# Logic and critical thinking

1. Jul 6, 2006

### williams747

I have somehow managed to maintain a "B" in this class, but I need help on this assignment. I have completed it and just need to know if it is wrong and if it is why?

Exercise 10

In the cartoon Doonesbury, the character of Boopsie claimed to be the reincarnated girl friend of the 16th century astrologer, Nostradamus. She explained to her husband B.D. that the world was going to come to an end as Nostradamus had predicted. On the eve of the predicted disaster, Boopsie and B. D. drove to the beach to spend their final moments together. The night passed and the sunrise came without the world coming to an end. Boopsie was puzzled. Why hadn’t the world come to an end as Nostradamus had predicted? B. D. suggested that Nostradamus didn’t really know anything about the end of the world, but Boopsie argued, “No, the world did come to an end, and we are now living in the after-life.”

Give a formal characterization of Boopsie’s reasoning such as illustrated in your textbook on pages 108-115. Identify Boopsie’s theory (5 points), her predicted observation (5 points), the actual observation (5 points), and the auxiliary hypothesis she uses to explain her predictive failure (5 points). Is her auxiliary hypothesis ad hoc? Explain why or why not (10 points). (Total of 30 points)

p=the world is coming to an end theory
q=the world ends predicted observation
-q=the world did not end actual observation
a=the world ended and the after-life began auxiliary hypothesis
Her auxiliary hypothesis would be considered ad hoc because it is compatible with the predicted observation even though no new evidence has been brought in. She is trying to validate a fallacy with her new hypothesis.

Exercise 11

The following passages contain arguments. Identify the form of the argument (5 points) and its name (if it has one) (5 points) and prove whether the argument is valid or invalid (5 points). (60 points total.) The relevant pages in the textbook are 97-101 and 116-120.

First Example: If I am doubting then I am thinking. If I am thinking then I exist. Therefore, if I am doubting then I exist.

p = I am doubting. Argument form: p  q
q = I am thinking. q  r
r = I exist. So, p  r

The argument is an instance of hypothetical syllogism (see page 117) and is valid. It is impossible for the premises of the argument to be true and the conclusion false. The conclusion is false only if p is assigned T and r is assigned F. The variable q must be assigned T to make the first premise true, but it must be assigned F to make the second premise true. Thus, there is no way to give a consistent assignment of truth values for the variables and to have true premises and a false conclusion.

Second Example: If the Bible is the word of God, then every statement asserted in it is true. Every statement asserted in the Bible is true. Therefore, the Bible is the word of God.

p = The Bible is the word of God Argument form: p  q
q = Every statement asserted in the q
Bible is true. So, p

The argument is an instance of affirming the consequent (see page 100). It is an invalid argument because it is possible for the premises to be true and the conclusion false. A truth table proves the case—in the third row of the truth table, the premises are true and the conclusion is false.

1st premise 2nd premise conclusion
p q p  q q p
T T T T T
T F F F T
F T T T F
F F T F F

1. The proposition that 1 is the lowest prime number if and only if 2 is the lowest prime number is false. But 1 is the lowest prime number. Therefore, 2 is not the lowest prime number.

p = 1 is the lowest prime number
q = 2 is not the lowest prime number
p↔q
p
therefore, q Valid
p and q have the same truth value Modus Ponendo Tollens

p q p ↔ q p q
T T T T T
T F F F f
F T T T f
F F T F F

2. If I know that most apples are red, then I believe that most apples are red. I do not know that most apples are red. Therefore I do not believe that most apples are red.

p = know most apples are red
q = believe most apples are red
(p→q)
-p
Therefore, -q
. Modus Tollens-valid

3. She loves me and she loves me not. Therefore, she loves me.
p = she loves me
q = she loves me not
p ^ q
therefore, p
Simplification-valid

4. If you are widely read then you read pornography. But if you are not widely read then you are illiterate. Therefore, either you read pornography or you are illiterate.

r = you are illiterate
p → q
-p → r
Therefore, either q or r
The argument is valid. It is a constructive dilemma with an unstated (and an unnecessary) premise, “p   p.”

