On 1/18/2025 2:29 AM, PGC wrote:
First I'll address the rest of your post as there's not really much to
talk about: Uncomputable inference rules (like the ω-rule) aren’t used
in standard physical theories much, so invoking them misses the core
point about Gödel’s incompleteness unless you have some incredible
non-standard result to show; in which case, prove/show it. Again, we can
simulate a finite system for N time steps, but Gödel’s result is not
about whether you can brute-force a finite trajectory—it’s about the
existence of statements in a sufficiently strong formal framework (one
that encodes arithmetic) which no consistent axiom system can decide.
Sufficiently strong means being able to construct self-referential
language in the system so that "This proposition is unprovable." is a
proposition of the system. Which isn't very interesting. Whether a
system has some interesting unprovable propositions is a separate question.
Brent
Consequently, if a “theory of everything” in physics is robust enough
to interpret integer arithmetic, then Gödel’s incompleteness theorems
apply. There's really nothing more I can say regarding all the
vagueness in your reply, because you clearly are performing rhetorical
moves to limit the generality of Gödel's contributions and separating
"modern physics" from it.
And doing the same while demanding “an example” for finite steps is
meaningless unless we specify exactly which formal system’s
provability we’re talking about— with the entire range of standard
specifications that the question omits, as if we were adding salt to a
dish or something. That omission reveals a misunderstanding of Gödel:
he never claimed you can’t compute discrete steps in a small system,
but rather that any consistent, arithmetic-level theory remains
incomplete about some statements. This conflation of “finite-step
computation” with “formal provability” underscores why your rhetorical
moves lack any sort of precision and ultimately
misrepresent/misunderstand not only Gödel’s theorems but the nuanced
notion of provability in basic terms. Because provability is relative
and computability is not. Your stock fell for me with this reply.
Please don't pretend to spoon feed me. You can play teacher with AG,
which is out-of-topic regarding ToE. AG can pay for lessons somewhere
and play "not convinced" twirling his moustache and adjusting his
monocle elsewhere and the trolling/grandstanding, playing god is so
abundant... moderate it guys. Passivity kills freedom and discourse.
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/cd5e1664-21de-4e46-97ef-329b9ef10ed3%40gmail.com.
