Description

For courses in Symbolic Logic

 

Designed for those who have no prior background in logic, philosophy, or mathematics, this comprehensive introduction covers all the standard topics of symbolic logic through relational predicate logic with identity.

 

Understanding Symbolic Logic, Fifth Edition, is completely reader-friendly. All concepts and theories are presented in small "bites," helping students to master the concepts of symbolic logic with confidence.

Features

How do you ensure that your students understand symbolic logic?

Understanding Symbolic Logic is a comprehensive text that has the tools your students need to truly understand and retain what they have learned. Special pedagogical features include

• Comprehensive coverage, including all the basics of symbolic logic, through relational predicate logic with identity.

• A logical organization. Each unit has an introduction, providing an overview of what is to come, as well as a set of learning objectives for that unit. Units are divided into separate sections, each covering a particular, limited topic. Most units have a set of definitions at the end, covering the most important concepts of that unit.
• Clear and thorough explanations of procedures and lots of in-text examples. This ensures that your students understand the procedures so that they can apply them. Very detailed explanations are given for the various techniques, as well as many illustrative examples.
• Clear and logically organized introduction to predicate logic.

• Topics broken down into small, manageable segments, with a clear, linear approach. 

•  A difficulty level that is intuitive to the needs of introductory students. This text is accessible, but with a range of topics of varying difficulty.
•  Thorough discussion of symbolization, with numerous examples worked out step-by-step.

How do you teach students to apply symbolic logic?Understanding Symbolic Logic offers plenty of opportunities for students to practice and check their work. Special pedagogical features include

• An abundance of exercises ranging from easy to very challenging.
• Answers provided in the back of the book for many of the exercises. This allows students to immediately check their work.
• Guidance through the proof process. This text has been lauded by reviewers for being very effective in guiding students through the proof process and helping them master it. The method of "working backward" is especially effective.

How do you prepare your course materials?Understanding Symbolic Logic has an Instructor's Manual and Prentice Hall's Test Generator software available to adopters of the text.New to the Fifth Edition

• New in-text examples have been added and numerous examples have been updated and clarified.
• New exercises have been added. There are additional exercises for Units 1,4,7,8,9,10,11,12,13,14, and 19.

• Improved symbolization.

• Clearer explanations for difficult concepts. i.e. form and substitution instances, arguments vs. assertions, deductive and inductive logic, truth-functional and non-truth-functional operators.

• The exercises in Units Seven (The Proof Method: Eight Basic Inference Rules) and Eight (Replacement Rules) split into sets of rules. This makes it possible for students to practice with just a few rules at once, instead of having to do problems right off the bat with the entire set of rules. 

• Formulas have been clarified by eliminating braces and using only parentheses and, where needed, brackets.
• Any misprints have been corrected.
• The difference between forms and substitution instances have been clarified and further explained.
• Changes to specific units
  • Unit 1: 
    • Expanded discussion of arguments, especially the distinction between arguments and mere assertions.
    • Expanded and clarified section on the difference between deductive and inductive arguments.
    • New exercise set, combining material from those two items.
  • Unit 4: 
    • Expanded discussion of the difference between truth-functional and non-truth-functional compounds.
    • New section on necessary and sufficient conditions, in the discussion of the conditional.
    • An expanded discussion of "unless".
  • Unit 6:
    • Clarification of the process for testing statements (instances) as opposed to forms.
    • Discussion of the connection between the rules in Units 7 and 8 and the concepts of logical implication and logical equivalence.
  • Unit 10: 
    • Expanded discussion of propositional functions and the difference between them and singular sentences.
  • Unit 11: 
    • Expanded discussion of bound variables.
  • Unit 12: 
    • New section explaining the rationale for using the conditional after the universal quantifier and the conjunction after the existential quantifier.
      
      

New to this Edition

New in-text examples have been added and numerous examples have been updated and clarified.

New exercises have been added. There are additional exercises for Units 1,4,7,8,9,10,11,12,13,14, and 19.

Improved symbolization.

Clearer explanations for difficult concepts. i.e. form and substitution instances, arguments vs. assertions, deductive and inductive logic, truth-functional and non-truth-functional operators.

The exercises in Units Seven (The Proof Method: Eight Basic Inference Rules) and Eight (Replacement Rules) split into sets of rules. This makes it possible for students to practice with just a few rules at once, instead of having to do problems right off the bat with the entire set of rules. 

Formulas have been clarified by eliminating braces and using only parentheses and, where needed, brackets.

Any misprints have been corrected.

The difference between forms and substitution instances have been clarified and further explained.

Changes to specific units

• Unit 1: 
  • Expanded discussion of arguments, especially the distinction between arguments and mere assertions.
  • Expanded and clarified section on the difference between deductive and inductive arguments.
  • New exercise set, combining material from those two items.
• Unit 4: 
  • Expanded discussion of the difference between truth-functional and non-truth-functional compounds.
  • New section on necessary and sufficient conditions, in the discussion of the conditional.
  • An expanded discussion of "unless".
• Unit 6:
  • Clarification of the process for testing statements (instances) as opposed to forms.
  • Discussion of the connection between the rules in Units 7 and 8 and the concepts of logical implication and logical equivalence.
• Unit 10: 
  • Expanded discussion of propositional functions and the difference between them and singular sentences.
• Unit 11: 
  • Expanded discussion of bound variables.
• Unit 12: 
  • New section explaining the rationale for using the conditional after the universal quantifier and the conjunction after the existential quantifier.

