On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote:
On 10/06/2026 06:09 AM, olcott wrote:Do you ever have any substantial original thought that >>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>
On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:Isomophisms are analogies.
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>Not certain if you realized it but this is a math group. >>>>>>>>>>>>>>>> Let's
dispense with talking about barking cats & talk about math. >>>>>>>>>>>>>>>
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind.
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>> offer ready avenues that are facile es descencis.
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>> one entry while they are yet the same word.
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in
a paleo-classical post-modern account with a thorough
account of reason and super-classical reasoning,
not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology.
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique
alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself.
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity,
and it's conserved, always-everywhere and always-becoming.
It is the theory of the biological process of of human pregnancy
that is distinct and different from anything that can described
in language? In other words it expressly includes the physical
sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts
of heno-theory make for theories like logic, and mathematics
with geometry and arithmetic, and language with language
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical.
heno-theory must be defined.
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements".
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through gestation
and out through delivery, is in the first hundred books on the shelf in >>>> the "A" section of the research university library, it's what starts
Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote:
On 10/06/2026 06:09 AM, olcott wrote:Do you ever have any substantial original thought that >>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>
On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math group. >>>>>>>>>>>>>>>>> Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>> one entry while they are yet the same word.
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in
a paleo-classical post-modern account with a thorough >>>>>>>>>>>>> account of reason and super-classical reasoning,
not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology.
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique
alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself.
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity,
and it's conserved, always-everywhere and always-becoming.
It is the theory of the biological process of of human pregnancy
that is distinct and different from anything that can described
in language? In other words it expressly includes the physical
sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts
of heno-theory make for theories like logic, and mathematics
with geometry and arithmetic, and language with language
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical.
heno-theory must be defined.
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements".
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through gestation >>>>> and out through delivery, is in the first hundred books on the
shelf in
the "A" section of the research university library, it's what starts >>>>> Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote:
On 10/06/2026 06:09 AM, olcott wrote:Do you ever have any substantial original thought that >>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>
On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math group. >>>>>>>>>>>>>>>>>> Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>> one entry while they are yet the same word.
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in
a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>> account of reason and super-classical reasoning,
not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology.
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique
alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself.
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity,
and it's conserved, always-everywhere and always-becoming.
It is the theory of the biological process of of human pregnancy >>>>>>> that is distinct and different from anything that can described
in language? In other words it expressly includes the physical
sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts
of heno-theory make for theories like logic, and mathematics
with geometry and arithmetic, and language with language
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical.
heno-theory must be defined.
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements".
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through gestation >>>>>> and out through delivery, is in the first hundred books on the
shelf in
the "A" section of the research university library, it's what starts >>>>>> Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote:
On 10/06/2026 06:09 AM, olcott wrote:Do you ever have any substantial original thought that >>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>
On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math group. >>>>>>>>>>>>>>>>>>> Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>> one entry while they are yet the same word.
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology.
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique
alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself.
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>> and it's conserved, always-everywhere and always-becoming.
It is the theory of the biological process of of human pregnancy >>>>>>>> that is distinct and different from anything that can described >>>>>>>> in language? In other words it expressly includes the physical >>>>>>>> sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts
of heno-theory make for theories like logic, and mathematics >>>>>>>>> with geometry and arithmetic, and language with language
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical.
heno-theory must be defined.
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through gestation >>>>>>> and out through delivery, is in the first hundred books on the
shelf in
the "A" section of the research university library, it's what starts >>>>>>> Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote:
On 10/06/2026 06:09 AM, olcott wrote:Do you ever have any substantial original thought that >>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>
On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math group. >>>>>>>>>>>>>>>>>>> Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>> one entry while they are yet the same word.
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology.
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique
alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself.
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>> and it's conserved, always-everywhere and always-becoming.
It is the theory of the biological process of of human pregnancy >>>>>>>> that is distinct and different from anything that can described >>>>>>>> in language? In other words it expressly includes the physical >>>>>>>> sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts
of heno-theory make for theories like logic, and mathematics >>>>>>>>> with geometry and arithmetic, and language with language
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical.
heno-theory must be defined.
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through gestation >>>>>>> and out through delivery, is in the first hundred books on the
shelf in
the "A" section of the research university library, it's what starts >>>>>>> Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
On 10/08/2026 04:55 PM, Ross Finlayson wrote:
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote: >>>>>>>>>>>>>>>>>> On 10/06/2026 06:09 AM, olcott wrote:
Do you ever have any substantial original thought that >>>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>>On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math >>>>>>>>>>>>>>>>>>>> group.
Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>>> one entry while they are yet the same word. >>>>>>>>>>>>>>>>>>
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology. >>>>>>>>>>>>>>>
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique >>>>>>>>>>>>> alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself. >>>>>>>>>>>>>
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>>> and it's conserved, always-everywhere and always-becoming. >>>>>>>>>>
It is the theory of the biological process of of human pregnancy >>>>>>>>> that is distinct and different from anything that can described >>>>>>>>> in language? In other words it expressly includes the physical >>>>>>>>> sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts >>>>>>>>>> of heno-theory make for theories like logic, and mathematics >>>>>>>>>> with geometry and arithmetic, and language with languageheno-theory must be defined.
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical. >>>>>>>>>
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through
gestation
and out through delivery, is in the first hundred books on the >>>>>>>> shelf in
the "A" section of the research university library, it's what
starts
Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
Also Heidegger is rather remarkably ridiculous.
Maybe this is showing some slant against Germans, Austrians, and Poles, Heidegger, Wittgenstein, and Tarski, yet, I don't need them for anything.
At least they're not "Russo-Hungarians" or even, "Bulgarians".
On 10/08/2026 04:55 PM, Ross Finlayson wrote:
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote: >>>>>>>>>>>>>>>>>> On 10/06/2026 06:09 AM, olcott wrote:
Do you ever have any substantial original thought that >>>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>>On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not incoherent >>>>>>>>>>>>>>>>>>>>> then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>>Not certain if you realized it but this is a math >>>>>>>>>>>>>>>>>>>> group.
Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>>> one entry while they are yet the same word. >>>>>>>>>>>>>>>>>>
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology. >>>>>>>>>>>>>>>
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique >>>>>>>>>>>>> alternatives to the textbook views of foundations.
If you can't explain it in simple words that proves
that you do not sufficiently understand it yourself. >>>>>>>>>>>>>
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>>> and it's conserved, always-everywhere and always-becoming. >>>>>>>>>>
It is the theory of the biological process of of human pregnancy >>>>>>>>> that is distinct and different from anything that can described >>>>>>>>> in language? In other words it expressly includes the physical >>>>>>>>> sensations of [human pregnancy] that cannot be expressed in
language?
It's a theory where as a heno-theory then various accounts >>>>>>>>>> of heno-theory make for theories like logic, and mathematics >>>>>>>>>> with geometry and arithmetic, and language with languageheno-theory must be defined.
and words (and probability and physics).
There's a modal, temporal relevance logic, that's classical. >>>>>>>>>
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through
gestation
and out through delivery, is in the first hundred books on the >>>>>>>> shelf in
the "A" section of the research university library, it's what >>>>>>>> starts
Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
Also Heidegger is rather remarkably ridiculous.
Maybe this is showing some slant against Germans, Austrians, and Poles, Heidegger, Wittgenstein, and Tarski, yet, I don't need them for anything.
At least they're not "Russo-Hungarians" or even, "Bulgarians".
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and >>>> found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to >>>> be unprovable. But none of that affects its meaning and meaningfulness. >>>> What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does not >>>>>> make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is
involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently,
is merely anything for which your proposed semantics fails to
supply an answer.
Within PTS any expression that is neither provable nor refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete
method to find out whether a sentence or its negation can be proven.
Consequently, it is not possible to construct a system that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently, >>>>>>>> is merely anything for which your proposed semantics fails to >>>>>>>> supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>> method to find out whether a sentence or its negation can be proven. >>>>>> Consequently, it is not possible to construct a system that rejects >>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It might be the case that its truth value is unknowable. I restricted
my system to "the body of general knowledge that can be expressed in language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
On 10/8/2026 6:58 PM, Ross Finlayson wrote:
On 10/08/2026 04:55 PM, Ross Finlayson wrote:
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote:
On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote: >>>>>>>>>>>>>>>>>>> On 10/06/2026 06:09 AM, olcott wrote:
Do you ever have any substantial original thought that >>>>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>>>On 10/6/2026 7:50 AM, Blaine wrote:
olcott wrote:
When we assume that the Liar Paradox is not >>>>>>>>>>>>>>>>>>>>>> incoherentNot certain if you realized it but this is a math >>>>>>>>>>>>>>>>>>>>> group.
then his proof succeeds. Likewise when we assume that >>>>>>>>>>>>>>>>>>>>>> "cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>>>
Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in language >>>>>>>>>>>>>>>>>>> of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>>>> one entry while they are yet the same word. >>>>>>>>>>>>>>>>>>>
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, though, >>>>>>>>>>>>>>>>> for example, I introduce something like an "original" as >>>>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the identity >>>>>>>>>>>>>>>>> dimension".
Attaining to "Truth" is a usual account of seeking wisdom, >>>>>>>>>>>>>>>>> then that accounts of "Foundations" have very, very strong >>>>>>>>>>>>>>>>> requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question.
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology. >>>>>>>>>>>>>>>>
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique >>>>>>>>>>>>>> alternatives to the textbook views of foundations. >>>>>>>>>>>>>>
If you can't explain it in simple words that proves >>>>>>>>>>>>>> that you do not sufficiently understand it yourself. >>>>>>>>>>>>>>
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>>>> and it's conserved, always-everywhere and always-becoming. >>>>>>>>>>>
It is the theory of the biological process of of human pregnancy >>>>>>>>>> that is distinct and different from anything that can described >>>>>>>>>> in language? In other words it expressly includes the physical >>>>>>>>>> sensations of [human pregnancy] that cannot be expressed in >>>>>>>>>> language?
