On 1/9/2023 10:01 PM, Richard Damon wrote:
> On 1/9/23 10:19 PM, olcott wrote:
>> The set of (analytical) expressions of (formal or natural language) have
>> a complete semantic connection to their truth maker axioms otherwise
>> they are simply untrue. Copyright 2022 PL Olcott
>
> Right, but such a connection can be based on an INFINTE number of
>

Mathematicians and logicians make sure to ignore the philosophical
foundation of these things. or we would never get this:

The conventional definition of incompleteness:
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

>>
>> Previously philosophers were trying to define truth maker for analytical
>> truth and empirical truth at the same time and in the same way.
>
> Nope. Just shows you are not understanding how logic works.
>
>>
>> This much is agreed: “x makes it true that p” is a construction that
>> signifies, if it signifies anything at all, a relation borne to a truth-
>> bearer by something else, a truth-maker. But it isn’t generally agreed
>> what that something else might be, or what truth-bearers are, or what
>> the character might be of the relationship that holds, if it does,
>> between them, or even whether such a relationship ever does hold.
>> https://plato.stanford.edu/entries/truthmakers/
>
> But note, that the statement x -> y is NOT a assertion that x MAKES y
> true, but that the Truth of x proves that Y is true.
>

x ⊨ y Aristotle's syllogism required a semantic connection based on
semantic categories.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure

> It is NOT a statement about "Causation", in fact, it is more a statement
> about sub-sets of models that might exist.
>

https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
In other words there is a semantic connection form an expression of
language to its truth maker axioms.

> The statement x -> y means that the set of possible conditions of truth
> values of all statements where x is true, is a subset of all the
> possible conditions of truth values of all statements where y is true.
>
> Thus, if we are in a condition where x is true, we know that y must also
> be true.
>
>>
>> *This means that Wittgenstein is correct*
>> 'True in Russell's system' means, as was said: proved in Russell's
>> system; and 'false in Russell's system' means:the opposite has been
>> proved in Russell's system.
>> https://www.liarparadox.org/Wittgenstein.pdf]
>
> Nope, not unless you are redefinig "Proof" to include an infinite set of
> connections, at which point you are in a totally new language.
>

Formal systems require finite proofs to truth or the expression is
untrue in the formal system. Unless and until there is a connection to
the axioms of the system the expression remains untrue in the system.
Curry calls these axioms: "elementary theorems of::T"

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

>>
>> If P is unprovable in Russell's system then P is simply untrue in
>> Russell's system.
>>
> Nope.
>

Yup. That mathematicians and logicians do not bother to pay attention to
the philosophical foundations of these things leads them astray. They
simply follow their learned-by-rote never realizing (or even caring)
that they are incoherent.

> If you hold to this, as has been pointed out, this means, unless you
> system is very small, that you can't talk about statements you haven't
> already proven as you don't know if they are Truth Beares.
>
> The Provablity of statements is not a Truth Bearr until you have proven
> that it is.
>

Curry agrees that the systems define "elementary theorems of::T" that
anchor the notion of truth in these systems, thus if there is no
connection from an expression to these anchors then it remains untrue.

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

On 1/9/23 11:50 PM, olcott wrote:
> On 1/9/2023 10:01 PM, Richard Damon wrote:
>> On 1/9/23 10:19 PM, olcott wrote:
>>> The set of (analytical) expressions of (formal or natural language) have
>>> a complete semantic connection to their truth maker axioms otherwise
>>> they are simply untrue. Copyright 2022 PL Olcott
>>
>> Right, but such a connection can be based on an INFINTE number of
>>
>
> Mathematicians and logicians make sure to ignore the philosophical
> foundation of these things. or we would never get this:
>
> The conventional definition of incompleteness:
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

Right, a system is incomplete if there exist a statement (which has a
Truth Value) but that statment can neither be proven or disproven in T.

Alternatively, a system is incomplete if there exists a TRUE statement
which can not be proven in T (the disproven half of the above becoming a
seperate piece as if the statement is false (not just "untrue") then we
can form the negation of the statement and not be able to prove that one.

>
>>>
>>> Previously philosophers were trying to define truth maker for analytical
>>> truth and empirical truth at the same time and in the same way.
>>
>> Nope. Just shows you are not understanding how logic works.
>>
>>>
>>> This much is agreed: “x makes it true that p” is a construction that
>>> signifies, if it signifies anything at all, a relation borne to a truth-
>>> bearer by something else, a truth-maker. But it isn’t generally agreed
>>> what that something else might be, or what truth-bearers are, or what
>>> the character might be of the relationship that holds, if it does,
>>> between them, or even whether such a relationship ever does hold.
>>> https://plato.stanford.edu/entries/truthmakers/
>>
>> But note, that the statement x -> y is NOT a assertion that x MAKES y
>> true, but that the Truth of x proves that Y is true.
>>
>
> x ⊨ y Aristotle's syllogism required a semantic connection based on
> semantic categories.
> https://en.wikipedia.org/wiki/Syllogism#Basic_structure

And Aristotle's logic system is only for CATEGORICAL statements, and
thus only a first order logic system.

Note, your "Semantic" connection here comes out as a neccesary condition
based on you being in CATEGORICAL logic.

Such a system can not express the required logic to create a full
description of the Natural Numbers.

>
>> It is NOT a statement about "Causation", in fact, it is more a
>> statement about sub-sets of models that might exist.
>>
>
> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
> In other words there is a semantic connection form an expression of
> language to its truth maker axioms.

(quoting and changing some symbols to make typable)

A Formula A is a semantic consequence within a formal system FS of a set
of statements L, if and only if there is no model M in which all of L
are True and A is false.

....

Or, in other words, the set of interpretations that makes all memebers
of L true is a subset of the set of interpretations that makes A true.

This is exactly what I said below

Note, "Semantic Consequence" doesn't actually make ANY reference to the
"Meaning of the Words".

This definition supports usages where A is an "ALWAYS TRUE" statement,
which will be a smantic consequence of ANY statement, or where the
statements L form a never true premise which creates a semantic
consequence to any statement.

>
>> The statement x -> y means that the set of possible conditions of
>> truth values of all statements where x is true, is a subset of all the
>> possible conditions of truth values of all statements where y is true.
>>
>> Thus, if we are in a condition where x is true, we know that y must
>> also be true.
>>
>>>
>>> *This means that Wittgenstein is correct*
>>> 'True in Russell's system' means, as was said: proved in Russell's
>>> system; and 'false in Russell's system' means:the opposite has been
>>> proved in Russell's system.
>>> https://www.liarparadox.org/Wittgenstein.pdf]
>>
>> Nope, not unless you are redefinig "Proof" to include an infinite set
>> of connections, at which point you are in a totally new language.
>>
>
> Formal systems require finite proofs to truth or the expression is
> untrue in the formal system. Unless and until there is a connection to
> the axioms of the system the expression remains untrue in the system.
> Curry calls these axioms: "elementary theorems of::T"

Finite connection to PROVE, not to make TRUE.

the "connection" for truth can be an infiinte chain.

Note also, Curry's "elementary theorems" are not a complete set of what
it "True" in the 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

yes, these statements are True, but not all statements that are True are
elementary statements.

Not, he also talks about how these make there Truth KNOWN, not about
what makes the True.

>
>>>
>>> If P is unprovable in Russell's system then P is simply untrue in
>>> Russell's system.
>>>
>> Nope.
>>
>
> Yup. That mathematicians and logicians do not bother to pay attention to
> the philosophical foundations of these things leads them astray. They
> simply follow their learned-by-rote never realizing (or even caring)
> that they are incoherent.

Nope.

You may think that the logic system use dy mathematics is "incoherent"
because it allows Truths to exist without being known, but they find it
useful to express the concepts they want to be able to handle.

It has been shown that any logic system that holds to the requirement
that all Truth must be provable either becomes inconsistent or is
incapbable of handling the concepts wanted to be represents.

It turns out this is a natural concequence of letting a system get "big"
enough, as a consequence of how infinites work.

Since we are finite, our proofs are finite, and some truths just become
to "big" to be proven. By accepting this Higher Logic, we can come to
understand things bigger than if we limit ourselves to only talking
about things that must be provable.

You just don't seem to understand this sort of thing, because you mind
is too small.

>
>> If you hold to this, as has been pointed out, this means, unless you
>> system is very small, that you can't talk about statements you haven't
>> already proven as you don't know if they are Truth Beares.
>>
>> The Provablity of statements is not a Truth Bearr until you have
>> proven that it is.
>>
>
> Curry agrees that the systems define "elementary theorems of::T" that
> anchor the notion of truth in these systems, thus if there is no
> connection from an expression to these anchors then it remains untrue.
>

No, you don't understand Curry. elementary theorems of ::T do NOT define
the whole set of the Truth of ::T, but relate more to Knowledge.

This is you classical error, you confuse what we can know about
something with what it True about it.

On 1/10/2023 6:56 AM, Richard Damon wrote:
> On 1/9/23 11:50 PM, olcott wrote:
>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>> On 1/9/23 10:19 PM, olcott wrote:
>>>> The set of (analytical) expressions of (formal or natural language)
>>>> have
>>>> a complete semantic connection to their truth maker axioms otherwise
>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>
>>> Right, but such a connection can be based on an INFINTE number of
>>>
>>
>> Mathematicians and logicians make sure to ignore the philosophical
>> foundation of these things. or we would never get this:
>>
>> The conventional definition of incompleteness:
>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>
> Right, a system is incomplete if there exist a statement (which has a
> Truth Value) but that statment can neither be proven or disproven in T.
>

Yet the above expression allows epistemological antinomies to show it is
incomplete, whereas epistemological antinomies are not truth bearers
thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

> Alternatively, a system is incomplete if there exists a TRUE statement
> which can not be proven in T

The set of (analytical) expressions of (formal or natural language) have
a complete semantic connection to their truth maker axioms otherwise
they are simply untrue. Copyright 2022 PL Olcott

If they are not true in a formal system because they are epistemological
antinomies thus self-contradictory, thus not truth bearers in this
formal system then they are simply not members of this formal system.

