/20/23 2:31 PM, olcott wrote:
>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>> eliminating
>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>
>>>>>>
>>>>>> You can't even remember that you said this?
>>>>>
>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>> connections to Truth.
>>>>>>
>>>>>>> WHERE in the definition of a "Formal System" does it say that the
>>>>>>> connecti0on must be finite.
>>>>>>
>>>>>> You said that formal system cannot have infinite proofs.
>>>>>> Did you change your mind?
>>>>>
>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>
>>>>> Truth can be based on an infinite chain of connections, proofs can
>>>>> not.
>>>>
>>>> Truth *in a formal system* cannot be based on infinite connections
>>>> because formal systems are not allowed to have infinite connections.
>>>
>>> Says Who ***FOR TRUTH***
>>>
>>> You reference does not provide that data, so I guess you are just
>>> making it up, and thus showing you to be a LIAR.
>>>
>>>>
>>>> Haskell Curry establishes that truth in a theory (AKA formal system)
>>>> is anchored in the elementary theorems (AKA axioms) of this formal
>>>> system.
>>>
>>> Right, ANCHORED TO, not limited to. Statments other than the
>>> elementary theorems are True, and they are true if they have a
>>> connection (not limited to finite) to these Truths.
>>>
>>> Where does he say True statements must have a FINITE connection to
>>> the elementary theorems.
>>>
>>>>
>>>> A theory (over (f) is defined as a conceptual class of these elementary
>>>> statements. Let::t be such a theory. Then the elementary statements
>>>> which belong to ::t we shall call the elementary theorems of::t; we
>>>> also
>>>> say that these elementary statements are true for::t. Thus, given ::t,
>>>> an elementary theorem is an elementary statement which is true. A
>>>> theory
>>>> is thus a way of picking out from the statements of (f a certain
>>>> subclass of true statements.
>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>
>>>> Perhaps you believe that you are enormously much brighter than
>>>> Haskell Curry ?
>>>>
>>>
>>> You don't understand what he is saying,
>>>
>>> He is saying these statements are True in F, as a given.
>>
>> Wrongo !!!
>>
>>     The terminology which has just been used implies that the
>>     elementary statements are not such that their truth and
>>     falsity are known to us without reference to::t.
>>
>>
>
> Right, they aren't just true in the Statement class, but are only
> considerdd true because we are in the Theory F.
>

F is not the theory T is the theory.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/20/23 5:16 PM, olcott wrote:
> On 1/20/2023 4:09 PM, Richard Damon wrote:
>> On 1/20/23 5:02 PM, olcott wrote:
>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>> eliminating
>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>
>>>>>>>
>>>>>>> You can't even remember that you said this?
>>>>>>
>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>> connections to Truth.
>>>>>>>
>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>> the connecti0on must be finite.
>>>>>>>
>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>> Did you change your mind?
>>>>>>
>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>
>>>>>> Truth can be based on an infinite chain of connections, proofs can
>>>>>> not.
>>>>>
>>>>> Truth *in a formal system* cannot be based on infinite connections
>>>>> because formal systems are not allowed to have infinite connections.
>>>>
>>>> Says Who ***FOR TRUTH***
>>>>
>>>> You reference does not provide that data, so I guess you are just
>>>> making it up, and thus showing you to be a LIAR.
>>>>
>>>>>
>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>> system) is anchored in the elementary theorems (AKA axioms) of this
>>>>> formal system.
>>>>
>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>> elementary theorems are True, and they are true if they have a
>>>> connection (not limited to finite) to these Truths.
>>>>
>>>> Where does he say True statements must have a FINITE connection to
>>>> the elementary theorems.
>>>>
>>>>>
>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>> elementary
>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>> which belong to ::t we shall call the elementary theorems of::t; we
>>>>> also
>>>>> say that these elementary statements are true for::t. Thus, given ::t,
>>>>> an elementary theorem is an elementary statement which is true. A
>>>>> theory
>>>>> is thus a way of picking out from the statements of (f a certain
>>>>> subclass of true statements.
>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>
>>>>> Perhaps you believe that you are enormously much brighter than
>>>>> Haskell Curry ?
>>>>>
>>>>
>>>> You don't understand what he is saying,
>>>>
>>>> He is saying these statements are True in F, as a given.
>>>
>>> Wrongo !!!
>>>
>>>     The terminology which has just been used implies that the
>>>     elementary statements are not such that their truth and
>>>     falsity are known to us without reference to::t.
>>>
>>>
>>
>> Right, they aren't just true in the Statement class, but are only
>> considerdd true because we are in the Theory F.
>>
>
> F is not the theory T is the theory.
>
>

Red Herring.

F is the Theory in Godels descussion.

You know what I meant, so you admit defeat by picking a nit.

YOU FAIL.

And actully, the Theory isn't "T", by a fancy script symbol that looks
like a T, or maybe an I.

So, you are wrong to to call it T.

On 1/20/2023 4:54 PM, Richard Damon wrote:
> On 1/20/23 5:16 PM, olcott wrote:
>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>> On 1/20/23 5:02 PM, olcott wrote:
>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>> eliminating
>>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>
>>>>>>>>
>>>>>>>> You can't even remember that you said this?
>>>>>>>
>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>> connections to Truth.
>>>>>>>>
>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>> the connecti0on must be finite.
>>>>>>>>
>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>> Did you change your mind?
>>>>>>>
>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>
>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>> can not.
>>>>>>
>>>>>> Truth *in a formal system* cannot be based on infinite connections
>>>>>> because formal systems are not allowed to have infinite connections.
>>>>>
>>>>> Says Who ***FOR TRUTH***
>>>>>
>>>>> You reference does not provide that data, so I guess you are just
>>>>> making it up, and thus showing you to be a LIAR.
>>>>>
>>>>>>
>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>> this formal system.
>>>>>
>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>> elementary theorems are True, and they are true if they have a
>>>>> connection (not limited to finite) to these Truths.
>>>>>
>>>>> Where does he say True statements must have a FINITE connection to
>>>>> the elementary theorems.
>>>>>
>>>>>>
>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>> elementary
>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>> we also
>>>>>> say that these elementary statements are true for::t. Thus, given
>>>>>> ::t,
>>>>>> an elementary theorem is an elementary statement which is true. A
>>>>>> theory
>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>> subclass of true statements.
>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>
>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>> Haskell Curry ?
>>>>>>
>>>>>
>>>>> You don't understand what he is saying,
>>>>>
>>>>> He is saying these statements are True in F, as a given.
>>>>
>>>> Wrongo !!!
>>>>
>>>>     The terminology which has just been used implies that the
>>>>     elementary statements are not such that their truth and
>>>>     falsity are known to us without reference to::t.
>>>>
>>>>
>>>
>>> Right, they aren't just true in the Statement class, but are only
>>> considerdd true because we are in the Theory F.
>>>
>>
>> F is not the theory T is the theory.
>>
>>
>
>
> Red Herring.
>
> F is the Theory in Godels descussion.

It is not a red herring at all. Curry proves that the mathematical
notion of incompleteness itself is incoherent in that Curry sustains
Wittgenstein's notion of true in a formal system.

That G is unprovable in F merely means that G is untrue in F a triviality.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/20/23 7:29 PM, olcott wrote:
> On 1/20/2023 4:54 PM, Richard Damon wrote:
>> On 1/20/23 5:16 PM, olcott wrote:
>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>> eliminating
>>>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You can't even remember that you said this?
>>>>>>>>
>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>> connections to Truth.
>>>>>>>>>
>>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>>> the connecti0on must be finite.
>>>>>>>>>
>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>> Did you change your mind?
>>>>>>>>
>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>
>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>> can not.
>>>>>>>
>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>> connections because formal systems are not allowed to have
>>>>>>> infinite connections.
>>>>>>
>>>>>> Says Who ***FOR TRUTH***
>>>>>>
>>>>>> You reference does not provide that data, so I guess you are just
>>>>>> making it up, and thus showing you to be a LIAR.
>>>>>>
>>>>>>>
>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>> this formal system.
>>>>>>
>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>> elementary theorems are True, and they are true if they have a
>>>>>> connection (not limited to finite) to these Truths.
>>>>>>
>>>>>> Where does he say True statements must have a FINITE connection to
>>>>>> the elementary theorems.
>>>>>>
>>>>>>>
>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>> elementary
>>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>>> we also
>>>>>>> say that these elementary statements are true for::t. Thus, given
>>>>>>> ::t,
>>>>>>> an elementary theorem is an elementary statement which is true. A
>>>>>>> theory
>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>> subclass of true statements.
>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>
>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>> Haskell Curry ?
>>>>>>>
>>>>>>
>>>>>> You don't understand what he is saying,
>>>>>>
>>>>>> He is saying these statements are True in F, as a given.
>>>>>
>>>>> Wrongo !!!
>>>>>
>>>>>     The terminology which has just been used implies that the
>>>>>     elementary statements are not such that their truth and
>>>>>     falsity are known to us without reference to::t.
>>>>>
>>>>>
>>>>
>>>> Right, they aren't just true in the Statement class, but are only
>>>> considerdd true because we are in the Theory F.
>>>>
>>>
>>> F is not the theory T is the theory.
>>>
>>>
>>
>>
>> Red Herring.
>>
>> F is the Theory in Godels descussion.
>
> It is not a red herring at all. Curry proves that the mathematical
> notion of incompleteness itself is incoherent in that Curry sustains
> Wittgenstein's notion of true in a formal system.
>
> That G is unprovable in F merely means that G is untrue in F a triviality.
>

Please point out WHERE in the page you have cited that he does this.

Remeber, the CLASS of statemeents he talks about as "Elementary
Statments" that he talks about is NOT a "exhaustive" list of statements
that can be formed, but a base set to start from.

This is clear from the line you have highlighted pointing out that these
statements of are called elementary statements to distinguish them from
other statements which we may form from them.

