Preface The Rational Decision Maker Words of Wisdom John von Neumann
13. Predecessors Introduction René Descartes There Is No “Is,” Only “Was” and “Will Be” Working Hypotheses RDM Reasoning David Hume Eudaimonia Financial Economic Discoveries Economic Analyses That Have Stood the Test of Time Constructive Skepticism Isaac Newton, Philosopher Fields Other Than Physics Karl Popper Mysticism Caveats Charles Peirce Immanuel Kant What an RDM Can Know A Priori
14. Deduction First Principles Introduction The Great Debate One More Reason for Studying Cantor’s Set Theory “Very Few Understood It” Finite Cardinal Arithmetic Relative Sizes of Finite Sets Finite Ordinal Arithmetic Standard Ordered Sets (SOSs) Finite Cardinal and Ordinal Numbers Cantor (101) Theorem Proof Corollary Proof Transfinite Cardinal Numbers The Continuum Hypothesis Transfinite Cardinal Arithmetic Lemma Transfinite Ordinal Numbers Examples of Well-Ordered and Not Well-Ordered Sets Transfinite Ordinal Arithmetic Extended SOSs Lemma Proof The Paradoxes (a.k.a. Antimonies) Three Directions From Aristotle to Hume to Hilbert British Empiricism versus Continental Rationalism Who Created What? Cantor Reconsidered Brouwer’s Objections Axiomatic Set Theory Peano’s Axioms (PAs) Hilbert’s Programs Whitehead and Russell Zermelo’s Axioms The “Axiom of Choice” The Trichotomy Equivalent to the Axiom of Choice Kurt Gödel (1906–1978) Thoralf Skolem (1887–1863)
15. Logic is Programming is Logic Introduction Terminology Number Systems and the EAS Structures Built on Them Deductive Systems as Programming Languages A Variety of Deductive DSSs Alternative Rules of Inference “Ladders” and “Fire Escapes” Organon 2000: From Ancient Greek to “Symbolic Logic” So, What’s New? Immediate Consequences Two Types of Set Ownership Modeling Modeling EAS-E Deduction: Status
16. The Infinite and The Infinitesimal Points and Lines Fields Constructing the Infinitesimals Infinite-Dimensional Utility Analysis The Algebraic Structure Called “A Field”
17. Induction Theory Introduction The Story Thus Far Concepts Basic Relationships Examples “Objective” Probability The Formal M59 Model Initial Consequences Bayes’s Rule A Bayesian View of MVA Judgment, Approximation and Axiom III (1) A Philosophical Difference between S54 and M59 Examples of Clearly “Objective” Probabilities” Propositions about Propositions A Problem with Axiom II Are the pj Probabilities the Scaling of the pj ? The pj “Mix on a Par” with Objective Probabilities
18. Induction Practice Introduction R. A. Fisher and Neyman-Pearson Hypothesis Tests The Likelihood Principle Andrei Kolmogorov A Model of Models The R.A. Fisher Argument Bayesian Conjugate Prior Procedures
19. Eudaimonia Review Eudaimonia for the Masses
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