Section 1-2: Logic and Informal Fallacies

Welcome to Professor Baker's Math Class! In this section, we're embarking on a journey into the realm of critical thinking. Specifically, we'll be covering Section 1.2 from "Quantitative Literacy: Thinking Between the Lines", focusing on logic and informal fallacies. Let's sharpen those minds!

Learning Objectives

  • Study of Logic: Understanding the principles that differentiate good reasoning from bad reasoning.
  • Informal Logical Fallacies: Examining common errors in reasoning.

What is Logic?

Logic is the study of the methods and principles used to distinguish correct reasoning from incorrect reasoning. A logical argument contains premises (hypotheses) and a conclusion. The premises are the assumptions we start with, and the argument is valid if the premises justify the conclusion.

Here's an example:

Premise 1: All wizards have white beards.

Premise 2: Gandalf is a wizard.

Conclusion: Therefore, Gandalf has a white beard.

This is a valid argument because the premises do lead to the conclusion.

Understanding Fallacies

A fallacy is an argument that may appear correct but is, in fact, incorrect. There are two main types:

  • Informal Fallacy: Arises from the content of the argument. The argument is incorrect because of what is said, not how it's said.
  • Formal Fallacy: Arises in the form or structure of the argument, independent of its content.

Common Informal Fallacies

Let's explore some common types of informal fallacies:

  1. Fallacies of Relevance: The premises are logically irrelevant to the conclusion. Examples include:
    • Appeal to Ignorance: Claiming something is true because it hasn't been proven false (or vice-versa).
      Example: "No one has proven that aliens haven't visited Earth, so they must have!"
    • Dismissal Based on Personal Attack (Ad Hominem): Attacking the person making the argument, rather than the argument itself.
      Example: "You can't trust his opinion on economics; he's a terrible person!"
    • False Authority: Citing an authority figure who isn't an expert on the topic.
      Example: "A famous actor says this medication is safe, so it must be!"
    • Straw Man: Misrepresenting an opponent's argument to make it easier to attack.
      Example: "My opponent wants to cut military spending, which means they want to leave our country defenseless!"
    • Appeal to Common Practice: Justifying something because it's popular.
      Example: "It's okay to cheat on your taxes because everyone does it."
  2. Fallacies of Presumption: These involve false or misleading assumptions. Examples include:
    • False Dilemma: Presenting only two options when more exist.
      Example: "You're either with us, or you're against us."
    • False Cause: Assuming that because two events are related, one causes the other.
      Example: "Since the new mayor took office, crime has increased. Therefore, the mayor is responsible for the increase in crime."
    • Circular Reasoning (Begging the Question): Restating the argument as the conclusion.
      Example: "This policy is right because it's the right thing to do."
    • Hasty Generalization: Drawing a conclusion based on insufficient evidence.
      Example: "I met two rude people from that town, so everyone from there must be rude."

Inductive vs. Deductive Reasoning

  • Deductive Argument: Draws a conclusion from premises based on logic. If the premises are true, the conclusion *must* be true.
    Example: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
  • Inductive Argument: Draws a conclusion from specific examples. The premises provide only *partial* evidence for the conclusion.
    Example: Every college football player I have ever seen is male. Therefore, all college football players are male.

By understanding these concepts, you'll be well-equipped to analyze arguments critically and avoid common pitfalls in reasoning. Keep practicing, and you'll become a logic master in no time!