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Gödel's 1931 incompleteness fails HOL
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olcott
Dec 2, 2023, 7:22:17 PM12/2/23
to
When PA is the n level of logic and metamathematics is the n+1 level of
logic in the same formal system then G <is> provable in this formal
system and incompleteness cannot exist. HOL can do this.
This sentence is not true: "This sentence is not true" is true.
The above is all there is to the Tarski Undefinability Theorem.
https://liarparadox.org/Tarski_275_276.pdf
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
logic in the same formal system then G <is> provable in this formal
system and incompleteness cannot exist. HOL can do this.
This sentence is not true: "This sentence is not true" is true.
The above is all there is to the Tarski Undefinability Theorem.
https://liarparadox.org/Tarski_275_276.pdf
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
Richard Damon
Dec 2, 2023, 10:09:06 PM12/2/23
to
On 12/2/23 7:22 PM, olcott wrote:
> When PA is the n level of logic and metamathematics is the n+1 level of
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
Except that incompleteness says that a given proposition that is true in
> When PA is the n level of logic and metamathematics is the n+1 level of
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
the system can't be proven in that system. Just because it is provable
in some higher power system, doesn't make that system complete.
So, you are just showing your ignorance of what you talk about, not
understanding what metalogic is actually about.
Note, you have an error in your logic, as the metamatematics of the n+1
level is a DIFFERENT (but related) formal system then the n level
system, because the meta system has additional "truthmakers" to it, that
provide information about the base system.
>
> This sentence is not true: "This sentence is not true" is true.
> The above is all there is to the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
>
What Tarski shows is that the assumption that Truth can be "defined" (in
the sense that there is a computable relationship that will tell you the
truth value of a sentence in the system) implies that ability to "prove"
that "This sentence is not true" is, in fact, true, (which implies that
it also must not be true) and thus the system is inconsistant.
olcott
Dec 2, 2023, 10:34:39 PM12/2/23
to
On 12/2/2023 6:22 PM, olcott wrote:
> When PA is the n level of logic and metamathematics is the n+1 level of
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
>
> This sentence is not true: "This sentence is not true" is true.
> The above is all there is to the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
>
When two formal systems are included in the same formal system
> When PA is the n level of logic and metamathematics is the n+1 level of
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
>
> This sentence is not true: "This sentence is not true" is true.
> The above is all there is to the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
>
as logic levels of n and n+1 then anything expressed in the
n level of PA is provable in the n+1 level of metamathematics
and incompleteness cannot exist.
If G is expressed at the n+1 level then the n+2 level proves G.
Richard Damon
Dec 2, 2023, 11:00:39 PM12/2/23
to
On 12/2/23 10:34 PM, olcott wrote:
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> When two formal systems are included in the same formal system
> as logic levels of n and n+1 then anything expressed in the
> n level of PA is provable in the n+1 level of metamathematics
> and incompleteness cannot exist.
>
> If G is expressed at the n+1 level then the n+2 level proves G.
>
Which means that level n was incomplete, as it didn't have enough
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> When two formal systems are included in the same formal system
> as logic levels of n and n+1 then anything expressed in the
> n level of PA is provable in the n+1 level of metamathematics
> and incompleteness cannot exist.
>
> If G is expressed at the n+1 level then the n+2 level proves G.
>
"logic" to prove the statement.
Note, G is expressed at the level of PA, and in the n+1 we can show that
G was true in PA, and that it was also unprofitable in PA, thus PA was
incomplete.
You just don't understand the requirements.
You also don't seem to understand how conversation works, and are just
proving yourself to be a dumb troll.
olcott
Dec 2, 2023, 11:24:00 PM12/2/23
to
On 12/2/2023 9:34 PM, olcott wrote:
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> When two formal systems are included in the same formal system
> as logic levels of n and n+1 then anything expressed in the
> n level of PA is provable in the n+1 level of metamathematics
> and incompleteness cannot exist.
>
> If G is expressed at the n+1 level then the n+2 level proves G.
>
A formal system having an unlimited number of logic levels cannot
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> When two formal systems are included in the same formal system
> as logic levels of n and n+1 then anything expressed in the
> n level of PA is provable in the n+1 level of metamathematics
> and incompleteness cannot exist.
>
> If G is expressed at the n+1 level then the n+2 level proves G.
>
possibly be incomplete in the Gödel sense. What-so-ever can be
expressed at the n level of logic can be proven at the n+1 level
of logic of this same formal system.
Richard Damon
Dec 2, 2023, 11:34:15 PM12/2/23
to
On 12/2/23 11:23 PM, olcott wrote:
> On 12/2/2023 9:34 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> When two formal systems are included in the same formal system
>> as logic levels of n and n+1 then anything expressed in the
>> n level of PA is provable in the n+1 level of metamathematics
>> and incompleteness cannot exist.
>>
>> If G is expressed at the n+1 level then the n+2 level proves G.
>>
>
> A formal system having an unlimited number of logic levels cannot
> possibly be incomplete in the Gödel sense. What-so-ever can be
> expressed at the n level of logic can be proven at the n+1 level
> of logic of this same formal system.
>
So you don't understand what those "logic levels" are, or what a "Formal
> On 12/2/2023 9:34 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> When two formal systems are included in the same formal system
>> as logic levels of n and n+1 then anything expressed in the
>> n level of PA is provable in the n+1 level of metamathematics
>> and incompleteness cannot exist.
>>
>> If G is expressed at the n+1 level then the n+2 level proves G.
>>
>
> A formal system having an unlimited number of logic levels cannot
> possibly be incomplete in the Gödel sense. What-so-ever can be
> expressed at the n level of logic can be proven at the n+1 level
> of logic of this same formal system.
>
Logic System" is. The different levels are DIFFERENT formal systems, so
no "formal system" has multiple "logic levels".
You are just proving you don't know what a "Formal Logic System" is.
olcott
Dec 3, 2023, 12:02:12 AM12/3/23
to
On 12/2/2023 10:23 PM, olcott wrote:
> On 12/2/2023 9:34 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> When two formal systems are included in the same formal system
>> as logic levels of n and n+1 then anything expressed in the
>> n level of PA is provable in the n+1 level of metamathematics
>> and incompleteness cannot exist.
>>
>> If G is expressed at the n+1 level then the n+2 level proves G.
>>
>
> A formal system having an unlimited number of logic levels cannot
> possibly be incomplete in the Gödel sense. What-so-ever can be
> expressed at the n level of logic can be proven at the n+1 level
> of logic of this same formal system.
>
HOL can have from 0 to N contiguous logic levels where N is a natural
> On 12/2/2023 9:34 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> When two formal systems are included in the same formal system
>> as logic levels of n and n+1 then anything expressed in the
>> n level of PA is provable in the n+1 level of metamathematics
>> and incompleteness cannot exist.
>>
>> If G is expressed at the n+1 level then the n+2 level proves G.
>>
>
> A formal system having an unlimited number of logic levels cannot
> possibly be incomplete in the Gödel sense. What-so-ever can be
> expressed at the n level of logic can be proven at the n+1 level
> of logic of this same formal system.
>
number, yet not a fixed constant.
Richard Damon
Dec 3, 2023, 7:17:35 AM12/3/23
to
On 12/3/23 12:02 AM, olcott wrote:
> On 12/2/2023 10:23 PM, olcott wrote:
>> On 12/2/2023 9:34 PM, olcott wrote:
>>> On 12/2/2023 6:22 PM, olcott wrote:
>>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>>> logic in the same formal system then G <is> provable in this formal
>>>> system and incompleteness cannot exist. HOL can do this.
>>>>
>>>> This sentence is not true: "This sentence is not true" is true.
>>>> The above is all there is to the Tarski Undefinability Theorem.
>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>
>>>
>>> When two formal systems are included in the same formal system
>>> as logic levels of n and n+1 then anything expressed in the
>>> n level of PA is provable in the n+1 level of metamathematics
>>> and incompleteness cannot exist.
>>>
>>> If G is expressed at the n+1 level then the n+2 level proves G.
>>>
>>
>> A formal system having an unlimited number of logic levels cannot
>> possibly be incomplete in the Gödel sense. What-so-ever can be
>> expressed at the n level of logic can be proven at the n+1 level
>> of logic of this same formal system.
>>
>
> HOL can have from 0 to N contiguous logic levels where N is a natural
> number, yet not a fixed constant.