> (the disproven half of the above becoming a
> seperate piece as if the statement is false (not just "untrue") then we
> can form the negation of the statement and not be able to prove that one.
>
>>
>>>>
>>>> Previously philosophers were trying to define truth maker for
>>>> analytical
>>>> truth and empirical truth at the same time and in the same way.
>>>
>>> Nope. Just shows you are not understanding how logic works.
>>>
>>>>
>>>> This much is agreed: “x makes it true that p” is a construction that
>>>> signifies, if it signifies anything at all, a relation borne to a
>>>> truth-
>>>> bearer by something else, a truth-maker. But it isn’t generally agreed
>>>> what that something else might be, or what truth-bearers are, or what
>>>> the character might be of the relationship that holds, if it does,
>>>> between them, or even whether such a relationship ever does hold.
>>>> https://plato.stanford.edu/entries/truthmakers/
>>>
>>> But note, that the statement x -> y is NOT a assertion that x MAKES y
>>> true, but that the Truth of x proves that Y is true.
>>>
>>
>> x ⊨ y Aristotle's syllogism required a semantic connection based on
>> semantic categories.
>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>
> And Aristotle's logic system is only for CATEGORICAL statements, and
> thus only a first order logic system.
>
> Note, your "Semantic" connection here comes out as a neccesary condition
> based on you being in CATEGORICAL logic.
>
> Such a system can not express the required logic to create a full
> description of the Natural Numbers.
>
>
>>
>>> It is NOT a statement about "Causation", in fact, it is more a
>>> statement about sub-sets of models that might exist.
>>>
>>
>> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
>> In other words there is a semantic connection form an expression of
>> language to its truth maker axioms.
>
> (quoting and changing some symbols to make typable)
>
> A Formula A is a semantic consequence within a formal system FS of a set
> of statements L, if and only if there is no model M in which all of L
> are True and A is false.
>

*I am referring to the Haskell Curry notion of true in the 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

In this case we only need a syntactic connection from the expression to
its truth maker axioms, {AKA elementary theorems of 𝓣} otherwise the
expression is simply untrue in 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 Tuesday, January 10, 2023 at 11:43:05 AM UTC-6, olcott wrote:
> On 1/10/2023 6:56 AM, Richard Damon wrote:
> > On 1/9/23 11:50 PM, olcott wrote:
> >> On 1/9/2023 10:01 PM, Richard Damon wrote:
> >>> On 1/9/23 10:19 PM, olcott wrote:
> >>>> The set of (analytical) expressions of (formal or natural language)
> >>>> have
> >>>> a complete semantic connection to their truth maker axioms otherwise
> >>>> they are simply untrue. Copyright 2022 PL Olcott
> >>>
> >>> Right, but such a connection can be based on an INFINTE number of
> >>>
> >>
> >> Mathematicians and logicians make sure to ignore the philosophical
> >> foundation of these things. or we would never get this:
> >>
> >> The conventional definition of incompleteness:
> >> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
> >
> > Right, a system is incomplete if there exist a statement (which has a
> > Truth Value) but that statment can neither be proven or disproven in T.
> >
> Yet the above expression allows epistemological antinomies to show it is
> incomplete, whereas epistemological antinomies are not truth bearers
> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
> > Alternatively, a system is incomplete if there exists a TRUE statement
> > which can not be proven in T
> The set of (analytical) expressions of (formal or natural language) have
> a complete semantic connection to their truth maker axioms otherwise
> they are simply untrue. Copyright 2022 PL Olcott
> If they are not true in a formal system because they are epistemological
> antinomies thus self-contradictory, thus not truth bearers in this
> formal system then they are simply not members of this formal system.
> > (the disproven half of the above becoming a
> > seperate piece as if the statement is false (not just "untrue") then we
> > can form the negation of the statement and not be able to prove that one.
> >
> >>
> >>>>
> >>>> Previously philosophers were trying to define truth maker for
> >>>> analytical
> >>>> truth and empirical truth at the same time and in the same way.
> >>>
> >>> Nope. Just shows you are not understanding how logic works.
> >>>
> >>>>
> >>>> This much is agreed: “x makes it true that p” is a construction that
> >>>> signifies, if it signifies anything at all, a relation borne to a
> >>>> truth-
> >>>> bearer by something else, a truth-maker. But it isn’t generally agreed
> >>>> what that something else might be, or what truth-bearers are, or what
> >>>> the character might be of the relationship that holds, if it does,
> >>>> between them, or even whether such a relationship ever does hold.
> >>>> https://plato.stanford.edu/entries/truthmakers/
> >>>
> >>> But note, that the statement x -> y is NOT a assertion that x MAKES y
> >>> true, but that the Truth of x proves that Y is true.
> >>>
> >>
> >> x ⊨ y Aristotle's syllogism required a semantic connection based on
> >> semantic categories.
> >> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
> >
> > And Aristotle's logic system is only for CATEGORICAL statements, and
> > thus only a first order logic system.
> >
> > Note, your "Semantic" connection here comes out as a neccesary condition
> > based on you being in CATEGORICAL logic.
> >
> > Such a system can not express the required logic to create a full
> > description of the Natural Numbers.
> >
> >
> >>
> >>> It is NOT a statement about "Causation", in fact, it is more a
> >>> statement about sub-sets of models that might exist.
> >>>
> >>
> >> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
> >> In other words there is a semantic connection form an expression of
> >> language to its truth maker axioms.
> >
> > (quoting and changing some symbols to make typable)
> >
> > A Formula A is a semantic consequence within a formal system FS of a set
> > of statements L, if and only if there is no model M in which all of L
> > are True and A is false.
> >
> *I am referring to the Haskell Curry notion of true in the 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
> In this case we only need a syntactic connection from the expression to
> its truth maker axioms, {AKA elementary theorems of 𝓣} otherwise the
> expression is simply untrue in 𝓣.
> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

The only trouble with all of this is, it doesn't put food on the table.

On 1/10/23 12:43 PM, olcott wrote:
> On 1/10/2023 6:56 AM, Richard Damon wrote:
>> On 1/9/23 11:50 PM, olcott wrote:
>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>> The set of (analytical) expressions of (formal or natural language)
>>>>> have
>>>>> a complete semantic connection to their truth maker axioms otherwise
>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>
>>>> Right, but such a connection can be based on an INFINTE number of
>>>>
>>>
>>> Mathematicians and logicians make sure to ignore the philosophical
>>> foundation of these things. or we would never get this:
>>>
>>> The conventional definition of incompleteness:
>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>
>> Right, a system is incomplete if there exist a statement (which has a
>> Truth Value) but that statment can neither be proven or disproven in T.
>>
>
> Yet the above expression allows epistemological antinomies to show it is
> incomplete, whereas epistemological antinomies are not truth bearers
> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))

No, because an epistemological antinomie is not a "∀φ ∈ T", which my
verbal statement makes clear.

The elements of T are only those statements with a Truth Value in T.

>
>> Alternatively, a system is incomplete if there exists a TRUE statement
>> which can not be proven in T
>
> The set of (analytical) expressions of (formal or natural language) have
> a complete semantic connection to their truth maker axioms otherwise
> they are simply untrue. Copyright 2022 PL Olcott

Right, and that semantic connection can b infinite in length, and thus
not a proof.

>
> If they are not true in a formal system because they are epistemological
> antinomies thus self-contradictory, thus not truth bearers in this
> formal system then they are simply not members of this formal system.

Right, even you have agreed that a statement asking about the existance
of a proof of a statement WILL be a Truth Bearer, (as such a proof
either does or does not exist) a thus G, even in the meta-theory is a
Truth Bearer.

>
>> (the disproven half of the above becoming a seperate piece as if the
>> statement is false (not just "untrue") then we can form the negation
>> of the statement and not be able to prove that one.
>>
>>>
>>>>>
>>>>> Previously philosophers were trying to define truth maker for
>>>>> analytical
>>>>> truth and empirical truth at the same time and in the same way.
>>>>
>>>> Nope. Just shows you are not understanding how logic works.
>>>>
>>>>>
>>>>> This much is agreed: “x makes it true that p” is a construction that
>>>>> signifies, if it signifies anything at all, a relation borne to a
>>>>> truth-
>>>>> bearer by something else, a truth-maker. But it isn’t generally agreed
>>>>> what that something else might be, or what truth-bearers are, or what
>>>>> the character might be of the relationship that holds, if it does,
>>>>> between them, or even whether such a relationship ever does hold.
>>>>> https://plato.stanford.edu/entries/truthmakers/
>>>>
>>>> But note, that the statement x -> y is NOT a assertion that x MAKES
>>>> y true, but that the Truth of x proves that Y is true.
>>>>
>>>
>>> x ⊨ y Aristotle's syllogism required a semantic connection based on
>>> semantic categories.
>>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>
>> And Aristotle's logic system is only for CATEGORICAL statements, and
>> thus only a first order logic system.
>>
>> Note, your "Semantic" connection here comes out as a neccesary
>> condition based on you being in CATEGORICAL logic.
>>
>> Such a system can not express the required logic to create a full
>> description of the Natural Numbers.
>>
>>
>>>
>>>> It is NOT a statement about "Causation", in fact, it is more a
>>>> statement about sub-sets of models that might exist.
>>>>
>>>
>>> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
>>> In other words there is a semantic connection form an expression of
>>> language to its truth maker axioms.
>>
>> (quoting and changing some symbols to make typable)
>>
>> A Formula A is a semantic consequence within a formal system FS of a
>> set of statements L, if and only if there is no model M in which all
>> of L are True and A is false.
>>
>
> *I am referring to the Haskell Curry notion of true in the 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
>
> In this case we only need a syntactic connection from the expression to
> its truth maker axioms, {AKA elementary theorems of 𝓣} otherwise the
> expression is simply untrue in 𝓣.
>

Right, and True in the system can come from an infinite set of
connections, and thus not a proof.

You confuse True in the system with KNOWN in the system.