Then the "Elementary Theorems" are a SUBSET of these, that are defined
to be True in the Theory. Thus, these also are not a complete listing of
all true statements in the Theory, but only the set a base truths that
we are working from (in addition to the contensive statements that are
true indepentent of the Theory).

NOTHING on that page limits "True" statements to those things that are
provable or only having a FINITE connection to those Elemetary Theories.

All this shows is that you don't understand what you are reading, or are
just lying.

On Friday, January 20, 2023 at 5:24:00 PM UTC-8, Richard Damon wrote:
> On 1/20/23 7:29 PM, olcott wrote:
> > On 1/20/2023 4:54 PM, Richard Damon wrote:
> >> On 1/20/23 5:16 PM, olcott wrote:
> >>> On 1/20/2023 4:09 PM, Richard Damon wrote:
> >>>> On 1/20/23 5:02 PM, olcott wrote:
> >>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
> >>>>>> On 1/20/23 2:31 PM, olcott wrote:
> >>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
> >>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
> >>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
> >>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
> >>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
> >>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
> >>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
> >>>>>>>>>>>> have perposed that we think about infinite proofs.
> >>>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>> Formal systems cannot ever use infinite connections from their
> >>>>>>>>>>> expressions of language to their truth maker axioms thus
> >>>>>>>>>>> eliminating
> >>>>>>>>>>> these from consideration as any measure of true "in the system".
> >>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> Source? or is this just another of your made up "Facts"
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> You can't even remember that you said this?
> >>>>>>>>
> >>>>>>>> No, I said they can't have infinite PROOFS, not infinite
> >>>>>>>> connections to Truth.
> >>>>>>>>>
> >>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
> >>>>>>>>>> the connecti0on must be finite.
> >>>>>>>>>
> >>>>>>>>> You said that formal system cannot have infinite proofs.
> >>>>>>>>> Did you change your mind?
> >>>>>>>>
> >>>>>>>> Right ***PROOF*** not ***TRUTH***
> >>>>>>>>
> >>>>>>>> Truth can be based on an infinite chain of connections, proofs
> >>>>>>>> can not.
> >>>>>>>
> >>>>>>> Truth *in a formal system* cannot be based on infinite
> >>>>>>> connections because formal systems are not allowed to have
> >>>>>>> infinite connections.
> >>>>>>
> >>>>>> Says Who ***FOR TRUTH***
> >>>>>>
> >>>>>> You reference does not provide that data, so I guess you are just
> >>>>>> making it up, and thus showing you to be a LIAR.
> >>>>>>
> >>>>>>>
> >>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
> >>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
> >>>>>>> this formal system.
> >>>>>>
> >>>>>> Right, ANCHORED TO, not limited to. Statments other than the
> >>>>>> elementary theorems are True, and they are true if they have a
> >>>>>> connection (not limited to finite) to these Truths.
> >>>>>>
> >>>>>> Where does he say True statements must have a FINITE connection to
> >>>>>> the elementary theorems.
> >>>>>>
> >>>>>>>
> >>>>>>> A theory (over (f) is defined as a conceptual class of these
> >>>>>>> elementary
> >>>>>>> statements. Let::t be such a theory. Then the elementary statements
> >>>>>>> which belong to ::t we shall call the elementary theorems of::t;
> >>>>>>> we also
> >>>>>>> say that these elementary statements are true for::t. Thus, given
> >>>>>>> ::t,
> >>>>>>> an elementary theorem is an elementary statement which is true. A
> >>>>>>> theory
> >>>>>>> is thus a way of picking out from the statements of (f a certain
> >>>>>>> subclass of true statements.
> >>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
> >>>>>>>
> >>>>>>> Perhaps you believe that you are enormously much brighter than
> >>>>>>> Haskell Curry ?
> >>>>>>>
> >>>>>>
> >>>>>> You don't understand what he is saying,
> >>>>>>
> >>>>>> He is saying these statements are True in F, as a given.
> >>>>>
> >>>>> Wrongo !!!
> >>>>>
> >>>>> The terminology which has just been used implies that the
> >>>>> elementary statements are not such that their truth and
> >>>>> falsity are known to us without reference to::t.
> >>>>>
> >>>>>
> >>>>
> >>>> Right, they aren't just true in the Statement class, but are only
> >>>> considerdd true because we are in the Theory F.
> >>>>
> >>>
> >>> F is not the theory T is the theory.
> >>>
> >>>
> >>
> >>
> >> Red Herring.
> >>
> >> F is the Theory in Godels descussion.
> >
> > It is not a red herring at all. Curry proves that the mathematical
> > notion of incompleteness itself is incoherent in that Curry sustains
> > Wittgenstein's notion of true in a formal system.
> >
> > That G is unprovable in F merely means that G is untrue in F a triviality.
> >
> Please point out WHERE in the page you have cited that he does this.
>
> Remeber, the CLASS of statemeents he talks about as "Elementary
> Statments" that he talks about is NOT a "exhaustive" list of statements
> that can be formed, but a base set to start from.
>
> This is clear from the line you have highlighted pointing out that these
> statements of are called elementary statements to distinguish them from
> other statements which we may form from them.
>
> Then the "Elementary Theorems" are a SUBSET of these, that are defined
> to be True in the Theory. Thus, these also are not a complete listing of
> all true statements in the Theory, but only the set a base truths that
> we are working from (in addition to the contensive statements that are
> true indepentent of the Theory).
>
> NOTHING on that page limits "True" statements to those things that are
> provable or only having a FINITE connection to those Elemetary Theories.
>
>
> All this shows is that you don't understand what you are reading, or are
> just lying.

"They're just lying?"

On Saturday, January 21, 2023 at 10:29:32 AM UTC-6, Jeffrey Rubard wrote:
> On Friday, January 20, 2023 at 5:24:00 PM UTC-8, Richard Damon wrote:
> > On 1/20/23 7:29 PM, olcott wrote:
> > > On 1/20/2023 4:54 PM, Richard Damon wrote:
> > >> On 1/20/23 5:16 PM, olcott wrote:
> > >>> On 1/20/2023 4:09 PM, Richard Damon wrote:
> > >>>> On 1/20/23 5:02 PM, olcott wrote:
> > >>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
> > >>>>>> On 1/20/23 2:31 PM, olcott wrote:
> > >>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
> > >>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
> > >>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
> > >>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
> > >>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
> > >>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
> > >>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
> > >>>>>>>>>>>> have perposed that we think about infinite proofs.
> > >>>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>> Formal systems cannot ever use infinite connections from their
> > >>>>>>>>>>> expressions of language to their truth maker axioms thus
> > >>>>>>>>>>> eliminating
> > >>>>>>>>>>> these from consideration as any measure of true "in the system".
> > >>>>>>>>>>>
> > >>>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>>
> > >>>>>>>>>> Source? or is this just another of your made up "Facts"
> > >>>>>>>>>>
> > >>>>>>>>>
> > >>>>>>>>> You can't even remember that you said this?
> > >>>>>>>>
> > >>>>>>>> No, I said they can't have infinite PROOFS, not infinite
> > >>>>>>>> connections to Truth.
> > >>>>>>>>>
> > >>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
> > >>>>>>>>>> the connecti0on must be finite.
> > >>>>>>>>>
> > >>>>>>>>> You said that formal system cannot have infinite proofs.
> > >>>>>>>>> Did you change your mind?
> > >>>>>>>>
> > >>>>>>>> Right ***PROOF*** not ***TRUTH***
> > >>>>>>>>
> > >>>>>>>> Truth can be based on an infinite chain of connections, proofs
> > >>>>>>>> can not.
> > >>>>>>>
> > >>>>>>> Truth *in a formal system* cannot be based on infinite
> > >>>>>>> connections because formal systems are not allowed to have
> > >>>>>>> infinite connections.
> > >>>>>>
> > >>>>>> Says Who ***FOR TRUTH***
> > >>>>>>
> > >>>>>> You reference does not provide that data, so I guess you are just
> > >>>>>> making it up, and thus showing you to be a LIAR.
> > >>>>>>
> > >>>>>>>
> > >>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
> > >>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
> > >>>>>>> this formal system.
> > >>>>>>
> > >>>>>> Right, ANCHORED TO, not limited to. Statments other than the
> > >>>>>> elementary theorems are True, and they are true if they have a
> > >>>>>> connection (not limited to finite) to these Truths.
> > >>>>>>
> > >>>>>> Where does he say True statements must have a FINITE connection to
> > >>>>>> the elementary theorems.
> > >>>>>>
> > >>>>>>>
> > >>>>>>> A theory (over (f) is defined as a conceptual class of these
> > >>>>>>> elementary
> > >>>>>>> statements. Let::t be such a theory. Then the elementary statements
> > >>>>>>> which belong to ::t we shall call the elementary theorems of::t;
> > >>>>>>> we also
> > >>>>>>> say that these elementary statements are true for::t. Thus, given
> > >>>>>>> ::t,
> > >>>>>>> an elementary theorem is an elementary statement which is true. A
> > >>>>>>> theory
> > >>>>>>> is thus a way of picking out from the statements of (f a certain
> > >>>>>>> subclass of true statements.
> > >>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
> > >>>>>>>
> > >>>>>>> Perhaps you believe that you are enormously much brighter than
> > >>>>>>> Haskell Curry ?
> > >>>>>>>
> > >>>>>>
> > >>>>>> You don't understand what he is saying,
> > >>>>>>
> > >>>>>> He is saying these statements are True in F, as a given.
> > >>>>>
> > >>>>> Wrongo !!!
> > >>>>>
> > >>>>> The terminology which has just been used implies that the
> > >>>>> elementary statements are not such that their truth and
> > >>>>> falsity are known to us without reference to::t.
> > >>>>>
> > >>>>>
> > >>>>
> > >>>> Right, they aren't just true in the Statement class, but are only
> > >>>> considerdd true because we are in the Theory F.
> > >>>>
> > >>>
> > >>> F is not the theory T is the theory.
> > >>>
> > >>>
> > >>
> > >>
> > >> Red Herring.
> > >>
> > >> F is the Theory in Godels descussion.
> > >
> > > It is not a red herring at all. Curry proves that the mathematical
> > > notion of incompleteness itself is incoherent in that Curry sustains
> > > Wittgenstein's notion of true in a formal system.
> > >
> > > That G is unprovable in F merely means that G is untrue in F a triviality.
> > >
> > Please point out WHERE in the page you have cited that he does this.
> >
> > Remeber, the CLASS of statemeents he talks about as "Elementary
> > Statments" that he talks about is NOT a "exhaustive" list of statements
> > that can be formed, but a base set to start from.
> >
> > This is clear from the line you have highlighted pointing out that these
> > statements of are called elementary statements to distinguish them from
> > other statements which we may form from them.
> >
> > Then the "Elementary Theorems" are a SUBSET of these, that are defined
> > to be True in the Theory. Thus, these also are not a complete listing of
> > all true statements in the Theory, but only the set a base truths that
> > we are working from (in addition to the contensive statements that are
> > true indepentent of the Theory).
> >
> > NOTHING on that page limits "True" statements to those things that are
> > provable or only having a FINITE connection to those Elemetary Theories..
> >
> >
> > All this shows is that you don't understand what you are reading, or are
> > just lying.
> "They're just lying?"