Table of Contents

I. SENTENTIAL LOGIC

 

 1. Introduction to Logic    Why Study Logic?    What Logic Is All About    Induction and Deduction    Form and Validity    Truth and Validity    The Nature of Symbolic Logic    The Scope of Symbolic Logic    Definitions    Study Questions    Exercises
 2. The Structure of Sentential Logic    Simple and Compound Sentences    Sentential Operators    The Structure and Symbolism of Sentential Logic    Definitions    Study Questions    Exercises
 3. Computing Truth Values    Truth Tables for the Operators    Computing Truth Values    Truth-functional Operators    Non-truth-functional Operators    Definitions    Study Questions    Exercises
 4. Symbolizing English Sentences    Simple Sentences    Truth-functional and Non-truth-functional Compounds    Symbolizing Truth-functional English Operators    Symbolizing Multiply Complex Sentences    Exercises
 5. Truth Tables for Testing Validity    Constructing Base Columns for Truth Tables    The Truth Table Test for Validity    Shortcut Validity Tests    Mechanical Decision Procedures    Definitions    Study Questions    Exercises
 6. Further Applications of the Truth Table Method    Tautologies, Contradictions, and Contingencies    Logical Implication and Logical Equivalence    Rules of Inference, Logical Implication, and Logical Equivalence    Consistency    Four Kinds of Truth Table Problems and the Relations Between Them    Definitions    Study Questions    Exercises
 7. The Proof Method: Eight Basic Inference Rules    Form and Substitution Instance    The Proof Process    Eight Basic Inference Rules    Derivations and Proofs    Constructing Simple Proofs    Constructing More Complex Proofs    Summary of Rules of Inference    Definitions    Exercises
 8. Replacement Rules    The Structure of Replacement Rules    The Ten Replacement Rules    Constructing Simple Proofs with Replacement Rules    Strategies for More Complex Proofs    Summary of Replacement Rules    Exercises
 9. Conditional Proof and Indirect Proof    Conditional Proof    Indirect Proof    Discharging Assumptions; Restrictions on C.P. and I.P.    Using C.P. and I.P.    Proofs of Theorems    Invalidity    Truth and Proof    Summary of Rules of Conditional Proof and Indirect Proof    Definitions    Exercises

II. MONADIC PREDICATE LOGIC

 

10. Singular Sentences    Singular Sentences and Propositional Functions    Symbolizing Singular Sentences    Definitions    Exercises
11. Quantifiers    Universal and Existential Quantifiers    Free and Bound Variables; Scope of a Quantifier    Negated Quantifiers    Definitions    Exercises
12. Categorical Propositions    The Four Categorical Propositions    Individuals, Sets, and Properties    Venn Diagrams    Symbolizing Categorical Propositions    Negated Categorical Propositions    Deriving C.Q.N. Rules from Q.N. Rules    Symbolizing English Categorical Sentences    Summary of Categorical Propositions    Definitions    Exercises
13. Complex Subjects and Predicates    Complex Subjects and Predicates    Equivalent Symbolizations    Exercises
14. Quantifier Form and Truth-Functional Compounds of Quantifier Statements    Quantifier Form    Truth-functional Compounds and Quantifier Form    Symbolizing Truth-functional Compounds    Definitions    Exercises
15. Proofs in Predicate Logic    Preliminary Statement of the Four Quantifier Rules    Instances of Quantified Formulas    The Rules of Universal Instantiation (U.I.) and Existential Generalization (E.G.)    The Rules of Existential Instantiation (E.I.) adn Universal Generalization (U.G.); Flagging Restrictions    Constructing Proofs for "Pure" Quantifier Arguments    Constructing Proofs for Arguments Containing Truth-functional Compounds    Constructing Proofs of Quantifier Theorems    Statement of the Quantifier Rules, with All Necessary Restrictions    Exercises
16. Invalidity in Quantifier Logic    The Natural Interpretation Method    Truth Conditions for Quantifier Statements    The Model Universe Method    Definitions    Exercises

III. RELATIONAL PREDICATE LOGIC

 

17. Symbolization in Relational Predicate Logic    Relational Predicates and Singular Sentences    Multiple Quantifiers    Quantifier Negation    Categorical Relational Statements; Complex Subjects and Predicates    Symbolizing English Sentences    Exercises
18. Proofs and Invalidity for Relational Predicate Logic    Proofs in Relational Predicate Logic    Invalidity in Relational Predicate Logic    Exercises
19. Identity and Definite Descriptions    Identity Statements and Their Negations    Exceptives and "Only" Statements    Superlatives    Numerical Statements    Definite Descriptions    Exercises
20. Proofs Involving Identity    Rules for Identity    Proofs Containing Identity Statements    Summary of Identity Rules    Exercises

IV. EXTRA CREDIT UNITS

 

21. Well-Formed Formulas for Sentential Logic    Exercises
22. Proof Trees for Sentential Logic    Exercises
23. Using Venn Diagrams to Prove Validity    Exercises
24. Proof Trees for Predicate Logic    Exercises
Answers to Starred Exercises
Index

Back Cover

Understanding Symbolic Logic

Fifth Edition

Virginia Klenk

Designed for those who have no prior background in logic, philosophy, or mathematics, this comprehensive introduction covers all the standard topics of symbolic logic through relational predicate logic with identity. Understanding Symbolic Logic, Fifth Edition, is completely reader-friendly. All concepts and theories are presented in small "bites," helping you to master the concepts of symbolic logic with confidence.

Understanding Symbolic Logic, Fifth Edition, features:

• Explanations keyed to the difficulty of the topics covered
• Numerous worked-out examples; many detailed, step-by-step symbolizations; over 50 fully worked-out proofs; additional exercises
• "Extra credit" units offer a glimpse into alternative methods of logic and more advanced topics
• New for the Fifth Edition: Along with revisions for clarity, more examples have been added throughout, especially in sections on translation and relational predicate logic; symbolization has been improved; additional background has been added on the nature of identity relation