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ISBN 10: 0190861789
ISBN 13: 978-0190861780
Author: Russell Marcus
Rigorous yet intuitive and accessible, Introduction to Formal Logic provides a focused, “nuts-and-bolts” introduction to formal deductive logic that covers syntax, semantics, translation, and natural deduction for propositional and predicate logics.
For instructors who want to go beyond a basic introduction to explore the connection between formal logic techniques and philosophy, Oxford also publishes Introduction to Formal Logic with Philosophical Applications, an extended version of this text that incorporates two chapters of stand-alone essays on logic and its application in philosophy and beyond.
Introduction to Formal Logic 1st Table of contents:
Chapter 1: Introducing Logic
1.1: DEFINING ‘LOGIC’
1.2: LOGIC AND LANGUAGES
1.3: A SHORT HISTORY OF LOGIC
1.4: SEPARATING PREMISES FROM CONCLUSIONS
EXERCISES 1.4 Regiment each of the following arguments into premise conclusion form. The inspiration
1.5: VALIDITY AND SOUNDNESS
EXERCISES 1.5 Determine whether each of the following arguments is intuitively valid or invalid. For
KEY TERMS
Chapter 2: Propositional Logic: Syntax and Semantics
2.1: LOGICAL OPERATORS AND TRANSLATION
Negation
Conjunction
Disjunction
Material Implication (the Conditional)
The Biconditional
Translation and Ambiguity
Arguments and Numbered Premise-Conclusion Form
Summary
EXERCISES 2.1a Identify the antecedents and consequents of each of the following sentences.
EXERCISES 2.1b Translate each sentence into propositional logic using the propositional variables gi
EXERCISES 2.1c Translate each argument into propositional logic using the letters provided.
EXERCISES 2.1d Interpret the following sentences of propositional logic using the given translation
2.2: SYNTAX OF PL: WFFS AND MAIN OPERATORS
Summary
EXERCISES 2.2 Are the following formulas wffs? If so, which operator is the main operator? (For the
2.3: SEMANTICS OF PL: TRUTH FUNCTIONS
Negation
Conjunction
Disjunction
Material Implication
The Biconditional
Truth Values of Complex Propositions
Complex Propositions with Unknown Truth Values
Summary
EXERCISES 2.3a Assume A, B, C are true and X, Y, Z are false. Evaluate the truth values of each comp
EXERCISES 2.3b Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the tru
EXERCISES 2.3c As in Exercises 2.3b, assume A, B, C are true; X, Y, Z are false; and P and Q are unk
2.4: TRUTH TABLES
Determining the Size of a Truth Table
Summary
Constructing Truth Tables for Propositions with Any Number of Variables
EXERCISES 2.4 Construct truth tables for each of the following propositions.
2.5: CLASSIFYING PROPOSITIONS
Summary
EXERCISES 2.5a Construct truth tables for each of the following propositions and then classify each
EXERCISES 2.5b Construct truth tables for each of the following pairs of propositions. Then, for eac
2.6: VALID AND INVALID ARGUMENTS
Summary
EXERCISES 2.6 Construct truth tables to determine whether each argument is valid. If an argument is
2.7: INDIRECT TRUTH TABLES
Consistency and the Indirect Method
Summary
EXERCISES 2.7a Determine whether each of the following arguments is valid. If invalid, specify a cou
EXERCISES 2.7b Determine, for each given set of propositions, whether it is consistent. If it is, pr
KEY TERMS
Chapter 3: Inference in Propositional Logic
3.1: RULES OF INFERENCE 1
Modus Ponens (MP)
Modus Tollens (MT)
Disjunctive Syllogism (DS)
Hypothetical Syllogism (HS)
Using the Rules in Derivations
Summary
Rules Introduced
EXERCISES 3.1a Derive the conclusions of each of the following arguments using natural deduction.