It's a theory where as a heno-theory then various accounts >>>>>>>>>>> of heno-theory make for theories like logic, and mathematics >>>>>>>>>>> with geometry and arithmetic, and language with language >>>>>>>>>>> and words (and probability and physics).heno-theory must be defined.
There's a modal, temporal relevance logic, that's classical. >>>>>>>>>>
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through
gestation
and out through delivery, is in the first hundred books on the >>>>>>>>> shelf in
the "A" section of the research university library, it's what >>>>>>>>> starts
Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
Also Heidegger is rather remarkably ridiculous.
Maybe this is showing some slant against Germans, Austrians, and Poles,
Heidegger, Wittgenstein, and Tarski, yet, I don't need them for anything.
At least they're not "Russo-Hungarians" or even, "Bulgarians".
I don't need Tarski for anything except to show exactly
how, why and where he went wrong with his Undefinability
theorem. I have no need to stoop to denigrating him that
is far too lame.
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does not >>>>>>> make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is
involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently, >>>>>>> is merely anything for which your proposed semantics fails to
supply an answer.
Within PTS any expression that is neither provable nor refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete
method to find out whether a sentence or its negation can be proven. >>>>> Consequently, it is not possible to construct a system that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic meaning, whether grounded or not. Existence of a proof from some set
of axioms is irrelevant to the arithmetic meaning.
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:It truth value will be known as soon as its proof has been chekcked >>>>> and
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>
unknown unless and until it proof can be algorithmically compressed. >>>>>
found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the >>>>> knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
An obvious attempt to decive (this time a change of subject) does not
work. In order to decive one needs to behave as a honest person would.
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>> method to find out whether a sentence or its negation can be proven. >>>>>>> Consequently, it is not possible to construct a system that rejects >>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It might be the case that its truth value is unknowable. I restricted
my system to "the body of general knowledge that can be expressed in
language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
Does that include cases where X is Peano arithmetic and Y is a
proof that G is true about natural number?
On 10/08/2026 05:29 PM, olcott wrote:
On 10/8/2026 6:58 PM, Ross Finlayson wrote:
On 10/08/2026 04:55 PM, Ross Finlayson wrote:
On 10/08/2026 04:35 PM, olcott wrote:
On 10/8/2026 5:41 PM, Ross Finlayson wrote:
On 10/07/2026 12:46 PM, olcott wrote:
On 10/7/2026 2:25 PM, Ross Finlayson wrote:
On 10/07/2026 12:22 PM, olcott wrote:
On 10/7/2026 2:06 PM, Ross Finlayson wrote:
On 10/07/2026 11:28 AM, olcott wrote:
On 10/7/2026 11:51 AM, Ross Finlayson wrote:
On 10/06/2026 04:29 PM, olcott wrote:
On 10/6/2026 6:23 PM, Ross Finlayson wrote:
On 10/06/2026 12:44 PM, olcott wrote:
On 10/6/2026 2:04 PM, Ross Finlayson wrote:
On 10/06/2026 11:49 AM, olcott wrote:
On 10/6/2026 1:00 PM, Ross Finlayson wrote: >>>>>>>>>>>>>>>>>> On 10/06/2026 09:50 AM, olcott wrote:
On 10/6/2026 11:35 AM, Ross Finlayson wrote: >>>>>>>>>>>>>>>>>>>> On 10/06/2026 06:09 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>> On 10/6/2026 7:50 AM, Blaine wrote: >>>>>>>>>>>>>>>>>>>>>> olcott wrote:
Do you ever have any substantial original thought that >>>>>>>>>>>>>>>>>>> does not conform to some conventional textbook view? >>>>>>>>>>>>>>>>>>>
When we assume that the Liar Paradox is not >>>>>>>>>>>>>>>>>>>>>>> incoherentNot certain if you realized it but this is a math >>>>>>>>>>>>>>>>>>>>>> group.
then his proof succeeds. Likewise when we assume >>>>>>>>>>>>>>>>>>>>>>> that
"cats are dogs" then "cats bark" is entailed. >>>>>>>>>>>>>>>>>>>>>>
Let's
dispense with talking about barking cats & talk about >>>>>>>>>>>>>>>>>>>>>> math.
Isomophisms are analogies.
No they're accounts of "relations".
Yet another retro-finitist crankety troll sock-puppet >>>>>>>>>>>>>>>>>>>> with a howler-troll fallacy blowing in the wind. >>>>>>>>>>>>>>>>>>>>
Many of the easily-fooled and readily-satisfied variety >>>>>>>>>>>>>>>>>>>> have such sorts of premature reductionisms that seem to >>>>>>>>>>>>>>>>>>>> offer ready avenues that are facile es descencis. >>>>>>>>>>>>>>>>>>>>
Structure in model theory vis-a-vis accounts in >>>>>>>>>>>>>>>>>>>> language
of the loose sort like the analogy vis-a-vis "language >>>>>>>>>>>>>>>>>>>> geometry" make for that dictionaries may have more than >>>>>>>>>>>>>>>>>>>> one entry while they are yet the same word. >>>>>>>>>>>>>>>>>>>>
Get bent, bot.
Tarski is also a sort of retro-finitist reductionist. >>>>>>>>>>>>>>>>>>>
I'm a canonical dogmatic doctrinal researcher in >>>>>>>>>>>>>>>>>> a paleo-classical post-modern account with a thorough >>>>>>>>>>>>>>>>>> account of reason and super-classical reasoning, >>>>>>>>>>>>>>>>>> not an ingrate.
It's hard to say what would be "original" thought, >>>>>>>>>>>>>>>>>> though,
for example, I introduce something like an "original" as >>>>>>>>>>>>>>>>>> an "originary" analysis for mathematics like "the >>>>>>>>>>>>>>>>>> identity
dimension".
Attaining to "Truth" is a usual account of seeking >>>>>>>>>>>>>>>>>> wisdom,
then that accounts of "Foundations" have very, very >>>>>>>>>>>>>>>>>> strong
requirements for their satisfaction of being thorough. >>>>>>>>>>>>>>>>>>
So bottom line you very carefully with exacting precision >>>>>>>>>>>>>>>>> memorize the work of others. You never ever consider the >>>>>>>>>>>>>>>>> possibility that there might be a fundamentally different >>>>>>>>>>>>>>>>> approach?
This is (first of all) a yes or no question. >>>>>>>>>>>>>>>>>
So, the "paleo-classical post-modern" as "super-classical >>>>>>>>>>>>>>>>>> super-modern" makes for that historicity, metaphysics, >>>>>>>>>>>>>>>>>> and monism are present.
Anybody has their own philosophy and psychology. >>>>>>>>>>>>>>>>>
No, your reading comprehension is deficient.
You did fail to elaborate the details of your unique >>>>>>>>>>>>>>> alternatives to the textbook views of foundations. >>>>>>>>>>>>>>>
If you can't explain it in simple words that proves >>>>>>>>>>>>>>> that you do not sufficiently understand it yourself. >>>>>>>>>>>>>>>
https://www.youtube.com/@rossfinlayson
How about 200+ hours of unscripted lectures?
"Axiomless Principled Thea-theory"
So you can't sum up the essence of that in one
short simple paragraph?
I summed it up in "Axiomless Principled Thea-theory".
It's a "theory of everything" where "truth" is the quantity, >>>>>>>>>>>> and it's conserved, always-everywhere and always-becoming. >>>>>>>>>>>>
It is the theory of the biological process of of human pregnancy >>>>>>>>>>> that is distinct and different from anything that can described >>>>>>>>>>> in language? In other words it expressly includes the physical >>>>>>>>>>> sensations of [human pregnancy] that cannot be expressed in >>>>>>>>>>> language?
It's a theory where as a heno-theory then various accounts >>>>>>>>>>>> of heno-theory make for theories like logic, and mathematics >>>>>>>>>>>> with geometry and arithmetic, and language with language >>>>>>>>>>>> and words (and probability and physics).heno-theory must be defined.
There's a modal, temporal relevance logic, that's classical. >>>>>>>>>>>
A heno-theory is any account of a theory that intends to
interpret any other theory, in terms of their "primary elements". >>>>>>>>>>
It turns out to be far simpler to specify all of the
natural language degree of semantics in a single language
like CycL with no "interpretation" required. The yet
unresolved Liar Paradox confused Tarski into believing
that a separate meta-system and language were required.
The science of human pregnancy, from fertilization through >>>>>>>>>> gestation
and out through delivery, is in the first hundred books on the >>>>>>>>>> shelf in
the "A" section of the research university library, it's what >>>>>>>>>> starts
Library of Congress catalog section "A".
There are more than a hundred, ....
So your
10/7/2026 11:51 AM, Ross Finlayson wrote:
It's a "theory of everything"
Excludes physical sensations that cannot be encoded
in language. It also must exclude the actual infinite
set of every detail of all knowledge otherwise it
cannot possibly be physically implemented.
My system can include all of the details of situation
specific events over and above general knowledge. I
limit my system to "general knowledge" initially so
that it can be understood to be physically implementable.
Define "continuum" for "continuum mechanics".
What is the cross between and elephant and a rhinoceros?
Eleph-ino
and not relevant to Tarski Undefinability or the foundation of:
"true on the basis of meaning expressed in language"
And "infinity" for "mathematics".
Never mind, you already said they're un-know-able.
Your grandiosis is showing, and it's not pretty.
Tarski was a self-aggrandizing pill-popping schmuck.
A guy as smart as you doesn't know that ad hominem
is incorrect?
Nah, forget you, Tarski-trivial-true is a non-statement about
theorems of a theory or models in a model.
What I'm saying is that Tarski's kind of a dead-ender and
not saying much.