>
Nope. Not in the sense that you are using logic levels.
> On 12/2/2023 10:23 PM, olcott wrote:
>> On 12/2/2023 9:34 PM, olcott wrote:
>>> On 12/2/2023 6:22 PM, olcott wrote:
>>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>>> logic in the same formal system then G <is> provable in this formal
>>>> system and incompleteness cannot exist. HOL can do this.
>>>>
>>>> This sentence is not true: "This sentence is not true" is true.
>>>> The above is all there is to the Tarski Undefinability Theorem.
>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>
>>>
>>> When two formal systems are included in the same formal system
>>> as logic levels of n and n+1 then anything expressed in the
>>> n level of PA is provable in the n+1 level of metamathematics
>>> and incompleteness cannot exist.
>>>
>>> If G is expressed at the n+1 level then the n+2 level proves G.
>>>
>>
>> A formal system having an unlimited number of logic levels cannot
>> possibly be incomplete in the Gödel sense. What-so-ever can be
>> expressed at the n level of logic can be proven at the n+1 level
>> of logic of this same formal system.
>>
>
> HOL can have from 0 to N contiguous logic levels where N is a natural
> number, yet not a fixed constant.
>
The "level" (called "Order") in Higher Order Logic, deals with the sort
of predicate you can use. First Order Logic only allows predicates to
quantify on the variables of the logic system (there exists an x
that...), Second Order Logic allows adding quantification of
relationships (there exists an f(), such that f(x) ...).
The Levels of logic used in Tarski, are levels of meta-logic, where we
create a NEW Formal System which has all the axioms of the base level,
plus axioms about that base system that weren't derivable in the base.
This is something completely different.
Jim Burns
Dec 3, 2023, 7:46:47 AM12/3/23
to
On 12/2/2023 7:22 PM, olcott wrote:
> When PA is the n level of logic and
> metamathematics is the n+1 level of logic
> in the same formal system
> then
> G <is> provable in this formal system
> and incompleteness cannot exist.
> HOL can do this.
One PA.sentence not PA.provable
> When PA is the n level of logic and
> metamathematics is the n+1 level of logic
> in the same formal system
> then
> G <is> provable in this formal system
> and incompleteness cannot exist.
> HOL can do this.
makes PA incomplete.
One PA.sentence PA.provable
does not make PA complete.
One PA.sentence HOL.provable
does not make PA complete.
One PA.sentence HOL.provable
does not make HOL complete.
One HOL.sentence HOL.provable
does not make HOL complete.
One HOL.sentence not HOL.provable
makes HOL incomplete.
This one PA.sentence
|
| PA" preceded by its PA.quotation
| is not PA.provable "PA
| preceded by its PA.quotation
| is not PA.provable.
|
makes PA incomplete.
This one HOL.sentence
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
makes HOL incomplete.
> This sentence is not true:
> "This sentence is not true"
> is true.
> The above is all there is to
> the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
| This sentence is not true
|
| "preceded by its quotation is not true"
| preceded by its quotation is not true.
|
does not self-refer.
It self-describes.
olcott
Dec 3, 2023, 10:44:12 AM12/3/23
to
On 12/3/2023 6:46 AM, Jim Burns wrote:
> On 12/2/2023 7:22 PM, olcott wrote:
>
>> When PA is the n level of logic and
>> metamathematics is the n+1 level of logic
>> in the same formal system
>> then
>> G <is> provable in this formal system
>> and incompleteness cannot exist.
>> HOL can do this.
>
> One PA.sentence not PA.provable
> makes PA incomplete.
>
> One PA.sentence PA.provable
> does not make PA complete.
>
> One PA.sentence HOL.provable
> does not make PA complete.
>
> One PA.sentence HOL.provable
> does not make HOL complete.
>
> One HOL.sentence HOL.provable
> does not make HOL complete.
>
> One HOL.sentence not HOL.provable
> makes HOL incomplete.
>
>
> On 12/2/2023 7:22 PM, olcott wrote:
>
>> When PA is the n level of logic and
>> metamathematics is the n+1 level of logic
>> in the same formal system
>> then
>> G <is> provable in this formal system
>> and incompleteness cannot exist.
>> HOL can do this.
>
> One PA.sentence not PA.provable
> makes PA incomplete.
>
> One PA.sentence PA.provable
> does not make PA complete.
>
> One PA.sentence HOL.provable
> does not make PA complete.
>
> One PA.sentence HOL.provable
> does not make HOL complete.
>
> One HOL.sentence HOL.provable
> does not make HOL complete.
>
> One HOL.sentence not HOL.provable
> makes HOL incomplete.
>
>
HOL can have from 0 to N contiguous logic levels where N
is a natural number, yet not a fixed constant.
This sentence cannot be proved: "This sentence cannot be proven"
is a natural number, yet not a fixed constant.
can be proved.
HOL always has as many orders of logic needed so that anything
that can be specified can be proved.
Jim Burns
Dec 3, 2023, 12:10:17 PM12/3/23
to
This one HOL.sentence
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
can be specified.
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
It can't be both true and HOL.provable.
Displaying a different true sentence which
can be proved
doesn't contradict that.
olcott
Dec 3, 2023, 12:33:02 PM12/3/23
to
necessary because 2000 years later the received view does not even
yet understand the simple one: This sentence is not true.
The sentence that you provided is simply rejected as incoherent.
HOL.{This sentence cannot be proven}. on the basis that it has
a cycle in its evaluation directed graph.
The version that you provided is simply a screwy way to
indirectly refer to a sentence that is isomorphic to
referring to its by its variable name.
Jim Burns
Dec 3, 2023, 2:03:33 PM12/3/23
to
On 12/3/2023 12:32 PM, olcott wrote:
> On 12/3/2023 11:10 AM, Jim Burns wrote:
>> [...]
> On 12/3/2023 11:10 AM, Jim Burns wrote:
>
> The sentence that you provided
> The sentence that you provided
This one HOL.sentence
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
> is simply rejected as incoherent.
> HOL.{This sentence cannot be proven}.
> on the basis that it has
> a cycle in its evaluation directed graph.
> HOL.{This sentence cannot be proven}.
> on the basis that it has
> a cycle in its evaluation directed graph.
This one HOL.sentence
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
does not have a cycle in
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
its evaluation directed graph.
> The version that you provided
> The version that you provided
This one HOL.sentence
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
|
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
> is simply
> a screwy way to indirectly refer to
> a sentence that is isomorphic to
> referring to its by its variable name.
Whether that is or isn't so,
> a screwy way to indirectly refer to
> a sentence that is isomorphic to
> referring to its by its variable name.
the HOL.sentence I provided
meets your criterion for coherency:
no cyclic evaluation.
If the sentence I provided is true,
then it's not HOL.provable.
Therefore,
despite the existence of
various provable or incoherent sentences
which I didn't provide,
HOL is incomplete.
Richard Damon
Dec 3, 2023, 2:14:42 PM12/3/23
to
you are talking about.
"Orders" of logic are different then the meta-"Levels" of logic.
But of course, since you understand neither, you can't understand the
difference.
olcott
Dec 3, 2023, 2:24:06 PM12/3/23
to
it forms a cycle in the directed graph of its evaluation sequence.
It is simply another variation of the two sentence liar paradox.
The next sentence is not true.
The prior sentence is true.
"preceded by its HOL.quotation" is simply
a way to indirectly refer to a sentence by its name.
Jim Burns
Dec 3, 2023, 5:14:10 PM12/3/23
to
On 12/3/2023 2:24 PM, olcott wrote:
> On 12/3/2023 1:03 PM, Jim Burns wrote:
>> On 12/3/2023 12:32 PM, olcott wrote:
>>> The version that you provided
>>
>> This one HOL.sentence
>> |
>> | HOL" preceded by its HOL.quotation
>> | is not HOL.provable "HOL
>> | preceded by its HOL.quotation
>> | is not HOL.provable.
>>
>
> Is rejected as semantically unsound
> on the basis that
> it forms a cycle in the directed graph of
> its evaluation sequence.
Say that a hundred more times,
> On 12/3/2023 1:03 PM, Jim Burns wrote:
>> On 12/3/2023 12:32 PM, olcott wrote:
>>> The version that you provided
>>
>> This one HOL.sentence
>> |
>> | HOL" preceded by its HOL.quotation
>> | is not HOL.provable "HOL
>> | preceded by its HOL.quotation
>> | is not HOL.provable.