EXERCISES 3.1b Translate each of the following paragraphs into arguments written in PL. Then, derive
3.2: RULES OF INFERENCE 2
Conjunction (Conj) and Addition (Add)
Simplification (Simp)
Constructive Dilemma (CD)
Summary
Rules Introduced
EXERCISES 3.2a For each of the following arguments, determine which, if any, of the eight rules of i
EXERCISES 3.2b Derive the conclusions of each of the following arguments using the eight rules of in
EXERCISES 3.2c Translate each of the following paragraphs into arguments written in PL. Then, derive
3.3: RULES OF EQUIVALENCE 1
De Morgan’s Laws (DM)
Association (Assoc)
Distribution (Dist)
Commutativity (Com)
Double Negation (DN)
Rules of Equivalence and Rules of Inference
Summary
Rules Introduced
EXERCISES 3.3a Derive the conclusions of each of the following arguments using the rules of inferenc
EXERCISES 3.3b Translate each of the following paragraphs into arguments written in PL. Then, derive
3.4: RULES OF EQUIVALENCE 2
Contraposition (Cont)
Material Implication (Impl)
Material Equivalence (Equiv)
Exportation (Exp)
Tautology (Taut)
Summary
Rules Introduced
EXERCISES 3.4a For each of the following inferences, determine which single rule of equivalence of s
EXERCISES 3.4b Derive the conclusions of each of the following arguments using the rules of inferenc
EXERCISES 3.4c Translate each of the following paragraphs into arguments written in PL. Then, derive
3.5: PRACTICE WITH DERIVATIONS
Making Conditionals
Switching Antecedents of a Nested Conditional
Negated Conditionals
Simplifying Antecedents and Consequents
Combining Conditionals
A Statement Entailing Its Own Negation
Explosion
Summary
EXERCISES 3.5a Derive the conclusions of each of the following arguments using the rules of inferenc
EXERCISES 3.5b Translate each of the following paragraphs into arguments written in PL. Then, derive
3.6: THE BICONDITIONAL
Summary
Rules Introduced
EXERCISES 3.6a Derive the conclusions of each of the following arguments using the eighteen standard
EXERCISES 3.6b Derive the conclusions of each of the following arguments using the rules of inferenc
EXERCISES 3.6c Translate each of the following paragraphs into arguments written in PL. Then, derive
3.7: CONDITIONAL PROOF
Summary
EXERCISES 3.7a Derive the conclusions of each of the following arguments using the method of conditi
EXERCISES 3.7b Translate each of the following paragraphs into arguments written in PL. Then, derive
3.8: LOGICAL TRUTHS
A Common Error to Avoid in Using CP to Derive Logical Truths
Converting Ordinary Derivations into Logical Truths
Summary
EXERCISES 3.8a Convert each of the following arguments to a logical truth, using either of the metho
EXERCISES 3.8b Use conditional proof to derive each of the following logical truths.
3.9: INDIRECT PROOF
Three Derivation Methods
Summary
EXERCISES 3.9a Derive the conclusions of the following arguments using conditional proof and/or indi
EXERCISES 3.9b Translate each of the following paragraphs into arguments written in PL. Then, derive
EXERCISES 3.9c Use conditional or indirect proof to derive each of the following logical truths.
3.10: CHAPTER REVIEW
Proof Strategies
Logical Truth or Not?
Valid or Invalid?
EXERCISES 3.10a Determine whether each of the following arguments is valid or invalid. If it is vali
EXERCISES 3.10b Determine whether each of the following propositions is a logical truth. If it is a
KEY TERMS
Chapter 4: Monadic Predicate Logic
4.1: INTRODUCING PREDICATE LOGIC
Singular Terms and Predicates
Quantifiers
Quantified Sentences with Two Predicates
Languages of Predicate Logic
Summary
EXERCISES 4.1a: Translate each sentence into predicate logic using constants in each.
EXERCISES 4.1b Translate each sentence into predicate logic. Do not use constants.
4.2: TRANSLATION USING M
Quantified Sentences with More than Two Predicates
Things and People
Only
Propositions with More than One Quantifier
Adjectives
Summary
EXERCISES 4.2a Translate each sentence into predicate logic using the given translation keys.
EXERCISES 4.2b Use the given interpretations to translate the following arguments written in predica
4.3: SYNTAX FOR M
Vocabulary of M
Formation Rules for Wffs of M
How to Expand Our Vocabulary
Summary
EXERCISES 4.3 For each of the following wffs of M, answer each of the following questions:
4.4: DERIVATIONS IN M
Taking Off the Universal Quantifier
Rule #1: Universal Instantiation (UI)
Putting on the Universal Quantifier
Rule #2: Universal Generalization (UG)
Putting on the Existential Quantifier
Rule #3: Existential Generalization (EG)
Taking off the Existential Quantifier
Rule #4: Existential Instantiation (EI)
Which Singular Term Should I Use?
Instantiation and Generalization Rules and Whole Lines
Instantiating the Same Quantifier Twice
Summary
Rules Introduced
EXERCISES 4.4a Derive the conclusions of the following arguments.