Also Heidegger is rather remarkably ridiculous.
Maybe this is showing some slant against Germans, Austrians, and Poles,
Heidegger, Wittgenstein, and Tarski, yet, I don't need them for
anything.
At least they're not "Russo-Hungarians" or even, "Bulgarians".
I don't need Tarski for anything except to show exactly
how, why and where he went wrong with his Undefinability
theorem. I have no need to stoop to denigrating him that
is far too lame.
For being a pill-popping, self-aggrandizing schmuck?
These are well-known and characteristic in the Fefermans'
biography of Tarski.
Feferman, with "quantifier disambiguation", has a lot more to
say about "impredicativity" with regards to that's not
"un-define-ability".
Then, pointing out the deficiencies of his program is also fair.
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to object
to (Gödel, Tarski) make any claims about knowledge. Tarski is concerned with truth and Gödel with theoremhood.
André
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to object
to (Gödel, Tarski) make any claims about knowledge. Tarski is
concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski is
concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets are static entities defined by a binary membership operator, whereas 'the
entire body of general knowledge' is a loosely defined entity which
changes from day to day as new things
are learned and old things forgotten.Once in the system it is never forgotten.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
never going to be the basis for anything computable.
André
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski is >>>> concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets
are static entities defined by a binary membership operator, whereas
'the entire body of general knowledge' is a loosely defined entity
which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski
is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets
are static entities defined by a binary membership operator, whereas
'the entire body of general knowledge' is a loosely defined entity
which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you claiming
it is still part of 'the entire body of general knowledge'?
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General Relativity part of the body of general knowledge? Are the basic tenets
of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski
is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets
are static entities defined by a binary membership operator, whereas
'the entire body of general knowledge' is a loosely defined entity
which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you claiming
it is still part of 'the entire body of general knowledge'?
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General Relativity part of the body of general knowledge? Are the basic tenets
of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
On 10/09/2026 06:45 PM, André G. Isaak wrote:
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski >>>>>> is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets
are static entities defined by a binary membership operator, whereas
'the entire body of general knowledge' is a loosely defined entity
which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you claiming
it is still part of 'the entire body of general knowledge'?
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General
Relativity part of the body of general knowledge? Are the basic tenets
of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
Einstein has an aether in his theory, says it's obvious.
(Cf., "Sidelights in Relativity".)
Agreeably, there's that lies, hyperbole, exaggeration,
and other distortions of the truth make that "the body
of general knowledge" must include malice beyond ignorance,
then that besides, there's "science" involved that scientists
only say "not falsified".
Set-theory as you mentioned is nice and simple as a
theory-of-one-relation, there are others, first of all there are other set-theories,
then for example part-theory and class-theory, then for example various order-theory and ordering-theory, accounts of theories-of-one-relation.
Then, about all those being modeled by one of those, involves
"paradoxes" of, for examples:
induction
quantification
identity
infinity
continuity
and so on, then that there's a theory where it's part of the body
of knowledge that those are resolved for paradox-free reason.
GR and QM can be made compatible with real space-contraction and
real wave-collapse, providing "Lorentzians" and "Schroedingerians"
for "doubly-objective relativity theory" and "continuous quantum
mechanics".
It involves infinity and continuity in mathematics,
yet any account of motion and continuity already does.
On 10/9/2026 8:45 PM, André G. Isaak wrote:
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to
object to (Gödel, Tarski) make any claims about knowledge. Tarski >>>>>> is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set. Sets
are static entities defined by a binary membership operator, whereas
'the entire body of general knowledge' is a loosely defined entity
which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you
claiming it is still part of 'the entire body of general knowledge'?
You said forgotten. Try to use all of your words
as if they were a mathematical formalism.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General
Relativity part of the body of general knowledge? Are the basic tenets
of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
All of the details about them are general knowledge.
Unresolved conflicts are outside the scope of knowledge.
On 2026-10-09 20:37, olcott wrote:
On 10/9/2026 8:45 PM, André G. Isaak wrote:
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to >>>>>>> object to (Gödel, Tarski) make any claims about knowledge. Tarski >>>>>>> is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set.
Sets are static entities defined by a binary membership operator,
whereas 'the entire body of general knowledge' is a loosely defined >>>>> entity which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you
claiming it is still part of 'the entire body of general knowledge'?
You said forgotten. Try to use all of your words
as if they were a mathematical formalism.
So is the luminiferous ether part of 'general knowledge' or not? It definetely was at one point and you claim that things are never forgotten.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General
Relativity part of the body of general knowledge? Are the basic
tenets of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
All of the details about them are general knowledge.
Unresolved conflicts are outside the scope of knowledge.
Again, you don't answer the question. Are the basic tenets of relativity
and quantum mechanics part of general knowledge or not?
André
On 2026-10-09 20:37, olcott wrote:
On 10/9/2026 8:45 PM, André G. Isaak wrote:
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to >>>>>>> object to (Gödel, Tarski) make any claims about knowledge. Tarski >>>>>>> is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set.
Sets are static entities defined by a binary membership operator,
whereas 'the entire body of general knowledge' is a loosely defined >>>>> entity which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you
claiming it is still part of 'the entire body of general knowledge'?
You said forgotten. Try to use all of your words
as if they were a mathematical formalism.
So is the luminiferous ether part of 'general knowledge' or not? It definetely was at one point and you claim that things are never forgotten.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General
Relativity part of the body of general knowledge? Are the basic
tenets of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
All of the details about them are general knowledge.
Unresolved conflicts are outside the scope of knowledge.
Again, you don't answer the question. Are the basic tenets of relativity
and quantum mechanics part of general knowledge or not?
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>>> method to find out whether a sentence or its negation can be
proven.
Consequently, it is not possible to construct a system that rejects >>>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and
found good. The proof can be algorithmically compressed as soon as it is
found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to
be unprovable. But none of that affects its meaning and meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames known.
It is updated the same way that Pluto ceased to be a planet.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
Meaningless expressions are outside the body of knowledge.
My focus has always been on "the body of general knowledge
that can be expressed in language".
I never really cared that system X is too weak to fully express Y.
A weaker system has a larger scope of applications, which is often
quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where
its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation
graph
Never terminates thus never derives PTS semantic meaning.
is valid and describes a possible evaluation.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
I created the system of Minimal Type Theory for this exact same
purpose before I knew that Prolog could do this same thing.
There are many nice things that are quite simple with Prolog if one
knows Prolog and thinks a little about how.
So far as far as I know no one has derived that final
resolution of the Liar Paradox besides myself. We could
say that Kripke did this
On 2026-10-09 20:37, olcott wrote:
On 10/9/2026 8:45 PM, André G. Isaak wrote:
On 2026-10-09 19:31, olcott wrote:
On 10/9/2026 6:40 PM, André G. Isaak wrote:
On 2026-10-09 10:03, olcott wrote:
On 10/9/2026 10:25 AM, André G. Isaak wrote:
On 2026-10-09 09:02, olcott wrote:
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
The problem here is that none of the theorems which you seem to >>>>>>> object to (Gödel, Tarski) make any claims about knowledge. Tarski >>>>>>> is concerned with truth and Gödel with theoremhood.
André
There are several different aspects of my work
that has the final goal of:
Making "true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
The entire body of general knowledge is not a well-defined set.
Sets are static entities defined by a binary membership operator,
whereas 'the entire body of general knowledge' is a loosely defined >>>>> entity which changes from day to day as new things
It can be updated. Anything not known to be true
is outside the scope.
are learned and old things forgotten.Once in the system it is never forgotten.
So for example, in the nineteenth century the existence of the
luminiferous ether was well known and widely accepted. Are you
claiming it is still part of 'the entire body of general knowledge'?
You said forgotten. Try to use all of your words
as if they were a mathematical formalism.
So is the luminiferous ether part of 'general knowledge' or not? It definetely was at one point and you claim that things are never forgotten.
It is also filled with contradictory propositions, so this isIt will have knowledge of these propositions and with my work
how to resolve some if not all of them.
never going to be the basis for anything computable.
I don't follow what you mean by this. Are the basic tenets of General
Relativity part of the body of general knowledge? Are the basic
tenets of Quantum Mechanics part of the body of general knowledge?
Both are widely accepted but we know both cannot be entirely correct
since they contradict one another.
André
All of the details about them are general knowledge.
Unresolved conflicts are outside the scope of knowledge.
Again, you don't answer the question. Are the basic tenets of relativity
and quantum mechanics part of general knowledge or not?
André
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no
complete
method to find out whether a sentence or its negation can be >>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and
found good. The proof can be algorithmically compressed as soon as it is >>> found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to
be unprovable. But none of that affects its meaning and meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames known.
It is updated the same way that Pluto ceased to be a planet.
It is not updated unless somebody updates it. Also note that the process
that resulted to Pluto not being regarded as a planet was not simple and easy.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful.
I never really cared that system X is too weak to fully express Y.
Then you should not post to this discussion as its topic is whether
PA is too weak to fully express the proof of G.
A weaker system has a larger scope of applications, which is often
quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater
ability to exclude from the scope what is not wanted.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where
its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation
graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular definition does not present a meaning.
is valid and describes a possible evaluation.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
I created the system of Minimal Type Theory for this exact same
purpose before I knew that Prolog could do this same thing.
There are many nice things that are quite simple with Prolog if one
knows Prolog and thinks a little about how.
So far as far as I know no one has derived that final
resolution of the Liar Paradox besides myself. We could
say that Kripke did this
That you don't know what others have concluded does not matter.
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and >>>> found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to >>>> be unprovable. But none of that affects its meaning and meaningfulness. >>>> What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It is updated the same way that Pluto ceased to be a planet.It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames known. >>>
It is not updated unless somebody updates it. Also note that the process
that resulted to Pluto not being regarded as a planet was not simple and
easy.
