Book contents
- Frontmatter
- Contents
- Preface
- 1 What is deductive logic?
- 2 Validity and soundness
- 3 Forms of inference
- 4 Proofs
- 5 The counterexample method
- 6 Logical validity
- 7 Propositions and forms
- Interlude: From informal to formal logic
- 8 Three connectives
- 9 PL syntax
- 10 PL semantics
- 11 ‘P’s, ‘Q’s, ‘α’s, ‘β’s and form again
- 12 Truth functions
- 13 Expressive adequacy
- 14 Tautologies
- 15 Tautological entailment
- 16 More about tautological entailment
- 17 Explosion and absurdity
- 18 The truth-functional conditional
- 19 ‘If’s and ‘→’s
- Interlude: Why natural deduction?
- 20 PL proofs: conjunction and negation
- 21 PL proofs: disjunction
- 22 PL proofs: conditionals
- 23 PL proofs: theorems
- 24 PL proofs: metatheory
- Interlude: Formalizing general propositions
- 25 Names and predicates
- 26 Quantifiers in ordinary language
- 27 Quantifier-variable notation
- 28 QL languages
- 29 Simple translations
- 30 More on translations
- Interlude: Arguing in QL
- 31 Informal quantifier rules
- 32 QL proofs
- 33 More QL proofs
- 34 Empty domains?
- 35 Q-valuations
- 36 Q-validity
- 37 QL proofs: metatheory
- Interlude: Extending QL
- 38 Identity
- 39 QL= languages
- 40 Definite descriptions
- 41 QL= proofs
- 42 Functions
- Appendix Soundness and completeness
- The Greek alphabet
- Further reading
- Index
This chapter is part of a book that is no longer available to purchase from Cambridge Core
24 - PL proofs: metatheory
Book contents
- Frontmatter
- Contents
- Preface
- 1 What is deductive logic?
- 2 Validity and soundness
- 3 Forms of inference
- 4 Proofs
- 5 The counterexample method
- 6 Logical validity
- 7 Propositions and forms
- Interlude: From informal to formal logic
- 8 Three connectives
- 9 PL syntax
- 10 PL semantics
- 11 ‘P’s, ‘Q’s, ‘α’s, ‘β’s and form again
- 12 Truth functions
- 13 Expressive adequacy
- 14 Tautologies
- 15 Tautological entailment
- 16 More about tautological entailment
- 17 Explosion and absurdity
- 18 The truth-functional conditional
- 19 ‘If’s and ‘→’s
- Interlude: Why natural deduction?
- 20 PL proofs: conjunction and negation
- 21 PL proofs: disjunction
- 22 PL proofs: conditionals
- 23 PL proofs: theorems
- 24 PL proofs: metatheory
- Interlude: Formalizing general propositions
- 25 Names and predicates
- 26 Quantifiers in ordinary language
- 27 Quantifier-variable notation
- 28 QL languages
- 29 Simple translations
- 30 More on translations
- Interlude: Arguing in QL
- 31 Informal quantifier rules
- 32 QL proofs
- 33 More QL proofs
- 34 Empty domains?
- 35 Q-valuations
- 36 Q-validity
- 37 QL proofs: metatheory
- Interlude: Extending QL
- 38 Identity
- 39 QL= languages
- 40 Definite descriptions
- 41 QL= proofs
- 42 Functions
- Appendix Soundness and completeness
- The Greek alphabet
- Further reading
- Index
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- An Introduction to Formal Logic , pp. 216 - 227Publisher: Cambridge University PressPrint publication year: 2020