how can someone live if they're full of shit I mean it would be like they wouldn't have any of the necessary vital organs like a harder and liver and all that maybe is it because maybe like the phrase you're full of shit is just some kind of like you've euphemisms for simile year or association or something like that is another worse just kind of slang in the person really doesn't think the other guy is full of shit literally because then the person can live in in anyway, you know we really shouldn't call names like Donald Trump knows because if you call people names like that, you'll never be president

On 1/20/2023 4:54 PM, Richard Damon wrote:
> On 1/20/23 5:16 PM, olcott wrote:
>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>> On 1/20/23 5:02 PM, olcott wrote:
>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>> eliminating
>>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>
>>>>>>>>
>>>>>>>> You can't even remember that you said this?
>>>>>>>
>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>> connections to Truth.
>>>>>>>>
>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>> the connecti0on must be finite.
>>>>>>>>
>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>> Did you change your mind?
>>>>>>>
>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>
>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>> can not.
>>>>>>
>>>>>> Truth *in a formal system* cannot be based on infinite connections
>>>>>> because formal systems are not allowed to have infinite connections.
>>>>>
>>>>> Says Who ***FOR TRUTH***
>>>>>
>>>>> You reference does not provide that data, so I guess you are just
>>>>> making it up, and thus showing you to be a LIAR.
>>>>>
>>>>>>
>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>> this formal system.
>>>>>
>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>> elementary theorems are True, and they are true if they have a
>>>>> connection (not limited to finite) to these Truths.
>>>>>
>>>>> Where does he say True statements must have a FINITE connection to
>>>>> the elementary theorems.
>>>>>
>>>>>>
>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>> elementary
>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>> we also
>>>>>> say that these elementary statements are true for::t. Thus, given
>>>>>> ::t,
>>>>>> an elementary theorem is an elementary statement which is true. A
>>>>>> theory
>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>> subclass of true statements.
>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>
>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>> Haskell Curry ?
>>>>>>
>>>>>
>>>>> You don't understand what he is saying,
>>>>>
>>>>> He is saying these statements are True in F, as a given.
>>>>
>>>> Wrongo !!!
>>>>
>>>>     The terminology which has just been used implies that the
>>>>     elementary statements are not such that their truth and
>>>>     falsity are known to us without reference to::t.
>>>>
>>>>
>>>
>>> Right, they aren't just true in the Statement class, but are only
>>> considerdd true because we are in the Theory F.
>>>
>>
>> F is not the theory T is the theory.
>>
>>
>
>
> Red Herring.
>
> F is the Theory in Godels descussion.
>

https://en.wikipedia.org/wiki/Metamathematics
LP := ~True(LP) is untrue yet that does not make it true.

When we examine this at the meta level we escape the self-contradiction
and can say that it is true that LP is untrue.

https://plato.stanford.edu/entries/tarski-truth/#195DefOff

It looks like model theory is required to determine the truth of
some mathematical expressions, this had it origins in Tarski's
definition of truth.

∃n ∈ ℕ (N > 3) // does not seem to need model theory
∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory

G is true in F iff it cannot be shown that G is true in F

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 1/23/2023 9:18 AM, olcott wrote:
> On 1/20/2023 4:54 PM, Richard Damon wrote:
>> On 1/20/23 5:16 PM, olcott wrote:
>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>> eliminating
>>>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You can't even remember that you said this?
>>>>>>>>
>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>> connections to Truth.
>>>>>>>>>
>>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>>> the connecti0on must be finite.
>>>>>>>>>
>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>> Did you change your mind?
>>>>>>>>
>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>
>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>> can not.
>>>>>>>
>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>> connections because formal systems are not allowed to have
>>>>>>> infinite connections.
>>>>>>
>>>>>> Says Who ***FOR TRUTH***
>>>>>>
>>>>>> You reference does not provide that data, so I guess you are just
>>>>>> making it up, and thus showing you to be a LIAR.
>>>>>>
>>>>>>>
>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>> this formal system.
>>>>>>
>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>> elementary theorems are True, and they are true if they have a
>>>>>> connection (not limited to finite) to these Truths.
>>>>>>
>>>>>> Where does he say True statements must have a FINITE connection to
>>>>>> the elementary theorems.
>>>>>>
>>>>>>>
>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>> elementary
>>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>>> we also
>>>>>>> say that these elementary statements are true for::t. Thus, given
>>>>>>> ::t,
>>>>>>> an elementary theorem is an elementary statement which is true. A
>>>>>>> theory
>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>> subclass of true statements.
>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>
>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>> Haskell Curry ?
>>>>>>>
>>>>>>
>>>>>> You don't understand what he is saying,
>>>>>>
>>>>>> He is saying these statements are True in F, as a given.
>>>>>
>>>>> Wrongo !!!
>>>>>
>>>>>     The terminology which has just been used implies that the
>>>>>     elementary statements are not such that their truth and
>>>>>     falsity are known to us without reference to::t.
>>>>>
>>>>>
>>>>
>>>> Right, they aren't just true in the Statement class, but are only
>>>> considerdd true because we are in the Theory F.
>>>>
>>>
>>> F is not the theory T is the theory.
>>>
>>>
>>
>>
>> Red Herring.
>>
>> F is the Theory in Godels descussion.
>>
>
> https://en.wikipedia.org/wiki/Metamathematics
> LP := ~True(LP) is untrue yet that does not make it true.
>
> When we examine this at the meta level we escape the self-contradiction
> and can say that it is true that LP is untrue.
>
> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>
> It looks like model theory is required to determine the truth of
> some mathematical expressions, this had it origins in Tarski's
> definition of truth.
>
> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory

Typo corrected
∃n ∈ ℕ (n > 3) // does not seem to need model theory

> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>
> G is true in F iff it cannot be shown that G is true in F
>
>

--
Copyright 2023 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 1/23/23 10:18 AM, olcott wrote:
> On 1/20/2023 4:54 PM, Richard Damon wrote:
>> On 1/20/23 5:16 PM, olcott wrote:
>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE. Truth
>>>>>>>>>>>> can use infinte sets oc connections, proofs can't. Only YOU
>>>>>>>>>>>> have perposed that we think about infinite proofs.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>> eliminating
>>>>>>>>>>> these from consideration as any measure of true "in the system".
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You can't even remember that you said this?
>>>>>>>>
>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>> connections to Truth.
>>>>>>>>>
>>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>>> the connecti0on must be finite.
>>>>>>>>>
>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>> Did you change your mind?
>>>>>>>>
>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>
>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>> can not.
>>>>>>>
>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>> connections because formal systems are not allowed to have
>>>>>>> infinite connections.
>>>>>>
>>>>>> Says Who ***FOR TRUTH***
>>>>>>
>>>>>> You reference does not provide that data, so I guess you are just
>>>>>> making it up, and thus showing you to be a LIAR.
>>>>>>
>>>>>>>
>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>> this formal system.
>>>>>>
>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>> elementary theorems are True, and they are true if they have a
>>>>>> connection (not limited to finite) to these Truths.
>>>>>>
>>>>>> Where does he say True statements must have a FINITE connection to
>>>>>> the elementary theorems.
>>>>>>
>>>>>>>
>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>> elementary
>>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>>> we also
>>>>>>> say that these elementary statements are true for::t. Thus, given
>>>>>>> ::t,
>>>>>>> an elementary theorem is an elementary statement which is true. A
>>>>>>> theory
>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>> subclass of true statements.
>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>
>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>> Haskell Curry ?
>>>>>>>
>>>>>>
>>>>>> You don't understand what he is saying,
>>>>>>
>>>>>> He is saying these statements are True in F, as a given.
>>>>>
>>>>> Wrongo !!!
>>>>>
>>>>>     The terminology which has just been used implies that the
>>>>>     elementary statements are not such that their truth and
>>>>>     falsity are known to us without reference to::t.
>>>>>
>>>>>
>>>>
>>>> Right, they aren't just true in the Statement class, but are only
>>>> considerdd true because we are in the Theory F.
>>>>
>>>
>>> F is not the theory T is the theory.
>>>
>>>
>>
>>
>> Red Herring.
>>
>> F is the Theory in Godels descussion.
>>
>
> https://en.wikipedia.org/wiki/Metamathematics
> LP := ~True(LP) is untrue yet that does not make it true.
>
> When we examine this at the meta level we escape the self-contradiction
> and can say that it is true that LP is untrue.

Excpet that untrue is not ~True() in classical logic, which makes
statements either True or False, or makes them Not a Truth Bearer, which
makes them not in the domain of the True predicate.

You need to move to tri-value logic to do this, at which point you loose
the relationship that ~True(x) -> False(x)

Note, most of mathematics is based on the two-value logic system.

