6.6 Argument Forms

A sound deductive argument is valid and has true premises.

A deductive argument is one in which it is claimed that the conclusion necessarily follows from the premises. That is, it is claimed that it is valid.

A valid argument is one in which it is impossible for the premises to be true and the conclusion false.

Or,

If the premises are true, the conclusion must be true.

Or,

There is no line on the truth table (no possible world) where the premises are true and the conclusion is false.

Valid

If James does well on the LSAT, then he will go to law school. James does well on the LSAT; therefore, he will go to law school.

Valid

If James does well on the LSAT, then he will go to law school. James does well on the LSAT; therefore, he will go to law school.

P1. J LP2. JC. L

Valid

J L J L J LT T T T T

T F F T F

F T T F T

F F T F F

Invalid

If James does well on the LSAT, then he will go to law school. James will go to law school; so he does well on the LSAT.

Invalid

If James does well on the LSAT, then he will go to law school. James will go to law school; so he does well on the LSAT.

P1. J LP2. LC. J

Invalid

B D J L L JT T T T T

T F F F T

F T T T F

F F T F F

Valid

P1. J LP2. JC. L

Invalid

P1. J LP2. LC. J

Valid

P1. J LP2. JC. L

Invalid

P1. J LP2. LC. J

P1. If Renée is from CA, then she runs marathons.P2. Renée is from CA.So, she runs marathons.

P1. If God exists, then life has meaning. P2. God exists.C. Therefore, life has meaning.

P1. Monkeys eat tulips. P2. If monkeys eat tulips, then grape nuts are healthy.C. So, grape nuts are healthy.

P1. If Renée is from CA, then she runs marathons.P2. Renée is from CA.C. So, she runs marathons.

P1. If God exists, then life has meaning. P2. God exists.C. Therefore, life has meaning.

P1. Monkeys eat tulips. P2. If monkeys eat tulips, then grape nuts are

healthy.C. So, grape nuts are healthy.

Validity has to do with the form of the argument, not its content.

We can see the form by translating an argument into propositional logic.

Then, using a truth table we can see whether or not the argument is valid.

Valid Argument Forms

Arguments with certain forms are always valid.

P QPQ

Valid Argument Forms

Modus Ponens (MP)

P QPQVALID

Valid Argument Forms

Arguments with certain forms are always invalid.

P QQP

Valid Argument Forms

Affirming the consequent (AC)

P QQP INVALID

Valid Argument Forms

Modus Tollens (MT)

P Q~Q~PVALID

Valid Argument Forms

Modus Tollens (MT)

P Q / ~Q // ~P

Valid Argument Forms

Denying the Antecedent (DA)

P Q~P~QINVALID

Valid Argument Forms

Denying the Antecedent (DA)

P Q / ~P // ~Q

Disjunctive Syllogism (DS)

P v Q P v Q~P ~QQ P

VALID

Affirming a Disjunct (AD)

P v Q P v QP QQ (or ~Q)P (or ~P)

INVALID

(Pure) Hypothetical Syllogism (HS)

P QQ RP R

Constructive Dilemma (CD)

(P Q) • (R S)P v RQ v SVALID

Constructive Dilemma (CD)

(P Q) • (R S)P v RQ v SVALID

Constructive Dilemma (CD)

(P Q) • (R S)P v RQ v SVALID

Constructive Dilemma (CD)

(P Q) • (R S)P v RQ v SVALID

Destructive Dilemma (DD)

(P Q) • (R S)~Q v ~S~P v ~RVALID

Destructive Dilemma (DD)

(P Q) • (R S)~Q v ~S~P v ~RVALID

Destructive Dilemma (DD)

(P Q) • (R S)~Q v ~S~P v ~RVALID

Destructive Dilemma (DD)

(P Q) • (R S)~Q v ~S~P v ~RVALID

Recognize argument forms by recognizing types of statements, patterns

Recognize argument forms by recognizing types of statements

(F v P) (G O)(F v P)(G O)

Premises can be put in any order

D v (K • J)(D F) • [(K • J)

H]F v H

Premises can be put in any order

D v (K • J)(D F) • [(K • J)

H]F v H

Given a conjunction of 2 conditionals and the disjunction of each of their antecedents, one can validly derive the disjunction of each of their consequents.

Think of negations as “opposite truth value” or the “denial of P”

~A v B H ~S

A SB ~H

1.

N C~C~N

1. MT

N C~C~N

2.

S FF ~LS ~L

2. HS

S FF ~LS ~L

3.

A v ~Z~ZA

3. Invalid (AD)

A v ~Z~ZA

4.

(S ~P) • (~S D)S v ~S ~P v D

4. CD

(S ~P) • (~S D)S v ~S ~P v D

5.

~N~N TT

5. MP

~N~N TT

6.

M v ~B~M~B

6. DS

M v ~B~M~B

7.

(E N) • (~L ~K)~N v K~E v L

7. DD

(E N) • (~L ~K)~N v K~E v L

8.

W ~M~MW

8. INVALID (AC)

W ~M~MW

9.

~B ~LG ~BG ~L

9. HS

~B ~LG ~BG ~L

10.

F O~F~O

10. INVALID (DA)

F O~F~O