The Fundamental Circularity Theorem: Why Some Mathematical Behaviours Are Inherently Unprovable 2025-01-22T18:20:25.697Z

Comment by Alister Munday (alister-munday) on The Fundamental Circularity Theorem: Why Some Mathematical Behaviours Are Inherently Unprovable · 2025-01-27T13:58:23.744Z · LW · GW

While you're correct that arithmetic operations can be derived recursively from succession, the paper's core insight isn't about formal derivability. Rather, it suggests some mathematical behaviors are "irreducible" - they arise directly from how properties interact rather than from deeper patterns waiting to be discovered. This may explain why certain simple-looking conjectures resist proof: we're seeking deeper explanations when the behaviour itself IS the fundamental interaction.