On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>> existing foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>> the discussion shouldpeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>> the result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well- >>>>>>>>>>>>>>>>>>>> founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>> is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected. >>>>>>>>>>>>>>>>
True(L, X) := rea+o rea BaseFacts(L) (+o reo X) // copyright >>>>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does >>>>>>>>>>>>>>>> not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body >>>>>>>>>>>>>>> of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>>>> whether
rea+o rea BaseFacts(L) (+o reo X) for every X in some L. >>>>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X >>>>>>>>>>>>> to +o then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>>>> back-chained inference path from X to +o.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
On 04/16/2026 10:47 AM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
There's a thread here about 2003 "Factorial/Exponential Identity,
Infinity" where I arrived at not only an infinitary
factorial/exponential identity, also a new approximation for factorial,
then show that "Borel versus Combinatorics" makes that set theory's
account of descriptive set theory has conflicting ordinary accounts
of "Borel versus Combinatorics" about how many almost all/none of
infinite {0,1} sequences are absolutely normal, this shows that
whether "Borel" or "Combinatorics" holds is independent the
ordinary set theory's descriptive account of Archimedean numbers,
and naturally.
https://groups.google.com/g/sci.math/c/3AH5LXl76Cw
So, "Borel versus Combinatorics", then I later make it "Borel vis-a-vis Combinatorics", and make constructive developments that then live in the applied, while then I can take any account that invokes van der Waerden
or Roth and the like or Ramsey theory, and make it two theories.
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
On 04/16/2026 10:47 AM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
There's a thread here about 2003 "Factorial/Exponential Identity,
Infinity" where I arrived at not only an infinitary
factorial/exponential identity, also a new approximation for factorial,
then show that "Borel versus Combinatorics" makes that set theory's
account of descriptive set theory has conflicting ordinary accounts
of "Borel versus Combinatorics" about how many almost all/none of
infinite {0,1} sequences are absolutely normal, this shows that
whether "Borel" or "Combinatorics" holds is independent the
ordinary set theory's descriptive account of Archimedean numbers,
and naturally.
https://groups.google.com/g/sci.math/c/3AH5LXl76Cw
So, "Borel versus Combinatorics", then I later make it "Borel vis-a-vis Combinatorics", and make constructive developments that then live in the applied, while then I can take any account that invokes van der Waerden
or Roth and the like or Ramsey theory, and make it two theories.
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from >>>>>>>>>>> Goldbach
conjecture to the body of knowledge then how it is out of >>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, >>> since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model" >>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where >>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't. >>>>>>>>>
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where >>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point, >>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
On 4/17/26 10:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a
point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't. >>>>>>>>>
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
Right, because "Knowledge" and "Truth" are different things.
It seems you just admitted that you goal is unatainable, that there
*ARE* statements with a truth value (like the Goldbach Conjecture) that
can not be actually proven based on our current knowledge.
It isn't that the Goldbach Conjecture doesn't have a meaning, but it expresses something whose answer is currently not known, and might never
be known.
The problem is you can not exhaustively search the possible space it discusses to rule out that there is a counter example. No matter how
high you test, there are still larger numbers where a counter example
might be found. So unless you happen to be able to find an actual proof
of its truth, it might be unknowable.
This is the whole concept of incompleteness, a term I don't think you understand. Being "incomplete" doesn't make a system less usefull, and
in fact comes out of the fact that the power of the system to exprss
thins grew too rapidly for it to be able to analyize EVERYTHING, but it
still does more than a lessor system that can analyize everything it can express.
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>> there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
On 04/17/2026 07:58 AM, olcott wrote:
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>> model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>> whether or not according to the operations it's an even number, >>>>>>>>>>>> then as with regards to whether or not that is or isn't >>>>>>>>>>>> a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
On 04/17/2026 09:53 AM, olcott wrote:
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is >>>>>>>>>>>>>>>>>>> out of
scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>
*The above has been the question for 28 years* >>>>>>>>>>>>>>>> The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>>> model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about >>>>>>>>>>>>> the qualities of _the entire system_ where, for examples, >>>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is >>>>>>>>>>>>> empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>>> whether or not according to the operations it's an even >>>>>>>>>>>>> number,
then as with regards to whether or not that is or isn't >>>>>>>>>>>>> a sum of two primes, or about whether "addition" and >>>>>>>>>>>>> "multiplication", hold together "at infinity", for example >>>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path >>>>>>>>>>>>>>>>>>>> from
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>>>
Goldbach
conjecture to the body of knowledge then how it is >>>>>>>>>>>>>>>>>>>> out of
scope ?
The current path is not finite.
The current path is to search every even >>>>>>>>>>>>>>>>>>> natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>
*The above has been the question for 28 years* >>>>>>>>>>>>>>>>> The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>>>> model"
It states that every even natural number greater >>>>>>>>>>>>>>> than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about >>>>>>>>>>>>>> the qualities of _the entire system_ where, for examples, >>>>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is >>>>>>>>>>>>>> empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>>>> whether or not according to the operations it's an even >>>>>>>>>>>>>> number,
then as with regards to whether or not that is or isn't >>>>>>>>>>>>>> a sum of two primes, or about whether "addition" and >>>>>>>>>>>>>> "multiplication", hold together "at infinity", for example >>>>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE >>>>>>>>>>>>> does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves. >>>>>>>>>>>>
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
On 4/17/2026 9:13 PM, Ross Finlayson wrote:
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
I don't understand any of that stuff I do know
how to write a C program that would test this.
