1. 6.6 Argument Forms and Fallacies
Propositional Logic
6.6 Argument Forms and Fallacies

2. Arguments Forms and Fallacies
Disjunctive Syllogism p v q / q // ~p … test it with a truth table
p v q
~p__ q
Not to be confused with…
p v q
q__ ~p

3. Arguments Forms and Fallacies
Pure Hypothetical Syllogism Pure Hypothetical Syllogism requires a chain be made where the argument in red fails to make one.
p  q
q  r
p  r
Not to be confused with…
p  q
r  q
p  r

4. Arguments Forms and Fallacies
Modus Ponens (Method of Affirming) The fallacy in red is called Affirming the Consequent.
p  q
p___ q
Not to be confused with…
p  q
q___ p

5. Arguments Forms and Fallacies
Modus Tollens (Method of Destroying) The fallacy in red is called Denying the Antecedent.
p  q
~q___ ~p
Not to be confused with…
p  q
~p__ ~q

6. Arguments Forms and Fallacies
Constructive Dilemma Destructive Dilemma
(p  q) • (r  s)
p v r________
q v s
p  q
p___ q
See Modus Ponens in CD?
p  q
~q___ ~p
(p  q) • (r  s)
~q v ~s______
~p v ~r
See Modus Tollens in DD?

7. Arguments Forms and Fallacies
If we get Hillary, then we get socialism. If we get Obama, then we get naïveté. We’re going to get either Hillary or Obama as the next president. So, we’ll either have socialism or naïveté . Symbolizing… (H  S) • (O  N) H v O_________ S v N

8. Arguments Forms and Fallacies
To refute constructive and destructive dilemmas (you refute both the same way), you either
Grasp by the horns
Escape between the horns
For example,
Grasping by the Horns
Prove the conjunctive premise false by proving either conjunct false
(H  S) • (O  N)
T  F F
Show Hillary is a strong defender of free markets, say
For example,
Show, say, Edwards is going to win
Escaping between the Horns
Prove the disjunctive premise false
H v O
F F F

9. Refuting Constructive and Destructive Dilemmas
If we get Giuliani, then we get a philanderer. If we get Huckabee, then we get a religious nut. Either the US doesn’t want a philanderer or it doesn’t want a religious nut. So, we won’t get Giuliani or we won’t get Huckabee as president. Symbolizing… (G  P) • (H  N) ~P v ~N__________ ~G v ~H

10. Arguments Forms and Fallacies
To refute constructive and destructive dilemmas (you refute both the same way), you either
Grasp by the horns
Escape between the horns
For example,
Grasping by the Horns
Prove the conjunctive premise false by proving either conjunct false
(G  P) • (H  N)
F T  F
Show Huckabee has reasonable religious views
For example,
Show America minds neither philanderers nor religious nuts
Escaping between the Horns
Prove the disjunctive premise false
~P v ~N
F F F