Gödel's incompleteness theorems

Can a puzzle have missing pieces we can't see?

Imagine you're trying to finish a puzzle with a friend, but you realize there are pieces that you can't find, no matter how hard you search.

Gödel's incompleteness theorems show that in certain puzzles (formal systems), there are truths (pieces) that can't be found (proven) within the rules of the puzzle.

Example

You're searching for a piece that fits perfectly, but it's missing, even though you know it should be there.

Remember this

Some puzzles have missing pieces that we can't solve, no matter how well we understand the rules.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

Foundations of mathematics

Can math ever be truly complete and consistent?

Proof of impossibility

Can a perfect square root be neatly packaged as a simple fraction?

Problem of universals

Universals question independent existence

logical positivism collapsed

Can a philosophy prove itself scientifically?

Russell's paradox

What if you find a set that defies its own rules?

Logical positivism

Logical positivism's verification principle claims only empirically verifiable statements are meaningful

Swipe through 100 ML concepts daily

Open Pocket Polymath