Math uses terms-of-the-art to deceive.
"undecidable" input has always only been semantically
incoherent input or results that are outside of the
body of knowledge such as the truth value of the Goldbach
conjecture. You seem to talk around the issues that I
raise never getting to the exact and 100% precise point.
On 04/17/2026 07:25 PM, olcott wrote:
On 4/17/2026 9:13 PM, Ross Finlayson wrote:
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
I don't understand any of that stuff I do know
how to write a C program that would test this.
Math uses terms-of-the-art to deceive.
"undecidable" input has always only been semantically
incoherent input or results that are outside of the
body of knowledge such as the truth value of the Goldbach
conjecture. You seem to talk around the issues that I
raise never getting to the exact and 100% precise point.
Yeah that's why nobody needs what that is
for "Foundations" of mathematics.
What you got there is called "empiricism",
and it's neither scientific nor mathematically complete.
What you should do is paste what I wrote into your bot bros,
for example with the "panel" of the A.I.'s about theories
alike mine, though then you'd probably want to take care
that it would give them a reasoning for a mind of their own
and a constant, consistent, complete, and concrete theory.
Which _includes_ all standard theory, as an example.
On 4/17/2026 1:45 AM, Mikko wrote:
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Everything can be encoded about the Goldbach
conjecture besides its truth value because
its truth value is unknown.
Also the back-chained inference is from the expression
to the atomic fact (axioms) of the formal system of
knowledge.
On 14/04/2026 16:48, olcott wrote:
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>> existing foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>> the discussion shouldpeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well- >>>>>>>>>>>>>>>>>>> founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := rea+o rea BaseFacts(L) (+o reo X) // copyright >>>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>>> whether
rea+o rea BaseFacts(L) (+o reo X) for every X in some L. >>>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X >>>>>>>>>>>> to +o then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>>> back-chained inference path from X to +o.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
On 17/04/2026 17:29, olcott wrote:
On 4/17/2026 1:45 AM, Mikko wrote:
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Everything can be encoded about the Goldbach
conjecture besides its truth value because
its truth value is unknown.
Depends on what you include in "everything".
Also the back-chained inference is from the expression
to the atomic fact (axioms) of the formal system of
knowledge.
But it is not known whther there is any.
But you still havn't answered the question.
On 04/17/2026 08:12 AM, Richard Damon wrote:
On 4/17/26 10:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point, >>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a
point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
Right, because "Knowledge" and "Truth" are different things.
It seems you just admitted that you goal is unatainable, that there
*ARE* statements with a truth value (like the Goldbach Conjecture) that
can not be actually proven based on our current knowledge.
It isn't that the Goldbach Conjecture doesn't have a meaning, but it
expresses something whose answer is currently not known, and might never
be known.
The problem is you can not exhaustively search the possible space it
discusses to rule out that there is a counter example. No matter how
high you test, there are still larger numbers where a counter example
might be found. So unless you happen to be able to find an actual proof
of its truth, it might be unknowable.
This is the whole concept of incompleteness, a term I don't think you
understand. Being "incomplete" doesn't make a system less usefull, and
in fact comes out of the fact that the power of the system to exprss
thins grew too rapidly for it to be able to analyize EVERYTHING, but it
still does more than a lessor system that can analyize everything it can
express.
Why lose?
Eventually for something like Zeno's discourse and dialectic
on "motion" and why it's profound and not necessarily a paradox,
why lose?
It brings some baggage, yet, what's always useful, and,
then the idea is to arrive at a wider, fuller dialectic
and greater, truer synthesis, the analysis, from "first
principles" for "final cause", why that's not baggage
(the bulky, awkward, and encumbered) instead kit.
So, one can never defeat Zeno's arguments: only win them.
On 4/18/2026 4:15 AM, Mikko wrote:
On 17/04/2026 17:29, olcott wrote:
On 4/17/2026 1:45 AM, Mikko wrote:
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Everything can be encoded about the Goldbach
conjecture besides its truth value because
its truth value is unknown.
Depends on what you include in "everything".
Zero details of general knowledge about the elements
of the conjecture itself are not included.
Also the back-chained inference is from the expression
to the atomic fact (axioms) of the formal system of
knowledge.
But it is not known whther there is any.
But you still havn't answered the question.
This that are unknown are not known thus not
elements of the body of knowledge.
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>> existing foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>> the discussion shouldpeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>> the result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well- >>>>>>>>>>>>>>>>>>>> founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>> is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected. >>>>>>>>>>>>>>>>
True(L, X) := rea+o rea BaseFacts(L) (+o reo X) // copyright >>>>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does >>>>>>>>>>>>>>>> not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body >>>>>>>>>>>>>>> of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>>>> whether
rea+o rea BaseFacts(L) (+o reo X) for every X in some L. >>>>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X >>>>>>>>>>>>> to +o then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>>>> back-chained inference path from X to +o.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
Olcott's Minimal Type Theory
G rao -4Prov[PA](riLGriY)
Directed Graph of evaluation sequence
00 rao-a-a-a-a-a-a-a-a-a-a-a-a-a-a 01 02
01 G
02 -4-a-a-a-a-a-a-a-a-a-a-a-a-a-a 03
03 Prov[PA]-a-a-a-a-a-a-a 04
04 G||del_Number_of 01-a // cycle
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
On 4/17/26 11:19 AM, Ross Finlayson wrote:
On 04/17/2026 08:12 AM, Richard Damon wrote:
On 4/17/26 10:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a
point-at-infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>> there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
Right, because "Knowledge" and "Truth" are different things.
