When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot possibly be true under any circumstance.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make it true.
When we drop Gödel numbers thus have G directly asserting that itself is unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Any system outside of the scope of self contradiction can determine that
an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot possibly be true under any circumstance.
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make it true.
When we drop Gödel numbers thus have G directly asserting that itself is unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Any system outside of the scope of self contradiction can determine that
an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make it true.
When we drop Gödel numbers thus have G directly asserting that itself is unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Any system outside of the scope of self contradiction can determine that
an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system >>> is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make
it true.
When we drop Gödel numbers thus have G directly asserting that itself is
unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
Any system outside of the scope of self contradiction can determine that
an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal system >>> is incomplete.
This sentence is not true: "This sentence is not true" is true because
the outer sentence refers to a self-contradictory sentence that cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make
it true.
When we drop Gödel numbers thus have G directly asserting that itself is
unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
Any system outside of the scope of self contradiction can determine that
an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in
F because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true because >>>> the outer sentence refers to a self-contradictory sentence that cannot >>>> possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make
it true.
When we drop Gödel numbers thus have G directly asserting that itself is >>> unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
Any system outside of the scope of self contradiction can determine that >>> an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in >>>>>> F because it would be a proof in F that no such proof exists in F. >>>>>>
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true because >>>>> the outer sentence refers to a self-contradictory sentence that cannot >>>>> possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a proof >>>> in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable >>> in F, diagonalization only shows THAT G is unprovable in F, thus leaving >>> us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Any system outside of the scope of self contradiction can determine
that
an ill-formed expression of language is not true or provable because it >>>> is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in
F because it would be a proof in F that no such proof exists in F.
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true because >>>> the outer sentence refers to a self-contradictory sentence that cannot >>>> possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not make
it true.
When we drop Gödel numbers thus have G directly asserting that itself is >>> unprovable in F this cannot be proven in F because it would be a proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
Any system outside of the scope of self contradiction can determine that >>> an ill-formed expression of language is not true or provable because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven in >>>>>> F because it would be a proof in F that no such proof exists in F. >>>>>>
No self-contradictory expressions can ever be proven in any formal
system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true because >>>>> the outer sentence refers to a self-contradictory sentence that cannot >>>>> possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a proof >>>> in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is unprovable >>> in F, diagonalization only shows THAT G is unprovable in F, thus leaving >>> us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, then we know that it is not unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Any system outside of the scope of self contradiction can determine
that
an ill-formed expression of language is not true or provable because it >>>> is ill-formed. If we ignore the fact that G and LP are ill-formed we
might be conned into believing that F is incomplete.
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven
in F because it would be a proof in F that no such proof exists
in F.
No self-contradictory expressions can ever be proven in any formal >>>>>> system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true
because
the outer sentence refers to a self-contradictory sentence that
cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a proof >>>>> in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F >>>> that no such proof exists in F, then we know that it is not unprovable >>>> in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the
strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory
we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is invalidated.
Any system outside of the scope of self contradiction can determine
that
an ill-formed expression of language is not true or provable
because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we >>>>> might be conned into believing that F is incomplete.
On 4/1/2023 12:46 PM, olcott wrote:
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven >>>>>>>> in F because it would be a proof in F that no such proof exists >>>>>>>> in F.
No self-contradictory expressions can ever be proven in any formal >>>>>>> system because they are self-contradictory not because the formal >>>>>>> system
is incomplete.
This sentence is not true: "This sentence is not true" is true
because
the outer sentence refers to a self-contradictory sentence that
cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a
proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not >>>>>> because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F >>>>> that no such proof exists in F, then we know that it is not unprovable >>>>> in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F >>>> that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the
strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key
element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory
we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is
invalidated.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Every rebuttal of this is one kind of a lie or another.
If the above G is unprovable in F only because it is self-contradictory
in F then it is not unprovable in F because F is incomplete.
Every rebuttal of this is one kind of a lie or another.
On 4/1/2023 12:46 PM, olcott wrote:
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven >>>>>>>> in F because it would be a proof in F that no such proof exists >>>>>>>> in F.
No self-contradictory expressions can ever be proven in any formal >>>>>>> system because they are self-contradictory not because the formal >>>>>>> system
is incomplete.
This sentence is not true: "This sentence is not true" is true
because
the outer sentence refers to a self-contradictory sentence that
cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a
proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not >>>>>> because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F >>>>> that no such proof exists in F, then we know that it is not unprovable >>>>> in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F >>>> that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the
strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key
element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory
we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is
invalidated.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Every rebuttal of this is one kind of a lie or another.
