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Propositional Logic

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Propositional Logic

6.6 Argument 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

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

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

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

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?

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

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

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

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