>
> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>
> It looks like model theory is required to determine the truth of
> some mathematical expressions, this had it origins in Tarski's
> definition of truth.
>
> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory
> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>

∃ is a symbol out of model theory, so hard to not need model theory.

Quoting from your reference:

Model theory by contrast works with three levels of symbol. There are
the logical constants ( = , ¬ , & for example), the variables (as
before), and between these a middle group of symbols which have no fixed
meaning but get a meaning through being applied to a particular
structure. The symbols of this middle group include the nonlogical
constants of the language, such as relation symbols, function symbols
and constant individual symbols. They also include the quantifier
symbols ∀ and ∃, since we need to refer to the structure to see what
set they range over. This type of three-level language corresponds to
mathematical usage; for example we write the addition operation of an
abelian group as +, and this symbol stands for different functions in
different groups.

> G is true in F iff it cannot be shown that G is true in F
>

Nope, you don't understand what G is. The Definition of G in F does NOT
refer in any way determinable in F to the statement G.

Thus, you claim is obviously invalid.

You are just violating your own rules since your statement about G in F
can not be shown to have a connection in F to it, since it is using
information that is not IN F, showing that you are either totally Stupid
or a Liar.

G in F IS a complecated mathematical expression and not reducable
because F doesn't contain the axioms that give it that meaning, those
only exist in the specific Meta-F that was used to build the
relationship (that doesn't refer to anything in Meta-F that isn't in F,
so it has the same mathematical value in both).

That you don't understand that you don't understand this, shows your
stupidity, as the intelegent person not only knows what they know, but
also has an understanding of what things they do not know.

The ignorant person THINKS they know many things, when they do not.

On 1/23/2023 10:51 AM, Richard Damon wrote:
> On 1/23/23 10:18 AM, olcott wrote:
>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>> On 1/20/23 5:16 PM, olcott wrote:
>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs can't.
>>>>>>>>>>>>> Only YOU have perposed that we think about infinite proofs.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>> eliminating
>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>> system".
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>
>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>> connections to Truth.
>>>>>>>>>>
>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say that
>>>>>>>>>>> the connecti0on must be finite.
>>>>>>>>>>
>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>> Did you change your mind?
>>>>>>>>>
>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>
>>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>>> can not.
>>>>>>>>
>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>> infinite connections.
>>>>>>>
>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>
>>>>>>> You reference does not provide that data, so I guess you are just
>>>>>>> making it up, and thus showing you to be a LIAR.
>>>>>>>
>>>>>>>>
>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>>> this formal system.
>>>>>>>
>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>> elementary theorems are True, and they are true if they have a
>>>>>>> connection (not limited to finite) to these Truths.
>>>>>>>
>>>>>>> Where does he say True statements must have a FINITE connection
>>>>>>> to the elementary theorems.
>>>>>>>
>>>>>>>>
>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>> elementary
>>>>>>>> statements. Let::t be such a theory. Then the elementary statements
>>>>>>>> which belong to ::t we shall call the elementary theorems of::t;
>>>>>>>> we also
>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>> given ::t,
>>>>>>>> an elementary theorem is an elementary statement which is true.
>>>>>>>> A theory
>>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>>> subclass of true statements.
>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>
>>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>>> Haskell Curry ?
>>>>>>>>
>>>>>>>
>>>>>>> You don't understand what he is saying,
>>>>>>>
>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>
>>>>>> Wrongo !!!
>>>>>>
>>>>>>     The terminology which has just been used implies that the
>>>>>>     elementary statements are not such that their truth and
>>>>>>     falsity are known to us without reference to::t.
>>>>>>
>>>>>>
>>>>>
>>>>> Right, they aren't just true in the Statement class, but are only
>>>>> considerdd true because we are in the Theory F.
>>>>>
>>>>
>>>> F is not the theory T is the theory.
>>>>
>>>>
>>>
>>>
>>> Red Herring.
>>>
>>> F is the Theory in Godels descussion.
>>>
>>
>> https://en.wikipedia.org/wiki/Metamathematics
>> LP := ~True(LP) is untrue yet that does not make it true.
>>
>> When we examine this at the meta level we escape the self-contradiction
>> and can say that it is true that LP is untrue.
>
>
> Excpet that untrue is not ~True() in classical logic, which makes
> statements either True or False, or makes them Not a Truth Bearer, which
> makes them not in the domain of the True predicate.
>
> You need to move to tri-value logic to do this, at which point you loose
> the relationship that ~True(x) -> False(x)
>

True / false and not a truth bearer.

> Note, most of mathematics is based on the two-value logic system.
>
>

Thus forcing it to classify "not a truth bearer" incorrectly.
If all you have is a hammer the unscrewing a screw becomes quite
destructive.

>>
>> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>>
>> It looks like model theory is required to determine the truth of
>> some mathematical expressions, this had it origins in Tarski's
>> definition of truth.
>>
>> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory
>> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>>
>
> ∃ is a symbol out of model theory, so hard to not need model theory.
>
> Quoting from your reference:
>
> Model theory by contrast works with three levels of symbol. There are
> the logical constants ( = , ¬ , & for example), the variables (as
> before), and between these a middle group of symbols which have no fixed
> meaning but get a meaning through being applied to a particular
> structure. The symbols of this middle group include the nonlogical
> constants of the language, such as relation symbols, function symbols
> and constant individual symbols. They also include the quantifier
> symbols  ∀ and ∃, since we need to refer to the structure to see what
> set they range over.

I just showed how to explicitly specify what they range over: ∃n ∈ ℕ

>> G is true in F iff it cannot be shown that G is true in F
>>
>
> Nope, you don't understand what G is. The Definition of G in F does NOT
> refer in any way determinable in F to the statement G.
>

∃n ∈ ℕ (n > 3) // Is this true or false?
How do you know?

On 1/23/23 5:23 PM, olcott wrote:
> On 1/23/2023 10:51 AM, Richard Damon wrote:
>> On 1/23/23 10:18 AM, olcott wrote:
>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>>> On 1/20/23 5:16 PM, olcott wrote:
>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs can't.
>>>>>>>>>>>>>> Only YOU have perposed that we think about infinite proofs.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Formal systems cannot ever use infinite connections from their
>>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>>> eliminating
>>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>>> system".
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>>
>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>>> connections to Truth.
>>>>>>>>>>>
>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
>>>>>>>>>>>> that the connecti0on must be finite.
>>>>>>>>>>>
>>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>>> Did you change your mind?
>>>>>>>>>>
>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>>
>>>>>>>>>> Truth can be based on an infinite chain of connections, proofs
>>>>>>>>>> can not.
>>>>>>>>>
>>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>>> infinite connections.
>>>>>>>>
>>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>>
>>>>>>>> You reference does not provide that data, so I guess you are
>>>>>>>> just making it up, and thus showing you to be a LIAR.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>>>> this formal system.
>>>>>>>>
>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>>> elementary theorems are True, and they are true if they have a
>>>>>>>> connection (not limited to finite) to these Truths.
>>>>>>>>
>>>>>>>> Where does he say True statements must have a FINITE connection
>>>>>>>> to the elementary theorems.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>>> elementary
>>>>>>>>> statements. Let::t be such a theory. Then the elementary
>>>>>>>>> statements
>>>>>>>>> which belong to ::t we shall call the elementary theorems
>>>>>>>>> of::t; we also
>>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>>> given ::t,
>>>>>>>>> an elementary theorem is an elementary statement which is true.
>>>>>>>>> A theory
>>>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>>>> subclass of true statements.
>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>>
>>>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>>>> Haskell Curry ?
>>>>>>>>>
>>>>>>>>
>>>>>>>> You don't understand what he is saying,
>>>>>>>>
>>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>>
>>>>>>> Wrongo !!!
>>>>>>>
>>>>>>>     The terminology which has just been used implies that the
>>>>>>>     elementary statements are not such that their truth and
>>>>>>>     falsity are known to us without reference to::t.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Right, they aren't just true in the Statement class, but are only
>>>>>> considerdd true because we are in the Theory F.
>>>>>>
>>>>>
>>>>> F is not the theory T is the theory.
>>>>>
>>>>>
>>>>
>>>>
>>>> Red Herring.
>>>>
>>>> F is the Theory in Godels descussion.
>>>>
>>>
>>> https://en.wikipedia.org/wiki/Metamathematics
>>> LP := ~True(LP) is untrue yet that does not make it true.
>>>
>>> When we examine this at the meta level we escape the self-contradiction
>>> and can say that it is true that LP is untrue.
>>
>>
>> Excpet that untrue is not ~True() in classical logic, which makes
>> statements either True or False, or makes them Not a Truth Bearer,
>> which makes them not in the domain of the True predicate.
>>
>> You need to move to tri-value logic to do this, at which point you
>> loose the relationship that ~True(x) -> False(x)
>>
>
> True / false and not a truth bearer.

That is your TRI-value logic.

>
>> Note, most of mathematics is based on the two-value logic system.
>>
>>
>
> Thus forcing it to classify "not a truth bearer" incorrectly.
> If all you have is a hammer the unscrewing a screw becomes quite
> destructive.

Nope, a "statement" can be well formed, and thus MUST be a "Truth
Bearer" or it isn't and is NOT a "Truth Bearer"

By ignoring that mathematically defined statement ARE "Truth Bearers",
you logic system is just broken.