If no human mind knows a thing then it is outside
the body of knowledge.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
It is true, so that any attempt at proving that
it is false is incorrect.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful.
a mathematical property where changing the order of
the operands does not change the final result.
The proof that feline cats are a type of 15 story
office building comes up empty because it is false.
I never really cared that system X is too weak to fully express Y.
Then you should not post to this discussion as its topic is whether
PA is too weak to fully express the proof of G.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
A weaker system has a larger scope of applications, which is often
quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater
ability to exclude from the scope what is not wanted.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where
its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation
graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular
definition does not present a meaning.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
On 10/11/2026 06:00 AM, olcott wrote:
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:It truth value will be known as soon as its proof has been chekcked >>>>> and
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>
unknown unless and until it proof can be algorithmically compressed. >>>>>
found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the >>>>> knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be >>>>> > expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames
known.
It is updated the same way that Pluto ceased to be a planet.
It is not updated unless somebody updates it. Also note that the process >>> that resulted to Pluto not being regarded as a planet was not simple and >>> easy.
If no human mind knows a thing then it is outside
the body of knowledge.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
It is true, so that any attempt at proving that
it is false is incorrect.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful.
a mathematical property where changing the order of
the operands does not change the final result.
The proof that feline cats are a type of 15 story
office building comes up empty because it is false.
I never really cared that system X is too weak to fully express Y.
Then you should not post to this discussion as its topic is whether
PA is too weak to fully express the proof of G.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
A weaker system has a larger scope of applications, which is often
quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater
ability to exclude from the scope what is not wanted.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where >>>>>>> its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation >>>>> graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular
definition does not present a meaning.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
It's a formal fact that any declaration has at least two readings,
for examples, one where it's true and one where it's not, and for
a wider example, one where it's true for itself (the usual "tau-tology")
and one where it's as for "cosmic complement" given
an actual account of formal identity (the less-than-usual "identity").
Then, for examples, a declaration is all the questions it answers,
implicitly with all the other declarations (and all the other questions).
Questions may stay the same temporally, declarations their answers
change, with the times.
What's "true" is what remains invariant under alternatives,
tests and examinations, all the space of questions, all the
space of declarations, sentences with meaning are re-readable.
So, accounts of meaning or _significance_ vis-a-vis something like
Russell's "isolation" and "significance", about the signification
of statements, makes for mechanics in informatics and accounts of
work, then for both what statements "prove" or what can be inferred
from them, _and_ what "prove" them.
Then, "the meaning" of a declaration about the relate-able,
talking to yourself, then the relay-able, convey-able to others,
makes for that there's always again _another_ layer of meaning,
about the utterances and the utterers, and the audience, _another_
layer, point being usual accounts about "Sowa" and so on are
navel-gazing of the monomaniac variety.
Really, lots of people reject and refuse "Tarski-trivial" or "Wittgenstein-tautological" when it comes to "true",
Tarski as trivial, Wittgenstein as tautological.
There's Sheffer and Chwistek, and Huntington's universals, ....--
On 10/11/2026 11:36 AM, Ross Finlayson wrote:
On 10/11/2026 06:00 AM, olcott wrote:
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:It truth value will be known as soon as its proof has been
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>> unknown unless and until it proof can be algorithmically compressed. >>>>>>
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from
premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>
chekcked and
found good. The proof can be algorithmically compressed as soon as >>>>>> it is
found, even before the verification, though that is irrelevant to the >>>>>> knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth >>>>>> value is unknowable.
I restricted my system to "the body of general knowledge that can be >>>>>> > expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames
known.
It is updated the same way that Pluto ceased to be a planet.
It is not updated unless somebody updates it. Also note that the
process
that resulted to Pluto not being regarded as a planet was not simple
and
easy.
If no human mind knows a thing then it is outside
the body of knowledge.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
It is true, so that any attempt at proving that
it is false is incorrect.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful.
a mathematical property where changing the order of
the operands does not change the final result.
The proof that feline cats are a type of 15 story
office building comes up empty because it is false.
I never really cared that system X is too weak to fully express Y.
Then you should not post to this discussion as its topic is whether
PA is too weak to fully express the proof of G.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
A weaker system has a larger scope of applications, which is often >>>>>> quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater
ability to exclude from the scope what is not wanted.
Irrelevant to your attempt to deceive with an ireelevancy.For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where >>>>>>>> its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language" >>>>>>
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation >>>>>> graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular
definition does not present a meaning.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
It's a formal fact that any declaration has at least two readings,
for examples, one where it's true and one where it's not, and for
a wider example, one where it's true for itself (the usual "tau-tology")
and one where it's as for "cosmic complement" given
an actual account of formal identity (the less-than-usual "identity").
So its true that 5 equals 6 has more than one
correct truth value?
Then, for examples, a declaration is all the questions it answers,
implicitly with all the other declarations (and all the other questions).
Questions may stay the same temporally, declarations their answers
change, with the times.
What's "true" is what remains invariant under alternatives,
tests and examinations, all the space of questions, all the
space of declarations, sentences with meaning are re-readable.
So, accounts of meaning or _significance_ vis-a-vis something like
Russell's "isolation" and "significance", about the signification
of statements, makes for mechanics in informatics and accounts of
work, then for both what statements "prove" or what can be inferred
from them, _and_ what "prove" them.
Then, "the meaning" of a declaration about the relate-able,
talking to yourself, then the relay-able, convey-able to others,
makes for that there's always again _another_ layer of meaning,
about the utterances and the utterers, and the audience, _another_
layer, point being usual accounts about "Sowa" and so on are
navel-gazing of the monomaniac variety.
Too convoluted for yo top show that you understand
the exact meaning of my words.
Really, lots of people reject and refuse "Tarski-trivial" or
"Wittgenstein-tautological" when it comes to "true",
Tarski as trivial, Wittgenstein as tautological.
There was a time when there was a universal consensus
that the Earth was flat.
There's Sheffer and Chwistek, and Huntington's universals, ....
On 10/11/2026 10:27 AM, olcott wrote:
On 10/11/2026 11:36 AM, Ross Finlayson wrote:
On 10/11/2026 06:00 AM, olcott wrote:
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon as >>>>>>> it is
found, even before the verification, though that is irrelevant to >>>>>>> the
knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth >>>>>>> value is unknowable.
I restricted my system to "the body of general knowledge that
can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames >>>>>>> known.
It is updated the same way that Pluto ceased to be a planet.
It is not updated unless somebody updates it. Also note that the
process
that resulted to Pluto not being regarded as a planet was not simple >>>>> and
easy.
If no human mind knows a thing then it is outside
the body of knowledge.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and >>>>>>>>> unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove >>>>>>> that the commutativity law is false.
It is true, so that any attempt at proving that
it is false is incorrect.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful.
a mathematical property where changing the order of
the operands does not change the final result.
The proof that feline cats are a type of 15 story
office building comes up empty because it is false.
I never really cared that system X is too weak to fully express Y.
Then you should not post to this discussion as its topic is whether
PA is too weak to fully express the proof of G.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
A weaker system has a larger scope of applications, which is often >>>>>>> quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater
ability to exclude from the scope what is not wanted.
Irrelevant to your attempt to deceive with an ireelevancy.For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where >>>>>>>>> its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language" >>>>>>>
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly >>>>>>>>> circular definitions.
Like the cycle in the directed graph of the evaluation sequence >>>>>>>> of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation >>>>>>> graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular >>>>> definition does not present a meaning.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
It's a formal fact that any declaration has at least two readings,
for examples, one where it's true and one where it's not, and for
a wider example, one where it's true for itself (the usual "tau-tology") >>> and one where it's as for "cosmic complement" given
an actual account of formal identity (the less-than-usual "identity").
So its true that 5 equals 6 has more than one
correct truth value?
Then, for examples, a declaration is all the questions it answers,
implicitly with all the other declarations (and all the other
questions).
Questions may stay the same temporally, declarations their answers
change, with the times.
What's "true" is what remains invariant under alternatives,
tests and examinations, all the space of questions, all the
space of declarations, sentences with meaning are re-readable.
So, accounts of meaning or _significance_ vis-a-vis something like
Russell's "isolation" and "significance", about the signification
of statements, makes for mechanics in informatics and accounts of
work, then for both what statements "prove" or what can be inferred
from them, _and_ what "prove" them.
Then, "the meaning" of a declaration about the relate-able,
talking to yourself, then the relay-able, convey-able to others,
makes for that there's always again _another_ layer of meaning,
about the utterances and the utterers, and the audience, _another_
layer, point being usual accounts about "Sowa" and so on are
navel-gazing of the monomaniac variety.
Too convoluted for yo top show that you understand
the exact meaning of my words.
Really, lots of people reject and refuse "Tarski-trivial" or
"Wittgenstein-tautological" when it comes to "true",
Tarski as trivial, Wittgenstein as tautological.
There was a time when there was a universal consensus
that the Earth was flat.
There's Sheffer and Chwistek, and Huntington's universals, ....
In Tarski's theory of a flat earth it's flat,
and Wittgenstein says it doesn't matter anyways,
due _a priori_ truths like "a strict inequality
exists in ordinals as modeled by finite natural
integers" that "5 < 6 and 5 =/= 6 is a fact"
still has, for example, that neither five wrongs
nor six wrongs is anyways right.
Wittgenstein is a liar whose great contribution
to liars is "don't break the spell", Tarski is
a tabulator who has run out of fingers.
The "invincible ignorance of inductive inference"
is readily dis-spelled by deductive reasoning.
The polaricentric and other accounts of deductive
reasoning about space and space-time in the universals
and wider Mach-ian and wider LaGrange-ian is a sort of
ultimate refutation of "Flat-Earth".