>>
>
> Is rejected as semantically unsound
> on the basis that
> it forms a cycle in the directed graph of
> its evaluation sequence.
and it still won't be true.
We need to be able to express two properties
in our language-of-the-day for HOL
Arithmetic is sufficient for this, but
we can go further, as long as
we can still express it.
Proves(y,x)
if
y represents a proof in HOL of
a formula in HOL which x represents
then
Proves(y,x) is true. Otherwise, false.
Subst(x,y,z)
if
x represents a formula A(u) with
one variable not bound by a quantifier (free)
and z represents A(y)
AKA A(u) with y substituted for
free occurrences of u in A(u)
then
Subst(x,y,z) is true. Otherwise, false.
Subst(x,y,z) doesn't get much attention,
I guess. It seems to me to be
pretty much guaranteed to exist
if predicate Proves(y,x) exists
But Subst(x,y,z) is how we get
"preceded by its quotation is not provable"
to be preceded by its quotation.
These numbers representing formulas
the same as quotations:
things representing speech acts.
∃y(Subst(x,x,y) ∧ ¬∃z:Proves(z,y)))
is the HOL.predicate meaning
| x represents
| a formula A(u) such that,
| for A(x), represented here by y
| no proof, represented here by z,
| exists
For convenience, refer to
∃y(Subst(x,x,y) ∧ ¬∃z:Proves(z,y)))
as G(x)
Represent (ie, quote) G(x) as a number g
G(g) is a certain long arithmetical formula
G(g) _means_
| HOL" preceded by its HOL.quotation
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
If G(g) is true, G(g) is not provable,
| is not HOL.provable "HOL
| preceded by its HOL.quotation
| is not HOL.provable.
and not all true sentence of HOL
are provable.
> "preceded by its HOL.quotation" is simply
> a way to indirectly refer to a sentence
> by its name.
Your "proof" that that's so
is to
swap out G(g) and put something else in.
https://en.wikipedia.org/wiki/Straw_man
olcott
Dec 3, 2023, 5:48:45 PM12/3/23
to
On 12/3/2023 1:03 PM, Jim Burns wrote:
A convoluted mess that is indirectly rather than directly
self-referential.
The author of the paradox made the ridiculously stupid mistake of
not understanding that the term bachelor is defined in terms of
unmarried male yet did this so convincingly that most people to
this day reject the notion of epistemic foundationalism.
https://iep.utm.edu/quine-an/
olcott
Dec 3, 2023, 5:53:23 PM12/3/23
to
it is semantically unsound and must be rejected. Otherwise
an expression of language is provable or untrue. A proof
is a directed path from the leaves of a tree to its root.
Jim Burns
Dec 3, 2023, 10:57:41 PM12/3/23
to
On 12/3/2023 5:53 PM, olcott wrote:
> On 12/3/2023 4:14 PM, Jim Burns wrote:
>> We need to be able to express two properties
>> in our language-of-the-day for HOL
>> Arithmetic is sufficient for this, but
>> we can go further, as long as
>> we can still express it.
>>
>> Proves(y,x)
>> if
>> y represents a proof in HOL of
>> a formula in HOL which x represents
>> then
>> Proves(y,x) is true. Otherwise, false.
>>
>> Subst(x,y,z)
>> if
>> x represents a formula A(u) with
>> one variable not bound by a quantifier (free)
>> and z represents A(y)
>> AKA A(u) with y substituted for
>> free occurrences of u in A(u)
>> then
>> Subst(x,y,z) is true. Otherwise, false.
> On 12/3/2023 4:14 PM, Jim Burns wrote:
>> We need to be able to express two properties
>> in our language-of-the-day for HOL
>> Arithmetic is sufficient for this, but
>> we can go further, as long as
>> we can still express it.
>>
>> Proves(y,x)
>> if
>> y represents a proof in HOL of
>> a formula in HOL which x represents
>> then
>> Proves(y,x) is true. Otherwise, false.
>>
>> Subst(x,y,z)
>> if
>> x represents a formula A(u) with
>> one variable not bound by a quantifier (free)
>> and z represents A(y)
>> AKA A(u) with y substituted for
>> free occurrences of u in A(u)
>> then
>> Subst(x,y,z) is true. Otherwise, false.
> Whenever any proof contains cycles in
> its directed graph
> it is semantically unsound and must be rejected.
Do you think there are cycles in
> its directed graph
> it is semantically unsound and must be rejected.
Proves(y,x) or Subst(x,y,z) ?
If yes, why do you think that?
If no,
are there cycles in
∃y(Subst(x,x,y) ∧ ¬∃z:Proves(z,y)))
?
What cycles?
Note that
olcott
Dec 4, 2023, 12:01:15 AM12/4/23
to
https://en.wikipedia.org/wiki/Quine%27s_paradox
A convoluted mess that is indirectly rather than directly
self-referential.
The statement "'yields falsehood when preceded by its quotation'
A convoluted mess that is indirectly rather than directly
self-referential.
yields falsehood when preceded by its quotation" is false.
In other words, the sentence implies that it is false, which is
paradoxical—for if it is false, what it states is in fact true.
*Thus proving a cycle in its evaluation graph*
All proves are directed paths from leaves to a root.
Jim Burns
Dec 4, 2023, 9:15:39 AM12/4/23
to
On 12/4/2023 12:01 AM, olcott wrote:
> On 12/3/2023 9:57 PM, Jim Burns wrote:
>> [...]
> On 12/3/2023 9:57 PM, Jim Burns wrote:
>
> https://en.wikipedia.org/wiki/Quine%27s_paradox
> A convoluted mess that
> is indirectly rather than directly
> self-referential.
>
> | The statement
> | "'yields falsehood when preceded by its quotation'
> | yields falsehood when preceded by its quotation"
> | is false.
G(x) :⇔ ∃y(Subst(x,x,y) ∧ ¬∃z:STProves(z,y)))
> https://en.wikipedia.org/wiki/Quine%27s_paradox
> A convoluted mess that
> is indirectly rather than directly
> self-referential.
>
> | The statement
> | "'yields falsehood when preceded by its quotation'
> | yields falsehood when preceded by its quotation"
> | is false.
ST is: Empty.Set, Adjunct, Extensionality.
h := "H(x)"
G(h) means
| H(x) preceded by its quotation
| is not ST.provable.
g := "G(x)" ≠ "G(g)"
G(g) means
| G(x) preceded by its quotation
| is not ST.provable.
!
G(g) is G(x) preceded by its quotation.
or,
being cute,
| "preceded by its quotation
| is not ST.provable"
| preceded by its quotation
| is not ST.provable.
If G(g) is true, G(g) is not ST.provable.
g refers to G(x) not G(g)
> | In other words,
> | the sentence implies that it is false,
false ≠ not ST.provable
> | which is paradoxical
> | —for if it is false,
> | what it states is in fact true.
not even if you say it is
a hundred times.
> *Thus proving a cycle in its evaluation graph*
Show me a cycle.
> All proves are directed paths
> from leaves to a root.
calling the root
description of the topic-of-the-day and
calling the leaves
not-first-false claims augmenting
the description.
The finiteness of paths from leaves
back to root is implicit in
their being attached.
olcott
Dec 4, 2023, 5:02:59 PM12/4/23
to
to make it incomprehensible.
When one knows the foundation of formal proofs always
involves a directed path from the leaves of a tree
to its root then one has the basis to untangle the
fundamental nature of any formal proof once it has
been translated into its directed graph form.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
When it is understood that an epistemological antinomy
is merely a self-contradictory expression of language
then the above quote conclusively proves that Gödel had a
fundamental misconception about the way the formal proofs
actually work.
It is far too ridiculously stupid to believe that anyone
ever truly believed that a formal system must be able
to prove any self-contradictory expression of language.
Thus the Gödel proof becomes the Gödel ruse.
Richard Damon
Dec 4, 2023, 6:41:56 PM12/4/23
to
the simple straight forward ideas.
>
> When one knows the foundation of formal proofs always
> involves a directed path from the leaves of a tree
> to its root then one has the basis to untangle the
> fundamental nature of any formal proof once it has
> been translated into its directed graph form.
(possibly infinite) to the truth-makers of the system, can't be true.
