1. Introduction 2. The Problem of Irreproducibility 3. Validity of Biomedical Science, Reproducibility, and Irreproducibility 4. The Logic of Certainty versus the Logic of Discovery 5. The Logic of Probability and Statistics 6. Causation, Process Metaphor, and Reductionism 7. Case Studies in Clinical Biomedical Research 8. Case Studies in Basic Biomedical Research 9. Case Studies in Computational Biomedical Research 10. Case Studies in Machine Learning Artificial Intelligence (AI) 11. Reproducibility of translation from biomedical research to clinical care 12. Chaotic and Complex Systems, Statistics, and Far-from-Equilibrium Thermodynamics 13. The Nature of the Fundamental Challenges to Reproducibility in any Knowledge Discipline 14. Epilogue 15. Appendix: Types of lack of reproducibilityility