Note, When he says these statements are "True for 𝓣", he is NOT saying
that ONLY these statements are True for 𝓣, so this doesn't actually
define what True for 𝓣 actually means.

On 1/10/2023 5:38 PM, Richard Damon wrote:
> On 1/10/23 12:43 PM, olcott wrote:
>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>> On 1/9/23 11:50 PM, olcott wrote:
>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>> language) have
>>>>>> a complete semantic connection to their truth maker axioms otherwise
>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>
>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>
>>>>
>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>> foundation of these things. or we would never get this:
>>>>
>>>> The conventional definition of incompleteness:
>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>
>>> Right, a system is incomplete if there exist a statement (which has a
>>> Truth Value) but that statment can neither be proven or disproven in T.
>>>
>>
>> Yet the above expression allows epistemological antinomies to show it is
>> incomplete, whereas epistemological antinomies are not truth bearers
>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>
> No, because an epistemological antinomie is not a "∀φ ∈ T", which my
> verbal statement makes clear.
>
> The elements of T are only those statements with a Truth Value in T.

Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
The definition of incompleteness.

>
>>
>>> Alternatively, a system is incomplete if there exists a TRUE
>>> statement which can not be proven in T
>>
>> The set of (analytical) expressions of (formal or natural language)
>> have a complete semantic connection to their truth maker axioms
>> otherwise they are simply untrue. Copyright 2022 PL Olcott
>
> Right, and that semantic connection can b infinite in length, and thus
> not a proof.
>

It is not allowed to be infinite length within formal systems (and you
know this) no proof in T means untrue in T.

>>
>> If they are not true in a formal system because they are epistemological
>> antinomies thus self-contradictory, thus not truth bearers in this
>> formal system then they are simply not members of this formal system.
>
> Right, even you have agreed that a statement asking about the existance
> of a proof of a statement WILL be a Truth Bearer, (as such a proof
> either does or does not exist) a thus G, even in the meta-theory is a
> Truth Bearer.
>

A self-contradictory epistemological antinomy in one formal system can
be resolved in any formal system where it is not self-contradictory.

>>
>>> (the disproven half of the above becoming a seperate piece as if the
>>> statement is false (not just "untrue") then we can form the negation
>>> of the statement and not be able to prove that one.
>>>
>>>>
>>>>>>
>>>>>> Previously philosophers were trying to define truth maker for
>>>>>> analytical
>>>>>> truth and empirical truth at the same time and in the same way.
>>>>>
>>>>> Nope. Just shows you are not understanding how logic works.
>>>>>
>>>>>>
>>>>>> This much is agreed: “x makes it true that p” is a construction that
>>>>>> signifies, if it signifies anything at all, a relation borne to a
>>>>>> truth-
>>>>>> bearer by something else, a truth-maker. But it isn’t generally
>>>>>> agreed
>>>>>> what that something else might be, or what truth-bearers are, or what
>>>>>> the character might be of the relationship that holds, if it does,
>>>>>> between them, or even whether such a relationship ever does hold.
>>>>>> https://plato.stanford.edu/entries/truthmakers/
>>>>>
>>>>> But note, that the statement x -> y is NOT a assertion that x MAKES
>>>>> y true, but that the Truth of x proves that Y is true.
>>>>>
>>>>
>>>> x ⊨ y Aristotle's syllogism required a semantic connection based on
>>>> semantic categories.
>>>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>
>>> And Aristotle's logic system is only for CATEGORICAL statements, and
>>> thus only a first order logic system.
>>>
>>> Note, your "Semantic" connection here comes out as a neccesary
>>> condition based on you being in CATEGORICAL logic.
>>>
>>> Such a system can not express the required logic to create a full
>>> description of the Natural Numbers.
>>>
>>>
>>>>
>>>>> It is NOT a statement about "Causation", in fact, it is more a
>>>>> statement about sub-sets of models that might exist.
>>>>>
>>>>
>>>> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
>>>> In other words there is a semantic connection form an expression of
>>>> language to its truth maker axioms.
>>>
>>> (quoting and changing some symbols to make typable)
>>>
>>> A Formula A is a semantic consequence within a formal system FS of a
>>> set of statements L, if and only if there is no model M in which all
>>> of L are True and A is false.
>>>
>>
>> *I am referring to the Haskell Curry notion of true in the 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
>>
>> In this case we only need a syntactic connection from the expression to
>> its truth maker axioms, {AKA elementary theorems of 𝓣} otherwise the
>> expression is simply untrue in 𝓣.
>>
>
> Right, and True in the system can come from an infinite set of
> connections, and thus not a proof.
>

True within the system requires provable in the system.
True outside the system does not require provable within the system.

Gödel did not even attempt to show that G is true in F.
Gödel showed that G is true outside of F.

For this reason, the sentence GF is often said to be "true but
unprovable." (Raatikainen 2015). However, since the Gödel sentence
cannot itself formally specify its intended interpretation, the truth of
the sentence GF may only be arrived at via a meta-analysis from outside
the system.

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

> You confuse True in the system with KNOWN in the system.
>
> Note, When he says these statements are "True for 𝓣", he is NOT saying
> that ONLY these statements are True for 𝓣, so this doesn't actually
> define what True for 𝓣 actually means.
>

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

On 1/10/23 7:05 PM, olcott wrote:
> On 1/10/2023 5:38 PM, Richard Damon wrote:
>> On 1/10/23 12:43 PM, olcott wrote:
>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>> language) have
>>>>>>> a complete semantic connection to their truth maker axioms otherwise
>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>
>>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>>
>>>>>
>>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>>> foundation of these things. or we would never get this:
>>>>>
>>>>> The conventional definition of incompleteness:
>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>
>>>> Right, a system is incomplete if there exist a statement (which has
>>>> a Truth Value) but that statment can neither be proven or disproven
>>>> in T.
>>>>
>>>
>>> Yet the above expression allows epistemological antinomies to show it is
>>> incomplete, whereas epistemological antinomies are not truth bearers
>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>
>> No, because an epistemological antinomie is not a "∀φ ∈ T", which my
>> verbal statement makes clear.
>>
>> The elements of T are only those statements with a Truth Value in T.
>
> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
> The definition of incompleteness.

Except that the definiton of ⊬ is "Does not PROVE", not is not true (or
you are quoting the wrong definition of incompleteness"

This seems to be your standard problem.

> >>
>>>
>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>> statement which can not be proven in T
>>>
>>> The set of (analytical) expressions of (formal or natural language)
>>> have a complete semantic connection to their truth maker axioms
>>> otherwise they are simply untrue. Copyright 2022 PL Olcott
>>
>> Right, and that semantic connection can b infinite in length, and thus
>> not a proof.
>>
>
> It is not allowed to be infinite length within formal systems (and you
> know this) no proof in T means untrue in T.
>

Source of that claim?

For TRUTH (not proof)

Until you can document that, it isn't true, and you are just making
yourself to be a liar.

>>>
>>> If they are not true in a formal system because they are epistemological
>>> antinomies thus self-contradictory, thus not truth bearers in this
>>> formal system then they are simply not members of this formal system.
>>
>> Right, even you have agreed that a statement asking about the
>> existance of a proof of a statement WILL be a Truth Bearer, (as such a
>> proof either does or does not exist) a thus G, even in the meta-theory
>> is a Truth Bearer.
>>
>
> A self-contradictory epistemological antinomy in one formal system can
> be resolved in any formal system where it is not self-contradictory.
>

So? in F, G is just a statement about the existance of a number.

in Meta-F, G is that same staement, but from it you can prove that G
being true implies that G can not be proven

So, where is the "Self-Contradictory Statement"?

How can a question about the existance of a number meeting a certain
requirement be "Self-Contradictory?"

>>>
>>>> (the disproven half of the above becoming a seperate piece as if the
>>>> statement is false (not just "untrue") then we can form the negation
>>>> of the statement and not be able to prove that one.
>>>>
>>>>>
>>>>>>>
>>>>>>> Previously philosophers were trying to define truth maker for
>>>>>>> analytical
>>>>>>> truth and empirical truth at the same time and in the same way.
>>>>>>
>>>>>> Nope. Just shows you are not understanding how logic works.
>>>>>>
>>>>>>>
>>>>>>> This much is agreed: “x makes it true that p” is a construction that
>>>>>>> signifies, if it signifies anything at all, a relation borne to a
>>>>>>> truth-
>>>>>>> bearer by something else, a truth-maker. But it isn’t generally
>>>>>>> agreed
>>>>>>> what that something else might be, or what truth-bearers are, or
>>>>>>> what
>>>>>>> the character might be of the relationship that holds, if it does,
>>>>>>> between them, or even whether such a relationship ever does hold.
>>>>>>> https://plato.stanford.edu/entries/truthmakers/
>>>>>>
>>>>>> But note, that the statement x -> y is NOT a assertion that x
>>>>>> MAKES y true, but that the Truth of x proves that Y is true.
>>>>>>
>>>>>
>>>>> x ⊨ y Aristotle's syllogism required a semantic connection based on
>>>>> semantic categories.
>>>>> https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>>
>>>> And Aristotle's logic system is only for CATEGORICAL statements, and
>>>> thus only a first order logic system.
>>>>
>>>> Note, your "Semantic" connection here comes out as a neccesary
>>>> condition based on you being in CATEGORICAL logic.
>>>>
>>>> Such a system can not express the required logic to create a full
>>>> description of the Natural Numbers.
>>>>
>>>>
>>>>>
>>>>>> It is NOT a statement about "Causation", in fact, it is more a
>>>>>> statement about sub-sets of models that might exist.
>>>>>>
>>>>>
>>>>> https://en.wikipedia.org/wiki/Logical_consequence#Semantic_consequence
>>>>> In other words there is a semantic connection form an expression of
>>>>> language to its truth maker axioms.
>>>>
>>>> (quoting and changing some symbols to make typable)
>>>>
>>>> A Formula A is a semantic consequence within a formal system FS of a
>>>> set of statements L, if and only if there is no model M in which all
>>>> of L are True and A is false.
>>>>
>>>
>>> *I am referring to the Haskell Curry notion of true in the 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
>>>
>>> In this case we only need a syntactic connection from the expression to
>>> its truth maker axioms, {AKA elementary theorems of 𝓣} otherwise the
>>> expression is simply untrue in 𝓣.
>>>
>>
>> Right, and True in the system can come from an infinite set of
>> connections, and thus not a proof.
>>
>
> True within the system requires provable in the system.