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
utter ignroance.
> When it is understood that an epistemological antinomy
> is merely a self-contradictory expression of language
> then the above quote conclusively proves that Gödel had a
> fundamental misconception about the way the formal proofs
> actually work.
had a truth value, or even directly used it as a statement in the Theory
(or meta-theory) is irrelevent.
Your repeating that statement, after this has been pointed out to you,
just shows your stupidity.
>
> It is far too ridiculously stupid to believe that anyone
> ever truly believed that a formal system must be able
> to prove any self-contradictory expression of language.
> Thus the Gödel proof becomes the Gödel ruse.
>
are the stupid one.
And too ignorant to understand the actual truth.
olcott
Dec 4, 2023, 7:08:29 PM12/4/23
to
On 12/4/2023 8:15 AM, Jim Burns wrote:
is expressing in a language woefully insufficiently expressive
to say this he is saying:
...We are therefore confronted with a proposition which asserts its own
unprovability. 15 ...(Gödel 1931:43-44)
This does have a cycle---> G := (F ⊬ G)
olcott
Dec 4, 2023, 7:12:24 PM12/4/23
to
On 12/2/2023 6:22 PM, olcott wrote:
> When PA is the n level of logic and metamathematics is the n+1 level of
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
>
> This sentence is not true: "This sentence is not true" is true.
> The above is all there is to the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
>
> logic in the same formal system then G <is> provable in this formal
> system and incompleteness cannot exist. HOL can do this.
>
> This sentence is not true: "This sentence is not true" is true.
> The above is all there is to the Tarski Undefinability Theorem.
> https://liarparadox.org/Tarski_275_276.pdf
>
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
Dishonest people can "interpret" this as saying everyone
for a similar undecidability proof...(Gödel 1931:43-44)
knows that no one can ever base any formal proof on any
epistemological antinomy.
*the direct opposite of what he actually says*
olcott
Dec 4, 2023, 7:47:17 PM12/4/23
to
On 12/4/2023 6:12 PM, olcott wrote:
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
> Dishonest people can "interpret" this as saying everyone
> knows that no one can ever base any formal proof on any
> epistemological antinomy.
>
> *the direct opposite of what he actually says*
>
If
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
> Dishonest people can "interpret" this as saying everyone
> knows that no one can ever base any formal proof on any
> epistemological antinomy.
>
> *the direct opposite of what he actually says*
>
epistemological antinomies are not members of most Formal Systems Language.
Then Gödel was that much more stupid for saying this.
Jim Burns
Dec 4, 2023, 7:49:14 PM12/4/23
to
On 12/4/2023 5:02 PM, olcott wrote:
> On 12/4/2023 8:15 AM, Jim Burns wrote:
>> On 12/4/2023 12:01 AM, olcott wrote:
>>> *Thus proving a cycle in its evaluation graph*
>>
>> G(g)
>> Show me a cycle.
> On 12/4/2023 8:15 AM, Jim Burns wrote:
>> On 12/4/2023 12:01 AM, olcott wrote:
>>> *Thus proving a cycle in its evaluation graph*
>>
>> G(g)
>> Show me a cycle.
> One can make any idea sufficiently convoluted
> to make it incomprehensible.
I can try to make each step more comprehensible,
> to make it incomprehensible.
and take more, shorter steps.
Be aware that there may be a trade-off, though.
More short steps may well be less comprehensible
than fewer broad sweeps which clue one in on
how to think about this.
if
Subst("H(u)","H(u)",y)
is true, then
y = "H("H(u)")"
if
¬∃z:Provesˢᵗ(z,"H("H(u)")")
is true, then
H("H(u)") is not ST.provable.
if
∃y(Subst("H(u)","H(u)",y) ∧ ¬∃z:Provesˢᵗ(z,y)))
is true, then
y = "H("H(u)")" exists and
"H("H(u)") is not ST.provable
Abbreviate
G(u) := ∃y(Subst(u,u,y) ∧ ¬∃z:Provesˢᵗ(z,y)))
if
G("H(u)")
is true, then
y = "H("H(u)")" exists and
H("H(u)") is not ST.provable
if
G("G(u)")
is true, then
y = "G("G(u)")" exists and
G("G(u)") is not ST.provable
tl;dr
if G("G(u)") is true
then G("G(u)") is not ST.provable
olcott
Dec 4, 2023, 8:00:16 PM12/4/23
to
we cannot build its proof tree.
Richard Damon
Dec 4, 2023, 8:44:07 PM12/4/23
to
On 12/4/23 7:47 PM, olcott wrote:
> On 12/4/2023 6:12 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> ...14 Every epistemological antinomy can likewise be used
>> for a similar undecidability proof...(Gödel 1931:43-44)
>>
>> Dishonest people can "interpret" this as saying everyone
>> knows that no one can ever base any formal proof on any
>> epistemological antinomy.
>>
>> *the direct opposite of what he actually says*
>>
>
> If
> epistemological antinomies are not members of most Formal Systems Language.
>
> Then Gödel was that much more stupid for saying this.
He never said the epistemological antinomy was a member of the Formal
> On 12/4/2023 6:12 PM, olcott wrote:
>> On 12/2/2023 6:22 PM, olcott wrote:
>>> When PA is the n level of logic and metamathematics is the n+1 level of
>>> logic in the same formal system then G <is> provable in this formal
>>> system and incompleteness cannot exist. HOL can do this.
>>>
>>> This sentence is not true: "This sentence is not true" is true.
>>> The above is all there is to the Tarski Undefinability Theorem.
>>> https://liarparadox.org/Tarski_275_276.pdf
>>>
>>
>> ...14 Every epistemological antinomy can likewise be used
>> for a similar undecidability proof...(Gödel 1931:43-44)
>>
>> Dishonest people can "interpret" this as saying everyone
>> knows that no one can ever base any formal proof on any
>> epistemological antinomy.
>>
>> *the direct opposite of what he actually says*
>>
>
> If
> epistemological antinomies are not members of most Formal Systems Language.
>
> Then Gödel was that much more stupid for saying this.
System Language.
Try to show where he did.
You are just apparently too stupid to understand wha the is saying,
Richard Damon
Dec 4, 2023, 8:44:10 PM12/4/23
to
On 12/4/23 7:12 PM, olcott wrote:
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
> Dishonest people can "interpret" this as saying everyone
> knows that no one can ever base any formal proof on any
> epistemological antinomy.
>
> *the direct opposite of what he actually says*
>
So, you are agreing that your own "proof" is incorrect, as you can't
> On 12/2/2023 6:22 PM, olcott wrote:
>> When PA is the n level of logic and metamathematics is the n+1 level of
>> logic in the same formal system then G <is> provable in this formal
>> system and incompleteness cannot exist. HOL can do this.
>>
>> This sentence is not true: "This sentence is not true" is true.
>> The above is all there is to the Tarski Undefinability Theorem.
>> https://liarparadox.org/Tarski_275_276.pdf
>>
>
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof...(Gödel 1931:43-44)
>
> Dishonest people can "interpret" this as saying everyone
> knows that no one can ever base any formal proof on any
> epistemological antinomy.
>
> *the direct opposite of what he actually says*
>
base a proof on an epistemological antinomy, which you just did (at
least to a similar degree as Godel did).
Richard Damon
Dec 4, 2023, 8:44:12 PM12/4/23
to
> This does have a cycle---> G := (F ⊬ G)
>
face liar.
If you disagree, show where he ACTUALLY SAYS That is what G is.
If you quote that statement again, and don't show how its context
actually means what you claim, you will just contionuie to prove
yourself to be just a stupid liar.
Richard Damon
Dec 4, 2023, 8:44:14 PM12/4/23
to
statement.
The statement of G is: "There does not exist a Natural Number g that
statisfies <a particular Primative Recursive Relationship>"
There exist a proof tree for that (which is infinite in length) in F,
since that relationship can be computed for every Natural Number, and it
turns out that all the answers are that none of the numbers satisfies
the relationship. Thus, the statement IS true.
The fact that none of the numbers satisfies the relationship can't be
determined in F, except by testing every number individually, which,
because there is an infinite number of numbers, says that can't be the
needed finite proof.
It DOES turn out that in Meta-F, because of its additional knowledge
about the Primitive Recursive Relationship, we can prove that there, in
fact, is no number that matches the relationship, and by the nature of
the meta-relationship between F and meta-F, we establish that it also
must be true in F itself (because the relationship doesn't change).