5. Either agreeing with one’s government leaders is a necessary condition of being patriotic or it is a sufficient condition. Therefore, one cannot be patriotic and disagree with one’s government leaders.
p = one agreeing with one’s government leaders is a necessary condition of being patriotic
q = one agreeing with one’s government leaders is a sufficient condition
r = one cannot be patriotic
s = one cannot disagree with one’s government
p ۷ q
therefore, r ^ s

Exercise 12. Put the following dilemmas into symbolic form (5 points) and carefully identify the meaning of the sentence variables (5 points). Explain whether escaping between the horns or grasping the bull by the horns is the most promising approach to criticizing the arguments (10 points). The relevant passages in the book are pages 119-120. (Total 40 points)

Example: Jean Valjean is an escaped criminal who has found a new life as the mayor of a small town that prospers under his leadership. In a nearby town, a man is arrested and accused of being Valjean. Valjean struggles with his conscience about whether to turn himself in: “I am the master of hundreds of workers, they all look to me. How can they live if I am not free? If I speak, I am condemned. If I stay silent, I am damned. Must I lie? Can I condemn this man to slavery, pretend I’m not the man I used to be? If I speak, I am condemned. If I stay silent, I am damned.” [from the musical adaptation of Victor Hugo’s Les Misérables]

p = Valjean speaks. Constructive (p  q)  ( p  r)
q = Valjean is condemned. dilemma: p   p
 p = Valjean stays silent. So, q  r
r = Valjean is damned.

The second premise is a tautology and therefore cannot be false. Thus, it is impossible to escape between the horns of this dilemma. Valjean must try to grasp one of the horns of the dilemma. This involves one of the following: either he must show that p might be true and q false or that  p might be true (in which case p would be false) and r could be false. In the book (and the musical adaptation of the book) Valjean “speaks” by revealing his true identity. Because of this he is obliged to again run from the police as a condemned man. Thus, he does not succeed in avoiding the dilemma.

1. Either one’s parents are partly causative of who one is, or they are not. If they are, then God does not create persons “out of “nothing.” If one’s parents are not part-causes of who one is, then the creatures are never causes of anything. Therefore, either God does not create one “out of nothing” or the creatures are never causes of anything [from C. Hartshorne, Wisdom as Moderation].
p = one’s parents are partly causative of who one is proof by contratdiction (p→q)^(-p→r)
q = God does not create persons “out of nothing q v r
-p = one’s parents are not part-causes of who one is
r = creatures are never causes of anything

the first premise is a tautology and cannot be false. You have to grasp one of the horns of the dilemma. You would need to prove that q is false.

2. If he joins the resistance in Paris then he will violate his duty to his ailing mother for whom he has cared all these years. If he stays at home to take care of his mother then he will violate his duty to his country by not resisting the Nazis. Either he will join the resistance in Paris or stay at home to take care of his mother. In either case, he violates a duty. [from Jean-Paul Sartre, Existentialism is a Humanism].

2. Jul 6, 2006

### HallsofIvy

Staff Emeritus
Therefore what? You haven't said whether the argument is valid or not.

Are you sure about this? The statement given is that "1 is the lowest prime number if and only if 2 is the lowest prime number " is false. It that equivalent to "1 is the lowest prime number if and only if 2 is not the lowest prime number"? Suppose the intial statement had been "1 is the lowest prime number if and only if 3 is the lowest prime number" is false. Would that make "1 is the lowest prime number if and only if 3 is not the lowest prime number" true (be careful- 1 is not a prime number!).
Once again you are assuming that not(a^b) (a= is patriotic, b= agrees with one's government leaders) is the same as (not a)^(not b)- and that's not true.

Why haven't you done this one?

Last edited: Jul 6, 2006