ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Rebutting things that I did not actually say might seem like a rebuttal
to gullible fools.
People that are paying 100% complete attention will see that such
rebuttals are the strawman error even if unintentional.
People that physically don't have the capacity to pay close attention
may commit the strawman error much of the time and not even know it.
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological antinomies are excluded and unknowns are excluded and there is nothing
else left over.
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological antinomies are excluded and unknowns are excluded and there is nothing
else left over.
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>> and undecidability by redefining meaning of the term {formal system} >>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
Reviewers that don't give a rat's ass about truth and only want to stay
in rebuttal mode even if must lie to do it will refuse to acknowledge
that expressions that require infinite proofs to resolve their true
value are necessarily not truth bearers in formal systems that do not
allow infinite proofs.
Reviewers that don't give a rat's ass about truth and only want to stay
in rebuttal mode even if must lie to do it will refuse to acknowledge
that expressions that require infinite proofs to resolve their true
value are necessarily not truth bearers in formal systems that do not
allow infinite proofs.
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological antinomies are excluded and unknowns are excluded and there is nothing
else left over.
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>> and undecidability by redefining meaning of the term {formal system} >>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>> and undecidability by redefining meaning of the term {formal system} >>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
On 11/19/2023 7:03 PM, olcott wrote:
On 11/19/2023 6:15 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean >>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it >>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>> bother to notice that I was talking about the set of human knowledge. >>>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a
paradox or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.
On 11/19/2023 6:15 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a
paradox or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.
On 11/19/2023 6:15 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a
paradox or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 6:15 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a
paradox or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 7:03 PM, olcott wrote:
On 11/19/2023 6:15 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean >>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it >>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>> bother to notice that I was talking about the set of human knowledge. >>>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
Antinomy
...term often used in logic and epistemology, when describing a
paradox or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy
epistemological antinomies are unprovable because they are semantic
nonsense.
"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.
On the other hand honest reviewers would say of course you are right
about this. Expecting a formal system to prove an epistemological
antinomy is ridiculous. How could Gödel make such a huge mistake?
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
There is no way to correctly refute that Gödel was definitely wrong
about this.
I would go further and say the the strongest possible rebuttal cannot
do any better than complete nonsense. My reviewer already knows this.
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
There is no way to correctly refute that Gödel was definitely wrong
about this.
I would go further and say the the strongest possible rebuttal cannot
do any better than complete nonsense. My reviewer already knows this.
On 11/19/2023 9:58 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
There is no way to correctly refute that Gödel was definitely wrong
about this.
I would go further and say the the strongest possible rebuttal cannot
do any better than complete nonsense. My reviewer already knows this.
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
is terribly incorrect.
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
(such as the above sentence) is terribly incorrect.
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
(such as the above sentence) is terribly incorrect.
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
(such as the above sentence) is terribly incorrect.
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
(such as the above sentence) is terribly incorrect.
Hopefully the one lying about this does not get the eternal
incineration in the Revelation 21:8 lake of fire required for
"all liars" that seems far too harsh.
The Church of Jesus Christ of Latter day saints temporary purgatory
like option seems more appropriate.
On 11/20/2023 8:38 AM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
It is dead obvious that epistemological antinomies are semantic
nonsense thus anyone saying that any proof can be based on them
(such as the above sentence) is terribly incorrect.
Proof by contraction when one begins with a self-contradictory
expression is like trying to make an angel food cake from dog shit.
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be
used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
"Who said you started with a self contradictory expression?"
Gödel
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be
used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
"Who said you started with a self contradictory expression?"
Gödel just said that in the quote above when you understand that epistemological antinomies are self-contradictory expressions.
*Antinomy*
...term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by changing >>>>>> the meaning of the term {set theory} we can eliminate incompleteness >>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
When you understand that an epistemological antinomy is a self-
contradictory expression then the above quoted sentence is
understood to be a ridiculous error.
Even gullible fools will know that changing the subject away
from the above quoted sentence is such a lame attempt at deception
that they will reject such attempts as nonsense.
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>> Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate incompleteness >>>>>>> and undecidability by redefining meaning of the term {formal system} >>>>>>> as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>> not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing >>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by
changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal
system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge. >>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is rejected as >>>>> not a truth bearer, (within this formal system) thus epistemological >>>>> antinomies are excluded and unknowns are excluded and there is nothing >>>>> else left over.
When we stipulate that a truthmaker is what-so-ever makes an expression >>>> of language true then we can know by tautology that every truth has a
truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
On 11/20/2023 1:25 PM, olcott wrote:
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean >>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it >>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>> bother to notice that I was talking about the set of human knowledge. >>>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
"Note, As I have pointed out, Godel isn't saying that he is using an epistemological antinomy as a PREMISE to his proof, so your argument
doesn't apply to it."
*Since incompleteness already has a precise definition*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
then the epistemological antinomy cannot possibly be correctly
construed as anything besides x in the above expression.
On 11/20/2023 1:25 PM, olcott wrote:
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean >>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it >>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>> bother to notice that I was talking about the set of human knowledge. >>>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
"Note, As I have pointed out, Godel isn't saying that he is using an epistemological antinomy as a PREMISE to his proof, so your argument
doesn't apply to it."
*Since incompleteness already has a precise definition*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
then the epistemological antinomy cannot possibly be correctly
construed as anything besides x in the above expression.
