On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean.[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
"atomic facts" that correspond to things in the worldOne usually says "assumption" instead of "stipulation". The latter
only have stipulation as their basis in truth within
the formal system.
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>> happen before
In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
On 07/02/2026 07:45 AM, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>>> tautology. I said semantic tautology. That cats are defined to >>>>>>>> be animals is a semantic tautology. That cats are defined to be >>>>>>>> cats is a logical tautology. Here is a definition of that fits >>>>>>>> my definition of semantic tautology.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>>
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
Animals are {cats, dogs, wallabies, llamas, aardvarks, crustaceans,
...}, a potentially infinitary expression.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
On 07/02/2026 07:45 AM, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>>> tautology. I said semantic tautology. That cats are defined to >>>>>>>> be animals is a semantic tautology. That cats are defined to be >>>>>>>> cats is a logical tautology. Here is a definition of that fits >>>>>>>> my definition of semantic tautology.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>>
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
Animals are {cats, dogs, wallabies, llamas, aardvarks, crustaceans,
...}, a potentially infinitary expression.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
On 02/07/2026 17:45, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
computer science 101
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>> "cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
On 07/03/2026 11:17 AM, olcott wrote:
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>> an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
Most thinking beings are feeling beings
and most feeling beings are thinking beings.
Not all, though, ....
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
On 07/03/2026 11:17 AM, olcott wrote:
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>> an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
Most thinking beings are feeling beings
and most feeling beings are thinking beings.
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
On 03/07/2026 18:23, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
For some kind of formal semantics where the meaning of a fintite
string is another finite string (or perhaps, in some cases, the
same). That way does not get any real world semantics, though
it can extend real world semantics if you already have some.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
They come from experiences about uses of those words by other people. Likewise for most of commonly used words and phrases.
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In sci.math olcott <polcott333@gmail.com> wrote:
[ .... ]
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
Seems doubtful. Falsehoods can also be expressed in language, together
with that vast trove of expressions which are neither true nor false. In fact, when it comes to "everything that can be expressed in language", a
list of "atomic facts" would appear to be unhelpful, just as much as a
list of "atomic falsehoods" would be, whatever that might mean.
--
Copyright 2026 Olcott
On 7/4/2026 9:07 AM, Alan Mackenzie wrote:
In sci.math olcott <polcott333@gmail.com> wrote:
[ .... ]
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
Seems doubtful. Falsehoods can also be expressed in language, together with that vast trove of expressions which are neither true nor false. In fact, when it comes to "everything that can be expressed in language", a list of "atomic facts" would appear to be unhelpful, just as much as a
list of "atomic falsehoods" would be, whatever that might mean.
A complete finite list of "atomic facts" of general knowledge
only includes true truth bearers and only facts that cannot
be derived from anything else. This excludes falsehoods and
expressions that are neither true nor false. It is the axiomatic
basis of knowledge of the world.
----
Copyright 2026 Olcott
On 7/4/2026 2:22 AM, Mikko wrote:
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
You may use "cats are animals" as a part of the defintion of "cat"
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect. >>>>
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
It tells us exactly one thing.
On 7/4/2026 1:58 AM, Mikko wrote:
On 03/07/2026 18:23, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>> "cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
For some kind of formal semantics where the meaning of a fintite
string is another finite string (or perhaps, in some cases, the
same). That way does not get any real world semantics, though
it can extend real world semantics if you already have some.
All of meaning expressed in language works this same way.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
They come from experiences about uses of those words by other people.
Likewise for most of commonly used words and phrases.
If this was true then Chinese would not exist.
Stipulated relations between finite strings is
the only way that language acquires meaning.
On 04/07/2026 16:29, olcott wrote:
On 7/4/2026 2:22 AM, Mikko wrote:
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
You may use "cats are animals" as a part of the defintion of "cat"
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect. >>>>>
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
It tells us exactly one thing.
Which thing? If the meanings of the words are already known it does
not tell anything that is not obvious from those meanings.
On 04/07/2026 16:24, olcott wrote:
On 7/4/2026 1:58 AM, Mikko wrote:
On 03/07/2026 18:23, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>> an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
For some kind of formal semantics where the meaning of a fintite
string is another finite string (or perhaps, in some cases, the
same). That way does not get any real world semantics, though
it can extend real world semantics if you already have some.
All of meaning expressed in language works this same way.
There is nore meaning expessed in language than you seem to be aware of.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
They come from experiences about uses of those words by other people.
Likewise for most of commonly used words and phrases.
If this was true then Chinese would not exist.
There is no reason to think so. In particular, that cannot be inferred
from what is known to be true.
Stipulated relations between finite strings is
the only way that language acquires meaning.
The "only" above is not supported by anything we know. It is not
even possible to stipulate anything before at least several words
already have meanings.
On 7/6/2026 5:13 AM, Mikko wrote:
On 04/07/2026 16:24, olcott wrote:
On 7/4/2026 1:58 AM, Mikko wrote:
On 03/07/2026 18:23, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>>> an "animal" but there are other posiibilities. Conseqently, the >>>>>>>> sentence "cats are animals" can be a semantic tautology that tells >>>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world >>>>>> when a tautology is presented. But that impression is a consequence >>>>>> of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
For some kind of formal semantics where the meaning of a fintite
string is another finite string (or perhaps, in some cases, the
same). That way does not get any real world semantics, though
it can extend real world semantics if you already have some.
All of meaning expressed in language works this same way.
There is nore meaning expessed in language than you seem to be aware of.
