6.6 argument forms
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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. . - PowerPoint PPT PresentationTRANSCRIPT
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