EXERCISES 4.4b Translate each of the following paragraphs into arguments written in M, using the giv
EXERCISES 4.4c Find the errors in each of the following illicit inferences. Some of the arguments ar
4.5: QUANTIFIER EXCHANGE
Quantifier Exchange (QE)
Some Transformations Permitted by QE
Summary
Rules Introduced
EXERCISES 4.5a Derive the conclusions of each of the following arguments. Do not use CP or IP.
EXERCISES 4.5b Translate each of the following arguments into propositions of M. Then, derive the co
4.6: CONDITIONAL AND INDIRECT PROOF IN M
Derivations in Predicate Logic with CP
Derivations in Predicate Logic with IP
Logical Truths of M
Summary
EXERCISES 4.6a Derive the conclusions of the following arguments.
EXERCISES 4.6b Translate each of the following arguments into propositions of M. Then, derive the co
EXERCISES 4.6c Derive the following logical truths of M.
4.7: SEMANTICS FOR M
Interpretations, Satisfaction, and Models
Logical Truth: Semantic Arguments
Summary
EXERCISES 4.7a Construct models for each of the following theories by specifying a domain of interpr
EXERCISES 4.7b Show, semantically, that the following propositions selected from Exercises 4.6c are
4.8: INVALIDITY IN M
Domains of One Member
Domains of Two Members
Constants
Domains of Three or More Members
Propositions Whose Main Operator Is Not a Quantifier
Logical Truths
Overlapping Quantifiers
Negations of Quantified Formulas
Summary
EXERCISES 4.8a Show that each of the following arguments is invalid by generating a counterexample.
EXERCISES 4.8b Show that each of the invalid arguments from Exercises 4.4c, listed here, is invalid.
EXERCISES 4.8c For each argument, determine whether it is valid or invalid. If it is valid, derive t
EXERCISES 4.8d For each proposition, determine if it is a logical truth. If it is a logical truth, p
KEY TERMS
Chapter 5: Full First-Order Logic
5.1: TRANSLATION USING RELATIONAL PREDICATES
Quantifiers with Relational Predicates
People and Things and Using Relational Predicates Instead of Monadic Ones
Wide and Narrow Scope
More Translations
The Power of F
Summary
EXERCISES 5.1a Translate each of the following into predicate logic using relational predicates.
EXERCISES 5.1b Use the translation key to translate the formulas into natural English sentences.1
EXERCISE 5.1c, A WRITING ASSIGNMENT Consider the formalization in F of William Carlos Williams’s
5.2: SYNTAX, SEMANTICS, AND INVALIDITY IN F
Formation Rules for Wffs of F
Invalidity in F
Summary
EXERCISES 5.2a Construct models for each of the given theories by specifying a domain of interpretat
EXERCISES 5.2b Show that each of the following arguments is invalid by generating a counterexample.
5.3: DERIVATIONS IN F
The Restriction on UG
Accidental Binding
More Derivations
Logical Truths
Summary
EXERCISES 5.3a Derive the conclusions of each of the following arguments.
EXERCISES 5.3b Translate each of the following arguments into propositions of F using the indicated
EXERCISES 5.3c Derive the following logical truths of F.
EXERCISES 5.3d For each argument, determine whether it is valid or invalid. If it is valid, derive t
5.4: THE IDENTITY PREDICATE: TRANSLATION
Introducing Identity Theory
Syntax and Rules for Identity Statements
Translation
SIMPLE IDENTITY CLAIMS
EXCEPT AND ONLY
SUPERLATIVES
AT LEAST AND AT MOST
EXACTLY
DEFINITE DESCRIPTIONS
Summary
EXERCISES 5.4 Translate into first-order logic, using the identity predicate where applicable.
5.5: THE IDENTITY PREDICATE: DERIVATIONS
Rules Governing Identity
Conventions for Derivations with Dropped Brackets
Summary
Rules Introduced
EXERCISES 5.5a Derive the conclusions of each of the following arguments.
EXERCISES 5.5b Translate each of the following arguments into F, using the given terms and the ident
EXERCISES 5.5c Derive the following logical truths of identity theory.
5.6: TRANSLATION WITH FUNCTIONS
Vocabulary of FF
Formation Rules for wffs of FF
Semantics for FF
Translations into FF and Simple Arithmetic Functions
Summary
EXERCISES 5.6 Use the given key to translate the following sentences into FF.
5.7: DERIVATIONS WITH FUNCTIONS
Derivations and Functional Structure
Derivations with Functors
Summary
EXERCISES 5.7a Derive the conclusions of each of the following arguments.
