P or q
If p then r
If q then s
Therefore, r or s
Example,
Either George W. Bush will win the election or John Kerry will win the election.
If George W. Bush wins the election, Republicans will be happy
If John Kerry wins the election, Democrats will be happy
Therefore, either Republicans will be happy or Democrats will be happy.

Also known as indirect proof. Conclusions are established by showing that assuming the opposite of the conclusion leads to absurdity.
Example: If NAFTA is ratified, then wages will go down in the US. If NAFTA is not ratified, then manufacturers will not increase their profits. If manufacturers do not increase their profits, US wages will go down. Either NAFTA will be ratified or it will not. Thus, US wages will go down.

Step 1: Make a dictionary
N=NAFTA is ratified; D=wages will go down;
I= increase their profits
Step 2: Put the argument into logical form:
P1. If N Then D
P2. If not-N then not-I
P3. If not-I then D
P4. Either N or not-N
Therefore, D

Common Valid Deductive Forms: Reductio ad absurdum (continued)
Step 3: Use Reductio strategy
Assume opposite of conclusion :
P1. If N Then D
P2. If not-N then not-I
P3. If not-I then D
P4. Either N or not-N
Therefore, D
P5. Not-D
Now, make inferences from the remaining premises:

Common Valid Deductive Forms: Reductio ad absurdum (continued)
P1. If N Then D
P2. If not-N then not-I
P3. If not-I then D
P4. Either N or not-N
Therefore, D
P5. Not-D
6. Not-N (from P5 and P1 using modus tollens )
7. Not-I (from 6 and P2 using modus ponens )
8. D (from P3 and 7 using modus ponens )
Reductio: P5 and 8 .

Chapter 10: Fallacies
1. Either Men are superior to women or women are superior to men. Men are not superior to women. Hence, women are superior to men
False Dilemma
2. Castro is an anti-democratic dictator.
Everything he says should be taken with a grain of salt.

Chapter 10: Fallacies
3. Why shouldn’t we believe that extra-terrestrial life exists?
No has proven that ET’s don’t exist.
Appeal to Ignorance
4. Obviously, human beings have free will, since they have the power to make choices.
Begging the Question
5. Are you still dating that loser?
Complex question
6. These feminists deny all difference between male and female. But this is absurd, as anyone with eyes can see.
Straw Man

Chapter 10: Fallacies
7. If smoking is not harmful, it should not be maligned. The tobacco companies say that smoking is not harmful.
Therefore, smoking should not be maligned.
Appeal to Authority: take a look at rules 14-17 (pp. 24-31) to find the problem with this argument .
8. Left turn signals frequently occur before an automobile turns left. Right turn signals frequently occur before an automobile turns right. Consequently, turn signals cause automobiles to turn.
False Cause: take a look at rules 18-23 (pp. 32-39) to find the problem with this argument .

Chapter 10: Fallacies
9. If the Cubs acquire Ichiro, they will surely win the World
Series. The Cubs will not acquire Ichiro. Therefore, the
Cubs will not win the World Series.
Denying the antecedent .
BE CAREFUL: this invalid form looks a lot like modus tollens .
10. If I do well on this exam, I’m on my way to an ‘A’ for the semester. I’m on my way to an ‘A’ for the semester.
Therefore, I did well on this exam.
Affirming the Consequent
11. Either you’re with us or you’re against us!
False Dilemma

Fallacies (continued)
12. There are scientific laws. Where there are laws there must be a lawgiver. Hence there must be someone who set up the scientific laws to govern our universe, and this someone could only be G-d.
Equivocation (see chapter 1, rule 7).
13. Miracles are impossible because they simply can’t happen.
Circular argument (also, begging the question )
14. Atheism is absurd. Atheists deny G-d exists because they can’t see him. But, who has seen electrons either?
Straw Man