Can we know everything?

Gödel’s First Incompleteness Theorem states:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory.

It is often argued (you know, by nerds) that this theorem proves it is impossible for us to ever fully understand the world, since understanding it would imply we have a theory of it—and surely any theory about the world must include “basic arithmetic truths”!

These naysayers overlook one crucial loophole: Gödel’s theorem does not imply that our knowledge must be incomplete—only that it cannot be both complete and consistent. What if it’s inconsistent?

Maybe reality is inconsistent with itself. If so, I don’t believe anyone’s proven we are doomed to fail in striving to understand it. Ever think about that?

Ha! I didn’t think so.

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2 thoughts on “Can we know everything?

  1. Bragaadeesh says:

    Godel’s theorem as such is something similar to “Trust me, I’m a liar”
    If it has to be true, then his own theorem contradicts what he says since I see the theorem in a theoretical way.
    Enjoyed the post by the way. 🙂

    • Daniel says:

      Haha, I can see what you mean about the theorem. But I don’t think Godel really contradicts himself. The main point of it is just that no system can really be complete in the sense of every true statement being expressible within the system. So in the case of numbers, for example, there are going to be facts about numbers which are true but which cannot be captured by existing number theory (and if some new number theory were to come along that could capture these facts, it would still be incomplete in its own ways). One thing’s for sure: it is a frustrating theorem to really get your head around! By the way, on a related note, I highly recommend the book Godel, Escher, Bach by Hofstadter. It is really amazing.

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