So, we do have the tree in F, but it is infinite, so not a proof (since
the incompleteness thereom is for Formal System, which as true for most
normal systems, define "Proofs" as FINITE arguments.
Jim Burns
Dec 5, 2023, 12:52:38 PM12/5/23
to
On 12/4/2023 8:44 PM, Richard Damon wrote:
> On 12/4/23 8:00 PM, olcott wrote:
>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>> tl;dr
>>> if G("G(u)") is true
>>> then G("G(u)") is not ST.provable
ST has {}, x∪{y}, and set equality.
> On 12/4/23 8:00 PM, olcott wrote:
>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>> tl;dr
>>> if G("G(u)") is true
>>> then G("G(u)") is not ST.provable
>> Until you get down to "G is unprovable in F"
>> we cannot build its proof tree.
>
> Except that since that ISN'T the statment of G,
> we don't need that statement.
>
> The statement of G is:
> "There does not exist
> a Natural Number g that statisfies
> <a particular Primative Recursive Relationship>"
>
> There exist a proof tree for that
> (which is infinite in length) in F,
> since that relationship can be computed
> for every Natural Number,
> and it turns out that
> all the answers are that
> none of the numbers satisfies the relationship.
> Thus, the statement IS true.
>
> The fact that
> none of the numbers satisfies the relationship
> can't be determined in F, except by
> testing every number individually, which,
> because there is an infinite number of numbers,
> says that can't be the needed finite proof.
Is F True Arithmetic?
https://en.wikipedia.org/wiki/True_arithmetic
True Arithmetic takes infinitely-many sentences
as axioms. True Arithmetic is not a counter-
example to Gödel's reasoning.
What Olcott wants still seems to be a
massive-database of all human knowledge,
complete, of course, and
PO sees Gödel's reasoning as what prevents that,
somehow, and
he sees that complete massive-database
as essential to True AI and
True AI as essential to humanity.
I do not guarantee that my recollection is
100% correct or thoroughly up-to-date.
However, assuming IRC,
True Arithmetic does not serve Olcott's purpose
because
the most massively massive of massive-databases
is still finite, unlike True Arithmetic.
However,
I'm not sure what F means here.
olcott
Dec 5, 2023, 2:30:40 PM12/5/23
to
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Eliminates Tarski undefinability and Gödel incompleteness and forces the
concept of truth in math and logic to conform to the way that it works
everywhere else. True(x) ≡ (⊢ x)
The only way that we know that "cats are animals" is true is the
connection from the above expression to the definition of {cats} and
{animals}.
The lack of inference steps from axioms to an expression simply means
untrue. Incomplete(L) is merely a terribly misleading euphemism for
~True(L,x).
Jim Burns
Dec 5, 2023, 2:58:59 PM12/5/23
to
On 12/5/2023 2:30 PM, olcott wrote:
> On 12/5/2023 11:52 AM, Jim Burns wrote:
>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>> On 12/4/23 8:00 PM, olcott wrote:
>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>> tl;dr
>>>>> if G("G(u)") is true
>>>>> then G("G(u)") is not ST.provable
>>
>> ST has {}, x∪{y}, and set equality.
>>
>>>> Until you get down to "G is unprovable in F"
>>>> we cannot build its proof tree.
> On 12/5/2023 11:52 AM, Jim Burns wrote:
>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>> On 12/4/23 8:00 PM, olcott wrote:
>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>> tl;dr
>>>>> if G("G(u)") is true
>>>>> then G("G(u)") is not ST.provable
>>
>> ST has {}, x∪{y}, and set equality.
>>
>>>> Until you get down to "G is unprovable in F"
>>>> we cannot build its proof tree.
>> he sees that complete massive-database
>> as essential to True AI and
>> True AI as essential to humanity.
>
> ∀L ∈ Formal_System ∀x ∈ Language(L)
> True(L,x) ≡ (T ⊢ x)
> False(L,x) ≡ (T ⊢ ¬x)
What is F ?
>> as essential to True AI and
>> True AI as essential to humanity.
>
> ∀L ∈ Formal_System ∀x ∈ Language(L)
> True(L,x) ≡ (T ⊢ x)
> False(L,x) ≡ (T ⊢ ¬x)
Do I have your motivation correct?
olcott
Dec 5, 2023, 3:09:43 PM12/5/23
to
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
Jim Burns
Dec 5, 2023, 4:29:02 PM12/5/23
to
On 12/5/2023 3:09 PM, olcott wrote:
> On 12/5/2023 1:58 PM, Jim Burns wrote:
>> On 12/5/2023 2:30 PM, olcott wrote:
>>> On 12/5/2023 11:52 AM, Jim Burns wrote:
>>>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>>>> On 12/4/23 8:00 PM, olcott wrote:
>>>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>>>> tl;dr
>>>>>>> if G("G(u)") is true
>>>>>>> then G("G(u)") is not ST.provable
>>>>
>>>> ST has {}, x∪{y}, and set equality.
>>>>>> Until you get down to
>>>>>> "G is unprovable in F"
>>>>>> we cannot build its proof tree.
>> What is F ?
> On 12/5/2023 1:58 PM, Jim Burns wrote:
>> On 12/5/2023 2:30 PM, olcott wrote:
>>> On 12/5/2023 11:52 AM, Jim Burns wrote:
>>>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>>>> On 12/4/23 8:00 PM, olcott wrote:
>>>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>>>> tl;dr
>>>>>>> if G("G(u)") is true
>>>>>>> then G("G(u)") is not ST.provable
>>>>
>>>> ST has {}, x∪{y}, and set equality.
>>>>>> Until you get down to
>>>>>> "G is unprovable in F"
>>>>>> we cannot build its proof tree.
> F is the formal system that encodes Gödel’s G
> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
IIRC, the 1931 paper calls it P.
It is(?) a variation on the system PM in
_Principia Mathematica_
I'm not complaining about your calling it F
I just trying to to understand you.
I'm working with a much smaller axiom set,
the one for ST: {}, x∪{y}, and set equality.
ST is the system which I want to prove is
incomplete or inconsistent.
ST is still an important result, as small as
it is, because it is straightforward to
generalize the proof of ST's incompleteness
to a proof for systems which ST can describe.
And what ST can describe is Vast.
I know: that's not exactly how Godel's proof
goes. But the important thing is my proof goes.
My hope is that, shown multiple versions, you
will be able to triangulate on why it goes.
>>>> he sees that complete massive-database
>>>> as essential to True AI and
>>>> True AI as essential to humanity.
>>>
>>> ∀L ∈ Formal_System ∀x ∈ Language(L)
>>> True(L,x) ≡ (T ⊢ x)
>>> False(L,x) ≡ (T ⊢ ¬x)
olcott
Dec 5, 2023, 5:29:44 PM12/5/23
to
Eliminates Tarski undefinability and Gödel incompleteness and forces the
concept of truth in math and logic to conform to the way that it works
everywhere else in the body of human knowledge: True(x) ≡ (⊢ x)
concept of truth in math and logic to conform to the way that it works
This makes it possible for a formal axiomatic system to eventually
get on social media and argue against the two most dangerous lies
about election fraud and climate change at every language level so
that the liars look like ridiculous fools even to themselves.
When everyone in the world believes that there is no objective
and consistent measure of True(x) (Tarski proof) this is impossible.
The reasonably possible alternative is that humanity becomes
extinct simply because some people wanted to chase after one
more dollar bill.
My paper bypasses most of the climate change lies by anchoring
itself in direct measurements of CO2 for the last 800,000 years,
These direct measurements cannot be biased.
My paper shows several different measure of a huge spike in CO2 since
1950. The next fastest spike in 800,000 years took 7,500 years.
Severe anthropogenic climate change proven entirely with verifiable facts
https://www.researchgate.net/publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
Richard Damon
Dec 5, 2023, 6:39:46 PM12/5/23
to
On 12/5/23 2:30 PM, olcott wrote:
> ∀L ∈ Formal_System ∀x ∈ Language(L)
> True(L,x) ≡ (T ⊢ x)
> False(L,x) ≡ (T ⊢ ¬x)
> Eliminates Tarski undefinability and Gödel incompleteness and forces the
> concept of truth in math and logic to conform to the way that it works
> everywhere else. True(x) ≡ (⊢ x)
>
> The only way that we know that "cats are animals" is true is the
> connection from the above expression to the definition of {cats} and
> {animals}.
