Risk-Return Analysis Volume 3

 Preface 
The Rational Decision Maker
Words of Wisdom
John von Neumann

 Acknowledgments

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 

Notes 

References 

Index