
Risk-Return Analysis Volume 3
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Content
- Cover
- Title Page
- Copyright Page
- Contents
- 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
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