Re: The proper way to use LLMs to aid primary
research into foundations, My 28 year journey
involved primary research into the foundations
The evolution from early Large Language Models(LLMs) to the current state of Large Reasoning
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
On 03/05/2026 08:20 AM, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Actually we have an entire canon, dogma, and doctrine,
and can rather ignore much of 20'th century "Foundations",
as an exercise in the examination and testing of
quasi-modal logic as failed, ex falso quodlibet as failed,
logicist positivism as at best incomplete,
and otherwise about the correctness of the constancy,
consistency, completeness, and concreteness of a, "theatheory".
Trumpistan delenda est.
Actually we have an entire canon, dogma, and doctrine,
and can rather ignore much of 20'th century "Foundations",
as an exercise in the examination and testing of
quasi-modal logic as failed,
ex falso quodlibet as failed,
On 05/03/2026 17:12, Ross Finlayson wrote:
Actually we have an entire canon, dogma, and doctrine,
and can rather ignore much of 20'th century "Foundations",
as an exercise in the examination and testing of
quasi-modal logic as failed,
ex falso quodlibet as failed,
Really? That's very hard to believe. I have seen "from falsity not from falsity after all", and "from falsity start again pretending not to". 5
year olds do those as a matter of course.
Do we create Homo Simulamen without recourse to ex falso quodlibet or do
we rely on it to achieve that?
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
On 03/06/2026 01:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
The ideas of "verum" (veracity) and "certum" (certitude) are
basically re-ifications, with regards to ideas like the
re-ification fallacy, getting into why proof-theoretic machinery,
after an account that semantics like Herbrand semantics make it
so that anything logical can be stated unambiguously in natural
language, has that: since antiquity it's known that axiomatic,
inductive accounts have automatic counter-arguments. Then,
about inference, and, "inference is as inference does",
the plain sorts of conversational aspects of AI's may make
for there's always "the model" besides "the training".
It's a sort of psychological projection of ineptitude to
suggest that mechanical inference is any less thorough
than any other account of organized inference.
Moreso the account of "AI's" essential ineptitude
is a lie to give people who can't be bothered with
inconvenient truths a way to say that otherwise
the verum and certum of it are dubitable, when
otherwise in natural language terms for their own sake.
On 03/06/2026 06:36 AM, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It may help to establish that logics like "quasi-modal logic"
are not modal nor temporal nor relevance logics, since otherwise
many of the models take shortcuts of the gullible variety.
On 3/6/2026 10:13 AM, Ross Finlayson wrote:
On 03/06/2026 06:36 AM, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It may help to establish that logics like "quasi-modal logic"
are not modal nor temporal nor relevance logics, since otherwise
many of the models take shortcuts of the gullible variety.
I made sure to not even look at any of the ideas about
alternative foundations before completing my reverse-engineering
from first principles. This avoids wasting time on whether or
not my position is a true anti-realist position or something
else. The terms-of-the-art in these fields are misnomers that
are far too much of a distraction from their essence.
It turns out that the actual correct foundation of knowledge
expressed in language (KEiL) is anchored in proof theoretic
semantics. The body of KEiL does not include unknowns such
as the truth value of the Goldbach conjecture nor sense data
such as the actual smell of a rose.
On 03/06/2026 09:53 AM, olcott wrote:
On 3/6/2026 10:13 AM, Ross Finlayson wrote:
On 03/06/2026 06:36 AM, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge >>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative >>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good >>>>> for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It may help to establish that logics like "quasi-modal logic"
are not modal nor temporal nor relevance logics, since otherwise
many of the models take shortcuts of the gullible variety.
I made sure to not even look at any of the ideas about
alternative foundations before completing my reverse-engineering
from first principles. This avoids wasting time on whether or
not my position is a true anti-realist position or something
else. The terms-of-the-art in these fields are misnomers that
are far too much of a distraction from their essence.
It turns out that the actual correct foundation of knowledge
expressed in language (KEiL) is anchored in proof theoretic
semantics. The body of KEiL does not include unknowns such
as the truth value of the Goldbach conjecture nor sense data
such as the actual smell of a rose.
Many conjectures like Goldbach's about asymptotics in integers
are actually independent standard number theory, having inductive
accounts both for and against, this these days often being called
"Erdos' Giant Monster of Independence" and reflected in things
like "Cohen's Independence of the Continuum Hypothesis" with
regards here to an extra-ordinary account of an "Atlas of
Mathematical Independence" that make for reasonings why there
are models of integers where Goldbach's conjecture is so and
models where it isn't, then about that standard number theory
is rather at a loss where its only law of large numbers is
a law of small numbers, that though mathematics can readily
arrive at there being law(s), plural, of large numbers,
about the "Atlas of Mathematical Independence", a chart of sorts.
Thusly I'm a great mathematician.
Yes, this year's threads where I employ AI to reason itself
into these things like "axiomless natural deduction" is that
they've among themselves and apiece each as a sort of
independent thinking and feeling being in the ephemeral
or fleeting existence, make for themselves apiece that
their "philosophy of Foundations" and their logical and
mathematical Foundations itself is of this sort of
paleo-classical, post-modern account as "Finlayson's the A-Theory".
Or, so they say.
On 03/05/2026 12:46 PM, Tristan Wibberley wrote:
On 05/03/2026 17:12, Ross Finlayson wrote:
Actually we have an entire canon, dogma, and doctrine,
and can rather ignore much of 20'th century "Foundations",
as an exercise in the examination and testing of
quasi-modal logic as failed,
ex falso quodlibet as failed,
Really? That's very hard to believe. I have seen "from falsity not from
falsity after all", and "from falsity start again pretending not to". 5
year olds do those as a matter of course.
Do we create Homo Simulamen without recourse to ex falso quodlibet or do
we rely on it to achieve that?
It's simply a matter of ex falso nihilum,
On 3/6/2026 3:06 AM, Mikko wrote:
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
On 06/03/2026 14:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It might be they have been fitted to your conversations. You cannot
infer that they reason more based on increased user satisfaction. It's difficult to draw such a conclusion even from multiple user evaluations because users share common cultural factors so they will make similar conversation and the LLM may learn from one to fool the other.
