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.
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.