All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
have a well understood
meaning in Common Language if Olcott's system would ever be implemented.
But it would never be in the body of common knowledge.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
so it is not outside
of the body of knowledge. It has a well defined arithmetic meaning
so it is not incoherent. But it is undecidable in Peano arithmetic.
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
On 7/14/2026 4:12 AM, Mikko wrote:You're kidding yourself. They can't possibly not exist. You can't just "stipulate them away".
On 13/07/2026 18:46, olcott wrote:That stays the same in my system yet in my system
All undecidability is unmasked as semanticG||del's sentence is true about natural numbers.
incoherence or outside of the body of knowledge.
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semanticThat's a tactic deliberately designed to cause confusion. P reo Q has a
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.The second of these is not false, but true. It's your wilful failure to understand this that's got you swearing at other posters in this group.
(P reo -4P) reo Q is simply false.
--so it is not outside of the body of knowledge. It has a well defined arithmetic meaning so it is not incoherent. But it is undecidable in--
Peano arithmetic.
Copyright 2026 Olcott
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated that his
G could not be proven from the axioms of PA. Nor could -4G be proven from the axioms of PA. So it's really unclear what you are trying to say.
If that 'stay the same', as you say, then that simply confirms that PA
is incomplete.
Andr|-
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
You're kidding yourself. They can't possibly not exist. You can't just "stipulate them away".
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
That's a tactic deliberately designed to cause confusion.
P reo Q has a
well defined meaning.
Don't be surprised when other posters reject your
replacing it with a new meaning. I reject it. Also you would need to
give a new symbol to stand for what reo stands for in mathematics.
And you still haven't corrected the grammatical error in your cut and
paste.
PA reo G is simply false.
(P reo -4P) reo Q is simply false.
The second of these is not false, but true.
It's your wilful failure to
understand this that's got you swearing at other posters in this group.
so it is not outside of the body of knowledge. It has a well defined
arithmetic meaning so it is not incoherent. But it is undecidable in
Peano arithmetic.
--
Copyright 2026 Olcott
PA reo G is simply false.
(P reo -4P) reo Q is simply false.
The second of these is not false, but true.
Plug English words into P and Q and show how the
meaning of the words of P <semantically entail> Q.
Claims without supporting evidence cannot
be correctly accepted as true.
On 7/14/2026 2:48 PM, Andr|- G. Isaak wrote:
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated that
his G could not be proven from the axioms of PA. Nor could -4G be
proven from the axioms of PA. So it's really unclear what you are
trying to say.
If that 'stay the same', as you say, then that simply confirms that PA
is incomplete.
Andr|-
My system has zero undecidability and zero incompleteness.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
On 2026-07-14 14:01, olcott wrote:
On 7/14/2026 2:48 PM, Andr|- G. Isaak wrote:
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated that
his G could not be proven from the axioms of PA. Nor could -4G be
proven from the axioms of PA. So it's really unclear what you are
trying to say.
If that 'stay the same', as you say, then that simply confirms that
PA is incomplete.
Andr|-
My system has zero undecidability and zero incompleteness.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
You say your system has 'zero incompleteness'. Since you admit that PA reo
G is false are you now claiming that PA reo -4G is true?
Because that is
what would be required to get rid of incompleteness and yet G||del rather clearly shows that PA *cannot* show that rCoG is true.
Andr|-
On 7/14/2026 3:30 PM, Andr|- G. Isaak wrote:
On 2026-07-14 14:01, olcott wrote:
On 7/14/2026 2:48 PM, Andr|- G. Isaak wrote:
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated that >>>> his G could not be proven from the axioms of PA. Nor could -4G be
proven from the axioms of PA. So it's really unclear what you are
trying to say.
If that 'stay the same', as you say, then that simply confirms that
PA is incomplete.
Andr|-
My system has zero undecidability and zero incompleteness.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
You say your system has 'zero incompleteness'. Since you admit that PA
reo G is false are you now claiming that PA reo -4G is true?
PA does not says shit about any of that.
Because that is what would be required to get rid of incompleteness
and yet G||del rather clearly shows that PA *cannot* show that rCoG is true. >>
Andr|-
THIS SYSTEM MAKES UNDECIDABILITY AND INCOMPLETENESS IMPOSSIBLE
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language.-a This is the only inference steps allowed.
On 2026-07-14 14:42, olcott wrote:
On 7/14/2026 3:30 PM, Andr|- G. Isaak wrote:
On 2026-07-14 14:01, olcott wrote:
On 7/14/2026 2:48 PM, Andr|- G. Isaak wrote:
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated that >>>>> his G could not be proven from the axioms of PA. Nor could -4G be
proven from the axioms of PA. So it's really unclear what you are
trying to say.
If that 'stay the same', as you say, then that simply confirms that >>>>> PA is incomplete.