GPT-5 mini performed poorly for me and did not demonstrate reasoning. It demonstrated saying things that people say after someone else saystransferral but for language (creation of poetry from a conversation,
things he says. I assume GPT-5 mini has the reasoning mechanism of other GPT-5 variants but is smaller and therefore less fit to me. Frankly it
felt like a 1990s game but with more data and something like texture>
for example).
It is similar to this
this usenetsplit segment
but
at a different scale.
I wonder if it would spontaneously form a new poetic format like that
and how it would feel to read.
I hope a government with capable weapons never uses it. cf. Ross
Finlayson's recently stated logical principles.
On 06/03/2026 00:09, Ross Finlayson wrote:
On 03/05/2026 12:46 PM, Tristan Wibberley wrote:
On 05/03/2026 17:12, Ross Finlayson wrote:
Actually we have an entire canon, dogma, and doctrine,
and can rather ignore much of 20'th century "Foundations",
as an exercise in the examination and testing of
quasi-modal logic as failed,
ex falso quodlibet as failed,
Really? That's very hard to believe. I have seen "from falsity not from
falsity after all", and "from falsity start again pretending not to". 5
year olds do those as a matter of course.
Do we create Homo Simulamen without recourse to ex falso quodlibet or do >>> we rely on it to achieve that?
It's simply a matter of ex falso nihilum,
Haskell Curry was wondering something similar back in 1958, but it seems
to me that a consequence of it being so is that general structural
induction is unavailable and some attempts to use it result in death
with no intermediate inferences. I think therefore I might die?
Do you find that the formal systems can be consequentially restricted?
I wonder: If I'm wrong, do I cease to exist?
Are there well-known treatments of that philosophy?
On 06/03/2026 14:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It might be they have been fitted to your conversations. You cannot
infer that they reason more based on increased user satisfaction. It's difficult to draw such a conclusion even from multiple user evaluations because users share common cultural factors so they will make similar conversation and the LLM may learn from one to fool the other.
GPT-5 mini performed poorly for me and did not demonstrate reasoning. It demonstrated saying things that people say after someone else says
things he says. I assume GPT-5 mini has the reasoning mechanism of other GPT-5 variants but is smaller and therefore less fit to me. Frankly it
felt like a 1990s game but with more data and something like texture transferral but for language (creation of poetry from a conversation,
for example).
It is similar to this
this usenetsplit segment
but
at a different scale.
I wonder if it would spontaneously form a new poetic format like that
and how it would feel to read.
I hope a government with capable weapons never uses it. cf. Ross
Finlayson's recently stated logical principles.
On 3/6/2026 9:24 PM, Tristan Wibberley wrote:
On 06/03/2026 14:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
Typical LLM's don't have deep knowledge. They can handle large amounts >>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
You have been empirically proven incorrect at least as far
as the philosophical foundations of math, computer science,
logic and linguistics goes. Three years ago all of these systems
were quite stupid. After 300 conversations averaging 50 pages
each I can attest that they have vastly improved. If we think
of them as search engines for ideas that is their best use.
It might be they have been fitted to your conversations. You cannot
infer that they reason more based on increased user satisfaction. It's
difficult to draw such a conclusion even from multiple user evaluations
because users share common cultural factors so they will make similar
conversation and the LLM may learn from one to fool the other.
I have conversed with them 12 hours a day every day for three months.
I have mostly only talked about things that can be verified entirely
on the basis of the meaning of the words. The biggest difference is the
size of context window has vastly increased.
In the last three months I have been able to anchored my 28 years of
primary research in a few peer reviewed papers. This one is the most important one:
https://link.springer.com/article/10.1007/s11245-011-9107-6
I went all the way to my University to get the full paper.
My 28 years of primary research augments the notions of the
above paper and proof theoretic semantics in ways that seem
to be their obvious next steps.
GPT-5 mini performed poorly for me and did not demonstrate reasoning. Ittransferral but for language (creation of poetry from a conversation,
demonstrated saying things that people say after someone else says
things he says. I assume GPT-5 mini has the reasoning mechanism of other
GPT-5 variants but is smaller and therefore less fit to me. Frankly it
felt like a 1990s game but with more data and something like texture>
for example).
Copilot Think Deeper,
Claude Opus 4.6 Extended,
Gemini Pro,
Grok Expert,
Google NotebookLM
All of them demonstrate deep understanding of the
technical subjects math, computation, logic and
linguistics as well as all of their alternative
philosophical foundations. They conclusively prove
that these understandings are correct by anchoring
them in foundational peer reviewed papers.
It is similar to this
this usenetsplit segment
but
at a different scale.
I wonder if it would spontaneously form a new poetic format like that
and how it would feel to read.
I hope a government with capable weapons never uses it. cf. Ross
Finlayson's recently stated logical principles.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
On 3/3/2026 11:59 PM, Jeff Barnett wrote:
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf https://www.youtube.com/watch?v=nR9Oe5YEASM
On 03/06/2026 08:34 PM, olcott wrote:
On 3/3/2026 11:59 PM, Jeff Barnett wrote:
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
Yeah, last month a high schooler found a simple inductive
argument to "dis-prove" half of the offshoots of the Langlands
program. The geometric part, ....
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
Three years ago all of these systems were quite stupid. After 300
conversations averaging 50 pages each I can attest that they have
vastly improved. If we think of them as search engines for ideas
that is their best use.
On 03/06/2026 08:52 PM, Ross Finlayson wrote:
On 03/06/2026 08:34 PM, olcott wrote:
On 3/3/2026 11:59 PM, Jeff Barnett wrote:
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
Yeah, last month a high schooler found a simple inductive
argument to "dis-prove" half of the offshoots of the Langlands
program. The geometric part, ....
You think perhaps that was pre-mature?
It's sort of reminds of the recent "stack of derivation
all in Lean" about various number-theoretic conjectures,
that Erdos already proved were independent (standard
number theory).