Source!!!

That is the lie that you will DIE on

> True outside the system does not require provable within the system.

SOURCE.

>
> Gödel did not even attempt to show that G is true in F.
> Gödel showed that G is true outside of F.

No, In his proof he shows that due to the things that can be proved in
Meta-F, G must be true in F.

Try to actually READ his proof.

My guess is you are looking at the Cliff notes version because it is
beyond you, and yo aren't even understand those Cliff Notes.

>
> For this reason, the sentence GF is often said to be "true but
> unprovable." (Raatikainen 2015). However, since the Gödel sentence
> cannot itself formally specify its intended interpretation, the truth of
> the sentence GF may only be arrived at via a meta-analysis from outside
> the system.
>

On 1/10/2023 6:27 PM, Richard Damon wrote:
> On 1/10/23 7:05 PM, olcott wrote:
>> On 1/10/2023 5:38 PM, Richard Damon wrote:
>>> On 1/10/23 12:43 PM, olcott wrote:
>>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>> language) have
>>>>>>>> a complete semantic connection to their truth maker axioms
>>>>>>>> otherwise
>>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>>
>>>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>>>
>>>>>>
>>>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>>>> foundation of these things. or we would never get this:
>>>>>>
>>>>>> The conventional definition of incompleteness:
>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>
>>>>> Right, a system is incomplete if there exist a statement (which has
>>>>> a Truth Value) but that statment can neither be proven or disproven
>>>>> in T.
>>>>>
>>>>
>>>> Yet the above expression allows epistemological antinomies to show
>>>> it is
>>>> incomplete, whereas epistemological antinomies are not truth bearers
>>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>
>>> No, because an epistemological antinomie is not a "∀φ ∈ T", which my
>>> verbal statement makes clear.
>>>
>>> The elements of T are only those statements with a Truth Value in T.
>>
>> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>> The definition of incompleteness.
>
>
> Except that the definiton of ⊬ is "Does not PROVE", not is not true (or
> you are quoting the wrong definition of incompleteness"
>
> This seems to be your standard problem.
>
>> >>
>>>>
>>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>>> statement which can not be proven in T
>>>>
>>>> The set of (analytical) expressions of (formal or natural language)
>>>> have a complete semantic connection to their truth maker axioms
>>>> otherwise they are simply untrue. Copyright 2022 PL Olcott
>>>
>>> Right, and that semantic connection can b infinite in length, and
>>> thus not a proof.
>>>
>>
>> It is not allowed to be infinite length within formal systems (and you
>> know this) no proof in T means untrue in T.
>>
>
> Source of that claim?
>
> For TRUTH (not proof)
>
> Until you can document that, it isn't true, and you are just making
> yourself to be a liar.

You said that infinite proofs are not allowed are you changing your
mind? Did you forget that you said this?

>
>>>>
>>>> If they are not true in a formal system because they are
>>>> epistemological
>>>> antinomies thus self-contradictory, thus not truth bearers in this
>>>> formal system then they are simply not members of this formal system.
>>>
>>> Right, even you have agreed that a statement asking about the
>>> existance of a proof of a statement WILL be a Truth Bearer, (as such
>>> a proof either does or does not exist) a thus G, even in the
>>> meta-theory is a Truth Bearer.
>>>
>>
>> A self-contradictory epistemological antinomy in one formal system can
>> be resolved in any formal system where it is not self-contradictory.
>>
>
> So? in F, G is just a statement about the existance of a number.
>

G is not true in F. An expression is true in a formal system iff it is
provable from the axioms of this formal system.

> in Meta-F, G is that same staement, but from it you can prove that G
> being true implies that G can not be proven
>
> So, where is the "Self-Contradictory Statement"?
>

The G says of itself that it is unprovable in F is self-connradictory in F.

>> True within the system requires provable in the system.
>
> Source!!!
>
> That is the lie that you will DIE on
>
>> True outside the system does not require provable within the system.
>
> SOURCE.
>
>>
>> Gödel did not even attempt to show that G is true in F.
>> Gödel showed that G is true outside of F.
>
> No, In his proof he shows that due to the things that can be proved in
> Meta-F, G must be true in F.
>
> Try to actually READ his proof.
>
> My guess is you are looking at the Cliff notes version because it is
> beyond you, and yo aren't even understand those Cliff Notes.
>
>>
>> For this reason, the sentence GF is often said to be "true but
>> unprovable." (Raatikainen 2015). However, since the Gödel sentence
>> cannot itself formally specify its intended interpretation, the truth
>> of the sentence GF may only be arrived at via a meta-analysis from
>> outside the system.
>>
>
> No, the Godel sentence if F EXACTLY specifies its direct meaning in F.
>
> That no number exists that meets a certain criteria. PERIOD.
>
> The Truth of that statement is proven in Meta F.

"This sentence is not true" is proven true in meta F.

>
>> https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
>>
>>> You confuse True in the system with KNOWN in the system.
>>>
>>> Note, When he says these statements are "True for 𝓣", he is NOT
>>> saying that ONLY these statements are True for 𝓣, so this doesn't
>>> actually define what True for 𝓣 actually means.
>>>
>>
>

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

On 1/10/23 9:03 PM, olcott wrote:
> On 1/10/2023 6:27 PM, Richard Damon wrote:
>> On 1/10/23 7:05 PM, olcott wrote:
>>> On 1/10/2023 5:38 PM, Richard Damon wrote:
>>>> On 1/10/23 12:43 PM, olcott wrote:
>>>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>>> language) have
>>>>>>>>> a complete semantic connection to their truth maker axioms
>>>>>>>>> otherwise
>>>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>>>
>>>>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>>>>
>>>>>>>
>>>>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>>>>> foundation of these things. or we would never get this:
>>>>>>>
>>>>>>> The conventional definition of incompleteness:
>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>
>>>>>> Right, a system is incomplete if there exist a statement (which
>>>>>> has a Truth Value) but that statment can neither be proven or
>>>>>> disproven in T.
>>>>>>
>>>>>
>>>>> Yet the above expression allows epistemological antinomies to show
>>>>> it is
>>>>> incomplete, whereas epistemological antinomies are not truth bearers
>>>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>
>>>> No, because an epistemological antinomie is not a "∀φ ∈ T", which my
>>>> verbal statement makes clear.
>>>>
>>>> The elements of T are only those statements with a Truth Value in T.
>>>
>>> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>> The definition of incompleteness.
>>
>>
>> Except that the definiton of ⊬ is "Does not PROVE", not is not true
>> (or you are quoting the wrong definition of incompleteness"
>>
>> This seems to be your standard problem.
>>
>>> >>
>>>>>
>>>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>>>> statement which can not be proven in T
>>>>>
>>>>> The set of (analytical) expressions of (formal or natural language)
>>>>> have a complete semantic connection to their truth maker axioms
>>>>> otherwise they are simply untrue. Copyright 2022 PL Olcott
>>>>
>>>> Right, and that semantic connection can b infinite in length, and
>>>> thus not a proof.
>>>>
>>>
>>> It is not allowed to be infinite length within formal systems (and
>>> you know this) no proof in T means untrue in T.
>>>
>>
>> Source of that claim?
>>
>> For TRUTH (not proof)
>>
>> Until you can document that, it isn't true, and you are just making
>> yourself to be a liar.
>
> You said that infinite proofs are not allowed are you changing your
> mind? Did you forget that you said this?
>

You seem to have a brain short between the concepts of Truth and Proof.

I said TRUTH allows an infinite connection, but PROOFS do not.

SInce you just answered my requrest for your source of your claim that
TRUTH needed to be finite, I will take it as PROOF that no such source
exists, and every time you make that claim in the future, I can just
call youi a LIAR.

>>
>>>>>
>>>>> If they are not true in a formal system because they are
>>>>> epistemological
>>>>> antinomies thus self-contradictory, thus not truth bearers in this
>>>>> formal system then they are simply not members of this formal system.
>>>>
>>>> Right, even you have agreed that a statement asking about the
>>>> existance of a proof of a statement WILL be a Truth Bearer, (as such
>>>> a proof either does or does not exist) a thus G, even in the
>>>> meta-theory is a Truth Bearer.
>>>>
>>>
>>> A self-contradictory epistemological antinomy in one formal system
>>> can be resolved in any formal system where it is not self-contradictory.
>>>
>>
>> So? in F, G is just a statement about the existance of a number.
>>
>
> G is not true in F. An expression is true in a formal system iff it is
> provable from the axioms of this formal system.
>

Yes, it is. It is proven in the logic of the proof.

Again, you show you don't understand the defintion of TRUTH, as it is
NOT required for a statement to be proven to be True, and your LYING
about it just shows you don't know what you are talking about.

>> in Meta-F, G is that same staement, but from it you can prove that G
>> being true implies that G can not be proven
>>
>> So, where is the "Self-Contradictory Statement"?
>>
>
> The G says of itself that it is unprovable in F is self-connradictory in F.

Nope, G (in F) says that there does not exist a number g that satisfies
a specific primative recursive relationship.

G in th meta-theory says the same thing, that such a number does not
exist, but in the meta-Theory, we can show that the existance of such a
number is the equivaenet of a proof of G.

Note, this comes from the fact that in Meta-F we can show that this
specific primative recurcive relationship is a proof checker for a proof
encoded as a number per the rules of the meta-theory.