It seems you just admitted that you goal is unatainable, that there
*ARE* statements with a truth value (like the Goldbach Conjecture) that
can not be actually proven based on our current knowledge.
It isn't that the Goldbach Conjecture doesn't have a meaning, but it
expresses something whose answer is currently not known, and might never >>> be known.
The problem is you can not exhaustively search the possible space it
discusses to rule out that there is a counter example. No matter how
high you test, there are still larger numbers where a counter example
might be found. So unless you happen to be able to find an actual proof
of its truth, it might be unknowable.
This is the whole concept of incompleteness, a term I don't think you
understand. Being "incomplete" doesn't make a system less usefull, and
in fact comes out of the fact that the power of the system to exprss
thins grew too rapidly for it to be able to analyize EVERYTHING, but it
still does more than a lessor system that can analyize everything it can >>> express.
Why lose?
Who said "lose"?
Eventually for something like Zeno's discourse and dialectic
on "motion" and why it's profound and not necessarily a paradox,
why lose?
Who said "lose"?
It brings some baggage, yet, what's always useful, and,
then the idea is to arrive at a wider, fuller dialectic
and greater, truer synthesis, the analysis, from "first
principles" for "final cause", why that's not baggage
(the bulky, awkward, and encumbered) instead kit.
So, one can never defeat Zeno's arguments: only win them.
Sure you can. You just point out that "time" isn't measured in "steps of aruement", and that the sequence of steps add up to a total finite
period of time, so the limit point when the event happens, is actually reached.
Zeno's logic and methodology FAILS because it can't actually handle the infinity it wants to talk about.
Yes, it can take an infinite number of calculation steps to get to the
event, but that is only an issue if you can't handle infinite
calculations. Since the "time" that it represents is finite, even if the
sum of an infinite number of terms, we can reach that time in reality.
All Zeno showed is that is methodology can't handle that problem with
that method.
On 04/18/2026 09:13 AM, Richard Damon wrote:
On 4/17/26 11:19 AM, Ross Finlayson wrote:
On 04/17/2026 08:12 AM, Richard Damon wrote:
On 4/17/26 10:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>> model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a
point-at-infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>> whether or not according to the operations it's an even number, >>>>>>>>>>>> then as with regards to whether or not that is or isn't >>>>>>>>>>>> a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
Right, because "Knowledge" and "Truth" are different things.
It seems you just admitted that you goal is unatainable, that there
*ARE* statements with a truth value (like the Goldbach Conjecture) that >>>> can not be actually proven based on our current knowledge.
It isn't that the Goldbach Conjecture doesn't have a meaning, but it
expresses something whose answer is currently not known, and might
never
be known.
The problem is you can not exhaustively search the possible space it
discusses to rule out that there is a counter example. No matter how
high you test, there are still larger numbers where a counter example
might be found. So unless you happen to be able to find an actual proof >>>> of its truth, it might be unknowable.
This is the whole concept of incompleteness, a term I don't think you
understand. Being "incomplete" doesn't make a system less usefull, and >>>> in fact comes out of the fact that the power of the system to exprss
thins grew too rapidly for it to be able to analyize EVERYTHING, but it >>>> still does more than a lessor system that can analyize everything it
can
express.
Why lose?
Who said "lose"?
Eventually for something like Zeno's discourse and dialectic
on "motion" and why it's profound and not necessarily a paradox,
why lose?
Who said "lose"?
It brings some baggage, yet, what's always useful, and,
then the idea is to arrive at a wider, fuller dialectic
and greater, truer synthesis, the analysis, from "first
principles" for "final cause", why that's not baggage
(the bulky, awkward, and encumbered) instead kit.
So, one can never defeat Zeno's arguments: only win them.
Sure you can. You just point out that "time" isn't measured in "steps of
aruement", and that the sequence of steps add up to a total finite
period of time, so the limit point when the event happens, is actually
reached.
Zeno's logic and methodology FAILS because it can't actually handle the
infinity it wants to talk about.
Yes, it can take an infinite number of calculation steps to get to the
event, but that is only an issue if you can't handle infinite
calculations. Since the "time" that it represents is finite, even if the
sum of an infinite number of terms, we can reach that time in reality.
All Zeno showed is that is methodology can't handle that problem with
that method.
So, thusly, you'd agree that there are inductive arguments
that are never.first.false, to use the brief notation as
of that generally conscientious logician Burns, that furthermore
the realm of relevance would concur that it's furthermore not.ultimately.untrue.
Furthermore now you must agree that inductive accounts may not
complete themselves, only as of sorts of deductive accounts,
about matters of _infinity_ and correspondingly _continuity_,
that the completions are like so and that there's a case for
the "infinite limit" besides as usually given, the "inductive limit".
So, are inductive accounts "defeated", or deductive accounts "won"?
Seems you won't agree to be wrong, ..., thusly you must be making
an account where both of Zeno's conflicting counterarguments must
be true, each not.first.false, while yet ultimately.untrue, about
some greater account that's ultimately.true.
Now, instead you seem to claim that "time", as some continuous
quantity, has not the properties of measurement of time. So,
according to the language of the theory of magnitudes of the
time with regards to the infinitely-divisible and indivisibles,
that's not so.