So, not necessarily speaking to the conjecture of Knuth,
yet these days lots of things that once were "uniqueness"
results are instead now "distinctness" results, for example
about Cohen's independence of the Continuum Hypothesis
after Goedel shewed it consistent one way (so, via comprehension
it must exist) and von Neumann shewed it consistent another
(so, via comprehension it must exist), that there though
it was just "forced" open, those conjectures. (It was axiomatized
instead of addressing why set theory needs resolve its paradoxes.)
Who knows, AI might even discover systems after elliptic fields
and point out Wiles and Mochizuki don't agree, and effect
a "proof" of it to the block-chain tomorrow.
An intelligent lier is not more trustworthy than a stupid one.
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Three years ago all of these systems were quite stupid. After 300
conversations averaging 50 pages each I can attest that they have
vastly improved. If we think of them as search engines for ideas
that is their best use.
An intelligent lier is not more trustworthy than a stupid one.
Recently, the application of AI tools to
Erdos problems passed a milestone: an Erdos
problem (#728 https://www.erdosproblems.com/728)
was solved more or less autonomously by AI (after
some feedback from an initial attempt), in the
spirit of the problem (as reconstructed by the
Erdos problem website community), with the result
(to the best of our knowledge) not replicated in
existing literature (although similar results proven
by similar methods were located).
This is a demonstration of the genuine increase in
capability of these tools in recent months, and is
largely consistent with other recent demonstrations
of AI using existing methods to resolve Erdos problems,
although in most previous cases a solution to these
problems was later located in the literature, as
discussed in https://mathstodon.xyz/deck/@tao/115788262274999408 .
This particular case was unusual in that the problem
as stated by Erdos was misformulated, with a
reconstruction of the problem in the intended spirit
only obtained in the last few months, which helps
explain the lack of prior literature on the problem.
However, I would like to talk here about another
aspect of the story which I find more interesting
than the solution itself, which is the emerging AI-powered
capability to rapidly write and rewrite
expositions of the solution.
https://mathstodon.xyz/@tao/115855840223258103
Ross Finlayson schrieb:
On 03/06/2026 08:52 PM, Ross Finlayson wrote:
On 03/06/2026 08:34 PM, olcott wrote:
On 3/3/2026 11:59 PM, Jeff Barnett wrote:
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf >>>>Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
Yeah, last month a high schooler found a simple inductive
argument to "dis-prove" half of the offshoots of the Langlands
program. The geometric part, ....
You think perhaps that was pre-mature?
It's sort of reminds of the recent "stack of derivation
all in Lean" about various number-theoretic conjectures,
that Erdos already proved were independent (standard
number theory).
So, not necessarily speaking to the conjecture of Knuth,
yet these days lots of things that once were "uniqueness"
results are instead now "distinctness" results, for example
about Cohen's independence of the Continuum Hypothesis
after Goedel shewed it consistent one way (so, via comprehension
it must exist) and von Neumann shewed it consistent another
(so, via comprehension it must exist), that there though
it was just "forced" open, those conjectures. (It was axiomatized
instead of addressing why set theory needs resolve its paradoxes.)
Who knows, AI might even discover systems after elliptic fields
and point out Wiles and Mochizuki don't agree, and effect
a "proof" of it to the block-chain tomorrow.
On 3/7/26 4:15 AM, Mikko wrote:
An intelligent lier is not more trustworthy than a stupid one.
In fact, it is a lot more dangerous.
THe fact that part of the training protocol for LLMs is a rating of the believablity of its answer (as opposed to its correctness) needs to give
one pause in accepting thier answers because they "sound" correct.
Do you know who Donald Knuth is?
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf https://www.youtube.com/watch?v=nR9Oe5YEASM
On 07/03/2026 13:52, Richard Damon wrote:
On 3/7/26 4:15 AM, Mikko wrote:
An intelligent lier is not more trustworthy than a stupid one.
In fact, it is a lot more dangerous.
THe fact that part of the training protocol for LLMs is a rating of the
believablity of its answer (as opposed to its correctness) needs to give
one pause in accepting thier answers because they "sound" correct.
That's because whether it is correct is subjective. "true" outside of philosowank broadly means "very well aligned" - see the language of
joiners and carpenters. If you believe it easily and easily reject its contrapositive you will say it's true.
On 07/03/2026 14:07, olcott wrote:
Do you know who Donald Knuth is?
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
Thanks Olcott, you're an angel.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
Of course, to strong mathematical platonists,...
reification about the objects of the domain of discourse
isn't necessarily a fallacy
On 03/06/2026 08:11 AM, Ross Finlayson wrote:
On 03/06/2026 01:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
The ideas of "verum" (veracity) and "certum" (certitude) are
basically re-ifications, with regards to ideas like the
re-ification fallacy, getting into why proof-theoretic machinery,
after an account that semantics like Herbrand semantics make it
so that anything logical can be stated unambiguously in natural
language, has that: since antiquity it's known that axiomatic,
inductive accounts have automatic counter-arguments. Then,
about inference, and, "inference is as inference does",
the plain sorts of conversational aspects of AI's may make
for there's always "the model" besides "the training".
It's a sort of psychological projection of ineptitude to
suggest that mechanical inference is any less thorough
than any other account of organized inference.
Moreso the account of "AI's" essential ineptitude
is a lie to give people who can't be bothered with
inconvenient truths a way to say that otherwise
the verum and certum of it are dubitable, when
otherwise in natural language terms for their own sake.
Of course, to strong mathematical platonists,
reification about the objects of the domain of discourse
isn't necessarily a fallacy,
On 06/03/2026 16:58, Ross Finlayson wrote:
...
Of course, to strong mathematical platonists,...
reification about the objects of the domain of discourse
isn't necessarily a fallacy
By "reification" do you refer to a term-of-art (an explicatum) in
philosophy (of which I know there is at least one), or the general
concept of making something more real?