Andr|-
My system has zero undecidability and zero incompleteness.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
You say your system has 'zero incompleteness'. Since you admit that
PA reo G is false are you now claiming that PA reo -4G is true?
PA does not says shit about any of that.
No, but G||del's proof does.
Because that is what would be required to get rid of incompleteness
and yet G||del rather clearly shows that PA *cannot* show that rCoG is
true.
Andr|-
THIS SYSTEM MAKES UNDECIDABILITY AND INCOMPLETENESS IMPOSSIBLE
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language.-a This is the only inference steps allowed.
How does that follow? If P does not semantically entail Q and P also
does not semantically entail -4Q, then the system is incomplete. Your use
of the term 'semantically entails' rather than proves has no bearing on this.
Andr|-
On 7/14/2026 4:06 PM, Andr|- G. Isaak wrote:
On 2026-07-14 14:42, olcott wrote:
On 7/14/2026 3:30 PM, Andr|- G. Isaak wrote:
On 2026-07-14 14:01, olcott wrote:
On 7/14/2026 2:48 PM, Andr|- G. Isaak wrote:
On 2026-07-14 13:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
That was the whole *point* of G||delrCOs theorem. He demonstrated >>>>>> that his G could not be proven from the axioms of PA. Nor could -4G >>>>>> be proven from the axioms of PA. So it's really unclear what you
are trying to say.
If that 'stay the same', as you say, then that simply confirms
that PA is incomplete.
Andr|-
My system has zero undecidability and zero incompleteness.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
PA reo G is simply false.
You say your system has 'zero incompleteness'. Since you admit that
PA reo G is false are you now claiming that PA reo -4G is true?
PA does not says shit about any of that.
No, but G||del's proof does.
Because that is what would be required to get rid of incompleteness
and yet G||del rather clearly shows that PA *cannot* show that rCoG is >>>> true.
Andr|-
THIS SYSTEM MAKES UNDECIDABILITY AND INCOMPLETENESS IMPOSSIBLE
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language.-a This is the only inference steps allowed.
How does that follow? If P does not semantically entail Q and P also
does not semantically entail -4Q, then the system is incomplete. Your
use of the term 'semantically entails' rather than proves has no
bearing on this.
Andr|-
"sfsdf [pem,e35rty 456456" Is that "undecidable" or
just plain nonsense? It is not provable or refutable
on PA.
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
This is the only inference steps allowed.
PA reo G is simply false.
(P reo -4P) reo Q is simply false.
On 7/14/2026 2:57 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
You're kidding yourself.-a They can't possibly not exist.-a You can't just >> "stipulate them away".
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
That's a tactic deliberately designed to cause confusion.
It may cause confusion only when one considers conventional
views the infallible word-of-God thus alternatives to
conventional views inherently incorrect.
-aP reo Q has a
well defined meaning.
If I stipulated that is means "go fuck yourself" then that
is what it means in any dialogue with me.
On 7/14/2026 2:11 AM, Mikko wrote:Olcott has confirmed that he thinks that A is true.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
be rejected as pathological.
Op 14.jul.2026 om 20:18 schreef olcott:
On 7/14/2026 2:11 AM, Mikko wrote:Olcott has confirmed that he thinks that A is true.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
be rejected as pathological.
Now he says that Olcott's system will reject this finite string A,
because of a self-reference.
According to the system, A has no truth value.
So, Olcott and his system disagree about the truth value of A.
Olcott claims that his system will convince everybody about the truth.
We now see ourselves confronted with the ultimate test of the strength
of Olcott's system:
Is the system strong enough to make Olcott change his opinion about A?
Will he accept that we cannot prove that A is true?
If no.
If even Olcott himself does not accept the output of his own system, why would we believe that anybody else will accept it?
If yes.
If Olcott accepts that we cannot say that A is true, i.e. that his
system is correct, why would anyone change his opinion because of the
output of a system of which the correctness cannot be proven?
On 14/07/2026 22:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
If G||del's undecidable sentence does not exist in your system then
you cannot say in that system that it is true about natural numbers.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
The exact meaning reo depends on the context. When talking about G||del's sentence it means, unless defined otherwise, that the sentence Q can
be inferred from P according to the rules of ordinary formal logic.
This is the only inference steps allowed.
THere are equivalent ways to represent ordinary logic.
Some styles
use only one inference rule, usually modus ponens,
and a large set
of axioms and axiom rules. Others use a large set of inference
rules and a small set of axioms and axiom rules or even no axioms
and axiom rules at all.
PA reo G is simply false.
(P reo -4P) reo Q is simply false.
The latter is off-topic per the subject line. But in any context
people really car or need to care about (P reo -4P) reo Q is true,
On 14/07/2026 23:16, olcott wrote:
On 7/14/2026 2:57 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
You're kidding yourself.-a They can't possibly not exist.-a You can't just >>> "stipulate them away".