>
>>>
>>> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>>>
>>> It looks like model theory is required to determine the truth of
>>> some mathematical expressions, this had it origins in Tarski's
>>> definition of truth.
>>>
>>> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory
>>> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>>>
>>
>> ∃ is a symbol out of model theory, so hard to not need model theory.
>>
>> Quoting from your reference:
>>
>> Model theory by contrast works with three levels of symbol. There are
>> the logical constants ( = , ¬ , & for example), the variables (as
>> before), and between these a middle group of symbols which have no
>> fixed meaning but get a meaning through being applied to a particular
>> structure. The symbols of this middle group include the nonlogical
>> constants of the language, such as relation symbols, function symbols
>> and constant individual symbols. They also include the quantifier
>> symbols  ∀ and ∃, since we need to refer to the structure to see what
>> set they range over.
>
> I just showed how to explicitly specify what they range over: ∃n ∈ ℕ

On 1/23/2023 4:54 PM, Richard Damon wrote:
> On 1/23/23 5:23 PM, olcott wrote:
>> On 1/23/2023 10:51 AM, Richard Damon wrote:
>>> On 1/23/23 10:18 AM, olcott wrote:
>>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>>>> On 1/20/23 5:16 PM, olcott wrote:
>>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs can't.
>>>>>>>>>>>>>>> Only YOU have perposed that we think about infinite proofs.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Formal systems cannot ever use infinite connections from
>>>>>>>>>>>>>> their
>>>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>>>> eliminating
>>>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>>>> system".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>>>
>>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>>>> connections to Truth.
>>>>>>>>>>>>
>>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
>>>>>>>>>>>>> that the connecti0on must be finite.
>>>>>>>>>>>>
>>>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>>>> Did you change your mind?
>>>>>>>>>>>
>>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>>>
>>>>>>>>>>> Truth can be based on an infinite chain of connections,
>>>>>>>>>>> proofs can not.
>>>>>>>>>>
>>>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>>>> infinite connections.
>>>>>>>>>
>>>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>>>
>>>>>>>>> You reference does not provide that data, so I guess you are
>>>>>>>>> just making it up, and thus showing you to be a LIAR.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>>>> system) is anchored in the elementary theorems (AKA axioms) of
>>>>>>>>>> this formal system.
>>>>>>>>>
>>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>>>> elementary theorems are True, and they are true if they have a
>>>>>>>>> connection (not limited to finite) to these Truths.
>>>>>>>>>
>>>>>>>>> Where does he say True statements must have a FINITE connection
>>>>>>>>> to the elementary theorems.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>>>> elementary
>>>>>>>>>> statements. Let::t be such a theory. Then the elementary
>>>>>>>>>> statements
>>>>>>>>>> which belong to ::t we shall call the elementary theorems
>>>>>>>>>> of::t; we also
>>>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>>>> given ::t,
>>>>>>>>>> an elementary theorem is an elementary statement which is
>>>>>>>>>> true. A theory
>>>>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>>>>> subclass of true statements.
>>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>>>
>>>>>>>>>> Perhaps you believe that you are enormously much brighter than
>>>>>>>>>> Haskell Curry ?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> You don't understand what he is saying,
>>>>>>>>>
>>>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>>>
>>>>>>>> Wrongo !!!
>>>>>>>>
>>>>>>>>     The terminology which has just been used implies that the
>>>>>>>>     elementary statements are not such that their truth and
>>>>>>>>     falsity are known to us without reference to::t.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Right, they aren't just true in the Statement class, but are only
>>>>>>> considerdd true because we are in the Theory F.
>>>>>>>
>>>>>>
>>>>>> F is not the theory T is the theory.
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> Red Herring.
>>>>>
>>>>> F is the Theory in Godels descussion.
>>>>>
>>>>
>>>> https://en.wikipedia.org/wiki/Metamathematics
>>>> LP := ~True(LP) is untrue yet that does not make it true.
>>>>
>>>> When we examine this at the meta level we escape the self-contradiction
>>>> and can say that it is true that LP is untrue.
>>>
>>>
>>> Excpet that untrue is not ~True() in classical logic, which makes
>>> statements either True or False, or makes them Not a Truth Bearer,
>>> which makes them not in the domain of the True predicate.
>>>
>>> You need to move to tri-value logic to do this, at which point you
>>> loose the relationship that ~True(x) -> False(x)
>>>
>>
>> True / false and not a truth bearer.
>
> That is your TRI-value logic.
>

It is true by logical necessity.
Every expression of language must necessarily be
true, false, neither true nor false.

>>
>>> Note, most of mathematics is based on the two-value logic system.
>>>
>>>
>>
>> Thus forcing it to classify "not a truth bearer" incorrectly.
>> If all you have is a hammer the unscrewing a screw becomes quite
>> destructive.
>
> Nope, a "statement" can be well formed, and thus MUST be a "Truth
> Bearer" or it isn't and is NOT a "Truth Bearer"
>
> By ignoring that mathematically defined statement ARE "Truth Bearers",
> you logic system is just broken.
>
>>
>>>>
>>>> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
>>>>
>>>> It looks like model theory is required to determine the truth of
>>>> some mathematical expressions, this had it origins in Tarski's
>>>> definition of truth.
>>>>
>>>> ∃n ∈ ℕ (N > 3)       // does not seem to need model theory
>>>> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
>>>>
>>>
>>> ∃ is a symbol out of model theory, so hard to not need model theory.
>>>
>>> Quoting from your reference:
>>>
>>> Model theory by contrast works with three levels of symbol. There are
>>> the logical constants ( = , ¬ , & for example), the variables (as
>>> before), and between these a middle group of symbols which have no
>>> fixed meaning but get a meaning through being applied to a particular
>>> structure. The symbols of this middle group include the nonlogical
>>> constants of the language, such as relation symbols, function symbols
>>> and constant individual symbols. They also include the quantifier
>>> symbols  ∀ and ∃, since we need to refer to the structure to see what
>>> set they range over.
>>
>> I just showed how to explicitly specify what they range over: ∃n ∈ ℕ
>
> Which means you are using "Model Theory"
>
> Maybe you don't understand those words.

On 1/23/23 6:39 PM, olcott wrote:
> On 1/23/2023 4:54 PM, Richard Damon wrote:
>> On 1/23/23 5:23 PM, olcott wrote:
>>> On 1/23/2023 10:51 AM, Richard Damon wrote:
>>>> On 1/23/23 10:18 AM, olcott wrote:
>>>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>>>>> On 1/20/23 5:16 PM, olcott wrote:
>>>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs can't.
>>>>>>>>>>>>>>>> Only YOU have perposed that we think about infinite proofs.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Formal systems cannot ever use infinite connections from
>>>>>>>>>>>>>>> their
>>>>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>>>>> eliminating
>>>>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>>>>> system".
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>>>>
>>>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>>>>> connections to Truth.
>>>>>>>>>>>>>
>>>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
>>>>>>>>>>>>>> that the connecti0on must be finite.
>>>>>>>>>>>>>
>>>>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>>>>> Did you change your mind?
>>>>>>>>>>>>
>>>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>>>>
>>>>>>>>>>>> Truth can be based on an infinite chain of connections,
>>>>>>>>>>>> proofs can not.
>>>>>>>>>>>
>>>>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>>>>> infinite connections.
>>>>>>>>>>
>>>>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>>>>
>>>>>>>>>> You reference does not provide that data, so I guess you are
>>>>>>>>>> just making it up, and thus showing you to be a LIAR.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>>>>> system) is anchored in the elementary theorems (AKA axioms)
>>>>>>>>>>> of this formal system.
>>>>>>>>>>
>>>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>>>>> elementary theorems are True, and they are true if they have a
>>>>>>>>>> connection (not limited to finite) to these Truths.
>>>>>>>>>>
>>>>>>>>>> Where does he say True statements must have a FINITE
>>>>>>>>>> connection to the elementary theorems.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>>>>> elementary
>>>>>>>>>>> statements. Let::t be such a theory. Then the elementary
>>>>>>>>>>> statements
>>>>>>>>>>> which belong to ::t we shall call the elementary theorems
>>>>>>>>>>> of::t; we also
>>>>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>>>>> given ::t,
>>>>>>>>>>> an elementary theorem is an elementary statement which is
>>>>>>>>>>> true. A theory
>>>>>>>>>>> is thus a way of picking out from the statements of (f a certain
>>>>>>>>>>> subclass of true statements.
>>>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>>>>
>>>>>>>>>>> Perhaps you believe that you are enormously much brighter
>>>>>>>>>>> than Haskell Curry ?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You don't understand what he is saying,
>>>>>>>>>>
>>>>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>>>>
>>>>>>>>> Wrongo !!!
>>>>>>>>>
>>>>>>>>>     The terminology which has just been used implies that the
>>>>>>>>>     elementary statements are not such that their truth and
>>>>>>>>>     falsity are known to us without reference to::t.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right, they aren't just true in the Statement class, but are
>>>>>>>> only considerdd true because we are in the Theory F.
>>>>>>>>
>>>>>>>
>>>>>>> F is not the theory T is the theory.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>> Red Herring.
>>>>>>
>>>>>> F is the Theory in Godels descussion.
>>>>>>
>>>>>
>>>>> https://en.wikipedia.org/wiki/Metamathematics
>>>>> LP := ~True(LP) is untrue yet that does not make it true.
>>>>>
>>>>> When we examine this at the meta level we escape the
>>>>> self-contradiction
>>>>> and can say that it is true that LP is untrue.
>>>>
>>>>
>>>> Excpet that untrue is not ~True() in classical logic, which makes
>>>> statements either True or False, or makes them Not a Truth Bearer,
>>>> which makes them not in the domain of the True predicate.
>>>>
>>>> You need to move to tri-value logic to do this, at which point you
>>>> loose the relationship that ~True(x) -> False(x)
>>>>
>>>
>>> True / false and not a truth bearer.
>>
>> That is your TRI-value logic.
>>
>
> It is true by logical necessity.
> Every expression of language must necessarily be
> true, false, neither true nor false.

