The Structural Theory of Probability

1 Cultural Roots.- 1.1 Operational analysis.- 1.2 Networks.- 1.3 Innovative improvements.- 2 Critical Remarks.- 2.1 Random events overlooked.- 2.2 Ensemble model.- 2.3 Linguistic model.- 2.4 Which is the probability argument?.- 2.5 A new proposal.- 3 Events and Structures.- 3.1 Connecting is primitive.- 3.2 Entities, relationships and structures.- 3.3 Abstract algebra.- 3.4 Structural model.- 3.5 Structure’s advantages.- 3.6 Successful structures.- 4 Notes on Structural Analysis.- 4.1 Main mechanisms in events.- 4.2 Basic structural forms.- 4.3 Three singular cases.- 4.4 Why they do not have a general application.- 5 Certainty and Uncertainty.- 5.1 Difficulties in investigating the reality.- 5.2 Uncertain details.- 5.3 Structure of levels.- 5.4 What the levels make explicit.- 5.5 Certain and uncertain structures.- 5.6 Uncertainty and randomness.- 5.7 Progressive qualities of knowledge.- 6 Probability.- 6.1 The problem of being.- 6.2 Definition of probability.- 6.3 Advantages from the definition.- 7 Relative Frequency.- 7.1 Rounding.- 7.2 Experimental test.- 7.3 Frequency and probability are identical.- 7.4 Frequency and probability do not coincide.- 7.5 The Law of large numbers.- 7.6 Practical applications of the law.- 8 Objectivism and Subjectivism.- 8.1 The meaning of probability.- 8.2 Theoretical schools.- 8.3 Theory and praxis.- 8.4 Science of indeterminism.- 9 Probability Calculus.- 9.1 The Laplace formula.- 9.2 Function of probability.- 9.3 Theorem of compound probabilities.- 9.4 Theorem of total probabilities.- 9.5 Closing remarks.- 10 Conditional Probability.- 10.1 Effects from causes.- 10.2 Dependence and independence.- 10.3 Probability of the third singular case.- 10.4 The Bayes theorem.- 11 Stochastic Systems.- 11.1 Transition matrix.- 11.2Chapman-Kolmogorov’s theorem.- 11.3 State matrix.- 11.4 Evolution theorem.- 12 Distributions.- 12.1 Distribution functions.- 12.2 Constant distribution.- 12.3 Binomial distribution.- 12.4 Poisson’s distribution.- 12.5 Normal distribution.- 12.6 Compound distributions.- 13 Bivalent and Multivalent Logic.- 13.1 Probability and language.- 13.2 Values of truth and probability.- 13.3 Logic calculus.- 14 Two Applications.- 14.1 Exercise I.- 14.2 Exercise II.- Appendix: History’s Lessons.- 1 Classical culture.- 2 The rule of apodictic reasoning.- 3 Uncertainty appears in jurisprudence.- 4 People begin to calculate chances.- 5 Statistics emerges.- 6 Two veins merge.- 7 Toward a systematic study.- 8 Several fields are invaded.- 9 Multivalent logic.- 10 The fundamentals are still obscure.- Index of Subjects.- Index of Names.