Synopses & Reviews
This text is designed for those instructors who desire a comprehensive introduction to formal logic that is both rigorous and accessible to students encountering the subject for the first time. Numerous, carefully crafted exercise sets accompanied by clear, crisp exposition give students a firm grasp of basic concepts and take the student from sentential logic through first-order predicate logic, the theory of descriptions, and identity. As the title suggests, this is a book devoted not merely to logic; students will encounter an extraordinary amount of philosophy as well. Upon completing the first two parts of the text, a student will be well prepared for advanced courses in analytic philosophy. The last part deals with supplemental matters-informal fallacies, modal logic, and inductive logic, among others.
Synopsis
This text is designed for those instructors who desire a comprehensive introduction to formal logic that is both rigorous and accessible to students encountering the subject for the first time. Numerous, carefully crafted exercise sets accompanied by clear, crisp exposition give students a firm grasp of basic concepts and take the student from sentential logic through first-order predicate logic, the theory of descriptions, and identity. As the title suggests, this is a book devoted not merely to logic; students will encounter an extraordinary amount of philosophy as well. Upon completing the first two parts of the text, a student will be well prepared for advanced courses in analytic philosophy. The last part deals with supplemental matters?informal fallacies, modal logic, and inductive logic, among others.
Synopsis
This text is designed for those who desire a comprehensive introduction to logic which is both rigorous and student friendly. Numerous, carefully graded exercise sets accompanied by crisp, clear exposition take the student from sentential logic through first order predicate logic with identity. The rules are carefully motivated and compared to other systems of rules for sentential and predicate logic. The text includes a solid range of additional material, including chapters devoted to Aristotelian logic, informal logic, inductive logic, and modal, epistemic, and deontic logics. Through all editions, the goal has been to make symbolic logic understandable for the typical student. Careful explanation and pedagogy make this the easiest text from which to learn symbolic logic.
About the Author
Alan Hausman received a Ph.D. in philosophy from Iowa State University and now teaches philosophy at Hunter College. He has published extensively on history of early modern philosophy, especially on the work of Hume, and on the work of Nelson Goodman.Howard Kahane (deceased) is considered one of the founders of the critical thinking movement?an approach to logic that makes it less abstract and more practical as a tool for analyzing political and social issues.Paul Tidman received his Ph.D. in philosophy from the University of Notre Dame.
Table of Contents
Preface. 1. Introduction. The Elements of an Argument. Deduction and Induction.Deductive Argument Forms. Truth and Validity. Soundness. Consistency. Consistency and Validity Compared. Contexts of Discovery and Justification. The Plan of This Book. Part 1: SENTENTIAL LOGIC. 2. Symbolizing in Sentential Logic. Atomic and Compound Sentences. Truth Functions. Conjunctions. Nontruth-Functional Connectives. Variables and Constants. Negations. Parentheses and Brackets. Use and Mention. Disjunctions. "Not Both" and "Neither?Nor" Material Conditionals. Material Biconditionals. "Only if" and "Unless" Symbolizing Complex Sentences. Alternative Sentential Logic Symbols. 3. Truth Tables. Computing Truth-Values. Logical Form. Tautologies, Contradictions, and Contingent Sentences. Logical Equivalences. Truth Table Test of Validity. Truth Table Test of Consistency. Validity and Consistency. The Short Truth Table Test for Invalidity. The Short Truth Table Test for Consistency. A Method of Justification for the Truth Tables. 