Introduction

About This Book

Logic as a Tool for Thinking Carefully

The Value of Formal Reasoning Tools

Basic Concepts

Definitions and Conceptual Analysis

Four Kinds of Definitions

How to Define a Concept

Necessary and Sufficient Conditions

Finding Counterexamples

Sentences and Propositions

Evidence, Reasons, and Arguments

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

Types of Modality

Possible Worlds

Necessity De Dicto vs. Necessity De Re

Symbolizing Modal Propositions

Modal Equivalences

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 of Predicate Logic

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

Deduction vs. Induction

Types of Non-Deductive Inferences

Enumerative Induction

Statistical Syllogism

Inference to the Best Explanation

Argument by Analogy

Evaluating Non-Deductive Inferences

Evaluating Inductive and Statistical Inferences

Comparing Explanations

Assessing Analogies

Hume’s Problem of Induction

Goodman’s New Riddle of Induction

Confirmation Theory

Hempel’s Theory of Confirmation by Instances

Hypothetico-deductivism

A Primer on Probability

Bayesian Confirmation Theory

Conditionalization

Bayes’s Theorem

Bayesian Bar Diagrams

Bayes Bars with Multiple Hypotheses

Surprising Implications of Bayesianism

Limitations of Bayesianism

Uncertain Evidence

Old Evidence

The Problem of the Priors

Evidence and Rationality

Epistemic Rationality

Logical Consistency and Probabilistic Coherence

Following the Evidence

Probabilistic Models of Evidence

The Bayesian Definition of Evidence

The Likelihood Principle

Measuring the Strength of Evidence

Cumulative Evidence

Practical Rationality

Bayesian Decision Theory

Representing Subjective Value