LESSON #17

Rules and Fallacies

Reading Assignment: 5.3 (pp. 274-280)

Click here to skip the following discussion and go straight to the assignments.

Using the five rules to determine the validity/invalidity of categorical syllogisms is a very straight-forward and easy-to-apply method.

You may want to review Lesson #11. You will need to understand which statements are negative (E, O); which statements are universal (A, E); and which statements are particular (I, O).

You will also need to memorize what is distributed in each of the four types of statements (p. 274). You can do these exercises without fully understanding the concept of distribution, although it is always preferable to understand what you can. If a term is distributed, it means that you are saying something about every member of that class of things. For instance, to say that "All cats are furry animals," you are saying something about the entire class of cats, but not about the entire class of furry animals. If someone were to randomly choose one individual from the class of cats, without showing it to you, on the basis of this statement you would know one thing about it--it is a furry animal. But that isn't the case if they chose one individual from the class of furry animals. It could be a cat, but it could just as well be a skunk.

To begin each exercise you should underline or otherwise indicate the distributed terms in each syllogism. Then you should make a chart out to the side with the numbers 1-5. Then you simply go down the list of rules (see inside front cover of Hurley text). If the syllogism passes the rule, put a check mark under the corresponding number and if it breaks the rule, put an X. If it breaks any rule, then the argument is invalid. It must pass all five rules to be valid.

NOTE: When the syllogism is invalid, you should indicate each rule it broke, so you will need to go through all five rules each time.  This is so you'll get practice with all the rules not just the first couple, not because an argument can be "more invalid" if it breaks more than one rule (which isn't true).

 

Logic Coach Assignment: 5.3 I 1-10, II all.

Assignment 1:

Use the rule method to determine whether the following standard form categorical syllogisms are valid or invalid. If invalid, indicate each rule which was violated.

1. Some A are C
No C are B
Some B are not A 

 2. All E are D
 No E are F
Some F are D

3. Some G are H 
Some I are H
Some I are G 

4. All J are K
 Some L are J
Some L are K

5. Some M are not N 
All O are M 
All O are N

6. No P are Q
Some R are Q 
Some R are not P

Assignment 2: (10 points each)

Reconstruct the following syllogisms and use rule method to determine validity/invalidity.

1. AEI-4

2. AAA-2

3. IOA-3

4. AEE-2

EXTRA CREDIT: Check your answers using Venn diagrams (One point each).

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