>
> The lack of inference steps from axioms to an expression simply means
> untrue. Incomplete(L) is merely a terribly misleading euphemism for
> ~True(L,x).
>
And means that we can't have the Natural Numbers or anything higher.
> ∀L ∈ Formal_System ∀x ∈ Language(L)
> True(L,x) ≡ (T ⊢ x)
> False(L,x) ≡ (T ⊢ ¬x)
> Eliminates Tarski undefinability and Gödel incompleteness and forces the
> concept of truth in math and logic to conform to the way that it works
> everywhere else. True(x) ≡ (⊢ x)
>
> The only way that we know that "cats are animals" is true is the
> connection from the above expression to the definition of {cats} and
> {animals}.
>
> The lack of inference steps from axioms to an expression simply means
> untrue. Incomplete(L) is merely a terribly misleading euphemism for
> ~True(L,x).
>
So, you are just defining that Your idea of logic is too small to be useful.
Prove otherwise.
(Hint, if you have the Natural Numbers, then Godel's proof applies, and
proves there is either a statement that is True but not Provable, or
your system is inconsistent)
This just goes back your you lack of understand of how logic actually works.
Note, it also means you don't even know the meaning of the word "True"
in Natural Language, as things can be "True" even if not provable.
They can't be "Known True", but they can be "True"
You don't seem to understand the difference, probably because you don't
understand what Knowledge is.
Richard Damon
Dec 5, 2023, 9:27:03 PM12/5/23
to
that Olcott is using to (mis)understand Godel's proof. In F, we get a
statement of the form that G is the assertion that there does not exist
a Natuaral Number g that satisfies a particular Primative Recursive
Relationship. This relationship being derived in a meta-system of F that
enumerates the fundamental properties in F, and in which an encoding of
statements to numbers is defined, and the relationship is a Proof Tester
that accepts a number (and only those numbers) that encode a valid proof
of the statement G.
He seems to have a problem with the fact that SOME truths can't be
proven, and somehow thinks that means that this allows untruths to be
claimed as truth.
He seems to want there to be a massive database of all knowledge, and
then that will produce a list of everything that is actually True and
False, and thus somehow make lies go away. The irony is he atually uses
the methodology of the "fake news" crowd to try to push his idea to be
used to eliminate "fake news", because he just doesn't understand
Jim Burns
Dec 6, 2023, 12:21:54 PM12/6/23
to
On 12/5/2023 9:26 PM, Richard Damon wrote:
> On 12/5/23 12:52 PM, Jim Burns wrote:
>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>> On 12/4/23 8:00 PM, olcott wrote:
>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>> tl;dr
>>>>> if G("G(u)") is true
>>>>> then G("G(u)") is not ST.provable
> On 12/5/23 12:52 PM, Jim Burns wrote:
>> On 12/4/2023 8:44 PM, Richard Damon wrote:
>>> On 12/4/23 8:00 PM, olcott wrote:
>>>> On 12/4/2023 6:49 PM, Jim Burns wrote:
>>>>> tl;dr
>>>>> if G("G(u)") is true
>>>>> then G("G(u)") is not ST.provable
>>>> Until you get down to
>>>> "G is unprovable in F"
>>>> we cannot build its proof tree.
>>>> "G is unprovable in F"
>>>> we cannot build its proof tree.
>>> There exist a proof tree for that
>>> (which is infinite in length) in F,
>>> (which is infinite in length) in F,
>> However,
>> I'm not sure what F means here.
>
> F is the name of the Logic System used in
> the version of Godel's paper that
> Olcott is using to (mis)understand
> Godel's proof.
> In F,
> we get a statement of the form that
> G is the assertion that
> there does not exist
> a Natuaral Number g that satisfies
> a particular Primative Recursive Relationship.
> This relationship being derived in
> a meta-system of F that enumerates
> the fundamental properties in F,
> and in which
> an encoding of statements to numbers
> is defined,
> and the relationship is
> a Proof Tester that accepts
> a number (and only those numbers) that
> encode
> a valid proof of the statement G.
Thank you.
>> I'm not sure what F means here.
>
> F is the name of the Logic System used in
> the version of Godel's paper that
> Olcott is using to (mis)understand
> Godel's proof.
> In F,
> we get a statement of the form that
> G is the assertion that
> there does not exist
> a Natuaral Number g that satisfies
> a particular Primative Recursive Relationship.
> This relationship being derived in
> a meta-system of F that enumerates
> the fundamental properties in F,
> and in which
> an encoding of statements to numbers
> is defined,
> and the relationship is
> a Proof Tester that accepts
> a number (and only those numbers) that
> encode
> a valid proof of the statement G.
I hope you don't mind
my screwing around with your whitespace.
I'm experimenting with
prettyprinting natural language
in a manner intended to be similar to
prettyprinting computer code.
It seems to me that
natural language would benefit even more
from prettyprinting than code does.
The semantic graphs of natural language
can be at least as tangled as (good) code, but
we are expected to chalk the lines
with only a handful of pronouns instead of
unlimited-many variable names.
Anyway, thank you for answering my question.
> He seems to have a problem with the fact that
> SOME truths can't be proven, and
> somehow thinks that means that
> this allows untruths to be claimed as truth.
Maybe quantifier dyslexia?
> He seems to want there to be
> a massive database of all knowledge,
> and then that will produce a list of
> everything that is actually True and False,
> and thus somehow
> make lies go away.
> The irony is
> he atually uses the methodology of
> the "fake news" crowd to try to push
> his idea to be used to eliminate "fake news",
> because he just doesn't understand
olcott
Dec 6, 2023, 2:08:55 PM12/6/23
to
objective measure of True(x) that works consistently.
Whereas True(x) ≡ (⊢ x) does work consistently for
the entire body of analytical knowledge.
It includes everything known to be true on the basis
of its meaning and excludes unknown truths such as
the truth (or falsity) of the Goldbach conjecture.
Incomplete(L) is merely a terribly misleading euphemism for ~True(L,x).
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
The most important thing that True(L,x) ≡ (L ⊢ x) excludes
for a similar undecidability proof...(Gödel 1931:43-44)
are epistemological antinomies which form the essential
basis of Tarski's proof.
https://liarparadox.org/Tarski_275_276.pdf
(3) x ∉ Provable if and only if x ∈ True.
That is the false assumption step of the Tarski proof.
As soon as humans accept the correct measure of True(x)
then we can manually create formal proofs of English
statements. Until then all opinions including dangerous
lies are incorrectly thought to carry the same weight.
Jim Burns
Dec 6, 2023, 3:33:19 PM12/6/23
to
On 12/6/2023 2:08 PM, olcott wrote:
> On 12/6/2023 11:21 AM, Jim Burns wrote:
>> [...]
> On 12/6/2023 11:21 AM, Jim Burns wrote:
>
> True(x) ≡ (⊢ x)
> It includes everything known to be true on
> the basis of its meaning and excludes
> unknown truths
Unknown truths are at least as capable of
> the basis of its meaning and excludes
> unknown truths
killing you as known truths.
That is something our tiger-dodging ancestors
would have been able to explain well to you,
if they didn't give up and kick you out
into the dark, to let you find out for yourself,
for a short, adrenalized period of time.
> As soon as humans accept
> the correct measure of True(x)
> then we can manually create
> formal proofs of English statements.
| Q is not-first-false in
| ⟨… P∨Q ¬P Q …⟩
| t f t
| t t t
| t f f
| f t f
|
True(qnff) ?
¬True(qnff) ?
Consider the claim finseq =
| For finite sequence ⟨foo … bar⟩
| if ⟨foo … bar⟩ holds a false claim,
| then it holds a first false claim.
|
True(finseq) ?
¬True(finseq) ?
_Abbreviate_
| n ends ordered ⟨0,…,n⟩ such that,
| for each split Fᣔ<ᣔH of ⟨0,…,n⟩
| some i‖i+1 is last‖first in F‖H, and
| 0‖n is first‖last in ⟨0,…,n⟩
| for
| non-0 non-doppelgänger non-final i+1
as
| n is a natural number
Consider the claim natnum =
| n is a natural number
| if and only if
| n ends ordered ⟨0,…,n⟩ such that,
| for each split Fᣔ<ᣔH of ⟨0,…,n⟩
| some i‖i+1 is last‖first in F‖H, and
| 0‖n is first‖last in ⟨0,…,n⟩
| for
| non-0 non-doppelgänger non-final i+1
|
True(natnum) ?
