The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
  1. Abstract
  2. Mathematics and Physics Have the Same Foundations
  3. The Underlying Structure of Mathematics and Physics
  4. The Metamodeling of Axiomatic Mathematics
  5. Some Simple Examples with Mathematical Interpretations
  6. Metamathematical Space
  7. The Issue of Generated Variables
  8. Rules Applied to Rules
  9. Accumulative Evolution
  10. Accumulative String Systems
  11. The Case of Hypergraphs
  12. Proofs in Accumulative Systems
  13. Beyond Substitution: Cosubstitution and Bisubstitution
  14. Some First Metamathematical Phenomenology
  15. Relations to Automated Theorem Proving
  16. Axiom Systems of Present-Day Mathematics
  17. The Model-Theoretic Perspective
  18. Axiom Systems in the Wild
  19. The Topology of Proof Space
  20. Time, Timelessness and Entailment Fabrics
  21. The Notion of Truth
  22. What Can Human Mathematics Be Like?
  23. Going below Axiomatic Mathematics
  24. The Physicalized Laws of Mathematics
  25. Uniformity and Motion in Metamathematical Space
  26. Gravitational and Relativistic Effects in Metamathematics
  27. Empirical Metamathematics
  28. Invented or Discovered? How Mathematics Relates to Humans
  29. What Axioms Can There Be for Human Mathematics?
  30. Counting the Emes of Mathematics and Physics
  31. Some Historical (and Philosophical) Background
  32. Implications for the Future of Mathematics
  33. Some Personal History: The Evolution of These Ideas
  34. Notes & Thanks
  35. Graphical Key
  36. Glossary
  37. Bibliography
  38. Index

Physicalization of Metamathematics Graphical Key

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