Transcript Class #10

Philosophy 1100
Title:
Critical Reasoning
Instructor:
Paul Dickey
E-mail Address: [email protected]
Website:http://mockingbird.creighton.edu/NCW/dickey.htm
Today:
Class Essay is due.
Exercise 9-7
Student Portfolios returned.
Finish Chapter 9.
Tomorrow (11/12):
Final Exam will be posted on Quia. There will be some
exercises that may require drawing.
Next week:
No Physical Class. Submit Final Essay & FINAL
EXAM by email BEFORE 11/18, 6:00 P.M. For every
4 hours the essay and/or exam is late, a full grade
will be reduced. NO EXCEPTIONS.
1
Class Workshop (Long Method)
Exercise 9-7
Laziness is the Mother of Invention
However there is often an easier way to demonstrate
validity with truth tables. It is called the short truthtable method.
The basic principle of this method simply is to look for a
row that makes the argument invalid. As soon as you
find one, you are done. If you exhaust all
opportunities and can’t, then the argument is valid.
Consider the argument:
P -> Q
~Q -> R
~P -> R
The argument could be invalid only if the conclusion is
false while the premises are true.
P Q R
F T F
Thus, the argument is invalid.
Now, consider the argument:
(P v Q) -> R
S -> Q
S -> R
The argument could be invalid only if the conclusion is
false while the premises are true.
To make the conclusion false -P
Q
R
F
S
T
To make the second premise true -P
Q
T
R
F
S
T
But there is no way now to make the first premise
true, so the argument is valid.
Exercises 9-8
1.
K -> (L & G)
M -> (J & K)
B&M
B&G
To make the third premise true –
B
T
M
T
But to make premise 2 true
B
T
M
T
J K
T T
But to make premise 1 true,
B
T
M
T
J K L G
T T T T
But there is no way now to make the conclusion false, so the
argument is valid.
2.
L v (W -> S)
P v ~S
~L -> W
P
To make the conclusion false –
P_
F
But to make premise 2 true,
P S
F F
But to make premise 1 true, we have to introduce additional rows. There
are three ways compatible with the truth-table so far, such that
L & W can be assigned so that premise 3 is true.
P
F
F
F
S
F
F
F
L W (W->S)
T T
F
T F
T
F F
T
***
***
***
The first two of these rows makes premise 3 true, so the argument is
invalid.
Class Workshop (Short Method)
Exercise 9-7
Translation Exercise:
If Scarlet is guilty of the crime, then Ms. White
must have left the back door unlocked and the
colonel must have retired before ten o’clock.
However, either Ms. White did not leave the back
door unlocked, or the colonel did not retire before
ten. Therefore, Scarlet is not guilty of the crime.
Now, is is this valid? Look at page 318
for the long proof. Wow! Now, let’s be
“lazy”…
Deductive
Arguments:
Rules of Induction
Deduction: Group 1 Rules
The basic valid argument patterns of deductive logic
(If doubted, all the rules we discuss below can be confirmed by the
truth-table method) is another method to prove a deductive
argument (that is, to show that it is valid).
•
Modus Ponens (MP)
P -> Q
P____
Q
-- Affirming the antecedent
P
T
T
F
F
Q
T
F
T
F
P->Q
T
F
T
T
Deduction: Group 1 Rules
2.
Modus Tollens (MT)
P -> Q
~Q____
~P
-- Denying the consequent
Deduction: Group 1 Rules
Okay, now that we have two rules to play
with, let’s stop for a minute and see how we
prove an argument valid using the rules.
1.
2.
3.
4.
5.
(P & Q) -> R
S
S -> ~R
~R
~ (P & Q)
/ .’. ~ ( P&Q)
2,3, MP
1,4, MT
3.
Chain Argument
(CA)
P -> Q
Q -> R____
P -> R
4.
Disjunctive Argument
PvQ
~P
Q
5.
Simplification (SIM)
P&Q
P
6.
PvQ
~Q__
P
P&Q
Q
Conjunction (CONJ)
P
Q__
P&Q
(DA)
7.
Addition
P
PvQ
8.
(ADD)
Q
PvQ
Constructive Dilemma
(CD)
P –> Q
R -> S
P v R
Q v S
9.
Destructive Dilemma
P –> Q
R -> S
~Q v ~S
~P v ~R
(DD)
Exercises 9-10
#1
1.
2.
3.
R -> P
Q -> R
Q -> P
/ .’. Q -> P
1,2, CA
#2
1.
2.
3.
4.
P -> S
PvQ
Q -> R
SvR
/ .’. S v R
1,2,3, CD
#10
1.
2.
3.
4.
5.
6.
7.
(T v M) -> ~Q
(P -> Q) & (R-> S)
T
TvM
~Q
P -> Q
~P
/ .’. ~P
3, ADD
1, 4, MP
2, SIMP
5, 6, MT