Re: The proper way to use LLMs to aid primary research into foundations

On 3/6/2026 12:19 PM, Ross Finlayson wrote:

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

For my purposes this is irrelevant. The ONLY relevant thing
is that the truth value of the Goldbach conjecture is not an
element of the body of knowledge expressed in language.
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.

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.
 

--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable for the entire body of knowledge.<br><br>
This required establishing a new foundation<br>