(The basic math is the same in theory and meta-theory, only the added
interpreation as a proof checker is added in the meta-theory)

>
>>> True within the system requires provable in the system.
>>
>> Source!!!
>>
>> That is the lie that you will DIE on
>>
>>> True outside the system does not require provable within the system.
>>
>> SOURCE.
>>
>>>
>>> Gödel did not even attempt to show that G is true in F.
>>> Gödel showed that G is true outside of F.
>>
>> No, In his proof he shows that due to the things that can be proved in
>> Meta-F, G must be true in F.
>>
>> Try to actually READ his proof.
>>
>> My guess is you are looking at the Cliff notes version because it is
>> beyond you, and yo aren't even understand those Cliff Notes.
>>
>>>
>>> For this reason, the sentence GF is often said to be "true but
>>> unprovable." (Raatikainen 2015). However, since the Gödel sentence
>>> cannot itself formally specify its intended interpretation, the truth
>>> of the sentence GF may only be arrived at via a meta-analysis from
>>> outside the system.
>>>
>>
>> No, the Godel sentence if F EXACTLY specifies its direct meaning in F.
>>
>> That no number exists that meets a certain criteria. PERIOD.
>>
>> The Truth of that statement is proven in Meta F.
>
> "This sentence is not true" is proven true in meta F.

Nope, What is proven in the meta-theory is that no number can satisfy
the specified primative recursive relationship, as if such a number
existed, it would imply that one can prove a false statement (to be true).

You are just PROVING that you don't understand Godel's proof, or even
the Cliff Notes version of it.

>
>>
>>> https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
>>>
>>>> You confuse True in the system with KNOWN in the system.
>>>>
>>>> Note, When he says these statements are "True for 𝓣", he is NOT
>>>> saying that ONLY these statements are True for 𝓣, so this doesn't
>>>> actually define what True for 𝓣 actually means.
>>>>
>>>
>>
>

On 1/10/2023 9:26 PM, Richard Damon wrote:
> On 1/10/23 9:03 PM, olcott wrote:
>> On 1/10/2023 6:27 PM, Richard Damon wrote:
>>> On 1/10/23 7:05 PM, olcott wrote:
>>>> On 1/10/2023 5:38 PM, Richard Damon wrote:
>>>>> On 1/10/23 12:43 PM, olcott wrote:
>>>>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>>>> language) have
>>>>>>>>>> a complete semantic connection to their truth maker axioms
>>>>>>>>>> otherwise
>>>>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>>>>
>>>>>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>>>>>
>>>>>>>>
>>>>>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>>>>>> foundation of these things. or we would never get this:
>>>>>>>>
>>>>>>>> The conventional definition of incompleteness:
>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>
>>>>>>> Right, a system is incomplete if there exist a statement (which
>>>>>>> has a Truth Value) but that statment can neither be proven or
>>>>>>> disproven in T.
>>>>>>>
>>>>>>
>>>>>> Yet the above expression allows epistemological antinomies to show
>>>>>> it is
>>>>>> incomplete, whereas epistemological antinomies are not truth bearers
>>>>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>
>>>>> No, because an epistemological antinomie is not a "∀φ ∈ T", which
>>>>> my verbal statement makes clear.
>>>>>
>>>>> The elements of T are only those statements with a Truth Value in T.
>>>>
>>>> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>> The definition of incompleteness.
>>>
>>>
>>> Except that the definiton of ⊬ is "Does not PROVE", not is not true
>>> (or you are quoting the wrong definition of incompleteness"
>>>
>>> This seems to be your standard problem.
>>>
>>>> >>
>>>>>>
>>>>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>>>>> statement which can not be proven in T
>>>>>>
>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>> language) have a complete semantic connection to their truth maker
>>>>>> axioms otherwise they are simply untrue. Copyright 2022 PL Olcott
>>>>>
>>>>> Right, and that semantic connection can b infinite in length, and
>>>>> thus not a proof.
>>>>>
>>>>
>>>> It is not allowed to be infinite length within formal systems (and
>>>> you know this) no proof in T means untrue in T.
>>>>
>>>
>>> Source of that claim?
>>>
>>> For TRUTH (not proof)
>>>
>>> Until you can document that, it isn't true, and you are just making
>>> yourself to be a liar.
>>
>> You said that infinite proofs are not allowed are you changing your
>> mind? Did you forget that you said this?
>>
>
> You seem to have a brain short between the concepts of Truth and Proof.
>
> I said TRUTH allows an infinite connection, but PROOFS do not.
>

If an analytic expression of language is true or false there must be a
complete set of semantic connections making it true or false otherwise
it is not a truth bearer.

Because formal systems are only allowed to have finite proofs formal
systems are not allowed to have infinite connections to their semantic
truth maker. Thus an expression is only true in a formal system iff it
is provable within this system. Otherwise this expression is untrue
which may or may not include false.

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

On 1/12/23 8:56 PM, olcott wrote:
> On 1/10/2023 9:26 PM, Richard Damon wrote:
>> On 1/10/23 9:03 PM, olcott wrote:
>>> On 1/10/2023 6:27 PM, Richard Damon wrote:
>>>> On 1/10/23 7:05 PM, olcott wrote:
>>>>> On 1/10/2023 5:38 PM, Richard Damon wrote:
>>>>>> On 1/10/23 12:43 PM, olcott wrote:
>>>>>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>>>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>>>>> language) have
>>>>>>>>>>> a complete semantic connection to their truth maker axioms
>>>>>>>>>>> otherwise
>>>>>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>>>>>
>>>>>>>>>> Right, but such a connection can be based on an INFINTE number of
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Mathematicians and logicians make sure to ignore the philosophical
>>>>>>>>> foundation of these things. or we would never get this:
>>>>>>>>>
>>>>>>>>> The conventional definition of incompleteness:
>>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>
>>>>>>>> Right, a system is incomplete if there exist a statement (which
>>>>>>>> has a Truth Value) but that statment can neither be proven or
>>>>>>>> disproven in T.
>>>>>>>>
>>>>>>>
>>>>>>> Yet the above expression allows epistemological antinomies to
>>>>>>> show it is
>>>>>>> incomplete, whereas epistemological antinomies are not truth bearers
>>>>>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>
>>>>>> No, because an epistemological antinomie is not a "∀φ ∈ T", which
>>>>>> my verbal statement makes clear.
>>>>>>
>>>>>> The elements of T are only those statements with a Truth Value in T.
>>>>>
>>>>> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>> The definition of incompleteness.
>>>>
>>>>
>>>> Except that the definiton of ⊬ is "Does not PROVE", not is not true
>>>> (or you are quoting the wrong definition of incompleteness"
>>>>
>>>> This seems to be your standard problem.
>>>>
>>>>> >>
>>>>>>>
>>>>>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>>>>>> statement which can not be proven in T
>>>>>>>
>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>> language) have a complete semantic connection to their truth
>>>>>>> maker axioms otherwise they are simply untrue. Copyright 2022 PL
>>>>>>> Olcott
>>>>>>
>>>>>> Right, and that semantic connection can b infinite in length, and
>>>>>> thus not a proof.
>>>>>>
>>>>>
>>>>> It is not allowed to be infinite length within formal systems (and
>>>>> you know this) no proof in T means untrue in T.
>>>>>
>>>>
>>>> Source of that claim?
>>>>
>>>> For TRUTH (not proof)
>>>>
>>>> Until you can document that, it isn't true, and you are just making
>>>> yourself to be a liar.
>>>
>>> You said that infinite proofs are not allowed are you changing your
>>> mind? Did you forget that you said this?
>>>
>>
>> You seem to have a brain short between the concepts of Truth and Proof.
>>
>> I said TRUTH allows an infinite connection, but PROOFS do not.
>>
>
> If an analytic expression of language is true or false there must be a
> complete set of semantic connections making it true or false otherwise
> it is not a truth bearer.

Right, but the connect set can be infinite.

>
> Because formal systems are only allowed to have finite proofs formal
> systems are not allowed to have infinite connections to their semantic
> truth maker. Thus an expression is only true in a formal system iff it
> is provable within this system. Otherwise this expression is untrue
> which may or may not include false.
>
>

Right, FINITE PROOFS, says nothing about TRUTH.

This is just like you saying that Cats are Dogs, and makes just as much
sense.

You mind is unable to distinguish between the concepts of Proof and Truth.

This may be related to the fact that you don't understand how an
infinite works.

You mind is just too small.

