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Table of Contents

I. Introduction

II. The Semantics of Logic
1. Definitions of Semantic Concepts
2. Signs
3. Signification and Reference
4. Formalization
5. Logic, Logistic and Calculus

III. Classical Term Logic
6. Early History of Logic
7. Terms
8. Aristotle’s Theory of Predication
9. Logic and Metaphysics
10. Syllogisms

IV. Boole’s Calculus of Logic
11. The Project of Formalizing Logic
12. Boole’s Philosophical and Mathematical Aims
13. Boolean Semiotics
14. Fundamental Laws of Thought
15. Primary and Secondary Propositions
16. Boolean Rules of Inference
17. Probability Theory

V. Modern Predicate Logic
Frege and Russell
Propositions
Propositional Functions
Predicates
Connectives
Atomic and Well-Formed Formulas
Quantifiers
Axioms
Inferences
Higher Order Logic

VI. The Failure of Logicism
Russell’s Claims
Atomic Formulas and Free Variables
Representable, Recursive, and Decidable Theories
Strong Undecidability Theorem
Strong Incompleteness Theorem

VII. Set Theory and Universals
Sets and Elements
Classes, Types and Boolean Universals
Zermelo-Fraenkel Theory and Axiom of Choice
Russell’s Paradox
Structured Sets
Inadequacy of Set Theory

VIII. Improving Predicate Calculus and Set Theory
Commentary on Trotter
Improved Lower Predicate Calculus
New Set Theoretic Axioms

IX. Psychologism
Linguistic Reaction to Failure of Logicism
Psychological Naturalism of Language
Quine, Wittgenstein, Chomsky
Intensional Logic
Analytic Epistemology Presupposes Metaphysics
Limitations of Empiricism

X. Conclusion

© 2009-2012, 2018 Daniel J. Castellano. All rights reserved. http://www.arcaneknowledge.org