I. Principles of inference and definition : 1. The sentential connectives : Negation and conjunction ; Disjunction ; Implication: conditional sentences ; Equivalence: biconditional sentences ; Grouping and parentheses ; Truth tables and tautologies ; Tautological implication and equivalence --
2. Sentential theory of inference : Two major criteria of inference and sentential interpretations ; The three sentential rules of derivation ; Some useful tautological implications ; Consistency of premises and indirect proofs --
3. Symbolizing everyday language : Grammar and logic ; Terms ; Predicates ; Quantifiers ; Bound and free variables ; A final example --
4. General theory of inference : Inference involving only universal quantifiers ; Interpretations and validity ; Restricted inferences with existential quantifiers ; Interchange of quantifiers ; General inferences ; Summary of rules of inference --
5. Further rules of inference : Logic of identity ; Theorems of logic ; Derived rules of inference --
6. Postscript on use and mention : Names and things named ; Problems of sentential variables ; Juxtaposition of names --
7. Transition from formal to informal proofs : General considerations ; Basic number axioms ; Comparative examples of formal derivations and informal proofs ; Examples of fallacious informal proofs ; Further examples of informal proofs --
8. Theory of definition : Traditional ideas ; Criteria for proper definitions ; Rules for proper definitions ; Definitions which are identities ; The problem of division by zero ; Conditional definitions ; Five approaches to division by zero ; Padoa's principle and independence of primitive symbols. II. Elementary intuitive set theory : 9. Sets : Introduction ; Membership ; Inclusion ; The empty set ; Operations of sets ; Domains of individuals ; Translating everyday language ; Venn diagrams ; Elementary principles about operations on sets --
10. Relations : Ordered couples ; Definition of relations ; Properties of binary relations ; Equivalence relations ; Ordering relations ; Operations on relations --
11. Functions : Definition ; Operations on functions ; Church's lambda notation --
12. Set-theoretical foundations of the axiomatic method : Introduction ; Set-theoretical predicates and axiomatizations of theories ; Isomorphism of models for a theory ; Example: probability ; Example: mechanics.