Logic: A Very Short Introduction

Why this book

Most introductions to logic teach a system and drill its rules. Graham Priest's Logic: A Very Short Introduction does something more unusual and more interesting: it uses logic as a series of doorways into open philosophical problems. Each short topic takes one logical notion — validity, the conditional, necessity, self-reference, vagueness, probability — presents the standard textbook treatment, and then shows the reader exactly where that treatment strains or breaks. The book is short, but it is not simple; it is a guided tour of the places where logic stops being mechanical and starts being contested.

Priest is one of the world's leading logicians and a noted defender of heterodox positions (he is famous for taking some contradictions seriously). That perspective shapes the book: it is honest, throughout, that "the logic everyone learns" is one theory among several, and that the foundations are still argued over. The reader comes away not with a finished toolkit but with something better — an accurate sense of what logic is, what it can settle, and what it cannot.

What is at stake

The book turns on a few load-bearing ideas worth holding onto:

1. Validity is about form, not content. An inference is valid when its conclusion must be true if its premises are — and that "must" depends on the argument's structure, not its subject matter. Naming that structure is the first move of logic, and topic 1 is built on it.
2. The standard answers have known cracks. The material conditional misbehaves; self-reference generates paradox; vagueness defeats classical bivalence; probability hides a "reference class" problem. Priest does not paper over these — each is a topic.
3. A logical puzzle is usually a philosophical question in disguise. "Did the Greeks worship Zeus?" is about reference and existence. "Is time real?" rides on the logic of tense. "Is anything ever the same?" is the logic of identity and change. The topic titles are questions on purpose.
4. There is no single, settled logic. Classical logic is a powerful default, but the book repeatedly shows rival systems doing better on particular problems. Logic is a science with live disagreements, not a closed rulebook.

Who it is for

• Anyone who wants to know what "logic" actually means beyond the loose everyday sense — and is willing to think hard for a short book.
• Students of philosophy — the book is a map of which logical topics open onto which classic problems (existence, time, identity, knowledge).
• Readers of mathematics, computer science, or argumentation who know some formal logic and want to see its philosophical underside and its limits.
• Anyone who enjoyed the puzzle-driven topics of a book like Gödel, Escher, Bach and wants a rigorous, compact follow-up.

How to read this synthesis

The fifteen core topics are loosely cumulative; each is a self-contained puzzle, but later topics assume the vocabulary of earlier ones.

1. The core machinery (ch 1–4) — validity and logical form, truth functions, names and quantifiers, descriptions and existence.
2. The hard cases (ch 5–10) — self-reference, necessity and possibility, conditionals, time, identity and change, vagueness.
3. Reasoning under uncertainty (ch 11–13) — probability, inverse (Bayesian) probability, decision theory.
4. The limits of logic (ch 14–15) — computability and the halting problem, and the incompleteness results: truths that cannot be proved.
5. Back matter — a short history with further reading, plus a Problems set and worked solutions.

Read in order on a first pass. The synthesis preserves each topic's puzzle and can also be used as a reference grid afterward.

Topic index

1. 1. Validity: What Follows from What?
2. 2. Truth Functions — or Not?
3. 3. Names and Quantifiers: Is Nothing Something?
4. 4. Descriptions and Existence: Did the Greeks Worship Zeus?
5. 5. Self-Reference: What Is This Topic About?
6. 6. Necessity and Possibility: What Will Be Must Be?
7. 7. Conditionals: What's in an If?
8. 8. The Future and the Past: Is Time Real?
9. 9. Identity and Change: Is Anything Ever the Same?
10. 10. Vagueness: How Do You Stop Sliding Down a Slippery Slope?
11. 11. Probability: The Strange Case of the Missing Reference Class
12. 12. Inverse Probability: You Can't Be Indifferent About It!
13. 13. Decision Theory: Great Expectations
14. 14. Halt! What Goes There?
15. 15. Maybe It Is True — But You Can't Prove It!
16. A Little History and Further Reading