II. Appendix: Proofs of ResultsReferences; Chapter Ill. Axiomatic Quantitative Probability; IIIA. Introduction; IIIB. Overspecification in the Kolmogorov Setup: Sample Space and Event Field; IIIC. Overspecification in the Probability Axioms: View from Comparative Probability; IIID. Overspecìficatìon in the Probability Axioms: View from Measurement Theory; IIIE. Further Specification of the Event Field and Probability Measure; IIIF. Conditional Probability; IIIG. Independence; IIIH. The Status of Axiomatic Probability; References; Chapter IV. Relative-Frequency and Probability

IVA. IntroductionIVB. Search for a Physical Interpretation of Probability Based on Finite Data; IVC. Search for a Physical Interpretation of Probability Based on Infinite Data; IVD. Bernoulli/Borel Formalization of the Relation between Probability and Relative-Frequency: Strong Laws of Large Numbers; IVE. Von Mises' Formalization of the Relation between Probability and Relative-Frequency: The Collective; IVF. Role of Relative-Frequency in the Measurement of Probability; IVG. Prediction of Outcomes from Probability Interpreted as Relative-Frequency; IVH. The Argument of the ""Long Run""

IVI. Preliminary Conclusions and New DirectionsIVJ. Axiomatic Approaches to the Measurement of Probability; IVK. Measurement of Comparative Probability: Induction by Enumeration; IVL. Conclusion; References; Chapter V. Computational Complexity, Random Sequences, and Probability; VA. Introduction; VB. Definition of Random Finite Sequence Using Place-Selection Functions; VC. Definition of the Complexity of Finite Sequences; VD. Complexity and Statistics; VE. Definition of Random Finite Sequence Using Complexity; VF. Random Infinite Sequences; VG. Exchangeable and Bernoulli Finite Sequences

VH. Independence and ComplexityVI. Complexity-Based Approaches to Prediction and Probability; VJ. Reflections on Complexity and Randomness: Determinism versus Chance; VK. Potential Applications for the Complexity Approach; V. Appendix: Proofs of Results; References; Chapter VI. Classical Probability and its Renaissance; VIA. Introduction; VIB. Illustrations of the Classical Argument and Assignments of Equiprobability; VIC. Axiomatic Formulations of the Classical Approach; VID. Justifying the Classical Approach and Its Axiomatic Reformulations; VIE. Conclusions; References