Propositional Logic

1
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 q__ p
Not to be confused with
p v q p__ q
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 r ? q p ? r
Not to be confused with
p ? q q ? r p ? r
4
Arguments Forms and Fallacies

• Modus Ponens (Method of Affirming)
• The fallacy in red is called Affirming the
  Consequent.

p ? q q___ p
Not to be confused with
p ? q p___ q
5
Arguments Forms and Fallacies

• Modus Tollens (Method of Destroying)
• The fallacy in red is called Denying the
  Antecedent.

p ? q p__ q
Not to be confused with
p ? q q___ p
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.
• Were going to get either Hillary or Obama as the
  next president. So, well 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
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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 doesnt want a philanderer or it
  doesnt want a religious nut. So, we wont get
  Giuliani or we wont 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