Logic in the Wild

What Logic Actually Is (And What It Isn't)

Validity vs. truth. Why your gut feeling isn't an argument. What formal logic can and can't do for you.

Propositions — The Building Blocks

What a proposition is, cognitive vs. emotive meaning, intension and extension, and what makes a definition actually good.

Arguments — Premises, Conclusions, and the Space Between

Argument structure, deductive vs. inductive, validity vs. soundness, and how to map extended arguments.

Categorical Logic — Statements About Categories

The four categorical forms, the square of opposition, Venn diagrams, and the rules of the valid syllogism.

Logical Connectives — And, Or, Not, If-Then

AND, OR, NOT, IF-THEN, biconditional. Truth-functional definitions. Why "if-then" doesn't mean what most people think.

Truth Tables — The Machine That Settles Arguments

Constructing truth tables, testing for validity, tautologies, contradictions, and the indirect method shortcut.

Logical Equivalences and Why They Matter

De Morgan's Laws, double negation, contraposition, material implication. The moves that let you rewrite arguments cleanly.

Rules of Inference — The Valid Moves

Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, Constructive Dilemma, and more.

Building Proofs

Proof strategy, direct proof, indirect proof, conditional proof. Multiple worked examples from simple to complex.

Beyond Propositions — Predicates and Quantifiers

Predicates, variables, constants, ∀ and ∃. Translating English into predicate logic, including scope and the domain of discourse.

Quantifier Rules and Predicate Proofs

The four quantifier rules with restrictions. Predicate logic proofs and quantifier negation (¬∀ ≡ ∃¬).

Putting It All Together — A Complete Derivation

A full worked example using everything from the book — propositions, quantifiers, inference rules, proof strategy.

Relational Predicates and Identity

Multi-place predicates, overlapping quantifiers (∀x∃y vs ∃x∀y), the identity predicate, uniqueness claims.

When Certainty Isn't the Goal

Strong vs. cogent arguments. The four inductive forms: statistical generalization, analogy, causal inference, abduction. How deductive and inductive reasoning work together.

Formal Fallacies — The Invalid Moves That Look Valid

Affirming the Consequent, Denying the Antecedent, Undistributed Middle, Illicit Major/Minor, Existential Fallacy.

Informal Fallacies — The Tricks People Play

The thirteen fallacies of relevance: Ad Hominem, Genetic Fallacy, Tu Quoque, Appeal to Authority, Appeal to Force, Appeal to Pity, Appeal to Emotion, Bandwagon, Appeal to Tradition, Sunk Cost, Red Herring, Straw Man, Missing the Point.

Informal Fallacies — Assumption and Language

Fallacies of presumption, ambiguity, and illicit transference: Begging the Question, False Dilemma, Slippery Slope, Hasty Generalization, False Cause, Equivocation, Composition, Division, and more.

Logic in the Wild

Six extended case studies: an access control PR, a vendor deck, a political op-ed, a contract clause, a press release, and a job offer you can't decide on.