Book

Logic: A Complete Introduction: Teach Yourself (Complete Introductions)

What this book is

A self-study course in formal logic that takes the absolute beginner from "what is an argument?" through propositional and predicate logic in six steady topics. Lee writes for the reader who has heard logic mentioned in philosophy, mathematics, computer science, or law and wants to understand the actual machinery — not a popular-press gloss.

It is the Teach Yourself series volume: explicit definitions, worked examples at every step, exercises with answers, the assumption that you have no prior training. The pace is faster than a university course and slower than a reference text. By the last topic you can write predicate-logic translations of ordinary-language sentences and check arguments for validity.

The shape of the journey

Executive summary

The book makes three claims that shape how you think about reasoning afterwards.

Validity is about form, not content

A valid argument is one whose conclusion follows from its premises by virtue of the logical structure, regardless of what the sentences are about. "All Greeks are mortal; Socrates is Greek; therefore Socrates is mortal" is valid because of its shape — "All A are B; x is A; therefore x is B" — not because of who Socrates was. This single distinction unlocks the rest of formal logic.

Most everyday "bad arguments" are informal fallacies

Topic 3's catalogue of informal fallacies — ad hominem, straw man, ad populum, post hoc, false dilemma, slippery slope, and a few dozen others — covers what 90% of media and political argument actually does. Naming a fallacy doesn't refute a position, but it does isolate where the bad reasoning sits and gives you the vocabulary to ask the speaker to support the missing inferential step.

Propositional and predicate logic compose

Propositional logic treats whole sentences as atoms connected by "and", "or", "not", "if-then". That is enough for many inferences but too coarse for the "All A are B" pattern. Predicate logic refines this by introducing quantifiers ("for all", "there exists") and predicates over individuals — the machinery that lets you analyse arguments mathematics, science, and law actually use.

Who this is for

Topic index

Topic 1 — What is logic?Arguments, premises, conclusions; validity vs truth; deductive vs inductive; the goal of formal analysis.Topic 2 — MeaningThe relationship between language and logic — sense vs reference, definition, ambiguity, and the hidden assumptions inside ordinary sentences.Topic 3 — Informal fallaciesThe taxonomy of bad arguments: ad hominem, straw man, post hoc, false dilemma, slippery slope, and the rest.Topic 4 — Categorical logicAristotle's syllogistic system — A/E/I/O propositions, the square of opposition, valid figures, and Venn-diagram tests.Topic 5 — Propositional logicThe longest topic. Connectives, truth tables, tautology, contradiction, logical equivalence, and the standard inference rules.Topic 6 — Predicate logicQuantifiers, predicates, variables — translating English into formal notation and proving validity with quantified statements.

How to read these summaries

The topics build linearly. Topic 1 sets up the vocabulary every later topic uses; topics 4 and 5 are the two ways formal logic developed historically (Aristotle vs Frege/Russell) and topic 6 is the modern successor that incorporates both.

If you only have time for half the book, read topics 1, 3, and 5: foundations, the practical fallacies catalogue, and propositional logic.

Concept companions

ArgumentA set of premises offered as support for a conclusion — the basic unit of reasoning.ValidityThe property of an argument whose conclusion follows from its premises by logical structure — distinct from truth.Logical fallacyA defect in reasoning that makes an argument unpersuasive even when its conclusion is true.Propositional logicThe logic of compound sentences built from atomic propositions via 'and', 'or', 'not', 'if-then'.Predicate logicThe logic of quantified statements about individuals — 'for all x', 'there exists x'.