¬True(natnum) ?
Are you expecting these answers to change
if, for example, a proof of the Goldbach
conjecture is discovered?
Please explain.
olcott
Dec 6, 2023, 4:37:09 PM12/6/23
to
Can you try again and ask to have anything that you
don't understand explained?
I understand that the philosophy of logic stuff might
be new to you.
Jim Burns
Dec 6, 2023, 4:49:24 PM12/6/23
to
is
your most important point.
YMMV.
Unknown truths are at least as capable of
killing you as known truths.
> Can you try again and ask to have
> anything that you don't understand
> explained?
True(qnff) ?
> anything that you don't understand
> explained?
¬True(qnff) ?
True(finseq) ?
¬True(finseq) ?
True(natnum) ?
¬True(natnum) ?
olcott
Dec 6, 2023, 4:55:40 PM12/6/23
to
of the analytic / synthetic distinction. That excludes
physical reality where things can kill you.
>> Can you try again and ask to have
>> anything that you don't understand
>> explained?
>
> True(qnff) ?
> ¬True(qnff) ?
>
> True(finseq) ?
> ¬True(finseq) ?
>
> True(natnum) ?
> ¬True(natnum) ?
>
Do you understand what this steps of the Tarski proof says:
(3) x ∉ Provable if and only if x ∈ True.
(3) x ∉ Provable if and only if x ∈ True.
Jim Burns
Dec 6, 2023, 5:35:06 PM12/6/23
to
On 12/6/2023 4:55 PM, olcott wrote:
> On 12/6/2023 3:49 PM, Jim Burns wrote:
>> On 12/6/2023 4:37 PM, olcott wrote:
>>> It seems that you ignored all of
>>> my important points.
>>
>>>>> excludes unknown truths
>> is
>> your most important point.
>> YMMV.
>>
>> Unknown truths are at least as capable of
>> killing you as known truths.
>
> Philosophically I am only referring to
> the analytic side of
> the analytic / synthetic distinction.
> That excludes physical reality where
> things can kill you.
Fascinating.
> On 12/6/2023 3:49 PM, Jim Burns wrote:
>> On 12/6/2023 4:37 PM, olcott wrote:
>>> It seems that you ignored all of
>>> my important points.
>>
>>>>> excludes unknown truths
>> is
>> your most important point.
>> YMMV.
>>
>> Unknown truths are at least as capable of
>> killing you as known truths.
>
> Philosophically I am only referring to
> the analytic side of
> the analytic / synthetic distinction.
> That excludes physical reality where
> things can kill you.
Would you like me to tell you about
global warming?
>>> Can you try again and ask to have
>>> anything that you don't understand
>>> explained?
>>
>> True(qnff) ?
>> ¬True(qnff) ?
>>
>> True(finseq) ?
>> ¬True(finseq) ?
>>
>> True(natnum) ?
>> ¬True(natnum) ?
>
> That all seems to be gibberish to me.
qnff =
| Q is not-first false
finseq =
| If this finite sequence of claims
| holds a false claim,
| then it holds a first false claim.
Abbreviate
| then it holds a first false claim.
a definition of "n is a natural number"
as "n is a natrual number.
natnum =
| n is a natural number
| if and only if
----
> Do you understand what this steps of
> the Tarski proof says:
> (3) x ∉ Provable if and only if x ∈ True.
Here's the problem:
> the Tarski proof says:
> (3) x ∉ Provable if and only if x ∈ True.
You:
olcott
Dec 6, 2023, 6:08:30 PM12/6/23
to
My whole point pertains to True(L,x) and everything else
is off topic.
Everything about this must be able to be translated
into a clear, correct English sentence.
When G only has a meaning based on 85 instances of
indirect reference specified by 85 different math
formulas this *is not* specified clearly enough.
It must be as clear as this:
∃G ∈ WFF(F) (G ↔ (F ⊬ G))
To say that a Natural number is true or false is
nonsense and you know it.
Richard Damon
Dec 6, 2023, 7:03:28 PM12/6/23
to
connection to your claim.
>
> Everything about this must be able to be translated
> into a clear, correct English sentence.
>
> When G only has a meaning based on 85 instances of
> indirect reference specified by 85 different math
> formulas this *is not* specified clearly enough.
seems gibberish to you.
>
> It must be as clear as this:
> ∃G ∈ WFF(F) (G ↔ (F ⊬ G))
>
> To say that a Natural number is true or false is
> nonsense and you know it.
>
It is the EXISTANCE of the number that will be either true of false.
Or, do you think some definite things either both exist and not exist,
or neither exist and not exist?
olcott
Dec 6, 2023, 10:56:58 PM12/6/23
to
philosophy.
The Sapir–Whorf hypothesis shows that there may be some
concepts that cannot be expressed within the scope of the
terms of logic.
https://en.wikipedia.org/wiki/Linguistic_relativity
Everything that is true on the basis of its meaning:
https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
AKA the analytic side of the analytic / synthetic distinction
necessarily must have a connection from an expression
to this meaning as its truthmaker or it cannot possibly be true.
Although within the conventional terms of logic there
may be some truths that cannot be proven there cannot
be analytic expressions of language that are true without
something making them true.
Richard Damon
Dec 7, 2023, 7:24:17 AM12/7/23
to
This seems to be your big blindspot, there is a diffence in the
fundamental definitions of what it means something to be True, and
something to be Provable (or Known, which is also slightly different).
Truth can be established by infinite processes, because it is
independent of knowledge, which since we are finite, is limited by
finite processes.
Thus, the chain that makes a statement true, might not qualify as a
proof, since proofs need to be finite, as proofs are an instrument of
knowledge, and thus are restricted to be finite.
Mathematics deals with concepts that are infinite, and thus can generate
infinite chains to make things true, but since we are still finite, for
us to know them we need to find a finite path that establishes them.
Your mind just seems to be too small to understand that there are things
bigger than your minds ability to think, and thus you do not understand
such things.
The greatest height of understanding is understanding what is beyond
your understanding, a property that you seem to lack.
olcott
Dec 7, 2023, 11:21:49 AM12/7/23
to
and analytical knowledge the former may require an infinite sequence of
steps as its truthmaker.
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Eliminates Tarski undefinability and Gödel incompleteness and forces the
concept of truth in math and logic to conform to the way that it works
everywhere else in the body of human knowledge: True(x) ≡ (⊢ x)
If the Goldbach conjecture only has an infinite sequence of steps as
its truthmaker and formal proofs do not allow an infinite sequence of
steps then we have an analytical truth with no proof yet it still has a
truthmaker.
Richard Damon
Dec 7, 2023, 6:26:45 PM12/7/23
to
infinite sequencd of steps to its Truth Makers, while Proofs, to create
knowledge, must only allow a finite number of steps.
So your True isn't actually a predicate for "truth" but Knowledge".
>
> Eliminates Tarski undefinability and Gödel incompleteness and forces the
> concept of truth in math and logic to conform to the way that it works
> everywhere else in the body of human knowledge: True(x) ≡ (⊢ x)
>
> If the Goldbach conjecture only has an infinite sequence of steps as
> its truthmaker and formal proofs do not allow an infinite sequence of
> steps then we have an analytical truth with no proof yet it still has a
> truthmaker.
>
you don't understand a thing you have been talking about.
olcott
Dec 7, 2023, 7:11:35 PM12/7/23
to
refutes the Tarski Undecidability theorem.
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)
above quote: (3) x ∉ Provable if and only if x ∈ True.
https://liarparadox.org/Tarski_275_276.pdf
Epistemological antinomies cannot possibly have a truthmaker (not even
with an infinite number of steps) thus are simply untrue.
Richard Damon
Dec 7, 2023, 9:44:53 PM12/7/23
to
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
"guessing" how to interprete it.
>
> Tarski anchored his proof in an epistemological antinomy just like the
> above quote: (3) x ∉ Provable if and only if x ∈ True.
> https://liarparadox.org/Tarski_275_276.pdf
be true if we assume that there exists a "definition" of truth, that is
a finite algorithm that tells you if a given expression is true.