Furthermore, you claim then that induction is not un-bounded,
which is also not so, about the language of the theory of the
time about the "potential" as un-bounded, vis-a-vis an "actual",
infinity.
Both of those are making "losers" not "winners".
Now, you're free to carry that burden yourself,
not impose it on others. Furthermore, anyone
can make their own constructive arguments in their
course of "winning Zeno's race",
So, if you're going to "not lose", you can't be breaking
the rules.
Instead, there must be an actual account of why the inductive
limit is actually the infinite limit, in this particular case
of the geometric series.
Then, besides the usual setups of Zeno of thought experiments
and reasoning exercises (_not_ paradoxes since uniform motion
is obvious to any with sense and science, in _time_), each as
of about either the geometric series or related rates, then
there's another account besides as like "the ant's march",
of "the bee's flight(s)", that like Vitali makes what is
called a "non-measurable set" an account of "equi-decomposability"
that the "infinite limit" would be _twice_, exactly, what
the inductive account (co-induction, a reductio) used to
justify the usual inductive limit, would give.
So, besides that the usual account of "inductive limit" is
preferential to not being wrong, and a ready account is given
that that's incoherent and inconsistent, there's another
where that's twice wrong.
So, why lose? Furthermore, why make losers?
Aristotle won't be made a fool: and Zeno is not defeated, only won.
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and
there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem.
If a sentence of a first
order theory is undecidable then it is known that it is true is some
models of the theory and false in others. Whether is is true in a
particular may be known in some cases and unknown in others.
Whether Goldbach's conjecture is decidable is not known.
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and
there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem. If a sentence of a first
order theory is undecidable then it is known that it is true is some
models of the theory and false in others. Whether is is true in a
particular may be known in some cases and unknown in others.
Whether Goldbach's conjecture is decidable is not known.
On 04/20/2026 01:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and
there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't >>>> find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem. If a sentence of a first
order theory is undecidable then it is known that it is true is some
models of the theory and false in others. Whether is is true in a
particular may be known in some cases and unknown in others.
Whether Goldbach's conjecture is decidable is not known.
Yes, well put, " ... at this time", "... as is commonly known".
That defines "conjecture" vis-a-vis "theorem". The usual idea
of a conjecture is as being a predicate vis-a-vis well-formed
statements in the language of the theory, for "proven conjectures"
the theorems, vis-a-vis, "model results" the theorems, or if
models are "faithful" and make "witness" then as are "testaments"
in the language of the theory, that then a theorem, usable in
a proof, in the language of the theory.
"Independence" is another aspect of un-decide-ability, since it
may be that the theory is closed and cannot consistently decide
either way, vis-a-vis where it's consistent either way.
For example, where the theory has a standard model of integers,
that may simply be wrong about a setting where models of integers
are only (incomplete) fragments or (proper) extensions, neither
of which is a model of the standard model.
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and
there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't >>>> find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
then it is a yes or no question that has no correct yes
or no answer within the formal system.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and >>>>> there
is no method to find out.
I don't know about philosophers but mathematicians and logicians don't >>>>> find it interesting if all you can say that all knowledge is knowable >>>>> and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g. Goldbach's conjecture ?
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown
and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians
don't
find it interesting if all you can say that all knowledge is knowable >>>>>> and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither >>>> the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g.
Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown >>>>>>> and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians >>>>>>> don't
find it interesting if all you can say that all knowledge is
knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither >>>>> the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g.
Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown >>>>>>>> and there
is no method to find out.
I don't know about philosophers but mathematicians and logicians >>>>>>>> don't
find it interesting if all you can say that all knowledge is
knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that
neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g.
Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown >>>>>>>>> and there
is no method to find out.
I don't know about philosophers but mathematicians and
logicians don't
find it interesting if all you can say that all knowledge is >>>>>>>>> knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that
neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g. >>>>> Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown >>>>>>>>> and there
is no method to find out.
I don't know about philosophers but mathematicians and
logicians don't
find it interesting if all you can say that all knowledge is >>>>>>>>> knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that
neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a
yes or no answer but k-|nor known to lack such answer, either, e.g.
Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is
unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and
logicians don't
find it interesting if all you can say that all knowledge is >>>>>>>>>> knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that >>>>>>>> neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have >>>>>> good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is >>>>>> true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural >>>>>> numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a >>>>>> yes or no answer but k-|nor known to lack such answer, either, e.g. >>>>>> Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
This just means that the truth> value of Goldbach is outside of thebody of
knowledge thus outside of the scope of my project.While the truth value is not in the body of knowledge someone may
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and
logicians don't
find it interesting if all you can say that all knowledge is >>>>>>>>>>> knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that >>>>>>>>> neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have >>>>>>> good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is >>>>>>> true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural >>>>>>> numbers it may have an answer in the natural numbers themselves. >>>>>>>
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a >>>>>>> yes or no answer but k-|nor known to lack such answer, either,
e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it.
This just means that the truth> value of Goldbach is outside of thebody of
knowledge thus outside of the scope of my project.While the truth value is not in the body of knowledge someone may
some day find a way to infer it from what is known.
