#incompletenesstheorem — Public Fediverse posts

Fernando Rosas (unfortunately not on Mastodon) asked on bsky:

"Has anyone figured out what exactly is the relation between the ideas of feedback, recurrence, and self-reference?"

A really interesting question.

He pointed to this paper for ideas: https://arxiv.org/abs/1711.02456
"Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos"

I did some desk research and found this cool paper:
https://arxiv.org/abs/1112.2141
"Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic"
that argues there is no essential incompleteness in formal reasoning systems if you look closely enough (using a more elaborate formalism based on polynomial equations to represent and evaluate logical proposition).

I wonder if analogous construction could be created for related theorems like the halting problem in computability theory.

#DynamicalSystems #IncompletenessTheorem #PolynomialEquations #HaltingProblem #Undecidability #SelfReference #Recurrence

#Veritasium - #Math's #FundamentalFlaw

https://www.youtube.com/watch?v=HeQX2HjkcNo&ab_channel=Veritasium

#RussellParadox #BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects #Paradox #LogicalParadox #Contradiction #Contradictions #Incompleteness #IncompletenessTheorem #Goedel #Hilbert

#JeffreyKaplan - #RussellsParadox - A simple #Explanation of a profound #Problem

https://www.youtube.com/watch?v=ymGt7I4Yn3k&ab_channel=JeffreyKaplan

#BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects #Paradox #LogicalParadox #Contradiction #Contradictions #Incompleteness #IncompletenessTheorem #Goedel #Hilbert

#SethLloyd - Theorem of Human #Unpredictability

https://www.youtube.com/watch?v=AIWemQthcZg&ab_channel=SeriousScience

#Philosophy #Science #PhilosophyOfScience #FreeWill #HumanUnpredictability #Information #Computability #HaltingProblem #TheHaltingProblem #Programming #AI #ArtificialIntelligence #Recursion #SelfReference #Goedel #KurtGoedel #Incompleteness #IncompletenessTheorem