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 ExercisesIndex
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