On Mon, Jan 20, 2025 at 7:46 AM PGC <multiplecit...@gmail.com> wrote:
*> In truth, the “weakness” you ascribe to simpler formal systems—such as
> first-order logic without heavy axioms, or minimal forms of arithmetic—can
> lead to fascinating nonstandard models and subtle phenomena that arguably
> eclipse the raw computational yardstick you employ.*
>
*I don't understand why you put weakness in quotation marks, I make no
apology for calling First Order Logic weak. It's true that unlike Second
Order Logic, such as that employed in Zermelo–Fraenkel set theory, First
Order Logic CAN prove its own self consistency, and First Order Logic is
also complete, any grammatically correct logical statement can be proven or
disproven with first order logic. The problem is if you only used First
Order Logic then you couldn't pass a first grade arithmetic test, and
forget about algebra or calculus or number theory or topology. First Order
Logic is very good for some things but the range of its applicability is
extremely limited. *
> * > when you reduce mind-created constructs—especially those relating to
> numbers and formal proofs—to mere mechanisms,*
>
*I don't know what you mean by "mere" mechanism. The huge advancement in AI
over the last two years didn't come about by people who were navel gazing
and postulating about some mysterious secret sauce that produces mind,
instead they broke down the operation of a mind until they got to the
simplest possible part, and you can't get simpler than zero or one, that is
to say an on and off switch. They have provided definitive proof that like
it or not mind is a "mere" mechanism, and that mind is what a brain does.*
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
uq3
1po
>
>
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