Originally published in 1964. This book is concerned with general arguments, by which is meant broadly arguments that rely for their force on the ideas expressed by all, every, any, some, none and other kindred words or phrases. A main object of quantificational logic is to provide methods for evaluating general arguments. To evaluate a general argument by these methods we must first express it in a standard form. Quantificational form is dealt with in chapter one and in part of chapter three; in the remainder of the book an account is given of methods by which arguments when formulated quantificationally may be tested for validity or invalidity. Some attention is also paid to the logic of identity and of definite descriptions. Throughout the book an attempt has been made to give a clear explanation of the concepts involved and the symbols used; in particular a step-by-step and partly mechanical method is developed for translating complicated statements of ordinary discourse into the appropriate quantificational formulae. Some elementary knowledge of truth-functional logic is presupposed.
1. (1. Introduction 2. Direct and indirect evaluation . 3. Quantifier-matrix form of singular statements 4. An alternative formulation 5. Universes of discourse 6. Quantifier-matrix form of general statements 7. Predicate and argument 8. Predicate abbreviation and substitution 9. Quantificational form 10. The question of existential import 11. Definitions) 2. (1. Quantificational validity 2. Deduction 3. The rule EI*; dummy names 4. The rules EG*, UI* and UG* 5. The rules SD* and SQ*; the restriction in SQ* 6. Examples 7. Explanatory remarks about UG* 8. Replacement of starred rules by unstarred rules: EI, EG, UI, UG) 3. (1. List of rules 2. Interpretation of the rules 3. Principles of single quantification; deductions 4. Multiple quantification; introduction 5. Expressing multiply general statements in quantificational form 6. Principles of multiple quantification; deductions 7. Identity 8. Definite descriptions; the iota operator) 4. (1. Reformulated definitions of validity; proof of invalidity 2. Quantifier-free equivalents 3. Testing QFE’s for falsifiability 4. Predicate and subject 5. Special considerations relating to identity 6. Examples of invalidity proofs 7. Decision problems)