alt Hacker NewsI'm no mathematician, but doesn't this come up against Gödel's incompleteness theorem? My brain has that roughly as "If you have a system and a model of that system, but the model is also part of the same system, something something, impossible"
Replies
bananaflag • yesterday at 1:17 PM
No, this sort of self-reflection is exactly what makes Gödel/Turing/etc impossibility results work ("strange loops" and all that).
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tsimionescu • yesterday at 4:19 PM
Godel's incompleteness theorem is about the limits of proof / mathematical knowledge. Algebra is still useful and true, even though the proof shows it must be incomplete.
anthk • yesterday at 1:07 PM
Any decent Lisp can reimplement eval, apply and the rest of functions/atom within itself.
Isn't GIT you can have a statement that is valid in a system, but can't be proven this way or that given the systems' axioms? And this is true for all such axiom systems? In other words the axioms are an incomplete description of the system.
Maybe the problem is axiomative deduction, we need a new inference-ology?