On 1/23/2023 6:38 PM, Richard Damon wrote:
> On 1/23/23 6:39 PM, olcott wrote:
>> On 1/23/2023 4:54 PM, Richard Damon wrote:
>>> On 1/23/23 5:23 PM, olcott wrote:
>>>> On 1/23/2023 10:51 AM, Richard Damon wrote:
>>>>> On 1/23/23 10:18 AM, olcott wrote:
>>>>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>>>>>> On 1/20/23 5:16 PM, olcott wrote:
>>>>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs
>>>>>>>>>>>>>>>>> can't. Only YOU have perposed that we think about
>>>>>>>>>>>>>>>>> infinite proofs.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Formal systems cannot ever use infinite connections from
>>>>>>>>>>>>>>>> their
>>>>>>>>>>>>>>>> expressions of language to their truth maker axioms thus
>>>>>>>>>>>>>>>> eliminating
>>>>>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>>>>>> system".
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>>>>>
>>>>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>>>>>> connections to Truth.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
>>>>>>>>>>>>>>> that the connecti0on must be finite.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>>>>>> Did you change your mind?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>>>>>
>>>>>>>>>>>>> Truth can be based on an infinite chain of connections,
>>>>>>>>>>>>> proofs can not.
>>>>>>>>>>>>
>>>>>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>>>>>> infinite connections.
>>>>>>>>>>>
>>>>>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>>>>>
>>>>>>>>>>> You reference does not provide that data, so I guess you are
>>>>>>>>>>> just making it up, and thus showing you to be a LIAR.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA formal
>>>>>>>>>>>> system) is anchored in the elementary theorems (AKA axioms)
>>>>>>>>>>>> of this formal system.
>>>>>>>>>>>
>>>>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>>>>>> elementary theorems are True, and they are true if they have
>>>>>>>>>>> a connection (not limited to finite) to these Truths.
>>>>>>>>>>>
>>>>>>>>>>> Where does he say True statements must have a FINITE
>>>>>>>>>>> connection to the elementary theorems.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> A theory (over (f) is defined as a conceptual class of these
>>>>>>>>>>>> elementary
>>>>>>>>>>>> statements. Let::t be such a theory. Then the elementary
>>>>>>>>>>>> statements
>>>>>>>>>>>> which belong to ::t we shall call the elementary theorems
>>>>>>>>>>>> of::t; we also
>>>>>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>>>>>> given ::t,
>>>>>>>>>>>> an elementary theorem is an elementary statement which is
>>>>>>>>>>>> true. A theory
>>>>>>>>>>>> is thus a way of picking out from the statements of (f a
>>>>>>>>>>>> certain
>>>>>>>>>>>> subclass of true statements.
>>>>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> Perhaps you believe that you are enormously much brighter
>>>>>>>>>>>> than Haskell Curry ?
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> You don't understand what he is saying,
>>>>>>>>>>>
>>>>>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>>>>>
>>>>>>>>>> Wrongo !!!
>>>>>>>>>>
>>>>>>>>>>     The terminology which has just been used implies that the
>>>>>>>>>>     elementary statements are not such that their truth and
>>>>>>>>>>     falsity are known to us without reference to::t.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Right, they aren't just true in the Statement class, but are
>>>>>>>>> only considerdd true because we are in the Theory F.
>>>>>>>>>
>>>>>>>>
>>>>>>>> F is not the theory T is the theory.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> Red Herring.
>>>>>>>
>>>>>>> F is the Theory in Godels descussion.
>>>>>>>
>>>>>>
>>>>>> https://en.wikipedia.org/wiki/Metamathematics
>>>>>> LP := ~True(LP) is untrue yet that does not make it true.
>>>>>>
>>>>>> When we examine this at the meta level we escape the
>>>>>> self-contradiction
>>>>>> and can say that it is true that LP is untrue.
>>>>>
>>>>>
>>>>> Excpet that untrue is not ~True() in classical logic, which makes
>>>>> statements either True or False, or makes them Not a Truth Bearer,
>>>>> which makes them not in the domain of the True predicate.
>>>>>
>>>>> You need to move to tri-value logic to do this, at which point you
>>>>> loose the relationship that ~True(x) -> False(x)
>>>>>
>>>>
>>>> True / false and not a truth bearer.
>>>
>>> That is your TRI-value logic.
>>>
>>
>> It is true by logical necessity.
>> Every expression of language must necessarily be
>> true, false, neither true nor false.
>
> Nope. You can also use a two level division like you actually talk about.
>
> Statments are either Truth Bearers or they are Not
>
> Truth Bearers are either True or they are False.

On 1/23/23 10:46 PM, olcott wrote:
> On 1/23/2023 6:38 PM, Richard Damon wrote:
>> On 1/23/23 6:39 PM, olcott wrote:
>>> On 1/23/2023 4:54 PM, Richard Damon wrote:
>>>> On 1/23/23 5:23 PM, olcott wrote:
>>>>> On 1/23/2023 10:51 AM, Richard Damon wrote:
>>>>>> On 1/23/23 10:18 AM, olcott wrote:
>>>>>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
>>>>>>>> On 1/20/23 5:16 PM, olcott wrote:
>>>>>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
>>>>>>>>>> On 1/20/23 5:02 PM, olcott wrote:
>>>>>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
>>>>>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
>>>>>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
>>>>>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
>>>>>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
>>>>>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs
>>>>>>>>>>>>>>>>>> can't. Only YOU have perposed that we think about
>>>>>>>>>>>>>>>>>> infinite proofs.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Formal systems cannot ever use infinite connections
>>>>>>>>>>>>>>>>> from their
>>>>>>>>>>>>>>>>> expressions of language to their truth maker axioms
>>>>>>>>>>>>>>>>> thus eliminating
>>>>>>>>>>>>>>>>> these from consideration as any measure of true "in the
>>>>>>>>>>>>>>>>> system".
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You can't even remember that you said this?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
>>>>>>>>>>>>>> connections to Truth.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
>>>>>>>>>>>>>>>> that the connecti0on must be finite.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You said that formal system cannot have infinite proofs.
>>>>>>>>>>>>>>> Did you change your mind?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Truth can be based on an infinite chain of connections,
>>>>>>>>>>>>>> proofs can not.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Truth *in a formal system* cannot be based on infinite
>>>>>>>>>>>>> connections because formal systems are not allowed to have
>>>>>>>>>>>>> infinite connections.
>>>>>>>>>>>>
>>>>>>>>>>>> Says Who ***FOR TRUTH***
>>>>>>>>>>>>
>>>>>>>>>>>> You reference does not provide that data, so I guess you are
>>>>>>>>>>>> just making it up, and thus showing you to be a LIAR.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA
>>>>>>>>>>>>> formal system) is anchored in the elementary theorems (AKA
>>>>>>>>>>>>> axioms) of this formal system.
>>>>>>>>>>>>
>>>>>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
>>>>>>>>>>>> elementary theorems are True, and they are true if they have
>>>>>>>>>>>> a connection (not limited to finite) to these Truths.
>>>>>>>>>>>>
>>>>>>>>>>>> Where does he say True statements must have a FINITE
>>>>>>>>>>>> connection to the elementary theorems.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> A theory (over (f) is defined as a conceptual class of
>>>>>>>>>>>>> these elementary
>>>>>>>>>>>>> statements. Let::t be such a theory. Then the elementary
>>>>>>>>>>>>> statements
>>>>>>>>>>>>> which belong to ::t we shall call the elementary theorems
>>>>>>>>>>>>> of::t; we also
>>>>>>>>>>>>> say that these elementary statements are true for::t. Thus,
>>>>>>>>>>>>> given ::t,
>>>>>>>>>>>>> an elementary theorem is an elementary statement which is
>>>>>>>>>>>>> true. A theory
>>>>>>>>>>>>> is thus a way of picking out from the statements of (f a
>>>>>>>>>>>>> certain
>>>>>>>>>>>>> subclass of true statements.
>>>>>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>>>>>>>>>>>
>>>>>>>>>>>>> Perhaps you believe that you are enormously much brighter
>>>>>>>>>>>>> than Haskell Curry ?
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> You don't understand what he is saying,
>>>>>>>>>>>>
>>>>>>>>>>>> He is saying these statements are True in F, as a given.
>>>>>>>>>>>
>>>>>>>>>>> Wrongo !!!
>>>>>>>>>>>
>>>>>>>>>>>     The terminology which has just been used implies that the
>>>>>>>>>>>     elementary statements are not such that their truth and
>>>>>>>>>>>     falsity are known to us without reference to::t.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Right, they aren't just true in the Statement class, but are
>>>>>>>>>> only considerdd true because we are in the Theory F.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> F is not the theory T is the theory.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Red Herring.
>>>>>>>>
>>>>>>>> F is the Theory in Godels descussion.
>>>>>>>>
>>>>>>>
>>>>>>> https://en.wikipedia.org/wiki/Metamathematics
>>>>>>> LP := ~True(LP) is untrue yet that does not make it true.
>>>>>>>
>>>>>>> When we examine this at the meta level we escape the
>>>>>>> self-contradiction
>>>>>>> and can say that it is true that LP is untrue.
>>>>>>
>>>>>>
>>>>>> Excpet that untrue is not ~True() in classical logic, which makes
>>>>>> statements either True or False, or makes them Not a Truth Bearer,
>>>>>> which makes them not in the domain of the True predicate.
>>>>>>
>>>>>> You need to move to tri-value logic to do this, at which point you
>>>>>> loose the relationship that ~True(x) -> False(x)
>>>>>>
>>>>>
>>>>> True / false and not a truth bearer.
>>>>
>>>> That is your TRI-value logic.
>>>>
>>>
>>> It is true by logical necessity.
>>> Every expression of language must necessarily be
>>> true, false, neither true nor false.
>>
>> Nope. You can also use a two level division like you actually talk about.
>>
>> Statments are either Truth Bearers or they are Not
>>
>> Truth Bearers are either True or they are False.
>
> Is this a trick? Did you just agree with me?

