A new axiom system called “Miniaturized Finitism” is a proposed workaround for achieving a fragmented sense of model consistency — even in the face of Gödel’s Second Incompleteness Theorem.
It’s able to achieve this self-consistency by dropping the assumption that multiplication is a total function and by curtailing the scope of modus ponens by forbidding it to operate across axiom levels.
Interestingly, the author has no direct ties to MIRI but concludes his work by discussing at length how valuable these extended-consistency systems will be for powerful future artificial reasoning systems.
4 Responses to “On the Significance of Self-Justifying Axiom Systems”
January 21
GuestSounds like you need to get this guy into one of the workshops!
January 21
Marius van VoordenSounds like you need to get this guy into one of the workshops!
January 21
Louie HelmEliezer, how similar is this to other ideas that are already out there? Would you say that weakening an axiom system by dropping multiplication as a total function is a grave loss when you’re still able to assume addition is a total function? It seems somewhat asinine, but maybe it’s NBD really. The trick he’s doing with modus ponens is also intuitively plausible but I’m less sure I understand/agree with it.
January 22
Brienne StrohlI really appreciate how you summarize articles in posts like this.