On 1/12/2023 8:37 PM, Richard Damon wrote:
> On 1/12/23 8:56 PM, olcott wrote:
>> On 1/10/2023 9:26 PM, Richard Damon wrote:
>>> On 1/10/23 9:03 PM, olcott wrote:
>>>> On 1/10/2023 6:27 PM, Richard Damon wrote:
>>>>> On 1/10/23 7:05 PM, olcott wrote:
>>>>>> On 1/10/2023 5:38 PM, Richard Damon wrote:
>>>>>>> On 1/10/23 12:43 PM, olcott wrote:
>>>>>>>> On 1/10/2023 6:56 AM, Richard Damon wrote:
>>>>>>>>> On 1/9/23 11:50 PM, olcott wrote:
>>>>>>>>>> On 1/9/2023 10:01 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/9/23 10:19 PM, olcott wrote:
>>>>>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>>>>>> language) have
>>>>>>>>>>>> a complete semantic connection to their truth maker axioms
>>>>>>>>>>>> otherwise
>>>>>>>>>>>> they are simply untrue. Copyright 2022 PL Olcott
>>>>>>>>>>>
>>>>>>>>>>> Right, but such a connection can be based on an INFINTE
>>>>>>>>>>> number of
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Mathematicians and logicians make sure to ignore the
>>>>>>>>>> philosophical
>>>>>>>>>> foundation of these things. or we would never get this:
>>>>>>>>>>
>>>>>>>>>> The conventional definition of incompleteness:
>>>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>
>>>>>>>>> Right, a system is incomplete if there exist a statement (which
>>>>>>>>> has a Truth Value) but that statment can neither be proven or
>>>>>>>>> disproven in T.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Yet the above expression allows epistemological antinomies to
>>>>>>>> show it is
>>>>>>>> incomplete, whereas epistemological antinomies are not truth
>>>>>>>> bearers
>>>>>>>> thus not members of any formal system: ∀φ ∈ T ((T ⊢ φ) ∨ (T ⊢ ¬φ))
>>>>>>>
>>>>>>> No, because an epistemological antinomie is not a "∀φ ∈ T", which
>>>>>>> my verbal statement makes clear.
>>>>>>>
>>>>>>> The elements of T are only those statements with a Truth Value in T.
>>>>>>
>>>>>> Yes thus negating: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>> The definition of incompleteness.
>>>>>
>>>>>
>>>>> Except that the definiton of ⊬ is "Does not PROVE", not is not true
>>>>> (or you are quoting the wrong definition of incompleteness"
>>>>>
>>>>> This seems to be your standard problem.
>>>>>
>>>>>> >>
>>>>>>>>
>>>>>>>>> Alternatively, a system is incomplete if there exists a TRUE
>>>>>>>>> statement which can not be proven in T
>>>>>>>>
>>>>>>>> The set of (analytical) expressions of (formal or natural
>>>>>>>> language) have a complete semantic connection to their truth
>>>>>>>> maker axioms otherwise they are simply untrue. Copyright 2022 PL
>>>>>>>> Olcott
>>>>>>>
>>>>>>> Right, and that semantic connection can b infinite in length, and
>>>>>>> thus not a proof.
>>>>>>>
>>>>>>
>>>>>> It is not allowed to be infinite length within formal systems (and
>>>>>> you know this) no proof in T means untrue in T.
>>>>>>
>>>>>
>>>>> Source of that claim?
>>>>>
>>>>> For TRUTH (not proof)
>>>>>
>>>>> Until you can document that, it isn't true, and you are just making
>>>>> yourself to be a liar.
>>>>
>>>> You said that infinite proofs are not allowed are you changing your
>>>> mind? Did you forget that you said this?
>>>>
>>>
>>> You seem to have a brain short between the concepts of Truth and Proof.
>>>
>>> I said TRUTH allows an infinite connection, but PROOFS do not.
>>>
>>
>> If an analytic expression of language is true or false there must be a
>> complete set of semantic connections making it true or false otherwise
>> it is not a truth bearer.
>
>
> Right, but the connect set can be infinite.
>
>>
>> Because formal systems are only allowed to have finite proofs formal
>> systems are not allowed to have infinite connections to their semantic
>> truth maker. Thus an expression is only true in a formal system iff it
>> is provable within this system. Otherwise this expression is untrue
>> which may or may not include false.
>>
>>
>
> Right, FINITE PROOFS, says nothing about TRUTH.
>

That it ridiculously false. Expressions of language that are proven to
have a connection to their truth maker axioms are a subset of all truth
and comprise the entire body of analytical knowledge.

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

On 1/12/23 10:04 PM, olcott wrote:
> On 1/12/2023 8:37 PM, Richard Damon wrote:
>> On 1/12/23 8:56 PM, olcott wrote:

>>> Because formal systems are only allowed to have finite proofs formal
>>> systems are not allowed to have infinite connections to their semantic
>>> truth maker. Thus an expression is only true in a formal system iff it
>>> is provable within this system. Otherwise this expression is untrue
>>> which may or may not include false.
>>>
>>>
>>
>> Right, FINITE PROOFS, says nothing about TRUTH.
>>
>
> That it ridiculously false. Expressions of language that are proven to
> have a connection to their truth maker axioms are a subset of all truth
> and comprise the entire body of analytical knowledge.
>

So, since proven statements are a SUBSET of all truth, what says that
all truths have to be proven.

that is like saying that since Dogs are a subset of Animals, all Animals
are Dogs.

You are just proving how little you understand about logic.

On 1/12/2023 9:35 PM, Richard Damon wrote:
> On 1/12/23 10:04 PM, olcott wrote:
>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>> On 1/12/23 8:56 PM, olcott wrote:
>
>>>> Because formal systems are only allowed to have finite proofs formal
>>>> systems are not allowed to have infinite connections to their semantic
>>>> truth maker. Thus an expression is only true in a formal system iff it
>>>> is provable within this system. Otherwise this expression is untrue
>>>> which may or may not include false.
>>>>
>>>>
>>>
>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>
>>
>> That it ridiculously false. Expressions of language that are proven to
>> have a connection to their truth maker axioms are a subset of all truth
>> and comprise the entire body of analytical knowledge.
>>
>
> So, since proven statements are a SUBSET of all truth, what says that
> all truths have to be proven.
>

Within a formal system where true requires finite proof to axioms the
lack of a finite proof to axioms means untrue.

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

On 1/12/23 10:52 PM, olcott wrote:
> On 1/12/2023 9:35 PM, Richard Damon wrote:
>> On 1/12/23 10:04 PM, olcott wrote:
>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>> On 1/12/23 8:56 PM, olcott wrote:
>>
>>>>> Because formal systems are only allowed to have finite proofs formal
>>>>> systems are not allowed to have infinite connections to their semantic
>>>>> truth maker. Thus an expression is only true in a formal system iff it
>>>>> is provable within this system. Otherwise this expression is untrue
>>>>> which may or may not include false.
>>>>>
>>>>>
>>>>
>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>
>>>
>>> That it ridiculously false. Expressions of language that are proven to
>>> have a connection to their truth maker axioms are a subset of all truth
>>> and comprise the entire body of analytical knowledge.
>>>
>>
>> So, since proven statements are a SUBSET of all truth, what says that
>> all truths have to be proven.
>>
>
> Within a formal system where true requires finite proof to axioms the
> lack of a finite proof to axioms means untrue.
>

Source of claim?

Since the DEFINITION just requires *A* connection, and doesn't specify
finite, where do you get the limitation that it must be.

Note, you can not use a philosophical argument that it needs to be,
because that isn't part of the formal system.

Yes, some philosophers want to claim it, but they have been proven WRONG.

You are just about a century behind in your logic.

On 1/12/2023 9:58 PM, Richard Damon wrote:
> On 1/12/23 10:52 PM, olcott wrote:
>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>> On 1/12/23 10:04 PM, olcott wrote:
>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>
>>>>>> Because formal systems are only allowed to have finite proofs formal
>>>>>> systems are not allowed to have infinite connections to their
>>>>>> semantic
>>>>>> truth maker. Thus an expression is only true in a formal system
>>>>>> iff it
>>>>>> is provable within this system. Otherwise this expression is untrue
>>>>>> which may or may not include false.
>>>>>>
>>>>>>
>>>>>
>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>
>>>>
>>>> That it ridiculously false. Expressions of language that are proven to
>>>> have a connection to their truth maker axioms are a subset of all truth
>>>> and comprise the entire body of analytical knowledge.
>>>>
>>>
>>> So, since proven statements are a SUBSET of all truth, what says that
>>> all truths have to be proven.
>>>
>>
>> Within a formal system where true requires finite proof to axioms the
>> lack of a finite proof to axioms means untrue.
>>
>
> Source of claim?
>

How else can it possibly work?

I figure these things out on the basis of categorically exhaustive
reasoning.

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

On 1/13/23 10:42 AM, olcott wrote:
> On 1/12/2023 9:58 PM, Richard Damon wrote:
>> On 1/12/23 10:52 PM, olcott wrote:
>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>
>>>>>>> Because formal systems are only allowed to have finite proofs formal
>>>>>>> systems are not allowed to have infinite connections to their
>>>>>>> semantic
>>>>>>> truth maker. Thus an expression is only true in a formal system
>>>>>>> iff it
>>>>>>> is provable within this system. Otherwise this expression is untrue
>>>>>>> which may or may not include false.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>
>>>>>
>>>>> That it ridiculously false. Expressions of language that are proven to
>>>>> have a connection to their truth maker axioms are a subset of all
>>>>> truth
>>>>> and comprise the entire body of analytical knowledge.
>>>>>
>>>>
>>>> So, since proven statements are a SUBSET of all truth, what says
>>>> that all truths have to be proven.
>>>>
>>>
>>> Within a formal system where true requires finite proof to axioms the
>>> lack of a finite proof to axioms means untrue.
>>>
>>
>> Source of claim?
>>
>
> How else can it possibly work?
>
> I figure these things out on the basis of categorically exhaustive
> reasoning.

Good, so you admit that it isn't based on any REAL theoretical basis but
only due to your limited (and flawed) thinkng ability.

Note, you CAN'T do a categorically exhaustive reasoning on this problem,
as its is an INFINITE domain. You just don't seem to understand the
nature of infinity, so you don't see that.

The Truth value is just based on the existance of a set on connections
to the axioms. Formal system or not, and NOTHING limits that to being
finite.

Proof is something different, Proof is a demonstration of Knowledge,
which since we are finite beings, means it needs to be a finite set of
connections, so we can know it.

Why shouldn't they be different.

Truth is NOT what we know, but what actually is, even in a purely
analytic "Universe". If there is a connection, ANY connection, even
infinite, to the Truth Makers within the system of interest.

In fact, the proofs that you appear not to be able to understand show
that any system based on an axiom that is equivalent to all Truth is
Provablye is strictly limited in the scope it can handle without
becoming inconsistent.

Inconsistent systems seem to also be a blind spot to you, as you don't
seem to understand that you can't just "disprove" a prove theory by
showing a proof of the opposite result, all that does is show that the
system that you used to prove that alternate result is inconsistent, by
definition, if you can't also validly show an actual ERROR in the
original proof.

Note, just CLAIMING an error, that isn't actually an error, doesn't count.

Claiming it can't be true becaue it counterdicts your ideas doesn't
count (just shows your ideas are inconsistenet).

Since G is about the existance of a number meeting a specific computable
set of properties, it must be a truth bearer in conventional logic.

All you are doing calling it not is proving you don't understand what
you are doing.

