Chapter 3. Thinking About Our Thinking: An Introduction to Logic

Summary

This chapter…

• Introduces the formal study of logic as the method for distinguishing correct from incorrect reasoning.
• Distinguishes between Deduction and Induction, identifying the two primary ways premises can support a conclusion.
• Explores the concepts of Validity and Soundness, providing a framework for evaluating the structure and truth of deductive arguments.
• Analyzes Inductive Strength and Cogency, explaining how to assess probability and evidence in non-conclusive reasoning.
• Identifies Common Logical Patterns, such as Modus Ponens, Modus Tollens, and Disjunctive Syllogisms.
• Addresses Formal Fallacies, specifically the errors of “Affirming the Consequent” and “Denying the Antecedent.”
• Discusses the “Reasonable Person” Standard, and how logical scaffolding helps overcome personal bias.
• Introduces Visualization Tools like Argument Mapping and Venn Diagrams to clarify complex logical structures.
• Ends with a summary of technical terms and a list of recommended references for mastering formal logic.

Key Terms

• Affirming the Consequent = An invalid logical form: If P, then Q; Q; therefore P.
• Antecedent = The first part of a conditional (“If”) statement.
• Categorical Logic = A system of logic based on the relations between categories or classes of things.
• Categorical Statement = A statement that puts things into classes or excludes them from classes (e.g., “All trout are fish” or “No dogs are reptiles”).
• Co-Premises = Multiple claims that work together as a single reason to support a conclusion.
• Cogent = An inductive argument that is both strong and has true premises.
• Conditional Statement = An “If-Then” statement.
• Consequent = The second part of a conditional (“Then”) statement.
• Deductive Reasoning = Reasoning that aims to provide conclusive, certain support for a conclusion.
• Denying the Antecedent = An invalid logical form: If P, then Q; Not P; therefore not Q.
• Disjunctive Syllogism = A valid logical form: Either P or Q; Not P; therefore Q.
• Independent Reasons = Separate reasons that support a claim regardless of whether other reasons are true.
• Inductive Reasoning = Reasoning that aims to provide probable support for a conclusion.
• Invalid = A deductive argument where the conclusion does not necessarily follow from the premises, even if they are true.
• Modus Ponens = A valid logical form (“Affirming the Antecedent”): If P, then Q; P; therefore Q.
• Modus Tollens = A valid logical form (“Denying the Consequent”): If P, then Q; Not Q; therefore not P.
• Objection = A claim or reason intended to lower confidence in another claim.
• Sound = A deductive argument that is valid and has true premises.
• Strength = The degree to which an inductive argument’s premises make the conclusion probable.
• Syllogism = A logical argument that applies deductive reasoning to arrive at a conclusion based on two or more premises.
• Valid = A deductive argument where, if the premises are true, the conclusion must be true.
• Venn Diagram = A visual tool using overlapping circles to represent the relationships between categories and evaluate validity.