EXERCISES 5.7b Translate each of the following arguments into FF. Then, derive the conclusion using
KEY TERMS
Chapter 6: Beyond Basic Logic
6.1: NOTES ON TRANSLATION WITH PL
Logical Equivalence and Translation
The Material Conditional and the Biconditional
Inclusive and Exclusive Disjunction
‘Unless’ and Exclusive Disjunction
Summary
For Further Research and Writing
Suggested Readings
6.2: CONDITIONALS
The Material Interpretation of the Natural-Language Conditional
Logical Truths and the Paradoxes of Material Implication
Dependent and Independent Conditionals
Nicod’s Criterion and the First Two Rows of the Truth Table
The Immutability of the Last Two Rows of the Truth Table for the Material Conditional
Subjunctive and Counterfactual Conditionals
Non-Truth-Functional Operators
Counterfactual Conditionals and Causal Laws
Summary
For Further Research and Writing
Suggested Readings
6.3: THREE-VALUED LOGICS
M1. Unproven Mathematical Statements
M2. Future Contingents
M3. Failure of Presupposition
M4. Nonsense
M5. Semantic Paradoxes
M6. The Paradoxes of the Material Conditional
M7. Vagueness
Three Three-Valued Logics
BOCHVAR (OR WEAK KLEENE) SEMANTICS (WK)
STRONG KLEENE SEMANTICS (K3)
ŁUKASIEWICZ SEMANTICS (L3)
Problems with Three-Valued Logics
Avoiding Three-Valued Logics
Summary
EXERCISES 6.3a
For Further Research and Writing
Suggested Readings
6.4: METALOGIC
Consistency
Soundness
Completeness
Decidability
Summary
For Further Research and Writing
Suggested Readings
6.5: MODAL LOGICS
Modal Operators
Formation Rules for Propositional Modal Logic (PML)
Alethic Operators and Their Underlying Concepts
Actual World Semantics
EXERCISES 6.5a Translate each of the following claims into English, and determine their truth values
Semantics for Other Worlds
EXERCISES 6.5b Determine the truth values of each of the following claims at w2 and w3, given the va
Possible World Semantics (Leibnizian)
EXERCISES 6.5c Determine the truth values of each of the following propositions given the values at
Different Worlds, Different Possibilities
Possible World Semantics (Kripkean)
EXERCISES 6.5d Determine the truth values of each of the following formulas, given the universe desc
System S5
Other Modal Logics
Modal Logic: Questions and Criticism
Summary
For Further Research and Writing
Suggested Readings
Solutions to Exercises 6.5a
Solutions to Exercises 6.5b
Solutions to Exercises 6.5c
Solutions to Exercises 6.5d
6.6: NOTES ON TRANSLATION WITH M
Universally Quantified Formulas and Existential Import
‘And’s and ‘Or’s and Universally Quantified Formulas
Quantifiers, Domains, and Charity
Summary
For Further Research and Writing
Suggested Readings
Appendix to 6.6
DERIVING 6.6.7 FROM 6.6.6
DERIVING 6.6.6 FROM 6.6.7
DERIVING 6.6.8 FROM 6.6.9
DERIVING 6.6.15 FROM 6.6.13
DERIVING 6.6.13 FROM 6.6.15
Chapter 7: Logic and Philosophy
7.1: DEDUCTION AND INDUCTION
Hume’s Problem of Induction
Three Problems of Induction
Summary: Logic, Ordinary Reasoning, and Scientific Reasoning
For Further Research and Writing
Suggested Readings
7.2: FALLACIES AND ARGUMENTATION
Formal Fallacies
Informal Fallacies
Irrelevant Premises
Unwarranted or Weak Premises
Causal Fallacies
Ambiguity
Summary
For Further Research and Writing
Suggested Readings
7.3: LOGIC AND PHILOSOPHY OF MIND: SYNTAX, SEMANTICS, AND THE CHINESE ROOM
Theories of the Mind
Functionalism and the Plausibility of AI
Searle and Strong AI
Syntax and Semantics
The Chinese Room
Searle’s Argument
Summary and Conclusion
For Further Research and Writing
Suggested Readings
7.4: LOGIC AND THE PHILOSOPHY OF RELIGION
The Ontological Argument
EXERCISE 7.4a
EXERCISE 7.4b
EXERCISE 7.4c
EXERCISE 7.4d
Evil, Error, Free Will
Theodicy
Summary
For Further Research and Writing
Suggested Readings
7.5: TRUTH AND LIARS
Truth
The Liar and Other Semantic Paradoxes
Explosion, or What’s So Bad About the Paradoxes?
