Introduction to Logic

Citation

Copi, I. M., Cohen, C., & Rodych, V. (2019). Introduction to Logic (15th ed.). Routledge.

Chapter Summary

The fifteenth edition has 722 pages and fourteen chapters in three parts, followed by appendices, a glossary-index and a set of "Logic Overviews". The publisher's contents also list a foreword, a preface and a short piece titled "A Very Brief History of Logic" ahead of Part I. Irving Copi, who studied under Bertrand Russell, wrote the original; Carl Cohen and Victor Rodych revised it for this edition. The descriptions below rest on the chapter titles and on the publisher's account of what changed in this edition.

Part I: Logic and Language (Chapters 1–4)

• Chapter 1: Basic Logical Concepts. The opening chapter. The publisher says it now uses a simpler and better definition of deductive validity, which the rest of the book, especially Chapters 8–10, relies on.
• Chapters 2–4: Analyzing Arguments; Language and Definitions; Fallacies. These chapters treat ordinary argument before any formal system appears: how arguments are analysed, how language and definitions bear on them, and fallacies.

Part II: Deduction (Chapters 5–10)

• Chapters 5–7: Categorical Propositions; Categorical Syllogisms; Syllogisms in Ordinary Language. The traditional logic of categorical statements and syllogisms, including how to recognise syllogisms in everyday language. The companion website offers Venn diagram testing of syllogisms.
• Chapter 8: Propositional Logic I: Truth-Functional Statements and Arguments. In this edition it has simpler definitions of simple and compound statements and more, and more detailed, examples of the Complete Truth-Table Method.
• Chapter 9: Propositional Logic II: Methods of Deduction. The most heavily revised chapter. The publisher lists a step-by-step account of the Shorter Truth-Table Method, with examples for conclusions of different types; a fuller account of Indirect Proof and a justification of it based on three ways in which an argument can be valid; a new section on Conditional Proof alongside the 19 Rules of Inference and Indirect Proof; proofs of tautologies; and a closing section on the difference between sound and demonstrative arguments.
• Chapter 10: Predicate Logic: Quantification Theory. The extension from propositional logic to quantified statements.

Part III: Induction (Chapters 11–14)

• Chapters 11–14: Analogical Reasoning; Causal Reasoning; Science and Hypothesis; Probability. The inductive half of the book, moving from reasoning by analogy and about causes to the logic of scientific hypotheses and to probability.

Appendices and Back Matter

Three appendices are new to this edition: one on making the Shorter Truth-Table Technique more efficient by choosing the most efficient sequence of steps, one on Step 1 calculations for multiple-line shorter truth tables, and one on unforced truth-value assignments, invalid arguments and Maxims III–V. Other listings of the book's contents also show an appendix on graduate-level admission tests and solutions to selected exercises; check which of these the edition in hand includes.

Key Concepts

Part I: Logic and Language

• Deductive validity: the central notion of Chapter 1, defined more simply in this edition.
• Fallacies: patterns of faulty reasoning, which have a chapter to themselves.

Part II: Deduction

• Categorical proposition and categorical syllogism: the statement forms and three-statement arguments of traditional logic.
• Truth-functional statements and the Complete Truth-Table Method: testing arguments by listing all possible truth-value assignments.
• Shorter Truth-Table Method: a faster test for validity that works backward from a conclusion assumed false.
• Rules of Inference, Indirect Proof and Conditional Proof: the formal proof methods of Chapter 9.
• Quantification theory: the logic of "all" and "some" in predicate logic.

Part III: Induction

• Analogical and causal reasoning: arguments that support their conclusions by similarity or by identifying causes.
• Hypothesis and probability: the logic of testing scientific claims and the measure of likelihood.

Critical Analysis

Strengths

• Wide scope in one volume. The contents run from informal argument analysis and fallacies, through traditional syllogistic logic and symbolic logic, to inductive reasoning. A single text can support either a critical reasoning course or a first course in formal logic.
• Gradual progression. The publisher says the revision of Chapters 1, 8 and 9 preserves the book's clear and gradual pedagogical approach, and the new step-by-step treatments of the Shorter Truth-Table Method and of Indirect Proof add worked detail where students usually struggle.
• Companion resources for practice. The publisher's companion website lists a proof checker, complete and shorter truth-table exercises, a truth-table video, Venn diagram testing of syllogisms and hundreds of true/false and multiple-choice questions, which suit self-study, with an instructor's manual and solutions manual for teachers.
• Detailed treatment of proof methods. The publisher says the account of Indirect Proof now justifies it separately for each of the three ways in which an argument can be valid, and adds Conditional Proof, so that students see why the methods work as well as how to apply them.
• A long-established text. The publisher says the book has served thousands of students for more than six decades, and the fifteenth edition is the product of repeated revision.

Limitations

• Length. At 722 pages the book contains more than most single courses can cover, and instructors have to choose among Parts I–III.
• No metatheory or non-classical logic. The chapter list contains no chapters on soundness and completeness, modal logic or other extensions; students who go on to these must turn to a more advanced text.
• Quantification comes late. Predicate logic is reached only at Chapter 10, after nine chapters of earlier material, so a course in modern logic that wants quantifiers early will need to rearrange the order.

Where It Fits in the Course

Copi is the broad first-course text in the logic list: it covers informal reasoning, traditional syllogistic logic, symbolic logic and induction in one volume. Barker-Plummer, Barwise and Etchemendy's Language, Proof and Logic is the alternative if the goal is a first-order logic course taught with software for truth tables, proofs and models, and its later chapters reach soundness, completeness and a sketch of Gödel's first incompleteness theorem, topics that do not appear in Copi's chapter list.

Theodore Sider's Logic for Philosophy is a second course that presupposes the basics Copi teaches and goes into modal logic and rigorous proofs about logical systems. Boolos, Burgess and Jeffrey's Computability and Logic is a mathematically rigorous text on computability and the metatheory of first-order logic, and is for later study.

How to Use This Book

The book is meant for undergraduates in philosophy, law, computer science and other fields with no previous logic; secondary-school mathematics is enough.

A practical plan:

• For a critical reasoning course: Part I (Chapters 1–4), the traditional logic of Chapters 5–7, and then Part III (Chapters 11–14).
• For a first course in formal logic: Chapter 1 for the central definitions, then Chapters 8–10 as the core. Work Chapter 8 until truth tables are routine before moving to the deductive methods of Chapter 9, and give Chapter 10 the remaining time.
• Practise actively: use the companion website's proof checker and truth-table exercises, and the solutions to selected exercises, if they are available in the edition in use. The appendices on the efficiency of the shorter truth-table technique are for readers who want to speed up.
• Use the "Logic Overviews" listed at the end of the book as a place to review the main definitions and methods before moving on, if the edition in hand includes them in that form.