If the above G is unprovable in F only because it is self-contradictory
in F then it is not unprovable in F because F is incomplete.
Every rebuttal of this is one kind of a lie or another.
Any system outside of the scope of self contradiction can
determine that
an ill-formed expression of language is not true or provable
because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we >>>>>> might be conned into believing that F is incomplete.
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven
in F because it would be a proof in F that no such proof exists
in F.
No self-contradictory expressions can ever be proven in any formal >>>>>> system because they are self-contradictory not because the formal
system
is incomplete.
This sentence is not true: "This sentence is not true" is true
because
the outer sentence refers to a self-contradictory sentence that
cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not
make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a proof >>>>> in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not
because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof in F >>>> that no such proof exists in F, then we know that it is not unprovable >>>> in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F
thus merely an example of the strawman deception dishonest dodge away
from the point at hand.
When we make a G in F that does assert its own unprovability in F then
this F right here that we just made is unprovable in F because it would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the
strawman deception to change the subject to a different F than the one
that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory
we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is invalidated.
Any system outside of the scope of self contradiction can determine
that
an ill-formed expression of language is not true or provable
because it
is ill-formed. If we ignore the fact that G and LP are ill-formed we >>>>> might be conned into believing that F is incomplete.
On 4/1/2023 1:18 PM, olcott wrote:
On 4/1/2023 12:46 PM, olcott wrote:
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven >>>>>>>>> in F because it would be a proof in F that no such proof exists >>>>>>>>> in F.
No self-contradictory expressions can ever be proven in any formal >>>>>>>> system because they are self-contradictory not because the
formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true >>>>>>>> because
the outer sentence refers to a self-contradictory sentence that >>>>>>>> cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not >>>>>>> make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a >>>>>>> proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not >>>>>>> because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof
in F
that no such proof exists in F, then we know that it is not
unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F >>>>> that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F >>>>> thus merely an example of the strawman deception dishonest dodge away >>>>> from the point at hand.
When we make a G in F that does assert its own unprovability in F then >>>> this F right here that we just made is unprovable in F because it would >>>> be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the >>>> strawman deception to change the subject to a different F than the one >>>> that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key
element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory >>> we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is >>> invalidated.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Every rebuttal of this is one kind of a lie or another.
If the above G is unprovable in F only because it is self-contradictory
in F then it is not unprovable in F because F is incomplete.
Every rebuttal of this is one kind of a lie or another.
When G
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
asserts that
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
is unprovable in F
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
cannot be proven in F
because it would be a proof in F that no such proof exists in F.
14 Every epistemological antinomy can likewise be used for a similar undecidability proof. (Gödel 1931:39-41)
Thus every equivalent proof that Gödel refers to does not prove that its formal system is incomplete, thus universally nullifying the notion of mathematical incompleteness for all of these equivalent proofs.
On 4/1/2023 1:56 PM, olcott wrote:
On 4/1/2023 1:18 PM, olcott wrote:
On 4/1/2023 12:46 PM, olcott wrote:
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be
proven in F because it would be a proof in F that no such
proof exists in F.
No self-contradictory expressions can ever be proven in any formal >>>>>>>>> system because they are self-contradictory not because the
formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true >>>>>>>>> because
the outer sentence refers to a self-contradictory sentence that >>>>>>>>> cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not >>>>>>>> make it true.
When we drop Gödel numbers thus have G directly asserting that >>>>>>>> itself is
unprovable in F this cannot be proven in F because it would be a >>>>>>>> proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not >>>>>>>> because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus >>>>>>> leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof >>>>>>> in F
that no such proof exists in F, then we know that it is not
unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof
in F
that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F >>>>>> thus merely an example of the strawman deception dishonest dodge away >>>>>> from the point at hand.
When we make a G in F that does assert its own unprovability in F then >>>>> this F right here that we just made is unprovable in F because it
would
be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the >>>>> strawman deception to change the subject to a different F than the one >>>>> that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key >>>> element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are
self-contradictory
we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked >>>> then every use of mathematical incompleteness by each and every
proof is
invalidated.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Every rebuttal of this is one kind of a lie or another.
If the above G is unprovable in F only because it is self-contradictory
in F then it is not unprovable in F because F is incomplete.
Every rebuttal of this is one kind of a lie or another.
