Unit 6: Formal fallacies

Introduction

Activity 1: Reading

Remember these three categories of formal fallacies.

Formal fallacies can be categorised into two main groups, namely:

• invalid arguments
• syllogistic fallacies

Each of these groups of formal fallacies are introduced in turn in this unit. We will also consider invalid references, which are usually classed as informal fallacies, but can be explained by reference to structure in conjunction with their content.

Invalid arguments

Activity 2: Thinking

Work alone or in pairs. Answer the following questions about the sentence.

If I speak, my mouth moves.
where P = If I speak, and Q = my mouth moves

P, Q

1. Which is the antecedent P or Q?
2. Which is the consequent P or Q?
3. Does deny mean stating something is true or false?
4. Does affirm mean stating something is true or false?

Activity 3: Thinking

Work alone or in pairs. Answer the following questions.

P　　　　 Q　　　not P 　　not Q

1. Which of the above is denying the antecedent?
2. Which of the above is denying the consequent?
3. Which of the above is affirming the antecedent?
4. Which of the above is affirming the consequent?

Activity 4: Reading

Work alone or in pairs. Answer the following questions.

There are three common invalid arguments, namely affirming the consequent, denying the antecedent and the undistributed middle term.

Examples

1. affirming the consequent If it rains, the street will be wet. The street is wet. Therefore, it rained.
2. denying the antecedent If he is in hospital, then he is sick. He is not in hospital. Therefore, he is not sick.
3. undistributed middle term Some Chinese attended the class. Aiko attended the class. Therefore, Aiko is Chinese.

Notation

1. affirming the consequent
   If P, then Q
   Q
   ∴P
2. denying the antecedent
   If P, then Q
   Not P
   ∴Not Q
3. undistributed middle term
   P -> Q
   R -> Q
   P -> R
   

Activity 5: Watching

Watch this excerpt of the animated version of Star Trek to find an example of affirming the consequent.

Watch this excerpt for three examples of denying the antecedent.

Syllogistic fallacies

Activity 6: Reading

Imperative.

There are four syllogistic fallacies, namely fallacy of four terms, illicit major, illicit minor and affirming a disjunct.

Examples

1. fallacy of four terms All questions have answers. All answers are correct. All professors are correct.
2. illicit major All men are human. No women are men. Therefore, no women are human.
3. illicit minor All English are football fans. All English are tea drinkers. Thus, all football fans are tea drinkers.
4. affirming a disjunct Xin is a professor or a doctor. Xin is a doctor. Therefore, Xin is not a professor.

Notation

1. fallacy of four terms
   SAM
   MAP
   XAP (syllogisms with two premises cannot have more than three terms)
2. illicit major
   All A are B
   No C are A
   ∴ No C are B
   B = major term (error: assuming all humans are men)
3. illicit minor
   All A are B
   All A are C
   ∴ All B are C
   A = major term (error: assuming all football fans are English)
4. affirming a disjunct
   P v Q
   P
   ∴ not Q
   Fallacy of equivocation - Logical disjunct vs. exclusive disjunct (and/or vs or) (v vs. v) (or vs. xor)

Activity 7: Watching

Watch this explanation of formal fallacies (14 min 53 sec). There are a number of examples for you to practice identifying and explaining formal fallacies.

Activity 8: Watching

Watch this explanation of using Venn diagrams to test the validity of logical syllogisms (8 min 02 sec).

Invalid references

Activity 9: Thinking

Read the following examples and explanations to understand the two invalid inferences.

There are two invalid inferences, namely fallacy of composition and fallacy of division. These fallacies are usually (but not always) grouped in informal fallacies by a number of logicians.

Examples

1. fallacy of composition Every sentence in these notes is correct. Therefore, these course notes are correct.
2. fallacy of division This sentence is written in English. Therefore, every sentence in these course notes is written in English.

Notation

1. fallacy of composition
   Let
   w = whole, p = part,　F = Fallacy
   p₁…, p_n are parts of w.
   p₁…, p_n have property F.
   Therefore, w has property F.
2. fallacy of division
   Let
   w = whole, p = part,　F = Fallacy
   w has property F.
   p₁…, p_n have are parts of w.
   Therefore,p₁…, p_n have have property F.

Activity 10: Identifying fallacies

Work alone or in pairs. Identify the fallacy in each of the following arguments.

1. If it rains, the street will be wet. The street is wet. Therefore, it rained.
2. If he is in hospital, then he is sick. He is not in hospital. Therefore, he is not sick.
3. Some Americans came to this university. Xiao Li came to this university. Therefore, Xiao Li is American.
4. All questions have answers. All answers are correct. All professors are correct.
5. All men are human. No women are men. Therefore, no women are human.
6. All English are football fans. All English are tea drinkers. Thus, all football fans are tea drinkers.
7. Xin is a professor or a doctor. Xin is a doctor. Therefore, Xin is not a professor.
8. Every sentence in these notes is correct. Therefore, these course notes are correct.
9. This sentence is written in English. Therefore, every sentence in these course notes is written in English.

Knowledge and application

Activity 11: Video recording

Submit a video (max: 150 seconds) in which you very briefly describe each of the 7 formal fallacies and 2 invalid references. The video must show your face at all times. Do NOT read from notes or the screen, etc. Submit the video clip through ELMS.