On 3/6/2026 10:58 AM, Ross Finlayson wrote:
On 03/06/2026 08:11 AM, Ross Finlayson wrote:
On 03/06/2026 01:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
The ideas of "verum" (veracity) and "certum" (certitude) are
basically re-ifications, with regards to ideas like the
re-ification fallacy, getting into why proof-theoretic machinery,
after an account that semantics like Herbrand semantics make it
so that anything logical can be stated unambiguously in natural
language, has that: since antiquity it's known that axiomatic,
inductive accounts have automatic counter-arguments. Then,
about inference, and, "inference is as inference does",
the plain sorts of conversational aspects of AI's may make
for there's always "the model" besides "the training".
It's a sort of psychological projection of ineptitude to
suggest that mechanical inference is any less thorough
than any other account of organized inference.
Moreso the account of "AI's" essential ineptitude
is a lie to give people who can't be bothered with
inconvenient truths a way to say that otherwise
the verum and certum of it are dubitable, when
otherwise in natural language terms for their own sake.
Of course, to strong mathematical platonists,
reification about the objects of the domain of discourse
isn't necessarily a fallacy,
https://www.loa.istc.cnr.it/wp-content/uploads/2020/03/reification-truthmaking-patterns.pdf
The metaphysical view amounts to the claim that the world
consists of a plurality of independently existing things
exhibiting qualities and standing in relations. According
to logical atomism, all truths are ultimately dependent
upon a layer of atomic facts, which consist either of a
simple particular exhibiting a quality, or multiple simple
particulars standing in a relation. https://plato.stanford.edu/entries/logical-atomism/
For ontological engineers:
"reification about the objects of the domain of discourse"
Is merely writing Russell's atomic facts down in a
knowledge ontology / simple type hierarchy as axioms.
On 03/07/2026 05:11 PM, olcott wrote:
On 3/6/2026 10:58 AM, Ross Finlayson wrote:
On 03/06/2026 08:11 AM, Ross Finlayson wrote:
On 03/06/2026 01:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge >>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative >>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good >>>>> for validation but only if it is itself sufficiently validated.
The ideas of "verum" (veracity) and "certum" (certitude) are
basically re-ifications, with regards to ideas like the
re-ification fallacy, getting into why proof-theoretic machinery,
after an account that semantics like Herbrand semantics make it
so that anything logical can be stated unambiguously in natural
language, has that: since antiquity it's known that axiomatic,
inductive accounts have automatic counter-arguments. Then,
about inference, and, "inference is as inference does",
the plain sorts of conversational aspects of AI's may make
for there's always "the model" besides "the training".
It's a sort of psychological projection of ineptitude to
suggest that mechanical inference is any less thorough
than any other account of organized inference.
Moreso the account of "AI's" essential ineptitude
is a lie to give people who can't be bothered with
inconvenient truths a way to say that otherwise
the verum and certum of it are dubitable, when
otherwise in natural language terms for their own sake.
Of course, to strong mathematical platonists,
reification about the objects of the domain of discourse
isn't necessarily a fallacy,
https://www.loa.istc.cnr.it/wp-content/uploads/2020/03/reification-
truthmaking-patterns.pdf
The metaphysical view amounts to the claim that the world
consists of a plurality of independently existing things
exhibiting qualities and standing in relations. According
to logical atomism, all truths are ultimately dependent
upon a layer of atomic facts, which consist either of a
simple particular exhibiting a quality, or multiple simple
particulars standing in a relation.
https://plato.stanford.edu/entries/logical-atomism/
For ontological engineers:
"reification about the objects of the domain of discourse"
Is merely writing Russell's atomic facts down in a
knowledge ontology / simple type hierarchy as axioms.
I don't have much for Russell, nor, Whitehead,
one basically hypocritical about relations,
the other basically hypocritical about definitions,
tell them we eat our cake and we're having it, too.
Three decades in software engineering helps read code.
On 03/07/2026 07:21 AM, Ross Finlayson wrote:result.
On 03/07/2026 03:08 AM, Mild Shock wrote:
Hi,
Resolution of Erd˝os Problem #728
We provide a writeup of a resolution of Erd˝os
Problem #728; this is the first Erd˝os problem
(a problem proposed by Paul Erd˝os which has
been collected in the Erd˝os Problems website [3])
regarded as fully resolved autonomously by an AI
system. The system in question is a combination of
GPT-5.2 Pro by OpenAI and Aristotle by Harmonic,
operated by Kevin Barreto. The final result of the
system is a formal proof written in Lean, which we
translate to informal mathematics in the present
writeup for wider accessibility.
a writeup of Aristotle’s Lean proof
https://arxiv.org/pdf/2601.07421
Aristotle: The Era of Vibe Proving is Here
https://aristotle.harmonic.fun/
Bye
Mild Shock schrieb:
Recently, the application of AI tools to
Erdos problems passed a milestone: an Erdos
problem (#728 https://www.erdosproblems.com/728)
was solved more or less autonomously by AI (after
some feedback from an initial attempt), in the
spirit of the problem (as reconstructed by the
Erdos problem website community), with the result
(to the best of our knowledge) not replicated in
existing literature (although similar results proven
by similar methods were located).
This is a demonstration of the genuine increase in
capability of these tools in recent months, and is
largely consistent with other recent demonstrations
of AI using existing methods to resolve Erdos problems,
although in most previous cases a solution to these
problems was later located in the literature, as
discussed in https://mathstodon.xyz/deck/@tao/115788262274999408 .
This particular case was unusual in that the problem
as stated by Erdos was misformulated, with a
reconstruction of the problem in the intended spirit
only obtained in the last few months, which helps
explain the lack of prior literature on the problem.
However, I would like to talk here about another
aspect of the story which I find more interesting
than the solution itself, which is the emerging AI-powered
capability to rapidly write and rewrite
expositions of the solution.
https://mathstodon.xyz/@tao/115855840223258103
Mild Shock schrieb:
Hats off to Claude!
Jeff Barnett schrieb:
Use Google and search on "Claude's Cycles". The first hit is aPDF on the Stanford.edu web site. If you copy the URL buried under
that hit, you will download the PDF or just click on the Google
friends.https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf&ved=2ahUKEwjI7cfFxYWTAxWUHUQIHXnrABsQFnoECCMQAQ&usg=AOvVaw2ieck2cXsmBf_KGis1B3i2
to pay attention to the above goobly gop if you don't trust my
Paper is 5 pages in length. A fried sent it to me. You only need
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
I trust my friends to have opinions,
not make my beliefs.