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>> logicians don't
find it interesting if all you can say that all knowledge is >>>>>>>>>>>> knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that >>>>>>>>>> neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already have >>>>>>>> good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no
undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then "sentence is >>>>>>>> true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural >>>>>>>> numbers it may have an answer in the natural numbers themselves. >>>>>>>>
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a >>>>>>>> yes or no answer but k-|nor known to lack such answer, either, >>>>>>>> e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system
is not in the scope of your system? OK, but shoudn't such questions >>>>>> be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it.
That is a correct correction.
Goldbach is known and possibly unknowable.
My system is only concerned with knowledge
expressed in language.
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all knowledge >>>>>>>>>>>>> is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether >>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>> because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known >>>>>>>>>>> that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already >>>>>>>>> have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no >>>>>>> undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then
"sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of natural >>>>>>>>> numbers it may have an answer in the natural numbers themselves. >>>>>>>>>
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to have a >>>>>>>>> yes or no answer but k-|nor known to lack such answer, either, >>>>>>>>> e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system >>>>>>> is not in the scope of your system? OK, but shoudn't such questions >>>>>>> be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture)
is provable or not. If you find a proof then you know it but it is
possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it.
That is a correct correction.
However, my correction is not complete. The question how your system
handles Goldbach's conjecture and similar cases is still unanswered.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all knowledge >>>>>>>>>>>>>> is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known >>>>>>>>>>>> that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference >>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that already >>>>>>>>>> have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no >>>>>>>> undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then
"sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yes
or no answer within the formal system.
Even if a question has no answer within a formal theory of >>>>>>>>>> natural
numbers it may have an answer in the natural numbers themselves. >>>>>>>>>>
My system is based on simple type theory and formalized
natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to >>>>>>>>>> have a
yes or no answer but k-|nor known to lack such answer, either, >>>>>>>>>> e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system >>>>>>>> is not in the scope of your system? OK, but shoudn't such questions >>>>>>>> be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find
out whether a particular sentence (for exmaple Goldbach conjecture) >>>>>> is provable or not. If you find a proof then you know it but it is >>>>>> possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it.
That is a correct correction.
However, my correction is not complete. The question how your system
handles Goldbach's conjecture and similar cases is still unanswered.
It is hard-coded to know that the truth value is not
currently known.
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
Yes that it correct.
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all knowledge >>>>>>>>>>>>>>> is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known >>>>>>>>>>>>> that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False >>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that
already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no >>>>>>>>> undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then
"sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory of >>>>>>>>>>> natural
numbers it may have an answer in the natural numbers themselves. >>>>>>>>>>>
My system is based on simple type theory and formalized >>>>>>>>>>>> natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to >>>>>>>>>>> have a
yes or no answer but k-|nor known to lack such answer, either, >>>>>>>>>>> e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system >>>>>>>>> is not in the scope of your system? OK, but shoudn't such
questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find >>>>>>> out whether a particular sentence (for exmaple Goldbach conjecture) >>>>>>> is provable or not. If you find a proof then you know it but it is >>>>>>> possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it.
That is a correct correction.
However, my correction is not complete. The question how your system
handles Goldbach's conjecture and similar cases is still unanswered.
It is hard-coded to know that the truth value is not
currently known.
So when the truth value is found out
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
Yes that it correct.
It also means that your system is incomplete and needs updates
whenever somebody discovers something (which happens many times
every day).
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
However, my correction is not complete. The question how your system
handles Goldbach's conjecture and similar cases is still unanswered.
It is hard-coded to know that the truth value is not
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
That Trump implemented this exact quote from Hitler's
Mein Kampf to convince people otherwise:
-a-a "The receptive powers of the masses are very
-a-a-a restricted, and their understanding is feeble.
-a-a-a On the other hand, they quickly forget. Such
-a-a-a being the case, all effective propaganda must
-a-a-a be confined to a few bare essentials and those
-a-a-a must be expressed as far as possible in stereotyped
-a-a-a formulas. These slogans should be persistently
-a-a-a repeated until the very last individual has come
-a-a-a to grasp the idea that has been put forward."
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
Yes that it correct.
It also means that your system is incomplete and needs updates
whenever somebody discovers something (which happens many times
every day).
If by incomplete you mean it is never the infallible
all knowing mind of God you would be correct.
If by incomplete you mean ever has less than 99% of
the sum total of all human general knowledge you
would be incorrect. Some of its knowledge of news
stories will remain provisional until fully vetted.
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:That is a correct correction.
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known >>>>>>>>>>>>>> that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False >>>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that >>>>>>>>>>>> already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no >>>>>>>>>> undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then >>>>>>>>>>>> "sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory of >>>>>>>>>>>> natural
numbers it may have an answer in the natural numbers
themselves.
My system is based on simple type theory and formalized >>>>>>>>>>>>> natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to >>>>>>>>>>>> have a
yes or no answer but k-|nor known to lack such answer, >>>>>>>>>>>> either, e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system >>>>>>>>>> is not in the scope of your system? OK, but shoudn't such >>>>>>>>>> questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find >>>>>>>> out whether a particular sentence (for exmaple Goldbach conjecture) >>>>>>>> is provable or not. If you find a proof then you know it but it is >>>>>>>> possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it. >>>>
However, my correction is not complete. The question how your system
handles Goldbach's conjecture and similar cases is still unanswered.
It is hard-coded to know that the truth value is not
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
That Trump implemented this exact quote from Hitler's
Mein Kampf to convince people otherwise:
-a-a "The receptive powers of the masses are very
-a-a-a restricted, and their understanding is feeble.