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
That's a tactic deliberately designed to cause confusion.
It may cause confusion only when one considers conventional
views the infallible word-of-God thus alternatives to
conventional views inherently incorrect.
-aP reo Q has a
well defined meaning.
If I stipulated that is means "go fuck yourself" then that
is what it means in any dialogue with me.
That's a big IF. Above you did not stipulate, you just coaimed.
On 7/15/2026 2:25 AM, Mikko wrote:
On 14/07/2026 22:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
If G||del's undecidable sentence does not exist in your system then
you cannot say in that system that it is true about natural numbers.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
The exact meaning reo depends on the context. When talking about G||del's
sentence it means, unless defined otherwise, that the sentence Q can
be inferred from P according to the rules of ordinary formal logic.
?Q" instead. When you reason about a system that doesn't have the |-predicate you can use it by the de faqto conventions of the group you're posting at.
On 7/15/2026 2:25 AM, Mikko wrote:
On 14/07/2026 22:41, olcott wrote:
PA reo G is simply false.
(P reo -4P) reo Q is simply false.
The latter is off-topic per the subject line. But in any context
people really car or need to care about (P reo -4P) reo Q is true,
Full English semantics thus the meaning of
the words of P forces the meaning of the words
of Q to be true, else not an inference step.
On 15/07/2026 16:14, olcott wrote:
On 7/15/2026 2:25 AM, Mikko wrote:
On 14/07/2026 22:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
If G||del's undecidable sentence does not exist in your system then
you cannot say in that system that it is true about natural numbers.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
The exact meaning reo depends on the context. When talking about G||del's >>> sentence it means, unless defined otherwise, that the sentence Q can
be inferred from P according to the rules of ordinary formal logic.
Really, it refers to inferences of a system with statements formed with
the unary predicate "|-" *or stipulated alternative presentations of the predicate*.
Godel's system P didn't stipulate the predicate so you don't have to be
very careful just because you're talking about Godel's sentence, you
have to be careful because there's such a commonly used meaning in logic
for "|-" which is derived from Frege's system and reformalised to
"A, B, C |- D" is short for "|-A & |-B & |-C => |-D".
When you say "in this chapter I relate two logistic systems, the
relating system has the '|-' symbol for the usual predicate but to distinguish their statements from it they have '!' and '?' in its place
in their statements, respectively," you are stipulating alternative presentations so you can have the union of the statements of the three
and you can't use P |- Q for inferences that have statements from the
two inferior systems for P or for Q - you'd have to say things like "!P
?Q" instead. When you reason about a system that doesn't have the |-predicate you can use it by the de faqto conventions of the group you're posting at.
On 15/07/2026 16:14, olcott wrote:
On 7/15/2026 2:25 AM, Mikko wrote:
On 14/07/2026 22:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
If G||del's undecidable sentence does not exist in your system then
you cannot say in that system that it is true about natural numbers.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
The exact meaning reo depends on the context. When talking about G||del's >>> sentence it means, unless defined otherwise, that the sentence Q can
be inferred from P according to the rules of ordinary formal logic.
Really, it refers to inferences of a system with statements formed with
the unary predicate "|-" *or stipulated alternative presentations of the predicate*.
Godel's system P didn't stipulate the predicate so you don't have to be
very careful just because you're talking about Godel's sentence, you
have to be careful because there's such a commonly used meaning in logic
for "|-" which is derived from Frege's system and reformalised to
"A, B, C |- D" is short for "|-A & |-B & |-C => |-D".
On 7/15/2026 4:11 AM, Fred. Zwarts wrote:
Op 14.jul.2026 om 20:18 schreef olcott:
On 7/14/2026 2:11 AM, Mikko wrote:Olcott has confirmed that he thinks that A is true.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
be rejected as pathological.
Now he says that Olcott's system will reject this finite string A,
because of a self-reference.
According to the system, A has no truth value.
So, Olcott and his system disagree about the truth value of A.
Olcott claims that his system will convince everybody about the truth.
You must bother to understand what properties that
a system having only basic facts would have. How
many actual facts are not true?
We now see ourselves confronted with the ultimate test of the strength
of Olcott's system:
Is the system strong enough to make Olcott change his opinion about A?
Will he accept that we cannot prove that A is true?
If no.
If even Olcott himself does not accept the output of his own system,
why would we believe that anybody else will accept it?
If yes.
If Olcott accepts that we cannot say that A is true, i.e. that his
system is correct, why would anyone change his opinion because of the
output of a system of which the correctness cannot be proven?
On 7/15/2026 2:35 AM, Mikko wrote:
On 14/07/2026 23:16, olcott wrote:
On 7/14/2026 2:57 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
You're kidding yourself.-a They can't possibly not exist.-a You can't >>>> just
"stipulate them away".