On Monday, January 23, 2023 at 8:39:20 PM UTC-8, Richard Damon wrote:
> On 1/23/23 10:46 PM, olcott wrote:
> > On 1/23/2023 6:38 PM, Richard Damon wrote:
> >> On 1/23/23 6:39 PM, olcott wrote:
> >>> On 1/23/2023 4:54 PM, Richard Damon wrote:
> >>>> On 1/23/23 5:23 PM, olcott wrote:
> >>>>> On 1/23/2023 10:51 AM, Richard Damon wrote:
> >>>>>> On 1/23/23 10:18 AM, olcott wrote:
> >>>>>>> On 1/20/2023 4:54 PM, Richard Damon wrote:
> >>>>>>>> On 1/20/23 5:16 PM, olcott wrote:
> >>>>>>>>> On 1/20/2023 4:09 PM, Richard Damon wrote:
> >>>>>>>>>> On 1/20/23 5:02 PM, olcott wrote:
> >>>>>>>>>>> On 1/20/2023 2:46 PM, Richard Damon wrote:
> >>>>>>>>>>>> On 1/20/23 2:31 PM, olcott wrote:
> >>>>>>>>>>>>> On 1/19/2023 8:34 PM, Richard Damon wrote:
> >>>>>>>>>>>>>> On 1/19/23 2:12 PM, olcott wrote:
> >>>>>>>>>>>>>>> On 1/17/2023 5:44 PM, Richard Damon wrote:
> >>>>>>>>>>>>>>>> On 1/17/23 11:39 AM, olcott wrote:
> >>>>>>>>>>>>>>>>> On 1/16/2023 7:51 PM, Richard Damon wrote:
> >>>>>>>>>>>>>>>>>> No, because I am showing that G is TRUE, not PROVABLE.
> >>>>>>>>>>>>>>>>>> Truth can use infinte sets oc connections, proofs
> >>>>>>>>>>>>>>>>>> can't. Only YOU have perposed that we think about
> >>>>>>>>>>>>>>>>>> infinite proofs.
> >>>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>> Formal systems cannot ever use infinite connections
> >>>>>>>>>>>>>>>>> from their
> >>>>>>>>>>>>>>>>> expressions of language to their truth maker axioms
> >>>>>>>>>>>>>>>>> thus eliminating
> >>>>>>>>>>>>>>>>> these from consideration as any measure of true "in the
> >>>>>>>>>>>>>>>>> system".
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> Source? or is this just another of your made up "Facts"
> >>>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> You can't even remember that you said this?
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> No, I said they can't have infinite PROOFS, not infinite
> >>>>>>>>>>>>>> connections to Truth.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>>> WHERE in the definition of a "Formal System" does it say
> >>>>>>>>>>>>>>>> that the connecti0on must be finite.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> You said that formal system cannot have infinite proofs.
> >>>>>>>>>>>>>>> Did you change your mind?
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> Right ***PROOF*** not ***TRUTH***
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> Truth can be based on an infinite chain of connections,
> >>>>>>>>>>>>>> proofs can not.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> Truth *in a formal system* cannot be based on infinite
> >>>>>>>>>>>>> connections because formal systems are not allowed to have
> >>>>>>>>>>>>> infinite connections.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Says Who ***FOR TRUTH***
> >>>>>>>>>>>>
> >>>>>>>>>>>> You reference does not provide that data, so I guess you are
> >>>>>>>>>>>> just making it up, and thus showing you to be a LIAR.
> >>>>>>>>>>>>
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> Haskell Curry establishes that truth in a theory (AKA
> >>>>>>>>>>>>> formal system) is anchored in the elementary theorems (AKA
> >>>>>>>>>>>>> axioms) of this formal system.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Right, ANCHORED TO, not limited to. Statments other than the
> >>>>>>>>>>>> elementary theorems are True, and they are true if they have
> >>>>>>>>>>>> a connection (not limited to finite) to these Truths.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Where does he say True statements must have a FINITE
> >>>>>>>>>>>> connection to the elementary theorems.
> >>>>>>>>>>>>
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> A theory (over (f) is defined as a conceptual class of
> >>>>>>>>>>>>> these elementary
> >>>>>>>>>>>>> statements. Let::t be such a theory. Then the elementary
> >>>>>>>>>>>>> statements
> >>>>>>>>>>>>> which belong to ::t we shall call the elementary theorems
> >>>>>>>>>>>>> of::t; we also
> >>>>>>>>>>>>> say that these elementary statements are true for::t. Thus,
> >>>>>>>>>>>>> given ::t,
> >>>>>>>>>>>>> an elementary theorem is an elementary statement which is
> >>>>>>>>>>>>> true. A theory
> >>>>>>>>>>>>> is thus a way of picking out from the statements of (f a
> >>>>>>>>>>>>> certain
> >>>>>>>>>>>>> subclass of true statements.
> >>>>>>>>>>>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> Perhaps you believe that you are enormously much brighter
> >>>>>>>>>>>>> than Haskell Curry ?
> >>>>>>>>>>>>>
> >>>>>>>>>>>>
> >>>>>>>>>>>> You don't understand what he is saying,
> >>>>>>>>>>>>
> >>>>>>>>>>>> He is saying these statements are True in F, as a given.
> >>>>>>>>>>>
> >>>>>>>>>>> Wrongo !!!
> >>>>>>>>>>>
> >>>>>>>>>>> The terminology which has just been used implies that the
> >>>>>>>>>>> elementary statements are not such that their truth and
> >>>>>>>>>>> falsity are known to us without reference to::t.
> >>>>>>>>>>>
> >>>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>> Right, they aren't just true in the Statement class, but are
> >>>>>>>>>> only considerdd true because we are in the Theory F.
> >>>>>>>>>>
> >>>>>>>>>
> >>>>>>>>> F is not the theory T is the theory.
> >>>>>>>>>
> >>>>>>>>>
> >>>>>>>>
> >>>>>>>>
> >>>>>>>> Red Herring.
> >>>>>>>>
> >>>>>>>> F is the Theory in Godels descussion.
> >>>>>>>>
> >>>>>>>
> >>>>>>> https://en.wikipedia.org/wiki/Metamathematics
> >>>>>>> LP := ~True(LP) is untrue yet that does not make it true.
> >>>>>>>
> >>>>>>> When we examine this at the meta level we escape the
> >>>>>>> self-contradiction
> >>>>>>> and can say that it is true that LP is untrue.
> >>>>>>
> >>>>>>
> >>>>>> Excpet that untrue is not ~True() in classical logic, which makes
> >>>>>> statements either True or False, or makes them Not a Truth Bearer,
> >>>>>> which makes them not in the domain of the True predicate.
> >>>>>>
> >>>>>> You need to move to tri-value logic to do this, at which point you
> >>>>>> loose the relationship that ~True(x) -> False(x)
> >>>>>>
> >>>>>
> >>>>> True / false and not a truth bearer.
> >>>>
> >>>> That is your TRI-value logic.
> >>>>
> >>>
> >>> It is true by logical necessity.
> >>> Every expression of language must necessarily be
> >>> true, false, neither true nor false.
> >>
> >> Nope. You can also use a two level division like you actually talk about.
> >>
> >> Statments are either Truth Bearers or they are Not
> >>
> >> Truth Bearers are either True or they are False.
> >
> > Is this a trick? Did you just agree with me?
> No. there are two DISTINT but connected binary values.
>
> Is it a Truth Bearer, and if so, what is the Truth Value.
>
> Once it has been made a Truth Bearer, the "untrue/unfalse" state is not
> available.
>
> Your "Tri-value" system seems to look the fact that some statements are,
> by definition, Truth Bearers.
>
> This just shows your lack of understanding.
> >
> >>
> >>>
> >>>
> >>>>>
> >>>>>> Note, most of mathematics is based on the two-value logic system.
> >>>>>>
> >>>>>>
> >>>>>
> >>>>> Thus forcing it to classify "not a truth bearer" incorrectly.
> >>>>> If all you have is a hammer the unscrewing a screw becomes quite
> >>>>> destructive.
> >>>>
> >>>> Nope, a "statement" can be well formed, and thus MUST be a "Truth
> >>>> Bearer" or it isn't and is NOT a "Truth Bearer"
> >>>>
> >>>> By ignoring that mathematically defined statement ARE "Truth
> >>>> Bearers", you logic system is just broken.
> >>>>
> >>>>>
> >>>>>>>
> >>>>>>> https://plato.stanford.edu/entries/tarski-truth/#195DefOff
> >>>>>>>
> >>>>>>> It looks like model theory is required to determine the truth of
> >>>>>>> some mathematical expressions, this had it origins in Tarski's
> >>>>>>> definition of truth.
> >>>>>>>
> >>>>>>> ∃n ∈ ℕ (N > 3) // does not seem to need model theory
> >>>>>>> ∃G ∈ F (G ↔ (F ⊬ G)) // does not seem to need model theory
> >>>>>>>
> >>>>>>
> >>>>>> ∃ is a symbol out of model theory, so hard to not need model theory.
> >>>>>>
> >>>>>> Quoting from your reference:
> >>>>>>
> >>>>>> Model theory by contrast works with three levels of symbol. There
> >>>>>> are the logical constants ( = , ¬ , & for example), the variables
> >>>>>> (as before), and between these a middle group of symbols which
> >>>>>> have no fixed meaning but get a meaning through being applied to a
> >>>>>> particular structure. The symbols of this middle group include the
> >>>>>> nonlogical constants of the language, such as relation symbols,
> >>>>>> function symbols and constant individual symbols. They also
> >>>>>> include the quantifier symbols ∀ and ∃, since we need to refer to
> >>>>>> the structure to see what set they range over.
> >>>>>
> >>>>> I just showed how to explicitly specify what they range over: ∃n ∈ ℕ
> >>>>
> >>>> Which means you are using "Model Theory"
> >>>>
> >>>> Maybe you don't understand those words.
> >>>
> >>> Model theory is used to define things that are not otherwise defined.
> >>> When they are otherwise defined there is no need for model theory.
> >>
> >> So, you don't understand what Model Theory is (or mixing different
> >> definitions)
> >
> > The most succinct definition seems to be saying that model theory merely
> > defines the semantics of elements expressions of language.
> No, perhaps the issue is that logic doesn't actual deal with "semantics"
> the way you want to talk about it. Meaning is NOT based on the "words"
> used to describe it, but the descrete properties attached to it.
>
> Items are defined as parts of classes.
>
> Cats are not mammels by the "meaning" of the words, but because the
> label "cats" is attached to a class of things, and "Mammels" is attached
> to another class of things, and the class of things called cats is
> defined to be a subset of the class of things called mammels.
> >
> > Sometimes we write or speak a sentence S that expresses nothing either
> > true or false, because some crucial information is missing about what
> > the words mean.
> >
> Which makes it not a logical statemen.
> > If we go on to add this information, so that S comes to express a true
> > or false statement, we are said to interpret S, and the added
> > information is called an interpretation of S.
> >
> > If the interpretation I happens to make S state something true, we say
