LESSON #25

Argument Forms and Fallacies

Reading Assignment: 6.6 (pp. 345-356)

Clich here to bypass the following discussion and go straight to the assignment.

Another way to determine whether an argument is valid or invalid is to recognize a particular form of an argument and to know that form is valid or invalid. In this section, you will become acquainted with the most common forms of valid arguments and with some invalid argument forms as well.

The argument forms you need to know are summarized on page 355 in the Hurley text. You should reflect upon the six valid argument forms and try to understand why they are valid. This has to do with the truth functional definitions of the connectives.

For example, consider disjunctive syllogism (DS). What it means for an "v" ("or") to be true is that at least one disjunct is true. Well, if you know that one disjunct is definitely not true (false), then it must be the case that the other side is the true side. Hence:

p v q       I am either dreaming or writing on the computer.
~p          I am not dreaming                    
q             I must be writing on the computer

You should try to think through each of these forms in the same way.

Important! -- Many people have trouble grasping this next point: When you see an argument form listed in a generic way, you must understand that the lower case letters (p, q, r, s) could stand for anything, even a very complex proposition with many letters, operators and parentheses. What is important is the main operator. Anytime you have a statement whose main operator is a "v" then, if you know that one whole side of that connective is false, then you know by disjunctive syllogism that the other side is true.

e.g.

(A · B) v ~(C v D) =   p v q
~(A · B)                =     ~p
~(C v D)                 =      q

We will begin working intensively with these argument forms in the next lesson. So don't rush through this section.

Try to memorize the forms and their names as much as you can. Understanding how they work will be of great help in memorizing them.

Logic Coach Assignment: 6.6 I 1-15.

Assignment:(10 points each)

Identify the forms of the following symbolized arguments, indicating whether the argument is valid or invalid.

2)    C É D
        ~C   
        ~D

3)    E É ~F
        E       
        ~F

4)    G v H
        H      
        ~G

5)   (X É Z) · (~V É W)
        ~Z v ~W             
        ~X v V

6)   I É J
    ~J      
    ~I

7)    (K v L) É M
        M          
        K v L

8)    N É ~O
       ~O É P
        N É P

9)    (Q É R) · (S É  ~P)
        Q v S          
        R v ~P

10)    [(T · U) v V] É (X v Y)
        ~(X v Y)
        ~[(T · U) v V]

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