Statements and declaration and interrogatives and
question in our rich natural language readily make
for that it's a formal fact that while transliterations
of words already have a "number", which is readily enough
their letters in their alphabet the word, they also have
a number that is infinite.
Matters of motion and continuity and other accounts of
ultimate universals make it so your mis-reading of Goedel
and Prawitz and so on then the ostrich-heading is bull-shit.
Quit trying, or change your ways.
On 10/11/2026 12:11 PM, Ross Finlayson wrote:
On 10/11/2026 10:27 AM, olcott wrote:
On 10/11/2026 11:36 AM, Ross Finlayson wrote:
On 10/11/2026 06:00 AM, olcott wrote:
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms >>>>>>>>>>>>> has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon as >>>>>>>> it is
found, even before the verification, though that is irrelevant to >>>>>>>> the
knowledge of its truth. Thought it is possible that it will be >>>>>>>> found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
However, these possibilities are irrelevant to the meaning of the
of the conjecture, which we do know in spite or our ignorance of
its provability and truth value.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth >>>>>>>> value is unknowable.
I restricted my system to "the body of general knowledge that >>>>>>>>> can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames >>>>>>>> known.
It is updated the same way that Pluto ceased to be a planet.
It is not updated unless somebody updates it. Also note that the
process
that resulted to Pluto not being regarded as a planet was not simple >>>>>> and
easy.
If no human mind knows a thing then it is outside
the body of knowledge.
Being meaningful is not a limitation, nor is the ability to prove >>>>>>>> that the commutativity law is false.each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and >>>>>>>>>> unporvable others.
That is merely a limitation of the individual formal systems. >>>>>>>>
It is true, so that any attempt at proving that
it is false is incorrect.
Meaningless expressions are outside the body of knowledge.
The commutativity law is not meaningless, whther provable or not.
My focus has always been on "the body of general knowledge
that can be expressed in language".
That should include the meanings of the commutativity law and its
negation nad that in some cases both are unprovable but meaningful. >>>>>>
a mathematical property where changing the order of
the operands does not change the final result.
The proof that feline cats are a type of 15 story
office building comes up empty because it is false.
I never really cared that system X is too weak to fully express Y. >>>>>>Then you should not post to this discussion as its topic is whether >>>>>> PA is too weak to fully express the proof of G.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
A weaker system has a larger scope of applications, which is often >>>>>>>> quite useful.
counter-factual. "Weaker" is stipulated to mean a reduced scope.
No, "stronger" is stipualted to mean a reduced scope, i.e., greater >>>>>> ability to exclude from the scope what is not wanted.
Irrelevant to your attempt to deceive with an ireelevancy.For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where >>>>>>>>>> its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language" >>>>>>>>
If all words are defined in terms of other words andThey are also meaningless if there are diretly or indirectly >>>>>>>>>> circular definitions.
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless. >>>>>>>>>>
Like the cycle in the directed graph of the evaluation sequence >>>>>>>>> of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic
evaluation
graph
Never terminates thus never derives PTS semantic meaning.
Irrelevant. A cyclic evaluation graph is not meaningless. A circular >>>>>> definition does not present a meaning.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
This is the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
It's a formal fact that any declaration has at least two readings,
for examples, one where it's true and one where it's not, and for
a wider example, one where it's true for itself (the usual "tau-
tology")
and one where it's as for "cosmic complement" given
an actual account of formal identity (the less-than-usual "identity"). >>>>
So its true that 5 equals 6 has more than one
correct truth value?
Then, for examples, a declaration is all the questions it answers,
implicitly with all the other declarations (and all the other
questions).
Questions may stay the same temporally, declarations their answers
change, with the times.
What's "true" is what remains invariant under alternatives,
tests and examinations, all the space of questions, all the
space of declarations, sentences with meaning are re-readable.
So, accounts of meaning or _significance_ vis-a-vis something like
Russell's "isolation" and "significance", about the signification
of statements, makes for mechanics in informatics and accounts of
work, then for both what statements "prove" or what can be inferred
from them, _and_ what "prove" them.
Then, "the meaning" of a declaration about the relate-able,
talking to yourself, then the relay-able, convey-able to others,
makes for that there's always again _another_ layer of meaning,
about the utterances and the utterers, and the audience, _another_
layer, point being usual accounts about "Sowa" and so on are
navel-gazing of the monomaniac variety.
Too convoluted for yo top show that you understand
the exact meaning of my words.
Really, lots of people reject and refuse "Tarski-trivial" or
"Wittgenstein-tautological" when it comes to "true",
Tarski as trivial, Wittgenstein as tautological.
There was a time when there was a universal consensus
that the Earth was flat.
There's Sheffer and Chwistek, and Huntington's universals, ....
In Tarski's theory of a flat earth it's flat,
and Wittgenstein says it doesn't matter anyways,
due _a priori_ truths like "a strict inequality
exists in ordinals as modeled by finite natural
integers" that "5 < 6 and 5 =/= 6 is a fact"
still has, for example, that neither five wrongs
nor six wrongs is anyways right.
Wittgenstein is a liar whose great contribution
to liars is "don't break the spell", Tarski is
a tabulator who has run out of fingers.
The "invincible ignorance of inductive inference"
is readily dis-spelled by deductive reasoning.
The polaricentric and other accounts of deductive
reasoning about space and space-time in the universals
and wider Mach-ian and wider LaGrange-ian is a sort of
ultimate refutation of "Flat-Earth".
Statements and declaration and interrogatives and
question in our rich natural language readily make
for that it's a formal fact that while transliterations
of words already have a "number", which is readily enough
their letters in their alphabet the word, they also have
a number that is infinite.
Matters of motion and continuity and other accounts of
ultimate universals make it so your mis-reading of Goedel
and Prawitz and so on then the ostrich-heading is bull-shit.
Quit trying, or change your ways.
Wittgenstein says things like "you can't talk about what's
not given in my theory" then "no-one can understand what
you say in your theory",
these are logically insane and
marks of a liar and abuser of language.
Now, a lot of people find it liberating to latch onto something that Wittgenstein says as giving them free-will when it's perceived accounts
like "determinism" or "natural order" or for that matter "positivism"
or even "nominalism" or "nominalist fictionalism" get in the way,
yet nobody needs Wittgenstein's permission or lack thereof for anything.
Tarski is the type to try to make a model of a logical theory--
that you can only follow not change. He failed trying to prove
he could make one.
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and >>>> found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to >>>> be unprovable. But none of that affects its meaning and meaningfulness. >>>> What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames known. >>>>
It is updated the same way that Pluto ceased to be a planet.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
Meaningless expressions are outside the body of knowledge.
Some knowledge about meaningful expression, their properties, and
relations between them is in the bdoy of knowledge.
Yes for example we already know that the Goldbach conjecture
is either true or false. Its actual truth value is currently
outside of the body of knowledge
counter-factual. "Weaker" is stipulated to mean a reduced scope.My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
A weaker system has a larger scope of applications, which is often
quite useful.
No, it is not. When applied to theories it is stipulated to mean lesser
provability.
The entire body of general knowledge expressed
in language can be fully encoded as two types
of relations between finite strings:
(a) Stipulated relations
(b) Semantic entailment specified syntactically.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where
its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation
graph
Never terminates thus never derives PTS semantic meaning.
THe main similatity is that both evaluation graphs and PTS semantic
meanings are irrelevant to PA and provability.
Not at all.
The entire body of general knowledge expressed
in language can be fully encoded as two types
of relations between finite strings:
(a) Stipulated relations
(b) Semantic entailment specified syntactically.
It has always been the case that the above notion of
Proof Theoretic Semantics has always been the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
is valid and describes a possible evaluation.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
I created the system of Minimal Type Theory for this exact same
purpose before I knew that Prolog could do this same thing.
There are many nice things that are quite simple with Prolog if one
knows Prolog and thinks a little about how.
So far as far as I know no one has derived that final
resolution of the Liar Paradox besides myself. We could
say that Kripke did this
No one, including you, has derived anything important about the liar
paradox during the last 2000 years. The only new results are attempts
to avoid the paradox in new systems, with variable success.
Kripke did define this same idea first with his: "The LP is ungrounded".
Outline of a Theory of Truth Saul Kripke (1975) https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/ files/2019/04/Outline-of-a-Theory-of-Truth.pdf
All that I did is make this same idea maximally succinct.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false. // Copyright 2018 and 2026 PL Olcott
*Truth as an Epistemic Notion (2011) Dag Prawitz*
What is the appropriate notion of truth for sentences
whose meanings are understood in epistemic terms
such as proof or ground for an assertion? It seems
that the truth of such sentences has to be identified
with the existence of proofs or grounds https://link.springer.com/article/10.1007/s11245-011-9107-6
The above seems to be consistent with Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's system'
means:the opposite has been proved in Russell's system. https://www.liarparadox.org/Wittgenstein.pdf
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:It truth value will be known as soon as its proof has been chekcked >>>>> and
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>
unknown unless and until it proof can be algorithmically compressed. >>>>>
found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the >>>>> knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
Unless you explicitly define the expression in every opus where you use
it the expession means it means in Common Language, which usually is
vague.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth
value is unknowable.
I restricted my system to "the body of general knowledge that can be >>>>> > expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames
known.
It is updated the same way that Pluto ceased to be a planet.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove
that the commutativity law is false.
Meaningless expressions are outside the body of knowledge.
Some knowledge about meaningful expression, their properties, and
relations between them is in the bdoy of knowledge.
Yes for example we already know that the Goldbach conjecture
is either true or false. Its actual truth value is currently
outside of the body of knowledge
And so is whether it will ever be found out.
counter-factual. "Weaker" is stipulated to mean a reduced scope.My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
A weaker system has a larger scope of applications, which is often
quite useful.
No, it is not. When applied to theories it is stipulated to mean lesser
provability.