4. Proofs. Argument Forms. The Method of Proof, Modus Ponens and Modus Tollens. Disjunctive Syllogism and Hypothetical Syllogism. Simplification and Conjunction. Addition and Constructive Dilemma. Principles of Strategy. Double Negation and DeMorgan's Theorem. Commutation, Association, and Distribution. Contraposition, Implication, and Exportation. Tautology and Equivalence. More Principles of Strategy. Common Errors in Problem Solving. 5. Conditional and Indirect Proofs. Conditional Proofs. Indirect Proofs. Strategy Hints for Using CP and IP. Zero Premise Deductions. Proving Premises Inconsistent. Adding Valid Argument Forms. The Completeness and Soundness of Sentential Logic. Introduction and Elimination Rules. 6. Sentential Logic Truth Trees. The Sentential Logic Truth Tree Method. The Truth Tree Rules. Details of Tree Construction. Normal Forms and Trees. Constructing Tree Rules for Any Function. Part II: PREDICATE LOGIC. 7. Predicate Logic Symbolization. Individuals and Properties. Quantifiers and Free Variables. Universal Quantifiers. Existential Quantifiers. Basic Predicate Logic Symbolizations. The Square of Opposition. Common Pitfalls in Symbolizing with Quantifiers. Expansions. Symbolizing "Only", "None but", and "Unless." 8. Predicate Logic Semantics. Interpretations in Predicate Logic. Proving Invalidity. Using Expansions to Prove Invalidity. Consistency in Predicate Logic. Validity and Inconsistency in Predicate Logic. 9. Predicate Logic Proofs. Proving Validity. The Four Quantifier Rules. The Five Main Restrictions. Precise Formulation of the Four Quantifier Rules. Mastering the Four Quantifier Rules. Quantifier Negation (QN). 10. Relational Predicate Logic. Relational Predicates. Symbolizations Containing Overlapping Quantifiers. Expansions and Overlapping Quantifiers. Places and Times. Symbolizing "Someone", "Somewhere", "Sometime", and So On. Invalidity and Consistency in Relational Predicate Logic. Relational Predicate Logic Proofs. Strategy for Relational Predicate Logic Proofs. Theorems and Inconsistency in Predicate Logic. Predicate Logic Metatheory. A Simpler Set of Quantifier Rules. 11. Rationale Behind the Precise Formulation of the Four Quantifier Rules. Cases Involving the Five Major Restrictions. One-to-One Correspondence Matters. Accidentally Bound Variables and Miscellaneous Cases. Predicate Logic Proofs with Flagged Constants. 12. Predicate Logic Truth Trees. Introductory Remarks. General Features of the Method. Specific Examples of the Method. Some Advantages of the Trees. Example of an Invalid Argument with at Least One Open Path. Metatheoretic Results. Strategy and Accounting. 13. Identity and Definite Descriptions. Identity. Definite Descriptions. Properties of Relations. Higher-Order Logics. Limitations of Predicate Logic. Philosophical Problems. Logical Paradoxes. 14. Aristotelian Logic. Categorical Propositions. Existential Import. The Square of Opposition. Conversion, Obversion, Contraposition. Syllogistic Logic?Not Assuming Existential Import. Venn Diagrams. Syllogisms. Determining Syllogism Validity. Venn Diagram Proofs of Validity or Invalidity. Five Rules for Determining Validity or Invalidity. Syllogistics Extended. Enthymemes. Sorites. Technical Restrictions and Limitations; Modern Logic and Syllogistic Logic Compared. Part 3: OTHER SYSTEMS OF LOGIC. 15. Informal Logic. The Nature of Fallacy. Fallacy Classification. 16. Inductive Logic. A Mistaken View of Induction and Deduction. Kinds of Inductive Arguments. Cause and Effect. Mill's Methods. Inductive Probability. The Probability Calculus. Bayes' Theorem. Induction Is Unjustified?The Old Riddle of Induction. Not All Instances of Theories Confirm Them?The New Riddle of Induction. 17. Axiom Systems. The Nature of an Axiom System. Interpreted and Uninterpreted Systems. Properties of Axiom Systems. Outline of an Axiom System for Sentential Logic. Axiom Systems for Predicate Logic. Other Kinds of Axiom Systems. 18. Alternative Logics. Modal Logic. Strict Implication. Modal Axioms. Modal Theorems. Modal Paradoxes. A Philosophical Problem. Modal Predicate Logic. Epistemic Logic: The Logic of Knowledge and Belief. Epistemic Theorems. Deontic Logic. Problems with Deontic Systems. Answers to Even-Numbered Exercise Items. Bibliography. Special Symbols. Index.