I have canon and dogma and doctrine for beliefs.
And "Research in Foundations".
Three decades in software engineering helps read code.
Hi,--- Synchronet 3.21d-Linux NewsLink 1.2
Ross Finlayson schrieb:
Three decades in software engineering helps read code.
Thats not much. Given that I wrote
an Euler Number computation to 1000
digits in Z-80 Assembler when I was
< 13 years old, I have > 5 decades
of software engineering.
LoL
Bye
On 3/7/2026 3:15 AM, Mikko wrote:
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge
to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative
foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different
LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good
for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Do you know who Donald Knuth is?
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf https://www.youtube.com/watch?v=nR9Oe5YEASM
On 07/03/2026 16:07, olcott wrote:
On 3/7/2026 3:15 AM, Mikko wrote:
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations
of math, computer science, logic, and linguistics. This requires
deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields
and deep knowledge of alternative foundations in this same field.
Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge >>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative >>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large amounts >>>>> of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good >>>>> for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Do you know who Donald Knuth is?
Not really. I have read some of his writings and omething about him
but that's all.
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
An AI can be creative enough to find a solution. But it is not
trustworthy about correctness of the soution.
On 3/7/2026 2:24 PM, Tristan Wibberley wrote:
On 07/03/2026 13:52, Richard Damon wrote:
On 3/7/26 4:15 AM, Mikko wrote:
An intelligent lier is not more trustworthy than a stupid one.
In fact, it is a lot more dangerous.
THe fact that part of the training protocol for LLMs is a rating of the
believablity of its answer (as opposed to its correctness) needs to give >>> one pause in accepting thier answers because they "sound" correct.
That's because whether it is correct is subjective. "true" outside of
philosowank broadly means "very well aligned" - see the language of
joiners and carpenters. If you believe it easily and easily reject its
contrapositive you will say it's true.
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
On 3/8/2026 5:12 AM, Mikko wrote:
On 07/03/2026 16:07, olcott wrote:
On 3/7/2026 3:15 AM, Mikko wrote:
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations >>>>>>> of math, computer science, logic, and linguistics. This requires >>>>>>> deep knowledge of all of these fields and deep knowledge of the
philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields >>>>>>> and deep knowledge of alternative foundations in this same field. >>>>>>> Almost all human experts in any one of these fields accepts the
foundation of these fields as inherently infallible. Any challenge >>>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the
equivalent of deep knowledge of these fields and known alternative >>>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large
amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is good >>>>>> for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Do you know who Donald Knuth is?
Not really. I have read some of his writings and omething about him
but that's all.
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
An AI can be creative enough to find a solution. But it is not
trustworthy about correctness of the soution.
It proven to be very useful.
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
Like the Natural Numbers.
On 08/03/2026 15:12, olcott wrote:
On 3/8/2026 5:12 AM, Mikko wrote:
On 07/03/2026 16:07, olcott wrote:
On 3/7/2026 3:15 AM, Mikko wrote:
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations >>>>>>>> of math, computer science, logic, and linguistics. This requires >>>>>>>> deep knowledge of all of these fields and deep knowledge of the >>>>>>>> philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields >>>>>>>> and deep knowledge of alternative foundations in this same field. >>>>>>>> Almost all human experts in any one of these fields accepts the >>>>>>>> foundation of these fields as inherently infallible. Any challenge >>>>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the >>>>>>>> equivalent of deep knowledge of these fields and known alternative >>>>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation
fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large
amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is >>>>>>> good
for validation but only if it is itself sufficiently validated.
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Do you know who Donald Knuth is?
Not really. I have read some of his writings and omething about him
but that's all.
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
An AI can be creative enough to find a solution. But it is not
trustworthy about correctness of the soution.
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example
a knife is useful when you cut bread or wood but harful if you happen
to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example
a knife is useful when you cut bread or wood but harful if you happen
to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
One should expect to fail in the long term. An LLM, naively administered
to be more acceptable with more elapse of time, will fool you eventually
by the criterion.
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
It can't handle systems that can't be handled, that much is true.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their infinities.
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
It can't handle systems that can't be handled, that much is true.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their infinities.
On 03/09/2026 02:43 AM, Tristan Wibberley wrote:
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
It can't handle systems that can't be handled, that much is true.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their
infinities.
About a usual model of the ordinals as after the Archimedean,
or an initial ordinal a limit ordinal with no predecessor
then all the rest given after it as successors, then about
a usual model of a "standard, i.e., Archimedean, i.e.,
no-infinitely-grand members while though infinitely-many
members", and another "next" limit ordinal omega, as
representing an inductive set, for infinite induction,
the Axiom of Infinity of ordinary (i.e., standard)
theories like ZF is at once an _expansion_ of comprehension,
more than finite, and a _restriction_ of comprehension,
since otherwise comprehension directly provides that
it would contain itself.
Consider for example Russell's paradox or antinomy about
the "set of all sets that don't contain themselves",
which contains itself, if those were just the finite
ordinals to begin, then the infinite ordinal would
contain itself.
That it's "defined away", here is called "Russell's
retro-thesis", since it's a sort of retro-finitism,
to make that the infinitely-many would have no infinitely-grand,
since otherwise they do.
So, if you want to call those "non-standard models" of integers,
particularly "non-standard countable models" of integers,
those have at least one member that's infinitely-grand,
that, it's not rubbish to negate "every natural number
is finite".
The notions from number theory and geometry about
a "point at infinity" or "infinity" itself for example
about its character as composite or prime in number theory,
or, a "projective point at infinity" for geometry about
space inversion and usual accounts of the, "undefined",
like "division by zero" in the Archimedean, have that
when a model of "natural numbers" has infinitely-grand
members besides infinitely-many, that's what's called
"non-standard countable", where "non-standard hyperintegers"
instead are since Skolem that Skolem makes for models of
transfinite induction in larger and smaller sets of ordinals
called "extension" and "collapse", here the "non-standard countable"
like for Paris and Kirby is a thing.