The entire body of general knowledge expressed
in language can be fully encoded as two types
of relations between finite strings:
(a) Stipulated relations
(b) Semantic entailment specified syntactically.
Irrelevant.
For example, it is not provable in a group
(where its negation isn't, either) nor in the quaternions (where >>>>>>> its negation is provable) but it is meaningful in both.
For
"true on the basis of meaning expressed in language"
when an expression cannot possibly connect to the
expressions that give it meaning then it never gets
any meaning.
That is not the basis in the above examples.
*This is the domain of my proposed system*
"the body of general knowledge that can be expressed in language"
Irrelevant to your attempt to deceive with an ireelevancy.
If all words are defined in terms of other words and
there is a string of symbols that it never assigned
any relation to other strings then it remains meaningless.
They are also meaningless if there are diretly or indirectly
circular definitions.
Like the cycle in the directed graph of the evaluation sequence
of the Liar Paradox formalized in Prolog.
Quite unlike. Circular definitions don't define. A cyclic evaluation >>>>> graph
Never terminates thus never derives PTS semantic meaning.
THe main similatity is that both evaluation graphs and PTS semantic
meanings are irrelevant to PA and provability.
Not at all.
The entire body of general knowledge expressed
in language can be fully encoded as two types
of relations between finite strings:
(a) Stipulated relations
(b) Semantic entailment specified syntactically.
It has always been the case that the above notion of
Proof Theoretic Semantics has always been the way that
"true on the basis of meaning expressed in language"
has always worked in actual reality.
No, it is not. Whether "true on the basis of meaning expressed in
language" has ever worked at all in actual reality is not clear
(mainly because you have not defined it sufficiently well), let
alone how.
is valid and describes a possible evaluation.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
I created the system of Minimal Type Theory for this exact same
purpose before I knew that Prolog could do this same thing.
There are many nice things that are quite simple with Prolog if one
knows Prolog and thinks a little about how.
So far as far as I know no one has derived that final
resolution of the Liar Paradox besides myself. We could
say that Kripke did this
No one, including you, has derived anything important about the liar
paradox during the last 2000 years. The only new results are attempts
to avoid the paradox in new systems, with variable success.
Kripke did define this same idea first with his: "The LP is ungrounded".
Outline of a Theory of Truth Saul Kripke (1975)
https://files.commons.gc.cuny.edu/wp-content/blogs.dir/1358/
files/2019/04/Outline-of-a-Theory-of-Truth.pdf
Kripke simply specifies that some sentences of some languages are
neither true not false and consequently for some languages no truth
predicate is possible.
For those languages a partial truth predicate
is the best one can have.
In order to have a partial predicate one
must use a logic system that can be soundly interpreted to have more
than two truth values.
All that I did is make this same idea maximally succinct.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false. // Copyright 2018 and 2026 PL Olcott
You dind't do even that. Those Prolog queries above are irrelevant.
*Truth as an Epistemic Notion (2011) Dag Prawitz*
What is the appropriate notion of truth for sentences
whose meanings are understood in epistemic terms
such as proof or ground for an assertion? It seems
that the truth of such sentences has to be identified
with the existence of proofs or grounds
https://link.springer.com/article/10.1007/s11245-011-9107-6
Epistemic notions are outside of the scope of formal logic.
The above seems to be consistent with Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's system'
means:the opposite has been proved in Russell's system.
https://www.liarparadox.org/Wittgenstein.pdf
That may be a reasonable interpretation of Russell's system but
it is not cosistent with what Wittgenstain would call "current
rules of the language game of logicians".
On 10/11/2026 4:02 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It truth value will be known as soon as its proof has been chekcked and >>>> found good. The proof can be algorithmically compressed as soon as
it is
found, even before the verification, though that is irrelevant to the
knowledge of its truth. Thought it is possible that it will be found to >>>> be unprovable. But none of that affects its meaning and meaningfulness. >>>> What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
That is one possibility, as already noted above. But it is also
possibe that a finite proof exists and is knowable but remains
forever unknown.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of general knowledge.
Anything unknown for any reason is not a member of the body of
knowledge.
On 10/9/2026 3:50 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>>> method to find out whether a sentence or its negation can be
proven.
Consequently, it is not possible to construct a system that rejects >>>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It might be the case that its truth value is unknowable. I restricted
my system to "the body of general knowledge that can be expressed in
language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
Does that include cases where X is Peano arithmetic and Y is a
proof that G is true about natural number?
Now I have (with the help of Gemini) finally totally
anchored my claim that in PTS the meaning of an
expression is only derived by the existence of a
canonical proof of it.
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently, >>>>>>>> is merely anything for which your proposed semantics fails to >>>>>>>> supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>> method to find out whether a sentence or its negation can be proven. >>>>>> Consequently, it is not possible to construct a system that rejects >>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic
meaning, whether grounded or not. Existence of a proof from some set
of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
On 15/10/2026 18:21, olcott wrote:
On 10/15/2026 4:45 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>> proposed semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>> as it is
found, even before the verification, though that is irrelevant to >>>>>>> the
knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
Unless you explicitly define the expression in every opus where you use
it the expession means it means in Common Language, which usually is
vague.
If no minds currently know a thing and this thing
is written down in language such that minds could
know this thing if they had access to this writing?
Yes that seems to count.
An AI could have semantic tautologies that no human
is aware of.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth >>>>>>> value is unknowable.
I restricted my system to "the body of general knowledge that >>>>>>>> can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames >>>>>>> known.
It is updated the same way that Pluto ceased to be a planet.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and >>>>>>>>> unporvable others.
That is merely a limitation of the individual formal systems.
Being meaningful is not a limitation, nor is the ability to prove >>>>>>> that the commutativity law is false.
Meaningless expressions are outside the body of knowledge.
Some knowledge about meaningful expression, their properties, and
relations between them is in the bdoy of knowledge.
Yes for example we already know that the Goldbach conjecture
is either true or false. Its actual truth value is currently
outside of the body of knowledge
And so is whether it will ever be found out.
The key most relevant point is that it is currently
outside of the body of knowledge.
The most relevant point is "currently". It means that the body of
knowledge is not constant in time. Therefore any system that uses
it needs be updated when new knowledge is found out. And that
means that someone must update it. THere must also be procedures
to make sure that updates don't add false knowledge to the system.
counter-factual. "Weaker" is stipulated to mean a reduced scope.My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
A weaker system has a larger scope of applications, which is often >>>>>>> quite useful.
No, it is not. When applied to theories it is stipulated to mean
lesser
provability.
The entire body of general knowledge expressed
in language can be fully encoded as two types
of relations between finite strings:
(a) Stipulated relations
(b) Semantic entailment specified syntactically.
Irrelevant.
The "Holy Grail" of AI is not irrelevant.
It is to stipulated meanings of terms of art, which was the topic of
the sentece you falsely pretended to comment.
On 09/10/2026 18:15, olcott wrote:
On 10/9/2026 3:50 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no
complete
method to find out whether a sentence or its negation can be >>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed.
It might be the case that its truth value is unknowable. I restricted
my system to "the body of general knowledge that can be expressed in
language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
Does that include cases where X is Peano arithmetic and Y is a
proof that G is true about natural number?
Now I have (with the help of Gemini) finally totally
anchored my claim that in PTS the meaning of an
expression is only derived by the existence of a
canonical proof of it.
Nevertheless, and arithmetic sentence has an arithmetic meaning,
whether provable or not. For example, 4 < 3 is not provable in
any natural number arithmetic but its meaning is clear.
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>> method to find out whether a sentence or its negation can be proven. >>>>>>> Consequently, it is not possible to construct a system that rejects >>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises
to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic
meaning, whether grounded or not. Existence of a proof from some set
of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or provability.
Perhaps you don't understand "Charlemagne received a
horn of a unicorn from Harun ar-Rashid" without a proof but many
others do.
On 10/9/2026 2:59 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:It truth value will be known as soon as its proof has been
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>> unknown unless and until it proof can be algorithmically compressed. >>>>>>
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>
chekcked and
found good. The proof can be algorithmically compressed as soon as >>>>>> it is
found, even before the verification, though that is irrelevant to the >>>>>> knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
An obvious attempt to decive (this time a change of subject) does not
work. In order to decive one needs to behave as a honest person would.
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
On 09/10/2026 18:02, olcott wrote:
On 10/9/2026 2:59 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>> proposed semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>> as it is
found, even before the verification, though that is irrelevant to >>>>>>> the
knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
An obvious attempt to decive (this time a change of subject) does not
work. In order to decive one needs to behave as a honest person would.
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
As Aristotle pointed out, words are sometimes used in an actual sense
and sometimes in an potential sense. In actual sense "knowledge" means something that is known, in potential sense something that can be
known. Both are important.
On 09/10/2026 18:02, olcott wrote:
On 10/9/2026 2:59 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>> proposed semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>> as it is
found, even before the verification, though that is irrelevant to >>>>>>> the
knowledge of its truth. Thought it is possible that it will be
found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
An obvious attempt to decive (this time a change of subject) does not
work. In order to decive one needs to behave as a honest person would.
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
As Aristotle pointed out, words are sometimes used in an actual sense
and sometimes in an potential sense. In actual sense "knowledge" means something that is known, in potential sense something that can be
known. Both are important.
On 10/20/2026 3:20 AM, Mikko wrote:
On 09/10/2026 18:02, olcott wrote:
On 10/9/2026 2:59 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>>> proposed semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system >>>>>>>>>>>>>> that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms >>>>>>>>>>>>> has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>>> as it is
found, even before the verification, though that is irrelevant >>>>>>>> to the
knowledge of its truth. Thought it is possible that it will be >>>>>>>> found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
An obvious attempt to decive (this time a change of subject) does not
work. In order to decive one needs to behave as a honest person would.
It seems incorrect to call anything "knowledge" that
no one has ever known. We can call it unknown truth.
