(Ebook) Introduction to Logical Theory 1st Edition by P F Strawson ISBN 0415618576 9780415618571

(Ebook) Introduction to Logical Theory 1st Edition by P F Strawson ISBN 0415618576 9780415618571

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ISBN 10: 0415618576 
ISBN 13: 9780415618571
Author: P F Strawson

First published in 1952, professor Strawson’s highly influential Introduction to Logical Theory provides a detailed examination of the relationship between the behaviour of words in common language and the behaviour of symbols in a logical system. He seeks to explain both the exact nature of the discipline known as Formal Logic, and also to reveal something of the intricate logical structure of ordinary unformalised discourse.

(Ebook) Introduction to Logical Theory 1st Table of contents:

Chapter 1. Logical Appraisal
1. Logical appraisal; and other kinds
I. Inconsistency
2. Words of logical appraisal have connected meanings
3. Contradicting oneself
4. Statements, not sentences, are inconsistent with one another
5. Incompatible predicates
6. Negation
7. Definition
8. Linguistic rules and logical relations
II. Reasoning
9. Arguing, proving, inferring: validity
10. Not all ‘valid steps’ are steps in reasoning
III. The Logician's Second-Order Vocabulary
11. Use to be made of logician's higher-order words
12. Contraries and contradictories
13. Entailment and inconsistency
14. Logically necessary statements; entailment and necessity
15. A problem
16. Logical equivalence; subcontrariety; necessary and sufficient conditions
Chapter 2. Formal Logic
1. The formal logician is not a list-maker
I. Generality. The Use Of Formulae
2. The generality of logicians’ entailment-statements
3. The use of formulae
4. Entailment between sentences and between formulae
5. The range of values of a variable
6. ‘Inconsistent’, ‘logically necessary’ applied to formulae
7. Misinterpretations of ‘⊃’
8. The point of using ‘⊃’
II. Form
9. The limitations implied by ‘formal’. Rules for representative patterns
10. Formal analogies and verbal frameworks
11. A formal analogy without a framework: transitivity
12. Logical constants
13. Logical forms of statements explained in terms of formal analogies
14. Logical form and logicians’ formulae
15. Mistakes about logical form
III. System
16. The logical ideal of system, and its effects
17. Methods of systematization
18. Abstract systems and their interpretation
Chapter 3. Truth-Functions
I. Truth Tables
1. Formation-rules
2. The meanings of the symbols of the system
3. Use of the tables in determining truth-conditions
4. Use of the tables for establishing logical relations and testing formulae
5. Some laws of the system
II. Truth-Functional Constants And Ordinary Words
6. The customary identifications
7. ‘~’ and ‘not’
8. ‘·’ and ‘and’
9. ‘⊃’ and ‘if’
10. ‘≡’ and ‘if and only if’
11. ‘v’ and ‘or’
III. Truth-Functional Constants And Logical Relations. The Deductive System Of Truth-Functions
12. ‘⊂’ and ‘entails’
13. The stroke-function
14. The deductive system of truth-functions
15. Examples of derivations
Chapter 4. Classes: An Alternative Interpretation Of The Tabular System
1. The system as an abstract exercise
2. An alternative interpretation. Class-expressions and class-constants
3. Class-statement formulae
4. The use of the tables to establish logical rules about class formulae
5. Parallels with ordinary speech. Re-expression of rules as entailments between class-membership formulae
6. Limitations of this use of the mechanism of the tables
Chapter 5. Predicative Formulae And Quantifiers
I. The Elements Of The Predicative System
1. Relations between the class and truth-functional systems
2. The paraphrasing of class-statement formulae in a new notation
3. Proofs in the new notation
4. Multiple quantification and relational predicates
II. THE PREDICATIVE SYSTEM AND ORDINARY SPEECH: PRELIMINARIES
5. The distinction between individual and predicative expressions: referring and describing
6. Claims made on behalf of the symbolism of the system
7. ‘(∃x)’ and tenses
Chapter 6. Subjects, Predicates, And Existence
I. The Traditional System Of Categorical Propositions
1. Formulae
2. Laws
3. Systematization
II. The Orthodox Criticisms Of The System
4. The dilemma of existence
5. The detail of the dilemma
III. Subjects And Predicates
5. A formalistic solution
6. The realistic solution: presupposition and entailment
7. Class-membership and class-inclusion. Subject-predicate statements
8. The relevance of the analysis of general statements as conjunctions of singular statements
9. Singular statements beginning with ‘the’ and ‘a’
10. “‘Exists’ is not a predicate”
11. Limitations of the traditional system
Chapter 7. General Statements And Relations
I. General Statements
1. The truth-conditions of general subject-predicate statements
2. Different kinds of general sentences
3. Law-statements
4. The impossibility of a neat classification of general sentences
II. Relations
5. Transitivity
6. Symmetry
7. Relations and their converses
8. The strained use of ‘relation’
9. Attempts to ‘reduce’ relational inferences
10. The logical forms of arguments
Chapter 8. Two Kinds Of Logic
I. Formal Logic: Applications And Limitations
1. Entailment-rules and referring rules
2. Logically ideal sentences
3. The use of modern logical symbolism in systems of necessary truth and natural law
II. Type-Differences And Formation-Rules
4. Formation-rules and rules of grammar
5. Non-grammatical type-restrictions
6. The metaphysical belief in basic types
III. The Logic Of Language
7. The fluidity of language
8. The logic of ordinary speech
Chapter 9. Inductive Reasoning And Probability
I. Support And Probability
1. Non-deductive reasoning
2. Degrees of support: the use of ‘probable’, etc.
3. Support and relative frequencies
4. Support and numerical chances
5. Degrees of support for generalizations
6. No precise rules for the assessment of evidence
II. The ‘Justification’ Of Induction
7. The doubt and its source
8. The desire for a supreme premise of inductions
9. The attempt to find a mathematical justification
10. The senselessness of the demand
11. Any successful method of finding things out must be inductively supported
12. The belief that the soundness of induction requires a ‘presupposition’ may rest upon the confused conflation of two questions
Index

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