Log In
Or create an account ->
Imperial Library
Home
About
News
Upload
Forum
Help
Login/SignUp
Index
Cover Page
Title Page
Copyright Page
Contents
Preface
Glossary of Special Symbols and Abbreviations
I. Mathematics, Formal Logic, and Names
1.1. Mathematics and mathematicians
1.2. Form and meaning
1.3. Use and mention
1.4. Statements about statements
II. The Statement Calculus
2.1. Statements and statement forms
2.2. Negation
2.3. Conjunction
2.4. Disjunction
2.5. The conditional
2.6. Statement formulas
2.7. Equivalence
2.8. Valid statement formulas
2.9. Notational conventions
2.10. Replacement
2.11. Substitution
2.12. Some useful valid formulas
2.13. A collection of valid statement formulas
2.14. Rules of inference
2.15. Collection of inference rules
III. Proof and Demonstration
3.1. Basic form of indirect proof
3.2. Special cases of the basic form of indirect proof
3.3. Proof by elimination
3.4. Proof by cases
3.5. Converses
3.6. Conversion in classical logic
3.7. Inverses
3.8. Demonstration and proof
3.9. Trees
3.10. Abbreviated demonstrations as proofs
3.11. Deduction principle
3.12. Conventional proofs in geometry
3.13. Analysis of a conventional proof
IV. Abstract Mathematical Systems
4.1. Mathematical models
4.2. A miniature geometry
4.3. Interpretations
V. The Restricted Predicate Calculus
5.1. Statement functions
5.2. Universal quantifier
5.3. Existential quantifier
5.4. Transformations of quantifiers
5.5. Free and bound variables
5.6. Inference rules for quantified statements
5.7. Inference of a statement function from a general statement
5.8. Inference rules of the statement calculus extended
5.9. Extension of the notion of valid statement formula
5.10. The generalization principle
5.11. Inference of a statement function from an existential statement: IE
5.12. Introduction of the existential quantifier
5.13. Use of the quantification inference rules
5.14. Statement functions of several variables
5.15. Extension of quantification inference rules
5.16. Final forms of the quantificational inference rules
5.17. Use of equality
5.18. Formal notion of equality
5.19. The scope of an assumption in a demonstration
VI. Applications of Logic in Mathematics
6.1. Introduction
6.2. Abstract groups
6.3. Isomorphic interpretations
6.4. Abstract field system
6.5. Interpretations of the abstract system
6.6. Further development of the abstract field system
6.7. Types of informality in proofs
6.8. Solution of a linear equation
6.9. Further theorems in the abstract field system
6.10. Solution of a quadratic equation
6.11. Subtraction and division
6.12. Solution of simultaneous linear equations
6.13. Negation vs. negative number
6.14. Ordered fields
6.15. Absolute value
6.16. Inequalities and absolute value
6.17. Applications to notions of limit
6.18. Restricted quantification
Appendix. Symbolic Treatment of the Miniature Geometry
Index
Back Cover
← Prev
Back
Next →
← Prev
Back
Next →