-a-a-a On the other hand, they quickly forget. Such
-a-a-a being the case, all effective propaganda must
-a-a-a be confined to a few bare essentials and those
-a-a-a must be expressed as far as possible in stereotyped
-a-a-a formulas. These slogans should be persistently
-a-a-a repeated until the very last individual has come
-a-a-a to grasp the idea that has been put forward."
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
Yes that it correct.
It also means that your system is incomplete and needs updates
whenever somebody discovers something (which happens many times
every day).
If by incomplete you mean it is never the infallible
all knowing mind of God you would be correct.
If by incomplete you mean ever has less than 99% of
the sum total of all human general knowledge you
would be incorrect. Some of its knowledge of news
stories will remain provisional until fully vetted.
On 26/04/2026 16:37, olcott wrote:
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:That is a correct correction.
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known >>>>>>>>>>>>>>> that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False >>>>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that >>>>>>>>>>>>> already have
good terms.
The result of undecidability proves that the current
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there is no >>>>>>>>>>> undecidability in the naive set theory.
If the sequence of inference steps is restricted to
valid inferences the term "True" as defined above then >>>>>>>>>>>>> "sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory of >>>>>>>>>>>>> natural
numbers it may have an answer in the natural numbers >>>>>>>>>>>>> themselves.
My system is based on simple type theory and formalized >>>>>>>>>>>>>> natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known to >>>>>>>>>>>>> have a
yes or no answer but k-|nor known to lack such answer, >>>>>>>>>>>>> either, e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
So the question whether something is in the scope of your system >>>>>>>>>>> is not in the scope of your system? OK, but shoudn't such >>>>>>>>>>> questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find >>>>>>>>> out whether a particular sentence (for exmaple Goldbach
conjecture)
is provable or not. If you find a proof then you know it but it is >>>>>>>>> possible that you never find, no matter how much you search.
Goldbach is unknowable if it is true because
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves it. >>>>>
However, my correction is not complete. The question how your system >>>>> handles Goldbach's conjecture and similar cases is still unanswered.
It is hard-coded to know that the truth value is not
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
In order to prove that climat change is true it is sufficient to
collect statistics of observation for a sufficiently long time
(at least 50 years, preferably 100) and to compute trends and
significancies. WHich will be doen anyway, regardless of anything
you can do.
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
That your system is unaware of any evidence of election fraud does
not mean that there aren't any. Peaple may have material that they
have not revealed.
That Trump implemented this exact quote from Hitler's
Mein Kampf to convince people otherwise:
-a-a-a "The receptive powers of the masses are very
-a-a-a-a restricted, and their understanding is feeble.
-a-a-a-a On the other hand, they quickly forget. Such
-a-a-a-a being the case, all effective propaganda must
-a-a-a-a be confined to a few bare essentials and those
-a-a-a-a must be expressed as far as possible in stereotyped
-a-a-a-a formulas. These slogans should be persistently
-a-a-a-a repeated until the very last individual has come
-a-a-a-a to grasp the idea that has been put forward."
Trump didn't implement it any more than Hitler did. It is just a
description of how people already are, and how to adapt to that.
Which the decidability and truth value of Goldbach's conjecture
will be if they ever will be known.
Yes that it correct.
It also means that your system is incomplete and needs updates
whenever somebody discovers something (which happens many times
every day).
If by incomplete you mean it is never the infallible
all knowing mind of God you would be correct.
If by incomplete you mean ever has less than 99% of
the sum total of all human general knowledge you
would be incorrect. Some of its knowledge of news
stories will remain provisional until fully vetted.
By incomplete I mean that there are questions that the system can
not answer.
Whether the truth value of Goldbach's conjecture can
be inferred from the known properties of natural numbers is one
example.
On 4/27/2026 4:04 AM, Mikko wrote:
On 26/04/2026 16:37, olcott wrote:
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:It is hard-coded to know that the truth value is not
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:Goldbach is unknowable if it is true because
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>> is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is >>>>>>>>>>>>>>>> known that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False >>>>>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that >>>>>>>>>>>>>> already have
good terms.
The result of undecidability proves that the current >>>>>>>>>>>>> foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
Hardly the same way as Russell's paradox proves that there >>>>>>>>>>>> is no
undecidability in the naive set theory.
So the question whether something is in the scope of your >>>>>>>>>>>> systemIf the sequence of inference steps is restricted to >>>>>>>>>>>>>> valid inferences the term "True" as defined above then >>>>>>>>>>>>>> "sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory of >>>>>>>>>>>>>> natural
numbers it may have an answer in the natural numbers >>>>>>>>>>>>>> themselves.
My system is based on simple type theory and formalized >>>>>>>>>>>>>>> natural language.
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
How does your system handle questions that are not known >>>>>>>>>>>>>> to have a
yes or no answer but k-|nor known to lack such answer, >>>>>>>>>>>>>> either, e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>
is not in the scope of your system? OK, but shoudn't such >>>>>>>>>>>> questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find >>>>>>>>>> out whether a particular sentence (for exmaple Goldbach
conjecture)
is provable or not. If you find a proof then you know it but >>>>>>>>>> it is
possible that you never find, no matter how much you search. >>>>>>>>>
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that proves >>>>>>>> it.
That is a correct correction.
