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 4/17/26 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 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 4/19/26 1:21 PM, 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.
Nope.
Undecidability can not come from Semantic Incoherence, as the definition
of Undecidability ia based on there being a coherent answer, just not
one that can be determined by a computation.
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, 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.
Nope.
Undecidability can not come from Semantic Incoherence, as the
definition of Undecidability ia based on there being a coherent
answer, just not one that can be determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the basic halting problem) involves a situations that have _no_ coherent answer, not just
one that can be known by not computed ...
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