As Aristotle pointed out, words are sometimes used in an actual sense
and sometimes in an potential sense. In actual sense "knowledge" means
something that is known, in potential sense something that can be
known. Both are important.
It is stipulated (by the meaning of its words) that
unknowns are not in the body of knowledge.
Within the system that I am specifying every sense
meaning of every word has a unique and immutable GUID.
This points to a static fixed set of relations to other
GUIDs that provide its fixed static meaning. Each of
these has a time/date_stamp. When Pluto got redefined
its GUID got a new time/date stamp.
On 10/19/2026 2:55 AM, Mikko wrote:
On 15/10/2026 18:21, olcott wrote:
On 10/15/2026 4:45 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>>> unknown unless and until it proof can be algorithmically
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>>> proposed semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>>>> complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system >>>>>>>>>>>>>> that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms >>>>>>>>>>>>> has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>>>> negation of the axioms and conclusion to a contradiction. >>>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>>>>
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>>> as it is
found, even before the verification, though that is irrelevant >>>>>>>> to the
knowledge of its truth. Thought it is possible that it will be >>>>>>>> found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
Unless you explicitly define the expression in every opus where you use >>>> it the expession means it means in Common Language, which usually is
vague.
If no minds currently know a thing and this thing
is written down in language such that minds could
know this thing if they had access to this writing?
Yes that seems to count.
An AI could have semantic tautologies that no human
is aware of.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its truth >>>>>>>> value is unknowable.
I restricted my system to "the body of general knowledge that >>>>>>>>> can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw becames >>>>>>>> known.
It is updated the same way that Pluto ceased to be a planet.
Being meaningful is not a limitation, nor is the ability to prove >>>>>>>> that the commutativity law is false.each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and >>>>>>>>>> unporvable others.
That is merely a limitation of the individual formal systems. >>>>>>>>
Meaningless expressions are outside the body of knowledge.
Some knowledge about meaningful expression, their properties, and
relations between them is in the bdoy of knowledge.
Yes for example we already know that the Goldbach conjecture
is either true or false. Its actual truth value is currently
outside of the body of knowledge
And so is whether it will ever be found out.
The key most relevant point is that it is currently
outside of the body of knowledge.
The most relevant point is "currently". It means that the body of
knowledge is not constant in time. Therefore any system that uses
it needs be updated when new knowledge is found out. And that
means that someone must update it. THere must also be procedures
to make sure that updates don't add false knowledge to the system.
Yes. Pluto is no longer a planet.
On 10/19/2026 3:05 AM, Mikko wrote:
On 09/10/2026 18:15, olcott wrote:
On 10/9/2026 3:50 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be
unknown unless and until it proof can be algorithmically compressed. >>>>> It might be the case that its truth value is unknowable. I restricted >>>>> my system to "the body of general knowledge that can be expressed
in language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is
The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
Does that include cases where X is Peano arithmetic and Y is a
proof that G is true about natural number?
Now I have (with the help of Gemini) finally totally
anchored my claim that in PTS the meaning of an
expression is only derived by the existence of a
canonical proof of it.
Nevertheless, and arithmetic sentence has an arithmetic meaning,
That can no longer be conflated with any meaning that is
not directly derived from the axioms of Peano Arithmetic.
whether provable or not. For example, 4 < 3 is not provable in
any natural number arithmetic but its meaning is clear.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
...the meaning of a sentence in terms of what
it is to know that the sentence is true, which
in mathematics amounts to having a proof of
the sentence
"Gentzen’s idea could be summarized by saying
that the meaning of a sentence is determined by
what counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
On 10/19/2026 3:12 AM, Mikko wrote:
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>>> method to find out whether a sentence or its negation can be
proven.
Consequently, it is not possible to construct a system that rejects >>>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic
meaning, whether grounded or not. Existence of a proof from some set
of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or
provability.
Perhaps you have never heard of the analytic / synthetic distinction.
This is very well known in philosophy yet unknown of other fields.
On 19/10/2026 17:50, olcott wrote:
On 10/19/2026 2:55 AM, Mikko wrote:
On 15/10/2026 18:21, olcott wrote:
On 10/15/2026 4:45 AM, Mikko wrote:
On 07/10/2026 16:10, polcott wrote:
On 10/7/2026 3:49 AM, Mikko wrote:
On 06/10/2026 15:32, olcott wrote:
On 10/6/2026 2:59 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:It turns out that automated proof systems expose
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of- >>>>>>>>>>>>>>>>> scope" does not make undecidability disappear. >>>>>>>>>>>>>>>>>Within PTS any expression that is neither provable nor >>>>>>>>>>>>>>>> refutable
For a formal theory T, "G is undecidable in T" simply >>>>>>>>>>>>>>>>> means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model >>>>>>>>>>>>>>>>> theory is involved.
And G is not "out-of-scope": it is a perfectly well- >>>>>>>>>>>>>>>>> formed sentence of the language of T. What is out-of- >>>>>>>>>>>>>>>>> scope, apparently, is merely anything for which your >>>>>>>>>>>>>>>>> proposed semantics fails to supply an answer. >>>>>>>>>>>>>>>>
never acquires any semantic meaning.
There is one more thing one needs to consider: there is >>>>>>>>>>>>>>> no complete
method to find out whether a sentence or its negation can >>>>>>>>>>>>>>> be proven.
Consequently, it is not possible to construct a system >>>>>>>>>>>>>>> that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms >>>>>>>>>>>>>> has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from >>>>>>>>>>>>> tne
negation of the axioms and conclusion to a contradiction. >>>>>>>>>>>>
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are
irrelevant to
The Goldbach conjecture is meaningful yet its truth value will be >>>>>>>>>> unknown unless and until it proof can be algorithmically
compressed.
It truth value will be known as soon as its proof has been
chekcked and
found good. The proof can be algorithmically compressed as soon >>>>>>>>> as it is
found, even before the verification, though that is irrelevant >>>>>>>>> to the
knowledge of its truth. Thought it is possible that it will be >>>>>>>>> found to
be unprovable. But none of that affects its meaning and
meaningfulness.
What PTS says about its meaning is irrelevant.
A finite proof might not exist.
It may forever remain unknowable
thus outside of the domain of knowledge.
Maybe, maybe not. If it ever will be found it is in the domain
of knowledge and has always been.
Unless at least one mind contains a truth such as
the ratio of the diameter to the circumference of
a circle back in caveman days I construe this as
outside of the domain of knowledge at the time.
Unless you explicitly define the expression in every opus where you >>>>> use
it the expession means it means in Common Language, which usually is >>>>> vague.
If no minds currently know a thing and this thing
is written down in language such that minds could
know this thing if they had access to this writing?
Yes that seems to count.
An AI could have semantic tautologies that no human
is aware of.
It might be the case that its truth value is unknowable.
It even might be possible that we can't ever know whether its >>>>>>>>> truth
value is unknowable.
I restricted my system to "the body of general knowledge that >>>>>>>>>> can be
expressed in language" to handle these edge cases.
Then your system needs be updated when something unknonw
becames known.
It is updated the same way that Pluto ceased to be a planet.
Being meaningful is not a limitation, nor is the ability to prove >>>>>>>>> that the commutativity law is false.each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and >>>>>>>>>>> unporvable others.
That is merely a limitation of the individual formal systems. >>>>>>>>>
Meaningless expressions are outside the body of knowledge.
Some knowledge about meaningful expression, their properties, and >>>>>>> relations between them is in the bdoy of knowledge.
Yes for example we already know that the Goldbach conjecture
is either true or false. Its actual truth value is currently
outside of the body of knowledge
And so is whether it will ever be found out.
The key most relevant point is that it is currently
outside of the body of knowledge.
The most relevant point is "currently". It means that the body of
knowledge is not constant in time. Therefore any system that uses
it needs be updated when new knowledge is found out. And that
means that someone must update it. THere must also be procedures
to make sure that updates don't add false knowledge to the system.
Yes. Pluto is no longer a planet.
It is in the body of knowledge that before the discovery of Pluto
an unknown planet was thought to exist farther than Neptunus, and
that when Pluto was discovered it was thought to be that planet.
More generally, false ideas are not knowledge but knowledge about
false ideas is.
Knowledge also covers meanings of words, including obsolete meanings.
On 19/10/2026 17:57, olcott wrote:
On 10/19/2026 3:05 AM, Mikko wrote:
On 09/10/2026 18:15, olcott wrote:
On 10/9/2026 3:50 AM, Mikko wrote:
On 04/10/2026 16:22, olcott wrote:
On 10/4/2026 6:30 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:The Goldbach conjecture is meaningful yet its truth value will be
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
Existence of a proof and existence of a meaning are irrelevant to >>>>>>
unknown unless and until it proof can be algorithmically compressed. >>>>>> It might be the case that its truth value is unknowable. I restricted >>>>>> my system to "the body of general knowledge that can be expressed >>>>>> in language" to handle these edge cases.
each other. For example, the sentence ∀x ∀y (x * y = y * x) is >>>>>>The Commutative Law For Multiplication
https://en.wikiversity.org/wiki/Basic_Laws_of_Algebra
meaningful in many theories and provable in some of them and
unporvable others.
That is merely a limitation of the individual formal systems.
My focus has always been on "the body of general knowledge
that can be expressed in language". I never really cared that
system X is too weak to fully express Y.
Does that include cases where X is Peano arithmetic and Y is a
proof that G is true about natural number?
Now I have (with the help of Gemini) finally totally
anchored my claim that in PTS the meaning of an
expression is only derived by the existence of a
canonical proof of it.
Nevertheless, and arithmetic sentence has an arithmetic meaning,
That can no longer be conflated with any meaning that is
not directly derived from the axioms of Peano Arithmetic.
Peano's axioms do not specify any meaning.
whether provable or not. For example, 4 < 3 is not provable in
any natural number arithmetic but its meaning is clear.