When G
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
asserts that
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
is unprovable in F
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
cannot be proven in F
because it would be a proof in F that no such proof exists in F.
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
Thus every equivalent proof that Gödel refers to does not prove that its
formal system is incomplete, thus universally nullifying the notion of
mathematical incompleteness for all of these equivalent proofs.
When I show that the generic notion of mathematical incompleteness is
bogus by showing that it is bogus for every equivalent proof that Gödel
just referred to this is not any kind of fallacy.
Because I just proved that I do know what epistemological antinomies
are by providing an epistemological antinomy proves that I know what
they are:
When G
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
asserts that
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
is unprovable in F
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Antinomy
...term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy
An empty unsupported claim that I am incorrect about this is the same as claims of election fraud without any evidence of election fraud, the
tactic used by liars in an attempt to fool the gullible.
On 4/1/2023 1:18 PM, olcott wrote:
On 4/1/2023 12:46 PM, olcott wrote:
On 4/1/2023 12:15 PM, olcott wrote:
On 4/1/2023 11:42 AM, olcott wrote:
On 4/1/2023 11:19 AM, olcott wrote:
On 4/1/2023 10:17 AM, olcott wrote:
On 4/1/2023 9:34 AM, olcott wrote:
On 4/1/2023 12:16 AM, olcott wrote:
When G asserts that it is unprovable in F this cannot be proven >>>>>>>>> in F because it would be a proof in F that no such proof exists >>>>>>>>> in F.
No self-contradictory expressions can ever be proven in any formal >>>>>>>> system because they are self-contradictory not because the
formal system
is incomplete.
This sentence is not true: "This sentence is not true" is true >>>>>>>> because
the outer sentence refers to a self-contradictory sentence that >>>>>>>> cannot
possibly be true under any circumstance.
"This sentence is not true" is indeed not true yet that does not >>>>>>> make it true.
When we drop Gödel numbers thus have G directly asserting that
itself is
unprovable in F this cannot be proven in F because it would be a >>>>>>> proof
in F that no such proof exists in F.
Thus G is unprovable in F because G is self-contradictory in F not >>>>>>> because F is incomplete.
Unless we drop Gödel numbers it is impossible to see WHY G is
unprovable
in F, diagonalization only shows THAT G is unprovable in F, thus
leaving
us free to simply guess WHY.
When we see that G is unprovable in F because it would be a proof
in F
that no such proof exists in F, then we know that it is not
unprovable
in F because F is incomplete.
When we see that G is unprovable in F because it would be a proof in F >>>>> that no such proof exists in F, this is all that we need to know.
Any reference to meta-F is not a proof in F that G is unprovable in F >>>>> thus merely an example of the strawman deception dishonest dodge away >>>>> from the point at hand.
When we make a G in F that does assert its own unprovability in F then >>>> this F right here that we just made is unprovable in F because it would >>>> be a proof in F that no such proof exists in F.
The only [fake] "rebuttal" to this requires the dishonest dodge of the >>>> strawman deception to change the subject to a different F than the one >>>> that we just specified. *There are no legitimate rebuttals to this*
Even though it is not precisely Gödel's G
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof. (Gödel 1931:39-41)
the above shows that Gödel did know that self-contradiction is the key
element of every equivalent proof.
Because epistemological antinomies are semantically ill-formed
expressions that are unprovable ONLY because they are self-contradictory >>> we know that they are not unprovable for any other reason.
Thus when the whole concept of mathematical incompleteness is debunked
then every use of mathematical incompleteness by each and every proof is >>> invalidated.
When G asserts that it is unprovable in F this cannot be proven in F
because it would be a proof in F that no such proof exists in F.
Every rebuttal of this is one kind of a lie or another.
If the above G is unprovable in F only because it is self-contradictory
in F then it is not unprovable in F because F is incomplete.
Every rebuttal of this is one kind of a lie or another.
When G
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
asserts that
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
is unprovable in F
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
cannot be proven in F
because it would be a proof in F that no such proof exists in F.
14 Every epistemological antinomy can likewise be used for a similar undecidability proof. (Gödel 1931:39-41)
Thus every equivalent proof that Gödel refers to does not prove that its formal system is incomplete, thus universally nullifying the notion of mathematical incompleteness for all of these equivalent proofs.
When G
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
asserts that
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
is unprovable in F
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
THIS G RIGHT HERE
cannot be proven in F
because it would be a proof in F that no such proof exists in F.
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