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language. This
is the only inference steps allowed.
That's a tactic deliberately designed to cause confusion.
It may cause confusion only when one considers conventional
views the infallible word-of-God thus alternatives to
conventional views inherently incorrect.
-aP reo Q has a
well defined meaning.
If I stipulated that is means "go fuck yourself" then that
is what it means in any dialogue with me.
That's a big IF. Above you did not stipulate, you just coaimed.
P <semantically entails> Q means syntactic derivation
implements semantic entailment encoded in syntactically
the language. This is the only inference steps allowed.
On 7/15/2026 2:25 AM, Mikko wrote:
On 14/07/2026 22:41, olcott wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
If G||del's undecidable sentence does not exist in your system then
you cannot say in that system that it is true about natural numbers.
P reo Q means syntactic derivation implements semantic
entailment encoded in syntactically the language.
The exact meaning reo depends on the context. When talking about G||del's
sentence it means, unless defined otherwise, that the sentence Q can
be inferred from P according to the rules of ordinary formal logic.
I am stipulating that it only means
<semantic entailment encoded syntactically>
Op 15.jul.2026 om 16:56 schreef olcott:
On 7/15/2026 4:11 AM, Fred. Zwarts wrote:
Op 14.jul.2026 om 20:18 schreef olcott:
On 7/14/2026 2:11 AM, Mikko wrote:Olcott has confirmed that he thinks that A is true.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
be rejected as pathological.
Now he says that Olcott's system will reject this finite string A,
because of a self-reference.
According to the system, A has no truth value.
So, Olcott and his system disagree about the truth value of A.
Olcott claims that his system will convince everybody about the truth.
You must bother to understand what properties that
a system having only basic facts would have. How
many actual facts are not true?
We now see ourselves confronted with the ultimate test of the
strength of Olcott's system:
Is the system strong enough to make Olcott change his opinion about
A? Will he accept that we cannot prove that A is true?
If no.
If even Olcott himself does not accept the output of his own system,
why would we believe that anybody else will accept it?
If yes.
If Olcott accepts that we cannot say that A is true, i.e. that his
system is correct, why would anyone change his opinion because of the
output of a system of which the correctness cannot be proven?
We see that Olcott disagrees with the results of his system, but he does
not want to choose whether he thinks it proves him wrong.
This unmasks Olcott's ideas as incoherent and useless.
"sfsdf [pem,e35rty 456456" is not a well-formed expression of
PA. G, on the other hand is.
In comp.theory olcott <polcott333@gmail.com> wrote:
On 7/14/2026 4:12 AM, Mikko wrote:
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
G||del's sentence is true about natural numbers.
That stays the same in my system yet in my system
undecidability and incompleteness cannot possibly exist.
You're kidding yourself. They can't possibly not exist. You can't just "stipulate them away".
On 7/14/2026 2:57 PM, Alan Mackenzie wrote:
-aP reo Q has a
well defined meaning.
If I stipulated that is means "go fuck yourself" then that
is what it means in any dialogue with me.
It is capable of processing this expression pair:
It is capable of processing this expression pair:
This sentence is not true: "This sentence is not true"
as the outer expression is true on the basis that the
inner expression has no truth value.
Op 16.jul.2026 om 11:01 schreef Fred. Zwarts:
Op 15.jul.2026 om 16:56 schreef olcott:
On 7/15/2026 4:11 AM, Fred. Zwarts wrote:
Op 14.jul.2026 om 20:18 schreef olcott:
On 7/14/2026 2:11 AM, Mikko wrote:Olcott has confirmed that he thinks that A is true.
On 13/07/2026 18:46, olcott wrote:
All undecidability is unmasked as semantic
incoherence or outside of the body of knowledge.
The sentence "Olcott's system is correct" would
be rejected as pathological.
Now he says that Olcott's system will reject this finite string A, because of a self-reference.
According to the system, A has no truth value.
So, Olcott and his system disagree about the truth value of A.
Olcott claims that his system will convince everybody about the truth. >>>>
You must bother to understand what properties that
a system having only basic facts would have. How
many actual facts are not true?
We now see ourselves confronted with the ultimate test of the strength of Olcott's system:
Is the system strong enough to make Olcott change his opinion about A? Will he accept that we
cannot prove that A is true?
If no.
If even Olcott himself does not accept the output of his own system, why would we believe that
anybody else will accept it?
If yes.
If Olcott accepts that we cannot say that A is true, i.e. that his system is correct, why would
anyone change his opinion because of the output of a system of which the correctness cannot be
proven?
We see that Olcott disagrees with the results of his system, but he does not want to choose
whether he thinks it proves him wrong.
This unmasks Olcott's ideas as incoherent and useless.
Olcott did not react. Probably, he does not know of a counter-argument. We may agree that this is
the final conclusion about his ideas.
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