§ The Metamathematical implications of the Strong Church Turing Thesis

• Thanks to Ben Przybocki, Meven, Arthur, and Anand for this enlightening fireside chat!
• I realized that my beliefs about computation and mathematics can be cleanly put as follows:
• Axiom: Strong Church Turing thesis: Computation everywhere "is the same".
• Axiom: Platonic realm: Mathematical objects "exist" out there.
• Given these two axioms, one must conclude that if one runs a physical computer to, for example, find proofs of consistency of ZFC in ZFC, and it actually halts in the real world, then we know for certain , in the mathematical world, that ZFC is inconsistent!
• In broader terms, computation "in the real world" enjoys a "transfer principle", where it behaves the same way also in the platonic universe.
• Another way of thinking about it: Computation is absolute, and must behave "similarly" in all realities, including all mathematical realities. Thus, any model of mathematics that induces strange computational principles that deviate from the real world can be ruled out!