On 1/13/2023 6:25 PM, Richard Damon wrote:
> On 1/13/23 10:42 AM, olcott wrote:
>> On 1/12/2023 9:58 PM, Richard Damon wrote:
>>> On 1/12/23 10:52 PM, olcott wrote:
>>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>>
>>>>>>>> Because formal systems are only allowed to have finite proofs
>>>>>>>> formal
>>>>>>>> systems are not allowed to have infinite connections to their
>>>>>>>> semantic
>>>>>>>> truth maker. Thus an expression is only true in a formal system
>>>>>>>> iff it
>>>>>>>> is provable within this system. Otherwise this expression is untrue
>>>>>>>> which may or may not include false.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>>
>>>>>>
>>>>>> That it ridiculously false. Expressions of language that are
>>>>>> proven to
>>>>>> have a connection to their truth maker axioms are a subset of all
>>>>>> truth
>>>>>> and comprise the entire body of analytical knowledge.
>>>>>>
>>>>>
>>>>> So, since proven statements are a SUBSET of all truth, what says
>>>>> that all truths have to be proven.
>>>>>
>>>>
>>>> Within a formal system where true requires finite proof to axioms the
>>>> lack of a finite proof to axioms means untrue.
>>>>
>>>
>>> Source of claim?
>>>
>>
>> How else can it possibly work?
>>
>> I figure these things out on the basis of categorically exhaustive
>> reasoning.
>
>
> Good, so you admit that it isn't based on any REAL theoretical basis but
> only due to your limited (and flawed) thinkng ability.
>
> Note, you CAN'T do a categorically exhaustive reasoning on this problem,
> as its is an INFINITE domain. You just don't seem to understand the
> nature of infinity, so you don't see that.
>
> The Truth value is just based on the existance of a set on connections
> to the axioms. Formal system or not, and NOTHING limits that to being
> finite.
>
In other words you are saying that it is *TRUE IN THE FORMAL SYSTEM*
even if it is *NOT TRUE IN THE FORMAL SYSTEM*.

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

On 1/14/23 3:28 PM, olcott wrote:
> On 1/13/2023 6:25 PM, Richard Damon wrote:
>> On 1/13/23 10:42 AM, olcott wrote:
>>> On 1/12/2023 9:58 PM, Richard Damon wrote:
>>>> On 1/12/23 10:52 PM, olcott wrote:
>>>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>>>
>>>>>>>>> Because formal systems are only allowed to have finite proofs
>>>>>>>>> formal
>>>>>>>>> systems are not allowed to have infinite connections to their
>>>>>>>>> semantic
>>>>>>>>> truth maker. Thus an expression is only true in a formal system
>>>>>>>>> iff it
>>>>>>>>> is provable within this system. Otherwise this expression is
>>>>>>>>> untrue
>>>>>>>>> which may or may not include false.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>>>
>>>>>>>
>>>>>>> That it ridiculously false. Expressions of language that are
>>>>>>> proven to
>>>>>>> have a connection to their truth maker axioms are a subset of all
>>>>>>> truth
>>>>>>> and comprise the entire body of analytical knowledge.
>>>>>>>
>>>>>>
>>>>>> So, since proven statements are a SUBSET of all truth, what says
>>>>>> that all truths have to be proven.
>>>>>>
>>>>>
>>>>> Within a formal system where true requires finite proof to axioms the
>>>>> lack of a finite proof to axioms means untrue.
>>>>>
>>>>
>>>> Source of claim?
>>>>
>>>
>>> How else can it possibly work?
>>>
>>> I figure these things out on the basis of categorically exhaustive
>>> reasoning.
>>
>>
>> Good, so you admit that it isn't based on any REAL theoretical basis
>> but only due to your limited (and flawed) thinkng ability.
>>
>> Note, you CAN'T do a categorically exhaustive reasoning on this
>> problem, as its is an INFINITE domain. You just don't seem to
>> understand the nature of infinity, so you don't see that.
>>
>> The Truth value is just based on the existance of a set on connections
>> to the axioms. Formal system or not, and NOTHING limits that to being
>> finite.
>>
> In other words you are saying that it is *TRUE IN THE FORMAL SYSTEM*
> even if it is *NOT TRUE IN THE FORMAL SYSTEM*.
>
>

No, it is TRUE in the formal system, because it has a connection to its
Truth Makers, but is not PROVEN (or even PROVABLE) becaue that
connection in not finte, as required for a PROOF, but not for Truth.

You are just proving your stupidity.

Note, it has been PROVEN (by proofs obviously too complicated for you)
that any system that tries to insist that all truth is provable, needs
to b STRICTLY limited in the material it tries to cover, or it becomes
inconsistent.

These strict limits include (as I recall) to being only a first order
logic system with a limit on the size of the domain.

The full properties of the Natural Numbers require going past these limits.

Not, you don't seem to understand the problem of inconsistent systems,
probably because your own system has gone inconsistent, and you can't
afford to look at that sort of issue.

On 1/14/2023 3:16 PM, Richard Damon wrote:
> On 1/14/23 3:28 PM, olcott wrote:
>> On 1/13/2023 6:25 PM, Richard Damon wrote:
>>> On 1/13/23 10:42 AM, olcott wrote:
>>>> On 1/12/2023 9:58 PM, Richard Damon wrote:
>>>>> On 1/12/23 10:52 PM, olcott wrote:
>>>>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>>>>
>>>>>>>>>> Because formal systems are only allowed to have finite proofs
>>>>>>>>>> formal
>>>>>>>>>> systems are not allowed to have infinite connections to their
>>>>>>>>>> semantic
>>>>>>>>>> truth maker. Thus an expression is only true in a formal
>>>>>>>>>> system iff it
>>>>>>>>>> is provable within this system. Otherwise this expression is
>>>>>>>>>> untrue
>>>>>>>>>> which may or may not include false.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>>>>
>>>>>>>>
>>>>>>>> That it ridiculously false. Expressions of language that are
>>>>>>>> proven to
>>>>>>>> have a connection to their truth maker axioms are a subset of
>>>>>>>> all truth
>>>>>>>> and comprise the entire body of analytical knowledge.
>>>>>>>>
>>>>>>>
>>>>>>> So, since proven statements are a SUBSET of all truth, what says
>>>>>>> that all truths have to be proven.
>>>>>>>
>>>>>>
>>>>>> Within a formal system where true requires finite proof to axioms the
>>>>>> lack of a finite proof to axioms means untrue.
>>>>>>
>>>>>
>>>>> Source of claim?
>>>>>
>>>>
>>>> How else can it possibly work?
>>>>
>>>> I figure these things out on the basis of categorically exhaustive
>>>> reasoning.
>>>
>>>
>>> Good, so you admit that it isn't based on any REAL theoretical basis
>>> but only due to your limited (and flawed) thinkng ability.
>>>
>>> Note, you CAN'T do a categorically exhaustive reasoning on this
>>> problem, as its is an INFINITE domain. You just don't seem to
>>> understand the nature of infinity, so you don't see that.
>>>
>>> The Truth value is just based on the existance of a set on
>>> connections to the axioms. Formal system or not, and NOTHING limits
>>> that to being finite.
>>>
>> In other words you are saying that it is *TRUE IN THE FORMAL SYSTEM*
>> even if it is *NOT TRUE IN THE FORMAL SYSTEM*.
>>
>>
>
> No, it is TRUE in the formal system, because it has a connection to its
> Truth Makers, but is not PROVEN (or even PROVABLE) becaue that
> connection in not finte, as required for a PROOF, but not for Truth.
>

How does the formal system know that an expression of language of this
formal system is true unless this expression of language has a
connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???

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

On 1/14/23 4:48 PM, olcott wrote:
> On 1/14/2023 3:16 PM, Richard Damon wrote:
>> On 1/14/23 3:28 PM, olcott wrote:
>>> On 1/13/2023 6:25 PM, Richard Damon wrote:
>>>> On 1/13/23 10:42 AM, olcott wrote:
>>>>> On 1/12/2023 9:58 PM, Richard Damon wrote:
>>>>>> On 1/12/23 10:52 PM, olcott wrote:
>>>>>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>>>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>>>>>
>>>>>>>>>>> Because formal systems are only allowed to have finite proofs
>>>>>>>>>>> formal
>>>>>>>>>>> systems are not allowed to have infinite connections to their
>>>>>>>>>>> semantic
>>>>>>>>>>> truth maker. Thus an expression is only true in a formal
>>>>>>>>>>> system iff it
>>>>>>>>>>> is provable within this system. Otherwise this expression is
>>>>>>>>>>> untrue
>>>>>>>>>>> which may or may not include false.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> That it ridiculously false. Expressions of language that are
>>>>>>>>> proven to
>>>>>>>>> have a connection to their truth maker axioms are a subset of
>>>>>>>>> all truth
>>>>>>>>> and comprise the entire body of analytical knowledge.
>>>>>>>>>
>>>>>>>>
>>>>>>>> So, since proven statements are a SUBSET of all truth, what says
>>>>>>>> that all truths have to be proven.
>>>>>>>>
>>>>>>>
>>>>>>> Within a formal system where true requires finite proof to axioms
>>>>>>> the
>>>>>>> lack of a finite proof to axioms means untrue.
>>>>>>>
>>>>>>
>>>>>> Source of claim?
>>>>>>
>>>>>
>>>>> How else can it possibly work?
>>>>>
>>>>> I figure these things out on the basis of categorically exhaustive
>>>>> reasoning.
>>>>
>>>>
>>>> Good, so you admit that it isn't based on any REAL theoretical basis
>>>> but only due to your limited (and flawed) thinkng ability.
>>>>
>>>> Note, you CAN'T do a categorically exhaustive reasoning on this
>>>> problem, as its is an INFINITE domain. You just don't seem to
>>>> understand the nature of infinity, so you don't see that.
>>>>
>>>> The Truth value is just based on the existance of a set on
>>>> connections to the axioms. Formal system or not, and NOTHING limits
>>>> that to being finite.
>>>>
>>> In other words you are saying that it is *TRUE IN THE FORMAL SYSTEM*
>>> even if it is *NOT TRUE IN THE FORMAL SYSTEM*.
>>>
>>>
>>
>> No, it is TRUE in the formal system, because it has a connection to
>> its Truth Makers, but is not PROVEN (or even PROVABLE) becaue that
>> connection in not finte, as required for a PROOF, but not for Truth.
>>
>
> How does the formal system know that an expression of language of this
> formal system is true unless this expression of language has a
> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>
>

Becaue the formal system doesn't need to KNOW what is true.