However, my correction is not complete. The question how your system >>>>>> handles Goldbach's conjecture and similar cases is still unanswered. >>>>>
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded
such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include
the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
In order to prove that climat change is true it is sufficient to
collect statistics of observation for a sufficiently long time
(at least 50 years, preferably 100) and to compute trends and
significancies. WHich will be doen anyway, regardless of anything
you can do.
Here is Exxon's own data that exactly correctly predicts
short term temperature increases correlated to CO2 increases. https://www.theguardian.com/business/2023/jan/12/exxon-climate-change- global-warming-research#img-2
https://www.theguardian.com/business/2023/jan/12/exxon-climate-change- global-warming-research
My own paper covers hundreds, thousands, and millions
of years many different ways
https://www.researchgate.net/ publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
Even the Heritage Foundation agrees
---the authors of project 2025---
Never any evidence of election fraud
that could possibly change the results:
1,600 total cases of election fraud in every election since 1981 https://electionfraud.heritage.org/search
If we could somehow magically increase these cases 15-fold
to give Trump the votes he needed in the closest two states
Trump was short 11,779 votes in Georgia
Trump was short 10,457 votes in Arizona
He would still lose the general election.
Trump is just copying Hitler's "big lie"
On 27/04/2026 17:38, olcott wrote:
On 4/27/2026 4:04 AM, Mikko wrote:
On 26/04/2026 16:37, olcott wrote:
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:It is hard-coded to know that the truth value is not
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:Goldbach is unknowable if it is true because
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is >>>>>>>>>>>>>>>>> known that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False >>>>>>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>>>>>> steps of expressions x or ~x reaching axioms
It is not useful to define new terms for comcepts that >>>>>>>>>>>>>>> already have
good terms.
The result of undecidability proves that the current >>>>>>>>>>>>>> foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had >>>>>>>>>>>>>> a glitch.
Hardly the same way as Russell's paradox proves that there >>>>>>>>>>>>> is no
undecidability in the naive set theory.
So the question whether something is in the scope of your >>>>>>>>>>>>> systemIf the sequence of inference steps is restricted to >>>>>>>>>>>>>>> valid inferences the term "True" as defined above then >>>>>>>>>>>>>>> "sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory >>>>>>>>>>>>>>> of natural
numbers it may have an answer in the natural numbers >>>>>>>>>>>>>>> themselves.
My system is based on simple type theory and formalized >>>>>>>>>>>>>>>> natural language.
This makes it a yes or no question that has no >>>>>>>>>>>>>>>> correct yes or no answer at all anywhere, thus >>>>>>>>>>>>>>>> an incorrect polar question.
How does your system handle questions that are not known >>>>>>>>>>>>>>> to have a
yes or no answer but k-|nor known to lack such answer, >>>>>>>>>>>>>>> either, e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
is not in the scope of your system? OK, but shoudn't such >>>>>>>>>>>>> questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to find >>>>>>>>>>> out whether a particular sentence (for exmaple Goldbach >>>>>>>>>>> conjecture)
is provable or not. If you find a proof then you know it but >>>>>>>>>>> it is
possible that you never find, no matter how much you search. >>>>>>>>>>
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that
proves it.
That is a correct correction.
However, my correction is not complete. The question how your system >>>>>>> handles Goldbach's conjecture and similar cases is still unanswered. >>>>>>
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded >>>>> -a> such as the biography of Goldbach.
More about those things may also be discovered. It is even possible
that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include >>>>>>> the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
In order to prove that climat change is true it is sufficient to
collect statistics of observation for a sufficiently long time
(at least 50 years, preferably 100) and to compute trends and
significancies. WHich will be doen anyway, regardless of anything
you can do.
Here is Exxon's own data that exactly correctly predicts
short term temperature increases correlated to CO2 increases.
https://www.theguardian.com/business/2023/jan/12/exxon-climate-change-
global-warming-research#img-2
https://www.theguardian.com/business/2023/jan/12/exxon-climate-change-
global-warming-research
That and other already publised articles cover the topic much better
than anything you can do.
My own paper covers hundreds, thousands, and millions
of years many different ways
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
Even the Heritage Foundation agrees
---the authors of project 2025---
Never any evidence of election fraud
that could possibly change the results:
They mean that no such evidence is public. It does not cover private knowledge nor undetected (but still potentially detectable) material evidence.
1,600 total cases of election fraud in every election since 1981
https://electionfraud.heritage.org/search
That is known cases. Unknown cases are not listed.
If we could somehow magically increase these cases 15-fold
to give Trump the votes he needed in the closest two states
Trump was short 11,779 votes in Georgia
Trump was short 10,457 votes in Arizona
Both number are small in comparison to the total number of voters.
He would still lose the general election.
And there are other states.
Trump is just copying Hitler's "big lie"
What has worked before can be expected to work again.
Anyway, you have not shown that your proposed system could add
anything to what is already known and understood.