On the Relation Between Heyting’s
and Gentzen’s Approaches to Meaning
Dag Prawitz (2013)
...the meaning of a sentence in terms of what
it is to know that the sentence is true, which
in mathematics amounts to having a proof of
the sentence
"Gentzen’s idea could be summarized by saying
that the meaning of a sentence is determined by
what counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
Irrelevant to the well known meaning of "4 < 3".
On 19/10/2026 18:07, olcott wrote:
On 10/19/2026 3:12 AM, Mikko wrote:
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no
complete
method to find out whether a sentence or its negation can be >>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>> to conclusion and an indirect proof is a similar chain from tne
negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic >>>>> meaning, whether grounded or not. Existence of a proof from some set >>>>> of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or
provability.
Perhaps you have never heard of the analytic / synthetic distinction.
This is very well known in philosophy yet unknown of other fields.
Philosphers amy have opinions about that distinction but I have
often pointed out when you have try to obscure the distinction,
though usually with different words according to each particular
error.
On 10/21/2026 2:43 AM, Mikko wrote:
On 19/10/2026 18:07, olcott wrote:
On 10/19/2026 3:12 AM, Mikko wrote:
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>> sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed >>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined arithemtic >>>>>> meaning, whether grounded or not. Existence of a proof from some set >>>>>> of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or
provability.
Perhaps you have never heard of the analytic / synthetic distinction.
This is very well known in philosophy yet unknown of other fields.
Philosphers amy have opinions about that distinction but I have
often pointed out when you have try to obscure the distinction,
though usually with different words according to each particular
error.
So you do not understand this well enough to discuss it.
On 10/5/2026 3:19 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does not >>>>>> make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is
involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently,
is merely anything for which your proposed semantics fails to
supply an answer.
Within PTS any expression that is neither provable nor refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete
method to find out whether a sentence or its negation can be proven.
Consequently, it is not possible to construct a system that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. Proofs are finite strings and strings don't contain
loops.
Unprovable and irrefutable in PA entails that
G never acquires semantic meaning in PA.
On 21/10/2026 16:57, olcott wrote:
On 10/21/2026 2:43 AM, Mikko wrote:
On 19/10/2026 18:07, olcott wrote:
On 10/19/2026 3:12 AM, Mikko wrote:
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from premises >>>>>>>>> to conclusion and an indirect proof is a similar chain from tne >>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined
arithemtic
meaning, whether grounded or not. Existence of a proof from some set >>>>>>> of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or
provability.
Perhaps you have never heard of the analytic / synthetic distinction.
This is very well known in philosophy yet unknown of other fields.
Philosphers amy have opinions about that distinction but I have
often pointed out when you have try to obscure the distinction,
though usually with different words according to each particular
error.
So you do not understand this well enough to discuss it.
That I can spot your errors indicates that I do understand well
enough.
On 05/10/2026 16:28, olcott wrote:
On 10/5/2026 3:19 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does not >>>>>>> make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is
involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently, >>>>>>> is merely anything for which your proposed semantics fails to
supply an answer.
Within PTS any expression that is neither provable nor refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete
method to find out whether a sentence or its negation can be proven. >>>>> Consequently, it is not possible to construct a system that rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. Proofs are finite strings and strings don't contain
loops.
Unprovable and irrefutable in PA entails that
G never acquires semantic meaning in PA.
Every formula in the language of PA has an arithmetic meaning.
Dunning/Kruger
On 10/23/2026 2:15 AM, Mikko wrote:
On 21/10/2026 16:57, olcott wrote:
On 10/21/2026 2:43 AM, Mikko wrote:
On 19/10/2026 18:07, olcott wrote:
On 10/19/2026 3:12 AM, Mikko wrote:
On 09/10/2026 17:22, olcott wrote:
On 10/9/2026 3:45 AM, Mikko wrote:
On 02/10/2026 14:55, olcott wrote:
On 10/2/2026 4:37 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" >>>>>>>>>>>>>> does not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means >>>>>>>>>>>>>>
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory >>>>>>>>>>>>>> is involved.
And G is not "out-of-scope": it is a perfectly well-formed >>>>>>>>>>>>>> sentence of the language of T. What is out-of-scope, >>>>>>>>>>>>>> apparently, is merely anything for which your proposed >>>>>>>>>>>>>> semantics fails to supply an answer.
Within PTS any expression that is neither provable nor >>>>>>>>>>>>> refutable
never acquires any semantic meaning.
There is one more thing one needs to consider: there is no >>>>>>>>>>>> complete
method to find out whether a sentence or its negation can be >>>>>>>>>>>> proven.
Consequently, it is not possible to construct a system that >>>>>>>>>>>> rejects
all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. A direct proof is either a forward chain from >>>>>>>>>> premises
to conclusion and an indirect proof is a similar chain from tne >>>>>>>>>> negation of the axioms and conclusion to a contradiction.
It turns out that automated proof systems expose
the correct details the most clearly. They used
back-chained inference. In any case when a finite
canonical proof is impossible then the expression
never gets semantically grounded.
A sentence of natural number arithmetic has a well defined
arithemtic
meaning, whether grounded or not. Existence of a proof from some >>>>>>>> set
of axioms is irrelevant to the arithmetic meaning.
**On the Relation Between Heyting’s**
**and Gentzen’s Approaches to Meaning**
"Gentzen’s idea could be summarized by saying that
the meaning of a sentence is determined by what
counts as a canonical proof of it..."
https://doi.org/10.1007/978-3-319-22686-6_2
In reality there is much meaning that does not depend on proofs or >>>>>> provability.
Perhaps you have never heard of the analytic / synthetic distinction. >>>>> This is very well known in philosophy yet unknown of other fields.
Philosphers amy have opinions about that distinction but I have
often pointed out when you have try to obscure the distinction,
though usually with different words according to each particular
error.
So you do not understand this well enough to discuss it.
That I can spot your errors indicates that I do understand well
enough.
Dunning/Kruger
On 10/23/2026 2:17 AM, Mikko wrote:
On 05/10/2026 16:28, olcott wrote:
On 10/5/2026 3:19 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope, apparently, >>>>>>>> is merely anything for which your proposed semantics fails to >>>>>>>> supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>> method to find out whether a sentence or its negation can be proven. >>>>>> Consequently, it is not possible to construct a system that rejects >>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. Proofs are finite strings and strings don't contain
loops.
Unprovable and irrefutable in PA entails that
G never acquires semantic meaning in PA.
Every formula in the language of PA has an arithmetic meaning.
That is not the way that it works in reality.
On 23/10/2026 16:27, olcott wrote:
On 10/23/2026 2:17 AM, Mikko wrote:
On 05/10/2026 16:28, olcott wrote:
On 10/5/2026 3:19 AM, Mikko wrote:
On 01/10/2026 17:47, olcott wrote:
On 10/1/2026 5:03 AM, Mikko wrote:
On 29/09/2026 19:31, olcott wrote:
On 9/29/2026 11:01 AM, Python wrote:
No, Pete. Calling an undecidable sentence "out-of-scope" does >>>>>>>>> not make undecidability disappear.
For a formal theory T, "G is undecidable in T" simply means
T |-/- G and T |-/- ~G
That is a statement entirely about proofs. No model theory is >>>>>>>>> involved.
And G is not "out-of-scope": it is a perfectly well-formed
sentence of the language of T. What is out-of-scope,
apparently, is merely anything for which your proposed
semantics fails to supply an answer.
Within PTS any expression that is neither provable nor refutable >>>>>>>> never acquires any semantic meaning.
There is one more thing one needs to consider: there is no complete >>>>>>> method to find out whether a sentence or its negation can be proven. >>>>>>> Consequently, it is not possible to construct a system that rejects >>>>>>> all undecidable sentences.
If back-chained inference from expression X to axioms
has a loop it is rejected.
Irrelevant. Proofs are finite strings and strings don't contain
loops.
Unprovable and irrefutable in PA entails that
G never acquires semantic meaning in PA.
Every formula in the language of PA has an arithmetic meaning.
That is not the way that it works in reality.
From the orignal purspose of PA follows that the primary meaning
of a sentence in PA is its arithmetic meaning. Whether that works
in reality is irrelevant.
On 10/23/2026 10:20 AM, André G. Isaak wrote:
On 2026-10-23 10:57, olcott wrote:
On 10/23/2026 11:15 AM, André G. Isaak wrote:
On 2026-10-23 07:21, olcott wrote:
Dunning/Kruger
My irony meter just exploded.
André
I know that I know that I am on the correct
side of that because I can finally explain
the key details that everyone else never noticed.
When we abandon the misleading terms:
(a) "Turing machine description" and replace it with
[Finite string source code for a Turing Machine]
(b) "Decider" and replace it with sequence of inference
steps that are applied to an input static finite string
that are syntactically or semantically relevant to the
decision criteria.
There's absolutely nothing misleading about either of the above terms.
The only reason you find them confusing is because you've never bothered
to learn the precise technical meanings of those terms and instead
interpret them in some incredibly vague way and then conclude you have
made some brilliant insight. That's classic Dunning-Kruger.
Concrete example of a decider where relevance is required.
int strcmp(const char *str1, const char *str2);
and the finite string inputs are the entire basis.
WE HAVE CORRECTED THE ERRORS AT THE FOUNDATION OF COMPUTATION.
At this point we only need to see what is semantically entailed
by these corrections.
You don't *understand* the foundations of computation and thus are in no
position to 'correct' them.
André
Can't fix stupid, ..., perhaps it would be more fruitful to
consider the non-standard arithmetic for example as after
Boolos and Jeffrey or the usual account of computability theory,
since the non-standard arithmetic makes for super-tasks the
cases of what happens in the asymptotic then the infinite.
Anyways, at some point in time it makes sense to not feed the troll.
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