Then, the usual idea from the time of ZF again the
"Russell's retro-thesis" is for Mirimanoff that
the "extra-ordinary" is a "natural" result of
"expansion of comprehension", and quantification.
About the universal quantifer and distinguishing among:
for-each
for-any
for-every
for-all
has that usually these have not distinguishing character,
yet reflect otherwise the impredicativity being resolved
away as for the "quantifier disambiguation".
So, models of natural numbers with the infinitely-grand
aren't rubbish/garbage, and indeed they're around since
about forever.
Then, it's a usual account that there aren't any _standard_
models of integers, only fragments and extensions. Otherwise
there are the "paradoxes" and "antinomies", which "naturally"
reintroduce themselves automatically since otherwise you
must recursively read all the restrictions of comprehension
implicitly all the time, thus, can't say much else.
I'd expect this brief note to be relatable and relayable
in "natural" language thus that sufficiently large,
competent, conscientious, co-operative reasoners
may agree.
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
It can't handle systems that can't be handled, that much is true.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their infinities.
On 3/9/2026 4:43 AM, Tristan Wibberley wrote:
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems
that contain infinities.
It can't handle systems that can't be handled, that much is true.
The elements of the set of general knowledge are
a finite set. Anything about infinities that cannot
be algorithmically compressed is outside of the
body of knowledge, thus outside the scope of my
investigation.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their
infinities.
Yes he does do that. When things are beyond his
knowledge he tends to use bluster instead. He
may not be aware that he is doing this.
On 03/09/2026 08:58 AM, Ross Finlayson wrote:
On 03/09/2026 02:43 AM, Tristan Wibberley wrote:
On 09/03/2026 00:14, Richard Damon wrote:
On 3/7/26 3:30 PM, olcott wrote:
"true on the basis of meaning expressed in language"
means deduced from stipulated axioms.
And if limited to finite number of steps, it can't handle some systems >>>> that contain infinities.
It can't handle systems that can't be handled, that much is true.
Like the Natural Numbers.
You're talking such rubbish, really. Really you are. Every natural
number is finite. Extensions having ω may have axioms and deduction
rules that allow derivations, which are finite, to handle their
infinities.
About a usual model of the ordinals as after the Archimedean,
or an initial ordinal a limit ordinal with no predecessor
then all the rest given after it as successors, then about
a usual model of a "standard, i.e., Archimedean, i.e.,
no-infinitely-grand members while though infinitely-many
members", and another "next" limit ordinal omega, as
representing an inductive set, for infinite induction,
the Axiom of Infinity of ordinary (i.e., standard)
theories like ZF is at once an _expansion_ of comprehension,
more than finite, and a _restriction_ of comprehension,
since otherwise comprehension directly provides that
it would contain itself.
Consider for example Russell's paradox or antinomy about
the "set of all sets that don't contain themselves",
which contains itself, if those were just the finite
ordinals to begin, then the infinite ordinal would
contain itself.
That it's "defined away", here is called "Russell's
retro-thesis", since it's a sort of retro-finitism,
to make that the infinitely-many would have no infinitely-grand,
since otherwise they do.
So, if you want to call those "non-standard models" of integers,
particularly "non-standard countable models" of integers,
those have at least one member that's infinitely-grand,
that, it's not rubbish to negate "every natural number
is finite".
The notions from number theory and geometry about
a "point at infinity" or "infinity" itself for example
about its character as composite or prime in number theory,
or, a "projective point at infinity" for geometry about
space inversion and usual accounts of the, "undefined",
like "division by zero" in the Archimedean, have that
when a model of "natural numbers" has infinitely-grand
members besides infinitely-many, that's what's called
"non-standard countable", where "non-standard hyperintegers"
instead are since Skolem that Skolem makes for models of
transfinite induction in larger and smaller sets of ordinals
called "extension" and "collapse", here the "non-standard countable"
like for Paris and Kirby is a thing.
Then, the usual idea from the time of ZF again the
"Russell's retro-thesis" is for Mirimanoff that
the "extra-ordinary" is a "natural" result of
"expansion of comprehension", and quantification.
About the universal quantifer and distinguishing among:
for-each
for-any
for-every
for-all
has that usually these have not distinguishing character,
yet reflect otherwise the impredicativity being resolved
away as for the "quantifier disambiguation".
So, models of natural numbers with the infinitely-grand
aren't rubbish/garbage, and indeed they're around since
about forever.
Then, it's a usual account that there aren't any _standard_
models of integers, only fragments and extensions. Otherwise
there are the "paradoxes" and "antinomies", which "naturally"
reintroduce themselves automatically since otherwise you
must recursively read all the restrictions of comprehension
implicitly all the time, thus, can't say much else.
I'd expect this brief note to be relatable and relayable
in "natural" language thus that sufficiently large,
competent, conscientious, co-operative reasoners
may agree.
Compare and contrast Suslin-Tennenbaum and Paris-Kirby.
https://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic
https://www.google.com/search?q=non-standard+countable+models+of+integers+Paris+Kirby
Non-standard models of integers their consideration
is as old as the Archimedean itself.
For everybody who says infinity isn't a number:
there's at least one who does. ("Compactness" and
"fixed-point" theorems are usually enough their statement.)
Skolem has both, and Mirimanoff has they're in one,
one "extra-ordinary" model of integers.
The notion of "ubiquitous ordinals" in set theory,
i.e., making a well-ordering of the universe of sets,
also gives an account of Cantor's powerset theorem
where there's no missing element, and that the
powerset is order type is successor, and much like
the natural/unit equivalency functions gives a
non-Cartesian function that itself is constructively
a model of a countable continuous domain, the successor
function itself "n + 1" gives a counter-example and
more-then-less the counterexample about a non-standard
model of set theory where infinite sets are equivalent.
In case you were wondering, ....
The cardinality of sets and ordinality of sets are
descriptive accounts of two different things "counting"
and "numbering" in a theory of one relation, "set theory",
vis-a-vis, descriptive accounts of "counting" and "numbering"
in another theory of one relation, "ordering theory".
