Critical Thinking: A User’s Manual Chapter 7 Evaluating Categorical Arguments

Categorical Arguments A categorical argument is a deductive argument that contains categorical claims. A categorical claim is a claim that relates two categories of things.

Categorical Claims All cats are mammals. No cats are dogs. Some mammals are cats. Some mammals are not cats.

Anatomy of Categorical Claims All cats are mammals. copula Quantifier Subject Term Predicate Term

Your turn! Identify the subject term, the predicate term, and the copula for the following claim. No dogs are fish.

Categorical Claims The quantifier indicates the quantity and quality of the claim. Quantity may be universal or particular. Quality may be affirmative or negative.

Standard Form A claim: Universal Affirmative All S are P E claim: Universal Negative No S are P I claim: Particular Affirmative Some S are P O claim: Particular Negative Some S are not P

Translating Categorical Claims Both the subject and predicate terms must be translated into plural nouns. Whoever should be expressed in terms of people. Whatever should be expressed in terms of things. Wherever should be expressed in terms of places. Whenever should be expressed in terms of times. Claims about individuals should be translated using the phrase identical to.

Your turn! Translate the following claim into standard form. Wherever extreme poverty exists, life expectancy is low.

Your turn! Translate the following claim into standard form. General Motors is in economic trouble.

Translating Categorical Claims The predicate category cannot be a subset of the subject category.

Your turn! Translate the following claim into standard form. All zebras are living on the African continent.

Translating Categorical Claims Only or none but introduces the predicate of an A claim. The only introduces the subject of an A claim.

Your turn! Translate the following claim into standard form. Only Porsches are true sports cars.

Your turn! Translate the following claim into standard form. The only true sports cars are Porsches.

Categorical Syllogisms A categorical syllogism is a categorical argument containing two premises and a conclusion.

Anatomy of Categorical Syllogisms All cats are mammals. All mammals are animals. All cats are animals. Middle Term Minor Term Major Term

Your turn! Using dogs as the major term, mammals as the minor term, and animals as the middle term, properly insert the terms into the syllogism. All _____ are _____.

Evaluating Categorical Arguments Categorical arguments may be valid or invalid. Demonstrate using a Venn diagram Demonstrate using Rules for Valid Syllogisms

Your turn!

A Claim: All S are P

E Claim: No S are P

I Claim: Some S are P

O Claim: Some S are not P

Labeling a Venn diagram Middle Term Major Term Minor Term

Anatomy of a Venn diagram All cats are mammals. All mammals are animals. All cats are animals.

What does each section represent?

How to Draw Venn Diagrams Step 1: State the argument as a standard form categorical syllogism. Step 2: Draw and label three intersecting circles. Step 3: Shade the sections to represent the universal premises. Step 4: Place an X in the section or on the line to represent any particular premises. Step 5: Determine validity by checking whether the conclusion is represented in the diagram.

We’re certain that Tony’s friend, Jason, is taking drugs We’re certain that Tony’s friend, Jason, is taking drugs. His eyes are always red, and we all know that people on drugs have red eyes.

Rules for Valid Syllogisms The middle term must be distributed at least once. Any term that is distributed in the conclusion must be distributed in a premise. If a premise is negative, the conclusion must be negative, and vice-versa. A valid argument cannot have two negative premises. A valid argument cannot have two universal premises when the conclusion is particular.

Distribution A subject or predicate term is distributed if the claim refers to every member of the group. A claim: All S are P. E claim: No S are P. I claim: Some S are P. O claim: Some S are not P.

We’re certain that Tony’s friend, Jason, is taking drugs We’re certain that Tony’s friend, Jason, is taking drugs. His eyes are always red, and we all know that people on drugs have red eyes.

Completing Enthymemes Step 1: Determine whether the missing claim is a premise or a conclusion. Step 2: Identify which two terms are in the missing claim. Step 3: Determine whether the claim will be affirmative or negative. Step 4: Make sure that terms are properly distributed. Step 5: Verify that all rules for valid syllogisms are followed.

Completing Enthymemes All people identical to Jason are people who have red eyes. All people identical to Jason are people who are on drugs.

Your turn! Find the patterns for term distribution. Both universal claims distribute _______ terms.   Neither particular claim distributes _______ terms. Both negative claims distribute _______ terms. Neither affirmative claim distributes _______ terms.

Complete Analysis plus Evaluation Step 1: Write a Basic Analysis of the passage. Identify the passage. Analyze the passage. Step 2: If it is an argument, determine whether it commits a fallacy. Identify the fallacy, and explain how it is committed. Step 3: If it is a nonfallacious argument, diagram it. Verify that your diagram is consistent with your Basic Analysis.

Complete Analysis plus Evaluation Step 4: Identify the kind of argument. If the argument is deductive, identify it as a categorical argument or a truth-functional argument. If the argument is inductive, identify it as an analogical argument, an inductive generalization, or a causal argument. Step 5: Evaluate the argument. If the argument is categorical, state the syllogism in standard form, and demonstrate whether the argument is valid or invalid using either a Venn diagram or the rules for valid syllogisms.

We’re certain that Tony’s friend, Jason, is taking drugs We’re certain that Tony’s friend, Jason, is taking drugs. His eyes are always red, and we all know that people on drugs have red eyes. This passage contains an argument. The issue is whether Tony’s friend, Jason, is taking drugs. The conclusion is that Tony’s friend, Jason, is taking drugs. The first premise is that Jason’s eyes are always red. The second premise is that people on drugs have red eyes.

We’re certain that  Tony’s friend, Jason, is taking drugs We’re certain that  Tony’s friend, Jason, is taking drugs.  His eyes are always red, and we all know that  people on drugs have red eyes.  +   

This passage contains an argument This passage contains an argument. The issue is whether Tony’s friend, Jason, is taking drugs. The conclusion is that Tony’s friend, Jason, is taking drugs. The first premise is that Jason’s eyes are always red. The second premise is that people on drugs have red eyes. This passage contains a deductive categorical argument. Its standard form is: All people identical to Jason are people who have red eyes. All people who are on drugs are people who have red eyes. All people identical to Jason are people who are on drugs. The argument is invalid because the middle term is not distributed.

The argument is invalid according to the following Venn diagram.