On 11/20/2023 1:25 PM, olcott wrote:
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean >>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it >>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>> bother to notice that I was talking about the set of human knowledge. >>>>>>
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this arbitrarily >>>>> limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
"Note, As I have pointed out, Godel isn't saying that he is using an epistemological antinomy as a PREMISE to his proof, so your argument
doesn't apply to it."
*Since incompleteness already has a precise definition*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
then the epistemological antinomy cannot possibly be correctly
construed as anything besides x in the above expression.
On 11/20/2023 2:08 PM, olcott wrote:
On 11/20/2023 1:25 PM, olcott wrote:
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by >>>>>>>>> epistemological antinomies by redefining meaning of the term >>>>>>>>> {formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects >>>>>>>>> input D that is defined to do the opposite of whatever Boolean >>>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies} >>>>>>>>> cannot possibly create incompleteness or undecidability when it >>>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>>> bother to notice that I was talking about the set of human
knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this
arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
"Note, As I have pointed out, Godel isn't saying that he is using an
epistemological antinomy as a PREMISE to his proof, so your argument
doesn't apply to it."
*Since incompleteness already has a precise definition*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
then the epistemological antinomy cannot possibly be correctly
construed as anything besides x in the above expression.
"So, you are presuming (INCORRECTLY) that the x in this
formula is an epistemological antinomy in Godel's Proof"
*I am presuming nothing* There is no possible other place
to correctly insert the epistemological antinomy in the
definition of incompleteness besides x.
Also again and again and again I have only been talking
about this one freaking quote in everyone of my last
very many messages:
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
On 11/20/2023 2:08 PM, olcott wrote:
On 11/20/2023 1:25 PM, olcott wrote:
On 11/20/2023 12:56 PM, olcott wrote:
On 11/19/2023 5:32 PM, olcott wrote:
On 11/19/2023 3:49 PM, olcott wrote:
On 11/19/2023 10:19 AM, olcott wrote:
On 11/18/2023 12:48 PM, olcott wrote:
On 11/18/2023 12:16 PM, olcott wrote:
On 11/18/2023 10:32 AM, olcott wrote:
ZFC was able to reject epistemological antinomies by screening >>>>>>>>>> out the pathological self-reference derived by sets as members >>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set >>>>>>>>>> theory differently.
In the same way that Russell's Paradox was eliminated we can >>>>>>>>>> get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically >>>>>>>>>> unsound.
When we define True(L, x) as (L ⊢ x) provable from the axioms >>>>>>>>>> of L, then epistemological antinomies become simply untrue and >>>>>>>>>> no longer show incompleteness or undecidability.
Since we have already fixed the undecidability issue of Russell's >>>>>>>>>> Paradox by redefining set theory the precedent has already been >>>>>>>>>> set that we can correct these issues by redefining the meaning >>>>>>>>>> of their terms.
Because the undecidability of Russell's Paradox was fixed by >>>>>>>>>> changing
the meaning of the term {set theory} we can eliminate
incompleteness
and undecidability by redefining meaning of the term {formal >>>>>>>>>> system}
as detailed above.
We can eliminate incompleteness and undecidability derived by >>>>>>>>> epistemological antinomies by redefining meaning of the term >>>>>>>>> {formal system} as detailed above.
For the halting problem H(D,D) simply screens out and rejects >>>>>>>>> input D that is defined to do the opposite of whatever Boolean >>>>>>>>> value that H returns.
Pathological self-reference {AKA epistemological antinomies} >>>>>>>>> cannot possibly create incompleteness or undecidability when it >>>>>>>>> is simply screened out as erroneous.
When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.
This is the way that human knowledge actually works:
True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)
This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not >>>>>>> bother to notice that I was talking about the set of human
knowledge.
then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.
Every expression that is neither provable nor refutable is
rejected as
not a truth bearer, (within this formal system) thus epistemological >>>>>>> antinomies are excluded and unknowns are excluded and there is
nothing
else left over.
When we stipulate that a truthmaker is what-so-ever makes an
expression
of language true then we can know by tautology that every truth has a >>>>>> truthmaker.
When we arbitrarily limit the set of truthmakers then this
arbitrarily
limit screws everything up.
To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.
My most important point of all this is that epistemological antinomies >>>>> are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
...14 Every epistemological antinomy
AKA every self-contradictory expression
can likewise be used for a similar undecidability proof...
AKA can likewise be used to provide a sequence of
inference steps proving that self-contradictory
expressions cannot be proven.
"By this logic, any proof that mentions epistemological
antinomies are invalid"
Not at all. I didn't say anything like that.
...14 Every epistemological antinomy can likewise be used
for a similar undecidability proof...(Gödel 1931:43-44)
*The above sentence proves that the above sentence is incorrect*
"Note, As I have pointed out, Godel isn't saying that he is using an
epistemological antinomy as a PREMISE to his proof, so your argument
doesn't apply to it."
*Since incompleteness already has a precise definition*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
then the epistemological antinomy cannot possibly be correctly
construed as anything besides x in the above expression.
*I have only been referring to this one quote*
*I have only been referring to this one quote*
*I have only been referring to this one quote*
...14 Every epistemological antinomy can likewise be
used for a similar undecidability proof...(Gödel 1931:43-44)
*I have not been referring to anything else*
*I have not been referring to anything else*
*I have not been referring to anything else*
"So, you are presuming (INCORRECTLY) that the x in this
formula is an epistemological antinomy in Godel's Proof"
*I am presuming nothing* There is no possible other place
to correctly insert the above quoted epistemological antinomy
in the definition of incompleteness besides x.
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