KNOWLEDGE is a different question then TRUTH.

Yes, if you do things right, everything that you KNOW will be TRUE, but
there is no requirement that you are able to KNOW everything that is
actually TRUE.

You don't seem to understand the difference between truth and knowledge
or even what is a Formal System. Maybe you should read about them, like
at https://en.wikipedia.org/wiki/Formal_system

In essence, a formal system is where you have defined:

1) A finite set of symbols, known as the alphabet, which are
concatenated into finite strings called formulas.

2) A grammar consisting of rules to form formulas from simpler formulas.
A formula is said to be well-formed if it can be formed using the rules
of the formal grammar. It is often required that there be a decision
procedure for deciding whether a formula is well-formed.

3) A set of axioms, or axiom schemata, consisting of well-formed formulas.

4) A set of inference rules. A well-formed formula that can be inferred
from the axioms is known as a theorem of the formal system.

There is nothing in that which implies you need to know everything that
is true as a result of these formalisms.

Note, one of the ey points of a formal system is that you start with the
complete set of axioms of the system, so you can't add more later
(except by creating a new formal system that is an extension of the
original).

Thus, unless your formal system actually STARTS with an axiom that says
that all Truth is Provalbe, you can't add it later without creating a
NEW formal system.

And, as has been pointed out previously, a Formal System with such an
axiom needs to be careful what other axioms and inference rules it also
contains, or it becomes inconsistent (and thus worthless).

On 1/14/2023 4:26 PM, Richard Damon wrote:
> On 1/14/23 4:48 PM, olcott wrote:
>> On 1/14/2023 3:16 PM, Richard Damon wrote:
>>> On 1/14/23 3:28 PM, olcott wrote:
>>>> On 1/13/2023 6:25 PM, Richard Damon wrote:
>>>>> On 1/13/23 10:42 AM, olcott wrote:
>>>>>> On 1/12/2023 9:58 PM, Richard Damon wrote:
>>>>>>> On 1/12/23 10:52 PM, olcott wrote:
>>>>>>>> On 1/12/2023 9:35 PM, Richard Damon wrote:
>>>>>>>>> On 1/12/23 10:04 PM, olcott wrote:
>>>>>>>>>> On 1/12/2023 8:37 PM, Richard Damon wrote:
>>>>>>>>>>> On 1/12/23 8:56 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>>>>> Because formal systems are only allowed to have finite
>>>>>>>>>>>> proofs formal
>>>>>>>>>>>> systems are not allowed to have infinite connections to
>>>>>>>>>>>> their semantic
>>>>>>>>>>>> truth maker. Thus an expression is only true in a formal
>>>>>>>>>>>> system iff it
>>>>>>>>>>>> is provable within this system. Otherwise this expression is
>>>>>>>>>>>> untrue
>>>>>>>>>>>> which may or may not include false.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Right, FINITE PROOFS, says nothing about TRUTH.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> That it ridiculously false. Expressions of language that are
>>>>>>>>>> proven to
>>>>>>>>>> have a connection to their truth maker axioms are a subset of
>>>>>>>>>> all truth
>>>>>>>>>> and comprise the entire body of analytical knowledge.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So, since proven statements are a SUBSET of all truth, what
>>>>>>>>> says that all truths have to be proven.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Within a formal system where true requires finite proof to
>>>>>>>> axioms the
>>>>>>>> lack of a finite proof to axioms means untrue.
>>>>>>>>
>>>>>>>
>>>>>>> Source of claim?
>>>>>>>
>>>>>>
>>>>>> How else can it possibly work?
>>>>>>
>>>>>> I figure these things out on the basis of categorically exhaustive
>>>>>> reasoning.
>>>>>
>>>>>
>>>>> Good, so you admit that it isn't based on any REAL theoretical
>>>>> basis but only due to your limited (and flawed) thinkng ability.
>>>>>
>>>>> Note, you CAN'T do a categorically exhaustive reasoning on this
>>>>> problem, as its is an INFINITE domain. You just don't seem to
>>>>> understand the nature of infinity, so you don't see that.
>>>>>
>>>>> The Truth value is just based on the existance of a set on
>>>>> connections to the axioms. Formal system or not, and NOTHING limits
>>>>> that to being finite.
>>>>>
>>>> In other words you are saying that it is *TRUE IN THE FORMAL SYSTEM*
>>>> even if it is *NOT TRUE IN THE FORMAL SYSTEM*.
>>>>
>>>>
>>>
>>> No, it is TRUE in the formal system, because it has a connection to
>>> its Truth Makers, but is not PROVEN (or even PROVABLE) becaue that
>>> connection in not finte, as required for a PROOF, but not for Truth.
>>>
>>
>> How does the formal system know that an expression of language of this
>> formal system is true unless this expression of language has a
>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>
>>
>
> Becaue the formal system doesn't need to KNOW what is true.
>

So PA has no idea that:
successor(successor(0)) == successor(0) + successor(0) is true ???

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

On 1/14/23 5:31 PM, olcott wrote:
> On 1/14/2023 4:26 PM, Richard Damon wrote:
>> On 1/14/23 4:48 PM, olcott wrote:
>>> How does the formal system know that an expression of language of this
>>> formal system is true unless this expression of language has a
>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>
>>>
>>
>> Becaue the formal system doesn't need to KNOW what is true.
>>
>
> So PA has no idea that:
> successor(successor(0)) == successor(0) + successor(0) is true ???
>

Why do you say that.

Just because truth doesn't NEED to be proven for it to be true, doesn't
mean it can't be.

In fact, your statement just comes out of a simple application of the
addition AXIOMS of PA.

a + 0 = a
a + Successor(b) = Successor(a + b)

So it is a PROVABLE statement, and thus actually KNOWN to be true.

You seem to have a lot of things backwards.

This just shows how LITTLE you understand how logic works, likely becaue
you didn't actually study it, but made up your own based on what little
you did understand of the bits and pieces you say.

On 1/14/2023 4:55 PM, Richard Damon wrote:
> On 1/14/23 5:31 PM, olcott wrote:
>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>> On 1/14/23 4:48 PM, olcott wrote:
>>>> How does the formal system know that an expression of language of this
>>>> formal system is true unless this expression of language has a
>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>
>>>>
>>>
>>> Becaue the formal system doesn't need to KNOW what is true.
>>>
>>
>> So PA has no idea that:
>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>
>
> Why do you say that.
>
> Just because truth doesn't NEED to be proven for it to be true, doesn't
> mean it can't be.
>
> In fact, your statement just comes out of a simple application of the
> addition AXIOMS of PA.
>
> a + 0 = a
> a + Successor(b) = Successor(a + b)
>
> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>

Unless a formal system has a syntactic connection from an expression of
its language to its truth maker axioms the expression is untrue in that
formal system.

Try and show an expression of language that is true in a formal system
(not just true somewhere else) that does not have any connection to
truth maker axioms in this formal system. You must show why it is true
in this formal system not merely that it is true somewhere else.

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

On 1/14/23 6:19 PM, olcott wrote:
> On 1/14/2023 4:55 PM, Richard Damon wrote:
>> On 1/14/23 5:31 PM, olcott wrote:
>>> On 1/14/2023 4:26 PM, Richard Damon wrote:
>>>> On 1/14/23 4:48 PM, olcott wrote:
>>>>> How does the formal system know that an expression of language of this
>>>>> formal system is true unless this expression of language has a
>>>>> connection to truth maker axioms *IN THIS FORMAL SYSTEM* ???
>>>>>
>>>>>
>>>>
>>>> Becaue the formal system doesn't need to KNOW what is true.
>>>>
>>>
>>> So PA has no idea that:
>>> successor(successor(0)) == successor(0) + successor(0) is true ???
>>>
>>
>> Why do you say that.
>>
>> Just because truth doesn't NEED to be proven for it to be true,
>> doesn't mean it can't be.
>>
>> In fact, your statement just comes out of a simple application of the
>> addition AXIOMS of PA.
>>
>> a + 0 = a
>> a + Successor(b) = Successor(a + b)
>>
>> So it is a PROVABLE statement, and thus actually KNOWN to be true.
>>
>
> Unless a formal system has a syntactic connection from an expression of
> its language to its truth maker axioms the expression is untrue in that
> formal system.

Right, but the connection can be infinite in length, and thus not provable.

>
> Try and show an expression of language that is true in a formal system
> (not just true somewhere else) that does not have any connection to
> truth maker axioms in this formal system. You must show why it is true
> in this formal system not merely that it is true somewhere else.
>

The connection might be infinite, and thus not SHOWABLE as a proof
strictly in the formal system.

If the connection exists as an infinite connection within the system,
then it is TRUE in the system.

Note, that if there is such an infinite connection, which thus can not
be proven within the formal system, it is still possible, that another
system, related to that system, with more knowledge, might be able to
show that there does exist within the original formal system such an
infinte connection.

This is what happens to G in F and meta-F

G states that there does not exist a Natural Number g that meets a
specific requirement (expressed as a primative recursive relationship).

This statement turns out to be true, because it turns out that no number
g does meet that requirement, but it can't be proven in F that this is
true, because in F, to show this we need to test every natuarl number,
which requires an infinite number of steps (finite for each number, but
an infinite number of numbers to test).

In meta-F, we can do better, because due to additional knowledge in
meta-F, we can show that if a number g could be found, then that number
g could be converted into a proof, in F, of the statement G (which says
that such a number does not exist).

Thus, in meta-F, we can prove that G is true, and also show that no
proof of it can exist in F.

Note, the key to this is that the primative recursive relationship is
built from the complete listing of axioms in F, and how to build ANY
proof in F based on the logic of meta-F, and is a "proof checker" for
the statement G, when so interpreted in meta-F

A number g that satisfies it is able to be shown by the logic of meta-F
to define a proof of G in F.