Table of Contents

This is a work in progress. I’ll upload sections and chapters as I finish them.

Introduction

About This Book

Logic as a Tool for Thinking Carefully

The Value of Formal Reasoning Tools

Basic Concepts

Evidence, Reasons, and Arguments

Sentences and Propositions

Recognizing Premises and Conclusions

Propositional Logic

Truth-functional Connectives

Well-formed Formulas (WFFs) of Propositional Logic

Symbolizing English Sentences

Truth Values

Calculating the Truth Value of a Compound Proposition

Calculating Truth Values When Some Components are Unknown

Calculating the Truth Values of Component Propositions

Truth Tables

Properties of Arguments: Validity and Soundness

Basic Concepts

The Truth Table Test for Validity

The Truth Assignment Test for Validity

Properties of Propositions: Tautologies, Contradictions, and Contingencies

Relations between Propositions: Consistency, Entailment, and Equivalence

Inference Rules

Formal Fallacies

Equivalence Rules

Proofs

Proof by Reductio ad Absurdum

Limitations of Propositional Logic

Modal Logic

Possibility and Necessity

Possible World Semantics

Well-formed Formulas (WFFs) of Modal Logic

Symbolizing Modal Propositions

Modal Equivalence Rules

Modal Models

Using Models to Test Validity

Modal Arguments with Non-modal Propositions

Counterfactuals

Predicate Logic

Subjects and Predicates

Variables and Quantifiers

Well-formed Formulas (WFFs) of Predicate Logic

Categorical Propositions

Venn Diagrams

Symbolizing Simple Categorical Propositions

Symbolizing Complex Categorical Propositions

Symbolizing Non-categorical Propositions

The Domain of Quantification

Relational Predicates

Inference and Equivalence Rules

Proofs in Predicate Logic

Non-deductive Inferences

Deductive vs. Inductive Arguments

Inductive Generalization (Enumerative Induction)

Inference to the Best Explanation

Analogical Inferences

Statistical Inferences

Probabilistic Reasoning

Probabilities and Credences

Epistemic and Practical Rationality

Probabilism

Bayesianism

Bayesian Decision Theory

Probabilistic Models of Evidence

The Bayesian Model

The Likelihood Principle