On 4/28/2026 2:51 AM, Mikko wrote:
On 27/04/2026 17:38, olcott wrote:
On 4/27/2026 4:04 AM, Mikko wrote:
On 26/04/2026 16:37, olcott wrote:
On 4/26/2026 3:17 AM, Mikko wrote:
On 25/04/2026 15:19, olcott wrote:
On 4/25/2026 3:18 AM, Mikko wrote:
On 24/04/2026 18:01, olcott wrote:
On 4/24/2026 1:08 AM, Mikko wrote:
On 23/04/2026 16:32, olcott wrote:
On 4/23/2026 1:35 AM, Mikko wrote:
On 22/04/2026 10:45, olcott wrote:Goldbach is unknowable if it is true because
On 4/22/2026 2:03 AM, Mikko wrote:
On 21/04/2026 16:22, olcott wrote:
On 4/21/2026 1:30 AM, Mikko wrote:
On 20/04/2026 16:31, olcott wrote:
On 4/20/2026 3:49 AM, Mikko wrote:
On 19/04/2026 20:21, olcott wrote:When we skip model theory and and define True and False >>>>>>>>>>>>>>>>> as the existence of a back chained sequence of inference >>>>>>>>>>>>>>>>> steps of expressions x or ~x reaching axioms
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is >>>>>>>>>>>>>>>>>> known that neither
the sentence nor its negation is a theorem. >>>>>>>>>>>>>>>>>
It is not useful to define new terms for comcepts that >>>>>>>>>>>>>>>> already have
good terms.
The result of undecidability proves that the current >>>>>>>>>>>>>>> foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had >>>>>>>>>>>>>>> a glitch.
Hardly the same way as Russell's paradox proves that there >>>>>>>>>>>>>> is no
undecidability in the naive set theory.
So the question whether something is in the scope of your >>>>>>>>>>>>>> systemIf the sequence of inference steps is restricted to >>>>>>>>>>>>>>>> valid inferences the term "True" as defined above then >>>>>>>>>>>>>>>> "sentence is
true" is just another way to say "sentence is a theorem". >>>>>>>>>>>>>>>>
then it is a yes or no question that has no correct yes >>>>>>>>>>>>>>>>> or no answer within the formal system.
Even if a question has no answer within a formal theory >>>>>>>>>>>>>>>> of natural
numbers it may have an answer in the natural numbers >>>>>>>>>>>>>>>> themselves.
My system is based on simple type theory and formalized >>>>>>>>>>>>>>>>> natural language.
This makes it a yes or no question that has no >>>>>>>>>>>>>>>>> correct yes or no answer at all anywhere, thus >>>>>>>>>>>>>>>>> an incorrect polar question.
How does your system handle questions that are not known >>>>>>>>>>>>>>>> to have a
yes or no answer but k-|nor known to lack such answer, >>>>>>>>>>>>>>>> either, e.g. Goldbach's conjecture ?
out-of-scope of the body of knowledge.
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
is not in the scope of your system? OK, but shoudn't such >>>>>>>>>>>>>> questions
be answerable anyway?
The truth value of the Goldbach conjecture might
be unknowable if it is true and the only way to
prove it is true is an infinite number of steps.
Peano arithmetic is unsolvable, i.e., there is no method to >>>>>>>>>>>> find
out whether a particular sentence (for exmaple Goldbach >>>>>>>>>>>> conjecture)
is provable or not. If you find a proof then you know it but >>>>>>>>>>>> it is
possible that you never find, no matter how much you search. >>>>>>>>>>>
verifying that it is true requires an infinite
number of steps.
That is not known. Perhaps there is an unknown proof that >>>>>>>>>> proves it.
That is a correct correction.
However, my correction is not complete. The question how your >>>>>>>> system
handles Goldbach's conjecture and similar cases is still
unanswered.
It is hard-coded to know that the truth value is not
currently known.
So when the truth value is found out
It is updated.
Everything else about the Goldbach conjecture is also hard-coded >>>>>> -a> such as the biography of Goldbach.
More about those things may also be discovered. It is even possible >>>>>> that something we thought we know will be found to be false.
Yes.
Goldbach is known and possibly unknowable.
Everthing is that is known is knowable. But that does not include >>>>>>>> the decidability and truth value of Goldbach's conjecture.
My system is only concerned with knowledge
expressed in language.
So essentially an ecyclopedia + a search engine.
Not exactly. When fully implemented it can conclusively
prove that climate change is real, that people saying
otherwise are liars and not merely mistaken.
In order to prove that climat change is true it is sufficient to
collect statistics of observation for a sufficiently long time
(at least 50 years, preferably 100) and to compute trends and
significancies. WHich will be doen anyway, regardless of anything
you can do.
Here is Exxon's own data that exactly correctly predicts
short term temperature increases correlated to CO2 increases.
https://www.theguardian.com/business/2023/jan/12/exxon-climate-
change- global-warming-research#img-2
https://www.theguardian.com/business/2023/jan/12/exxon-climate-
change- global-warming-research
That and other already publised articles cover the topic much better
than anything you can do.
My own paper covers hundreds, thousands, and millions
of years many different ways
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
That there was no actual evidence of election fraud
that could have possibly changed the results of the
2020 presidential election.
Even the Heritage Foundation agrees
---the authors of project 2025---
Never any evidence of election fraud
that could possibly change the results:
They mean that no such evidence is public. It does not cover private
knowledge nor undetected (but still potentially detectable) material
evidence.
1,600 total cases of election fraud in every election since 1981
https://electionfraud.heritage.org/search
That is known cases. Unknown cases are not listed.
THERE IS NO ACTUAL EVIDENCE OF ELECTION FRAUD THAT
COULD HAVE POSSIBLE CHANGED THAT OUTCOME OF THE
2020 ELECTION THUS TRUMP IS A DAMNED LIAR WHEN HE
CLAIM OTHERWISE.
With a system that objectively computes truth liesLies will be powerful as long as there are sufficiently many people
lose all of their power.
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