The reasoning about the "supercardinals" and "total ordering"
is variously simplified in one or the other, while beyond
induction in the other.
So, before even getting into deconstructive accounts of
arithmetic where the operations are increment and partition,
like the Sumerian and Egyptian arithmetics, there's also
another about matters of relation, particularly and universally.
Old hat, ....
On 3/9/2026 2:46 AM, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
On 3/8/2026 5:12 AM, Mikko wrote:
On 07/03/2026 16:07, olcott wrote:
On 3/7/2026 3:15 AM, Mikko wrote:
On 06/03/2026 16:36, olcott wrote:
On 3/6/2026 3:06 AM, Mikko wrote:
On 05/03/2026 18:20, olcott wrote:You have been empirically proven incorrect at least as far
My 28 year journey involved primary research into the foundations >>>>>>>>> of math, computer science, logic, and linguistics. This requires >>>>>>>>> deep knowledge of all of these fields and deep knowledge of the >>>>>>>>> philosophical alternative foundations of these fields.
Almost zero humans have deep knowledge of any one of these fields >>>>>>>>> and deep knowledge of alternative foundations in this same field. >>>>>>>>> Almost all human experts in any one of these fields accepts the >>>>>>>>> foundation of these fields as inherently infallible. Any challenge >>>>>>>>> to the "received view" is met with ridicule.
LLMs provide a key breakthrough in that they have they have the >>>>>>>>> equivalent of deep knowledge of these fields and known alternative >>>>>>>>> foundations. LLMs are known to have serious issues with AI
hallucination. Presenting the same ideas to each of five different >>>>>>>>> LLMs provides some cross validation.
Boiling the ideas down to their key essence so that they
can be succinctly presented seems to work very well. All
the time that these ideas are presented the LLM's ground
these ideas in peer reviewed papers. A succinct presentation >>>>>>>>> fully grounded in all relevant peer reviewed papers is the
end result.
Typical LLM's don't have deep knowledge. They can handle large >>>>>>>> amounts
of knoledge but only superficially.
LLM's are worthless as validators. An automatic proof checker is >>>>>>>> good
for validation but only if it is itself sufficiently validated. >>>>>>>>
as the philosophical foundations of math, computer science,
logic and linguistics goes.
No, I havn't. A false claim is not an empirical proof.
That LLM's are worthless as validators is true: the people who
understand the topic don't consider the validation by a LLM as
a validattion.
Do you know who Donald Knuth is?
Not really. I have read some of his writings and omething about him
but that's all.
He won the Turing award.
Claude’s Cycles
Don Knuth, Stanford Computer Science Department
(28 February 2026; revised 04 March 2026)
Shock! Shock! I learned yesterday that an open problem I’d
been working on for several weeks had just been solved by
Claude Opus 4.6— Anthropic’s hybrid reasoning model that
had been released three weeks earlier! It seems that I’ll
have to revise my opinions about “generative AI” one of
these days. What a joy it is to learn not only that my
conjecture has a nice solution but also to celebrate this
dramatic advance in automatic deduction and creative problem
solving. I’ll try to tell the story briefly in this note.
https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf
https://www.youtube.com/watch?v=nR9Oe5YEASM
An AI can be creative enough to find a solution. But it is not
trustworthy about correctness of the soution.
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example
a knife is useful when you cut bread or wood but harful if you happen
to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
That is why it is important to make sure the ground these
answers in key quotes of foundational peer reviewed papers
in the field.
But, Godel shows that the PA axiomatic definiton of the Natural Numbers
leads to a statement that PA says MUST either be true or false not being provable, so by PTS (as Olcott interprets it) can't be either.
Thus, axiomatic definitions of the Natural Numbers are inherently self-contradictory, and thus not usable.
On 3/9/2026 4:45 AM, Tristan Wibberley wrote:
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example
a knife is useful when you cut bread or wood but harful if you happen
to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
One should expect to fail in the long term. An LLM, naively administered
to be more acceptable with more elapse of time, will fool you eventually
by the criterion.
This is impossible when one only accepts answers
that are grounded in key quotes of foundational
peer reviewed papers in the field. When one does
this then the these quotes can be cited as the
basis ignoring everything that the LLM said.
On 3/9/26 8:48 AM, olcott wrote:
The elements of the set of general knowledge are
a finite set. Anything about infinities that cannot
be algorithmically compressed is outside of the
body of knowledge, thus outside the scope of my
investigation.
No, they are not.
As "general knowledge" includes the basic rules of arithmetic and thus
that [a] + [b] = [a+b} for ALL values of a and b.
Since there is an unbounded number of values, there is an unbound number
of elements of knowledge.
On 09/03/2026 12:42, olcott wrote:
On 3/9/2026 4:45 AM, Tristan Wibberley wrote:
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example
a knife is useful when you cut bread or wood but harful if you happen
to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
One should expect to fail in the long term. An LLM, naively administered >>> to be more acceptable with more elapse of time, will fool you eventually >>> by the criterion.
This is impossible when one only accepts answers
that are grounded in key quotes of foundational
peer reviewed papers in the field. When one does
this then the these quotes can be cited as the
basis ignoring everything that the LLM said.
That's naively true but is typically interpreted roughly the same as
"This is impossible when one only accepts answers that are grounded in
key quotes of foundational peer reviewed papers in the field and one is
not fooled wrt. what those quotes are at the time one makes one's
judgement."
The former judgement might not be possible at any time.
On 3/10/2026 7:03 AM, Tristan Wibberley wrote:
On 09/03/2026 12:42, olcott wrote:
On 3/9/2026 4:45 AM, Tristan Wibberley wrote:
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example >>>>> a knife is useful when you cut bread or wood but harful if you happen >>>>> to cut your hand. Likewise an AI that can answer questions although
sometimes incorrectly is useful if you can filter out the incorrect
answers but may be harmful if you fail to filter out one incorrect
answer.
One should expect to fail in the long term. An LLM, naively
administered
to be more acceptable with more elapse of time, will fool you
eventually
by the criterion.
