Unsubstantiated fear = obsessive thought processes = increased unsubstantiated fear = increasingly obsessive thought processes = even more unsubstantiated fear = uncontrollably obsessive thought processes = psychosis.
Welcome to an infinitely recursive argument. →⊢.
It corresponds to the type of fix:
fix :: forall a. (a -> a) -> a
fix f = f (fix f)
fix is the fixed-point function. It can be used to implement arbitrary recursion. This means it can lead to infinite loops! It can also be used to implement any type, which means it corresponds to a proof for any proposition. You could even prove the proposition false.
fix id :: forall a. a
fix id :: Void
According to Curry-Howard, circular logic is like unrestricted recursion. Adding circular logic turns your programming language into a Turing-complete one and, equivalently, turns your logic into an inconsistent one. Meaning, you can use it to prove anything. Not very useful for making coherent arguments!
This manner of thinking is also called rumination: conclusions about reality based on repeated feelings or situations in your life.
Does this sound familiar to anyone? No? We do this when we create affirmations.
Rumination: noun, a deep or considered thought about something.
Affirmation: noun, positively loaded phrases, or statements that are used to challenge unhelpful or negative thoughts.
The main difference? Rumination is given to you from outside sources.