I don't want to keep repeating all the details
that prove this hundreds and hundreds of times.
If you cannot remember what I already told you 20
times then you are too disrespectful.
On 7/6/2026 2:10 AM, Mikko wrote:The computer does not know that there is a real world.
On 04/07/2026 16:29, olcott wrote:
On 7/4/2026 2:22 AM, Mikko wrote:
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily
incorrect.
You may use "cats are animals" as a part of the defintion of "cat" >>>>>> or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
It tells us exactly one thing.
Which thing? If the meanings of the words are already known it does
not tell anything that is not obvious from those meanings.
"cats" ⊂ "animals"
"animals" ⊃ "cats"
Is to be construed as the first time that anyone
has every seen those finite strings.
We are defining the English meaning of words
to a computer program that starts as a completely
blank slate.
The end result of defining every "atomic fact"
of empirical general knowledge is that the computer
has complete general knowledge of the world.
On 06/07/2026 16:51, olcott wrote:
On 7/6/2026 2:10 AM, Mikko wrote:The computer does not know that there is a real world.
On 04/07/2026 16:29, olcott wrote:
On 7/4/2026 2:22 AM, Mikko wrote:
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily
incorrect.
You may use "cats are animals" as a part of the defintion of "cat" >>>>>>> or of the definition of "animal" but not both. However, above you >>>>>>> have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
It tells us exactly one thing.
Which thing? If the meanings of the words are already known it does
not tell anything that is not obvious from those meanings.
"cats" ⊂ "animals"
"animals" ⊃ "cats"
Is to be construed as the first time that anyone
has every seen those finite strings.
We are defining the English meaning of words
to a computer program that starts as a completely
blank slate.
The end result of defining every "atomic fact"
of empirical general knowledge is that the computer
has complete general knowledge of the world.
It just does wbat it is made to do.
On 7/8/2026 2:35 AM, Mikko wrote:
On 06/07/2026 16:51, olcott wrote:
On 7/6/2026 2:10 AM, Mikko wrote:The computer does not know that there is a real world.
On 04/07/2026 16:29, olcott wrote:
On 7/4/2026 2:22 AM, Mikko wrote:
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily
incorrect.
You may use "cats are animals" as a part of the defintion of "cat" >>>>>>>> or of the definition of "animal" but not both. However, above you >>>>>>>> have done neither, so you haven't excluded the possibility that >>>>>>>> "cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting >>>>>> about the real world.
It tells us exactly one thing.
Which thing? If the meanings of the words are already known it does
not tell anything that is not obvious from those meanings.
"cats" ⊂ "animals"
"animals" ⊃ "cats"
Is to be construed as the first time that anyone
has every seen those finite strings.
We are defining the English meaning of words
to a computer program that starts as a completely
blank slate.
The end result of defining every "atomic fact"
of empirical general knowledge is that the computer
has complete general knowledge of the world.
It just does wbat it is made to do.
As I have said many many dozens of times we encode
all of the "basic facts" of general knowledge both
empirical (the facts of the actual world) and analytical
knowledge into a finite set of axioms.
On 6/22/2026 2:23 AM, Mikko wrote:
On 21/06/2026 23:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" yesterday.
You can find any number of terms. That doesn't mean you're
capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 incompleteness >>>>> fails.
I don't believe you. You have no respect for or understanding of the >>>> truth. If you really want to persuade anybody that PTS somehow causes >>>> Gödel's theorem not to hold, then cite an academic expert who'll have >>>> some credibility.
If they are mere gibberish words to you then you will not understand. >>>>You don't understand Proof-theoritic Semantics, and you certainly don't >>>> understand Gödel's Theorem, neither the theorem itself nor any proof of >>>> it.
in the atomic base of PA.
It is a verified fact that Gödel's completeness and incompleteness
theorems are inevitable consequences of Peano arithmetic.
Within the foundation of Truth Conditional Semantics
this is true. Within the foundation of strict Proof
Theoretic Semantics this is false.
[ Followup-To: set]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/20/2026 5:26 AM, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics)
https://plato.stanford.edu/entries/proof-theoretic-semantics/
Some people only memorize conventional views and
reject alternative views out-of-hand without review.
Whereas you are stuck to your own incoherent views and reject
alternative views out-of-hand without review.
Calling my views (anchored in proof theoretic semantics)
incoherent merely proves that you are too damned lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
I've spent a couple of hours reading that web page. It is abstract in >>>>> the extreme. One thing is utterly clear: its level of abstraction is >>>>> well beyond the comprehension capabilities of Peter Olcott, who can't >>>>> even understand proof by contradiction.
That page's level of abstraction is high enough that I can't be bothered >>>>> to read it any further. If it actually says anything at all, that
something is heavily disguised. From it's "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically exclusively been >>>>> | occupied with logical constants. Logical constants play a central role >>>>> | in reasoning and inference, but are definitely not the exclusive, and >>>>> | perhaps not even the most typical sort of entities that can be defined >>>>> | inferentially. A framework is needed that deals with inferential
| definitions in a wider sense and covers both logical and extra-logical >>>>> | inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is currently and in the
near future not useful as making it useful requires much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be useful for? What it
It makes "true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Taking a best guess at what that phrase is meant to mean, it doesn't. Or
at the very least, you have failed to meet your burden of proof that it
does.
We know that in any sufficiently powerful language (and the bar is not
high), there are statements which are "incomputable". If you doubt this,
and still believe PTS gives a different result, please show some
mathematical proof which comes out differently between standard logic and PTS, illustrating the essence of PTS which makes it so.
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