From Newsgroup: sci.lang
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, Andr|- G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
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.-a That doesn't mean you're >>>>>>>>>>>>> capable of
understanding them.
The above is the key reason why under PTS G||del 1931 >>>>>>>>>>>> incompleteness
fails.
I don't believe you.-a You have no respect for or
understanding of the
truth.-a If you really want to persuade anybody that PTS >>>>>>>>>>> somehow causes
G||del'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 G||del's Theorem, neither the theorem itself nor >>>>>>>>>>> any proof of
it.
It is a verified fact that G||del'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.
"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.
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.
They use a tree structure for concepts. But why would one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
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?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
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.
--
Copyright 2026 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.
The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.
My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.
(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).
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