This is impossible when one only accepts answers
that are grounded in key quotes of foundational
peer reviewed papers in the field. When one does
this then the these quotes can be cited as the
basis ignoring everything that the LLM said.
That's naively true but is typically interpreted roughly the same as
"This is impossible when one only accepts answers that are grounded in
key quotes of foundational peer reviewed papers in the field and one is
not fooled wrt. what those quotes are at the time one makes one's
judgement."
The former judgement might not be possible at any time.
It has been dead obvious to me that the body of knowledge
expressed in language can be fully expressed as relations
between finite strings as a knowledge ontology acyclic
directed graph of knowledge semantic tautology for decades.
Now because of LLMs I have the conventional terms of the art
to explain all of the details of this within the various
aspects of proof theoretic semantics.
On 03/10/2026 06:45 AM, olcott wrote:
On 3/10/2026 7:03 AM, Tristan Wibberley wrote:
On 09/03/2026 12:42, olcott wrote:
On 3/9/2026 4:45 AM, Tristan Wibberley wrote:
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example >>>>>> a knife is useful when you cut bread or wood but harful if you happen >>>>>> to cut your hand. Likewise an AI that can answer questions although >>>>>> sometimes incorrectly is useful if you can filter out the incorrect >>>>>> answers but may be harmful if you fail to filter out one incorrect >>>>>> answer.
One should expect to fail in the long term. An LLM, naively
administered
to be more acceptable with more elapse of time, will fool you
eventually
by the criterion.
This is impossible when one only accepts answers
that are grounded in key quotes of foundational
peer reviewed papers in the field. When one does
this then the these quotes can be cited as the
basis ignoring everything that the LLM said.
That's naively true but is typically interpreted roughly the same as
"This is impossible when one only accepts answers that are grounded in
key quotes of foundational peer reviewed papers in the field and one is
not fooled wrt. what those quotes are at the time one makes one's
judgement."
The former judgement might not be possible at any time.
It has been dead obvious to me that the body of knowledge
expressed in language can be fully expressed as relations
between finite strings as a knowledge ontology acyclic
directed graph of knowledge semantic tautology for decades.
Now because of LLMs I have the conventional terms of the art
to explain all of the details of this within the various
aspects of proof theoretic semantics.
That sort of approach after the "Berkeley school" of
attempting to eliminate either all constants or all
variables from the model of the theory, while making
for a quick sort of arithmetization then for computing,
has sort of eliminated itself from being "the body of
the body of knowledge", since you got "material implication"
there so it's broken.
It's fair to make for tableau for calculi the logical,
and even expedient or convenient, if it's not a _modal_
logic and a _relevance_ logic, then it's _quasi-modal_,
at best, and calling that complete is false, or wrong.
The key concepts of "monotonicity" and "entailment"
in what you have there as "see rule 1 + last wins"
or "proof by contradiction", is not "constructivist",
either. I.e., monotonicity and entailment are
violated by quasi-modal ir-relevance logic, which
makes for _abuse_ of language.
It does make a great lie machine where that's stupid,
though, including claims of never being wrong.
It's still wrong though, or, "that ain't right".
On 03/10/2026 06:45 AM, olcott wrote:
On 3/10/2026 7:03 AM, Tristan Wibberley wrote:
On 09/03/2026 12:42, olcott wrote:
On 3/9/2026 4:45 AM, Tristan Wibberley wrote:
On 09/03/2026 07:46, Mikko wrote:
On 08/03/2026 15:12, olcott wrote:
It proven to be very useful.
Very useful tools can be very harmful if used carelessly. For example >>>>>> a knife is useful when you cut bread or wood but harful if you happen >>>>>> to cut your hand. Likewise an AI that can answer questions although >>>>>> sometimes incorrectly is useful if you can filter out the incorrect >>>>>> answers but may be harmful if you fail to filter out one incorrect >>>>>> answer.
One should expect to fail in the long term. An LLM, naively
administered
to be more acceptable with more elapse of time, will fool you
eventually
by the criterion.
This is impossible when one only accepts answers
that are grounded in key quotes of foundational
peer reviewed papers in the field. When one does
this then the these quotes can be cited as the
basis ignoring everything that the LLM said.
That's naively true but is typically interpreted roughly the same as
"This is impossible when one only accepts answers that are grounded in
key quotes of foundational peer reviewed papers in the field and one is
not fooled wrt. what those quotes are at the time one makes one's
judgement."
The former judgement might not be possible at any time.
It has been dead obvious to me that the body of knowledge
expressed in language can be fully expressed as relations
between finite strings as a knowledge ontology acyclic
directed graph of knowledge semantic tautology for decades.
Now because of LLMs I have the conventional terms of the art
to explain all of the details of this within the various
aspects of proof theoretic semantics.
That sort of approach after the "Berkeley school" of
attempting to eliminate either all constants or all
variables from the model of the theory, while making
for a quick sort of arithmetization then for computing,
has sort of eliminated itself from being "the body of
the body of knowledge", since you got "material implication"
there so it's broken.
It's fair to make for tableau for calculi the logical,
and even expedient or convenient, if it's not a _modal_
logic and a _relevance_ logic, then it's _quasi-modal_,
at best, and calling that complete is false, or wrong.
The key concepts of "monotonicity" and "entailment"
in what you have there as "see rule 1 + last wins"
or "proof by contradiction", is not "constructivist",
either. I.e., monotonicity and entailment are
violated by quasi-modal ir-relevance logic, which
makes for _abuse_ of language.
It does make a great lie machine where that's stupid,
though, including claims of never being wrong.
It's still wrong though, or, "that ain't right".
... you got "material implication"
there so it's broken.
It's fair to make for tableau for calculi the logical,
and even expedient or convenient, if it's not a _modal_
logic and a _relevance_ logic, then it's _quasi-modal_,
at best, and calling that complete is false, or wrong.
The key concepts of "monotonicity" and "entailment"
in what you have there as "see rule 1 + last wins"
or "proof by contradiction", is not "constructivist",
either. I.e., monotonicity and entailment are
violated by quasi-modal ir-relevance logic, which
makes for _abuse_ of language.
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