>
> Epistemological antinomies cannot possibly have a truthmaker (not even
> with an infinite number of steps) thus are simply untrue.
>
statement in their language.
The fact that somehow you think they do shows you just don't understand
what you are talking about. You just totally don't understand how logic
works.
olcott
Dec 8, 2023, 12:32:32 AM12/8/23
to
true nor false thus calling them undecidable is a terrible euphemism
for non-truth-bearer.
Richard Damon
Dec 8, 2023, 7:33:42 AM12/8/23
to
Your problem is you don't actually understand the proof, so you don't
know what he actually means here, but are just guessing at what he
"must" mean, because it is the only thing you can think of. But that
isn't it, and just shows your stupidity.
If you want to show me wrong here, show the step in the ACTUAL proof,
and not the commentary on it, where he does this wrong thing.
Somewhere step in the proof where he uses the antinomy in a way that
requires it to have a truth value.
It seems on of your fundamental problems is you don't understand what a
Logical Proof actually is, only how to argue.
olcott
Dec 8, 2023, 12:19:56 PM12/8/23
to
Saying that Gödel did not screw up because other parts of
his paper did not screw up is the strawman deception.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
~True(L,x).
Richard Damon
Dec 8, 2023, 12:38:00 PM12/8/23
to
> Saying that Gödel did not screw up because other parts of
> his paper did not screw up is the strawman deception.
>
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof... (Gödel 1931:43-44)
>
> Thus Undecidable(L,x) is merely a terribly misleading euphemism for
> ~True(L,x).
>
You can't use "similar" without pulling in ALL of that which is referenced.
You are just showing how much of a stupid liar you are.
olcott
Dec 8, 2023, 1:35:40 PM12/8/23
to
The mathematical use of the term includes the inability to decide
whether a kitten is a 15 story office building or a 16 story office
building and no option to say "incorrect question".
Richard Damon
Dec 8, 2023, 1:48:43 PM12/8/23
to
One set of definitions:
Definition: A decision problem is a problem that requires a yes or no
answer.
Definition: A decision problem that admits no algorithmic solution is
said to be undecidable.
So, while it technically could be used of a "Decision Problem" that
requires a yes or no answer that doesn't exist (and thus no algorihmic
solution could be possible), it is more normally restricted to decision
problems that DO have an actual answer, but one that can not be
determined by a "algorithmic solution", which basically means by a
finite number of steps.
You are just proving that you don't really understand what you are
talking about but are going arround claiming victories for defeating an
the strawmen that you are putting up.
You are just proving your ignorance of what you talk about.
olcott
Dec 8, 2023, 2:03:05 PM12/8/23
to
an expression of language that is a self-contradictory
question this is incorrectly ruled as undecidable.
Richard Damon
Dec 8, 2023, 2:25:03 PM12/8/23
to
On 12/8/23 2:03 PM, olcott wrote:
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof... (Gödel 1931:43-44)
>
> When a decision problem requires a yes or no answer to
> an expression of language that is a self-contradictory
> question this is incorrectly ruled as undecidable.
>
SO, you are still showing you don't understand a thing he is talking about.
> ...14 Every epistemological antinomy can likewise be used
> for a similar undecidability proof... (Gödel 1931:43-44)
>
> When a decision problem requires a yes or no answer to
> an expression of language that is a self-contradictory
> question this is incorrectly ruled as undecidable.
>
You are just so stupid it is pitiful.
As I asked before, show exactly WHERE he is doing what you claim.
That sentence isn't it, as it doesn't show HOW the epistemoloigical
antinomy was "used" in the proof, and thus doesn't show that he is
asking for a self-contradictory question to be given an yes or no answer.
All you are doing is proving your ignorance.
olcott
Dec 8, 2023, 2:37:48 PM12/8/23
to
"As I asked before, show exactly WHERE he is doing what you claim."
As I have said 500 times! RIGHT HERE !!!
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof... (Gödel 1931:43-44)
The truth is that NO epistemological antinomies CAN EVER
for a similar undecidability proof... (Gödel 1931:43-44)
be used in ANY undecidability proof, not ever not even once.
Richard Damon
Dec 8, 2023, 3:33:39 PM12/8/23
to
Where in the PROOF is he doing this.
I will note, I have mentioned how that statement is supposed to be
interpreted, but that seems to be above your head.
You are just proving you are 500x stupid, and not knowing what you are
talking about.
You seem to think he is saying that you directly plug the epistemolgical
antinomy as the statement to be proven. but nowhere does he actually say
to do so, that is YOUR INCORRECT (and stupid) assumption of what he is
doing.
By your reasoning, the whole world is just blathering idiots.
The more like case is that you are just totally out of your league in
what you are trying to talk about and are totally misunderstanding what
everything is about.
If fact, I have show that this is true.
You are just continuing to prove your utter ignorance and stupdity, and
that you are just a pathological liar, because you just don't know what
"Truth" or a "ProoF" is.
Sorry you are so stupid, but it is just the facts.
By your logic, you have admitted that you are just a moron, so we can go
with that.
olcott
Dec 8, 2023, 3:50:37 PM12/8/23
to
about the subject matter of his paper.
Richard Damon
Dec 8, 2023, 4:14:47 PM12/8/23
to
understand because you can't even summarize it properly.
The statement you are quoting is about about alterations to the proof to
use the structure of other Epistemological Antinomies as the structure
of the statment that being processed. Note, the structure has a
transform on it which changes its semantics so it is no longer an
antinomy, so your charge doesn't apply, but then, you can't understand that.
YOU are the one not having a clue.
Jim Burns
Dec 9, 2023, 8:23:01 PM12/9/23
to
On 12/8/2023 12:29 AM, olcott wrote:
> On 12/7/2023 6:11 PM, olcott wrote:
>> On 12/7/2023 10:20 AM, olcott wrote:
>>> On 12/6/2023 9:56 PM, olcott wrote:
>>>> On 12/6/2023 4:35 PM, Jim Burns wrote:
>>>>> [...]
> On 12/7/2023 6:11 PM, olcott wrote:
>> On 12/7/2023 10:20 AM, olcott wrote:
>>> On 12/6/2023 9:56 PM, olcott wrote:
>>>> On 12/6/2023 4:35 PM, Jim Burns wrote:
>
> ...14
> Every epistemological antinomy can likewise
> be used for a similar undecidability proof...
> ...14
> Every epistemological antinomy can likewise
> be used for a similar undecidability proof...
> (Gödel 1931:43-44)
>
> Thus Gödel really screwed up.
> Epistemological antinomies
The epistemological antinomy
>
> Thus Gödel really screwed up.
> Epistemological antinomies
| This sentence is false
|
is not in Gödel's proof.
| This sentence is false
|
is the blueprint, which guides
Gödel placement of (metaphorically) actual
bricks and mortar.
You live in a building of some kind, I'd bet.
What odds would you give on whether
that building's blueprints are incorporated
into its construction?
If you ripped plaster off walls,
would you find particular sheets paper
holding up waterlines?
In note 14, Gödel is mentioning that
other blueprints can guide the placement of
(metaphorically) actual bricks and mortar
for other proofs.
Nor are those other blueprints incorporated
into those other proofs.
> Epistemological antinomies
> are neither
...here nor there.
olcott
Dec 9, 2023, 9:55:58 PM12/9/23
to
any proof at all Gödel proved that it didn't have a clue
about the subject matter of his paper.
https://liarparadox.org/Tarski_247_248.pdf
Tarski said that he used Gödel as a basis
and in the above link shows that he anchored
his whole proof in the actual Liar Paradox.
*Here is his actual proof*
https://liarparadox.org/Tarski_275_276.pdf
Richard Damon
Dec 10, 2023, 8:09:53 AM12/10/23
to
By your own logic, YOU are "using" an epistemological antinomy in your
"proof" that Godel is incorrect, so your own proof is shown to be invalid.
>
> https://liarparadox.org/Tarski_247_248.pdf
> Tarski said that he used Gödel as a basis
> and in the above link shows that he anchored
> his whole proof in the actual Liar Paradox.
Right, and where did he assume that the Liar was a true statement?
What he has shown is that the assumption that we can algorithmically
determine the truth value of a sentence (his "Definition of Truth") then
it would be possible to logically prove the Truth of the Liar. Since
this is impossible, the assumption can't be true.
You just don't understand how logic works.
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