> > that I is a model of S, or that I satisfies S, in symbols ‘I ⊨ S’.
> >
> > Another way of saying that I is a model of S is to say that S is true in
> > I, and so we have the notion of model-theoretic truth, which is truth in
> > a particular interpretation.
> >
> > https://plato.stanford.edu/entries/model-theory/#Basic
> Maybe that is the Philosphical view of model theory, but doesn't sound
> like what Mathematics calls Model Theory.
>
> I would have to study it more to see how compatible it is with the model
> theory used by mathematitians.
>
> As I said, one of your problems is you think that you can use Natural
> Language meaning of words, or don't understand that Technical Meanings
> can differ between Fields, and you need to use the rght definition.
> >
> >>>
> >>>>>
> >>>>>>> G is true in F iff it cannot be shown that G is true in F
> >>>>>>>
> >>>>>>
> >>>>>> Nope, you don't understand what G is. The Definition of G in F
> >>>>>> does NOT refer in any way determinable in F to the statement G.
> >>>>>>
> >>>>>
> >>>>> ∃n ∈ ℕ (n > 3) // Is this true or false?
> >>>>> How do you know?
> >>>>
> >>>> Simple, 4 exists (S(S(S(S(0)))), 4 > 3, 4 ∈ ℕ, thus the statement is
> >>>> True. Like many (but not all) True statements, it can be proven.
> >>>>
> >>>>>
> >>>>> Generically how does ascertain that that any logic expression is
> >>>>> true or
> >>>>> false?
> >>>>
> >>>> Note, "Ascertain" means you are talking about KNOWLEDGE, not Truth.
> >>>>
> >>>> Truth doesn't need to be ascertained to be true, it just is.
> >>>>
> >>>> It needs to be ascertained to be KNOWN.
> >>>>
> >>>> It is a TRUE statement that either all even numbers greater than 2
> >>>> are the sum of 2 primes or there exists at least one that is not. We
> >>>> don't know which one of them is true right now, but we do know that
> >>>> one of them is.
> >>>>
> >>>> This seems to be one of your core problems, confusing what can be
> >>>> known to be true with what IS true.
> >>>>
> >>>>>
> >>>>> Most generically an analytical expression of formal or natural
> >>>>> language is only true if it has a semantic connection to its truth
> >>>>> maker axioms.
> >>>>
> >>>> Right, but that connection might not be known, or might even be
> >>>> infinite.
> >>>>
> >>>> It is only KNOWLEDGE or PROOF that requires a finite connection.
> >>>>>
> >>>>> The "truth maker axioms" of natural language are the definition of the
> >>>>> meaning of its words.
> >>>>
> >>>>
> >>>> No, the accepted Truth Maker Axioms of the Theory (not what their
> >>>> words mean in Natural Language) determine what is true.
> >>>
> >>> of natural language such as English
> >>> of natural language such as English
> >>> of natural language such as English
> >>> of natural language such as English
> >>
> >> Which has been proven unsuitable for logic.
> >>
> >> Given the statement:
> >>
> >> If this sentence is true, Peter Olcott is a moron.
> >>
> >> This is a valid logical statement of natural language form.
> >>
> >> By the meaning of the words, it is TRUE, because if the sentence IS
> >> true, then by the DEFINITION of True, it must be actually True.
> >>
> >> Thus, since it HAS been proven true, its implication must be correct,
> >> and thus YOU ARE A MORON.
> >>
> >> The "flaw" in the statement is that Natural Language isn't suitable to
> >> fully express logic.
> >
> > Montague Grammar made great strides in formalizing natural language
> > semantics.
> Then it must not be "Natural Language" any more, you CAN'T "formalise" a
> language and keep it Natural, as the definition of Natural Language is
> the language evolved naturally without concious planning or premeditation..
> >
> >>>
> >>>>
> >>>> Your reliance on "Natural Language" is what has actually been proven
> >>>> to lead to problems.
> >>>>
> >>>
> >>> The entire body of all analytical knowledge can only be expressed using
> >>> language. Hardly any of this is currently expressed using formal
> >>> language. All knowledge is necessarily true by definition.
> >>
> >> Right, TECHNICAL/FORMAL language, not NATURAL language.
> >>
> >> You are incorrect that hardly any of this is expressed using formal
> >> language, and that is a major part of your problem. Words that are
> >> words in "Natuaral Language" are frequently refined to a formal
> >> definition for particular usage. If you don't understand that formal
> >> definition, or even more important WHICH formal definition is needed
> >> for a given statement, you won't understand it.
> >
> > Of the sum total of all of analytical human knowledge far less than 1%
> > has been formalized.
> >
> >>
> >> And All Knowledge being necessarily true is NOT a universal
> >> definition, in fact, one of the problems of the study of knowledge is
> >> how to avoid the introduction into "Knowledge" of things that we THINK
> >> are True but are actually incorrect. We WANT everything that we (think
> >> we) know to be actually true, but factually, since there IS a human
> >> element in the aquisition of knowledge, there is a possibility of
> >> error and of thinking we know something that isn't true.
> >>
> >
> > Once truth has been properly formalized the discerning truth from
> > falsehood or presumption is a mere computation.
> But it has been proven that you can't formaize truth in a manner that it
> can be universally tested.
> >
> >>>
> >>>>>
> >>>>> The truth maker axioms for the above expression is the definition
> >>>>> of the ordered set of natural numbers:
> >>>>>
> >>>>> https://www.britannica.com/science/Peano-axioms
> >>>>>
> >>>>
> >>>> You understand that Godel showed that under the Peano-axioms, he
> >>>> proved that their exists truths that can not be proven.
> >>>
> >>> We can make the Gödel number of "I just ate some chicken" using the
> >>> adjacent ASCII values. This too cannot be proven in the Peano-axioms.
> >>
> >> Nope. You don't understand what Godel does. Not understanding
> >> something does not make it not true, you are just serving your Herring
> >> with Red Sauce.
> >>
> >> Yes, you can set up a system where you use Godel's math to create a
> >> number that represents the statement "I just ate some chicken", but
> >> that statement has nothing to do with Godel's proof.
> >>
> >> The fact you can throw out Red Herring that means nothing doesn't
> >> discount the proof, it just proves you don't understand what you are
> >> talking about.
> >>
> >>>
> >>>> It becomes a consequence of the induction axiom that allows him to
> >>>> be able to define the primative recursive relationship that shows
> >>>> that you can not prove within the theory that no nmber exists that
> >>>> matches that theory, and also create an extention to that theory
> >>>> (that is used to create that relationship) that allows us to
> >>>> actually prove that statment must be true, and also that no proof of
> >>>> this can exist in the base theory.
> >>>>
> >>>
> >>> Its a mere gimmick.
> >>> He acknowledged that the Liar Paradox forms an equivalent proof.
> >>
> >> No, it isn't.
> >
> > He said that it is. That you reject this because you want to stay in
> > rebuttal mode is no actual rebuttal.
> No, he said he used it to build the proof, and a similar antinomy could
> be used as well.
>
> Just like a recipe for a cake might say that a similar cake could be
> made with other flowers, that doesn't make the cake the equivalent of
> flower.
> >
> >> If you think it is, then SHOW that it is.
> >
> > He said that it is.
> > He said that it is.
> > He said that it is.
> > He said that it is.
> > He said that it is.
> No, he did NOT say it was equivalent, it was USED it.
>
> Read what he said again.
> >
> >> But to do that, you need to understand what he did and where he "just
> >> used a gimmick"
> >>
> >> All your statments show is that you just don't understand what he is
> >> saying and are such a pathological liar that you will make up excuses
> >> to cover that.
> >>
> >
> > When you lack a proper rebuttal you resort to ad Hominem.
> > This may be quite convincing to gullible fools.
> >
> What proper rebutal?
>
> You claim Godel has said something that means what it doesn't
> > The conventional definition of incompleteness:
> > Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
> No, becaue for that definition φ must be a statment that is a Truth Bearer.
>
> This is the problem of combining the two step boolian value into a
> single tri-value, you lost the definitoin of the domain of the statement.
>
> THe other version of the Definition is that there exists a statment that
> is True which can not be proven (or by negation, a false statement that
> can not be refuted)
> >
> > Rejects all formal systems as incomplete on the basis that they cannot
> > prove that the Liar Paradox is true.
> Nope, The Liar Paradox is not in the required domain of the definition
> >
> > This is where he says that he uses the Liar Paradox as his basis:
> > https://www.liarparadox.org/247_248.pdf
> Firstt, you just switch topics mid-stream, we WERE talking about Godel
> and his statment G, and now you are talking about Tarski and his proof
> of no definition of Truth.
>
> If you think these are the same thing, you are even dumber that I thought..
>
> Yes, the proofs are similar, but there ARE subtle differences to get to
> their different conclusions.
>
> Note, the page you are pointing to never says he uses the Liar's Paradox
> to actually BUILD the proof, but that it is shown that the existance of
> a "Definition of Truth" (which I am not sure you understand what he is
> talking about) would create the ability to prove that the Liar's Paradox
> was a True STatement, which implies a contradiction, and thus the
> premise, the existance of the Defintion of Truth, can not be in a system
> that is stipulated to be consistent.
> >
> > This is his whole proof:
> > https://www.liarparadox.org/Tarski_275_276.pdf
> >
> > Tarski concluded that truth cannot be formally defined and he did this
> > on the basis that he could not prove that the Liar Paradox is true
> > within the formal system where it remains self-contradictory.
> >
> > He was able to prove that it is true outside of the formal system where
> > it is self-contradictory.
> >
> Nope, you don't understand his proof.