Tarski’s Solution
Collapsing the Hierarchy: Kripke’s Alternative
Is Truth Deflationary or Inflationary?
Summary: Did Tarski Present the Final Word on Truth?
For Further Research and Writing
Suggested Readings
7.6: NAMES, DEFINITE DESCRIPTIONS, AND LOGICAL FORM
Frege’s Puzzle, Names, and Other Denoting Phrases
The Problem of Empty Reference
Summary: Russell and Frege
Bonus Quote
For Further Research and Writing
Suggested Readings
7.7: LOGICISM
Two Aspects of the Logicist Project
Naive Set Theory
Frege’s Definitions
Russell’s Paradox
After the Paradox
Summary: Is Mathematics Logic?
For Further Research and Writing
Suggested Readings
Appendix on the Logical Equivalence of the Rules of Equivalence
Terms
Names of Languages
Symbols
Abbreviations for Rules
Solutions to Selected Exercises
EXERCISES 1.4
EXERCISES 1.5
EXERCISES 2.1a
EXERCISES 2.1b
EXERCISES 2.1c
EXERCISES 2.1d
EXERCISES 2.2
EXERCISES 2.3a
EXERCISES 2.3b
EXERCISES 2.3c
EXERCISES 2.4
EXERCISES 2.5a
EXERCISES 2.5b
EXERCISES 2.6
EXERCISES 2.7a
EXERCISES 2.7b
EXERCISES 3.1a
EXERCISES 3.1b: TRANSLATIONS
EXERCISES 3.1b: DERIVATIONS
EXERCISES 3.2a
EXERCISES 3.2b
EXERCISES 3.2c: TRANSLATIONS
EXERCISES 3.2c: DERIVATIONS
EXERCISES 3.3a
EXERCISES 3.3b: TRANSLATIONS
EXERCISES 3.3b: DERIVATIONS
EXERCISES 3.4a
EXERCISES 3.4b
EXERCISES 3.4c: TRANSLATIONS
EXERCISES 3.4c: DERIVATIONS
EXERCISES 3.5a
EXERCISES 3.5b: TRANSLATIONS
EXERCISES 3.5b: DERIVATIONS
EXERCISES 3.6a
EXERCISES 3.6b
EXERCISES 3.6c: TRANSLATIONS
EXERCISES 3.6c: DERIVATIONS
EXERCISES 3.7a
EXERCISES 3.7b: TRANSLATIONS
EXERCISES 3.7b: DERIVATIONS
EXERCISES 3.8a
EXERCISES 3.8b
EXERCISES 3.9a
EXERCISES 3.9b: TRANSLATIONS
EXERCISES 3.9b: DERIVATIONS
EXERCISES 3.9c
EXERCISES 3.10a
EXERCISES 3.10b
EXERCISES 4.1a
EXERCISES 4.1b
EXERCISES 4.2a
EXERCISES 4.2b
EXERCISES 4.3
EXERCISES 4.4a
EXERCISES 4.4b: TRANSLATIONS
EXERCISES 4.4b: DERIVATIONS
EXERCISES 4.4c
EXERCISES 4.5a
EXERCISES 4.5b: TRANSLATIONS
EXERCISES 4.5b: DERIVATIONS
EXERCISES 4.6a
EXERCISES 4.6b: TRANSLATIONS
EXERCISES 4.6b: DERIVATIONS
EXERCISES 4.6c
EXERCISES 4.7a
EXERCISES 4.7b
EXERCISES 4.8a
EXERCISES 4.8b
EXERCISES 4.8c
EXERCISES 4.8d
EXERCISES 5.1a
EXERCISES 5.1b
EXERCISES 5.2a
EXERCISES 5.2b
EXERCISES 5.3a
EXERCISES 5.3b: TRANSLATIONS
EXERCISES 5.3b: DERIVATIONS
EXERCISES 5.3c
EXERCISES 5.3d
EXERCISES 5.4
EXERCISES 5.5a
EXERCISES 5.5b: TRANSLATIONS
EXERCISES 5.5b: DERIVATIONS
EXERCISES 5.5c
EXERCISES 5.6
EXERCISES 5.7a
EXERCISES 5.7b: TRANSLATIONS
EXERCISES 5.7b: DERIVATIONS
Index
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