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1

a. T/F If an argument is deductively strong for one person, then it is deductively strong for everyone else.

False. An argument is deductively strong if it is valid and all the premises are reasonable to believe. A premise is reasonable to believe if your total evidence supports the premise. Since different people may have different evidence, an argument may be deductively strong for one person, but not for another.

2

T/F If an argument is deductively strong for you, then it is reasonable for you to believe the conclusion of the argument.

True. An argument is deductively strong if it is valid and all the premises are reasonable to believe. Being valid means that if the premises are true, the conclusion must be true. Thus, it would be entirely irrational not to believe the conclusion of an argument that is deductively strong for you.

3

T/F All valid arguments with true premises have true conclusions.

True. Being valid means that if the premises are true, the conclusion must be true.

4

T/F If an argument is valid and has true premises, then it is deductively strong for you.

False. A premise or premises may not be reasonable to believe.

5

2. A deductively strong argument can have a false conclusion. How can this happen?

It could happen if the one of the premises is false (but reasonable to believe).

6

3. All the following arguments are valid. For each argument, identify its pattern and then evaluate the strength of the argument.
1. Dr. Laverty doesn't like any violent movies that he sees.
2. Village of Shadows is a violent movie that Dr. Laverty saw.
3. Dr. Laverty didn't like Village of Shadows.

x: Village of Shadows.
A: Violent movies that Dr. Laverty has seen.
B: Things Dr. Laverty doesn’t like.
1. All As are Bs.
2. x is an A.
3. x is a B.

The argument is valid (it has a valid pattern), but since you have no evidence either way, premise 2 is unreasonable (you should suspend judgement), and thus the argument is weak.

7

identify its pattern and then evaluate the strength of the argument. 1. All philosophy students are male.
2. All philosophy students are male.

1. All As are Bs.
2. All As are Bs.

The argument is valid as it has a valid pattern, but premise 1 is unreasonable. Katherine is a counter example. Therefore, the argument is weak.

8

. For each argument, identify its pattern and then evaluate the strength of the argument.
1. If the Liberals don't win the next Ontario election, then either the New Democrats or the Conservatives will.
2. The Liberals won't win the next Ontario election.
3. The New Democrats or the Conservatives will win the next Ontario

P: The Liberals will win the next Ontario election.
Q: The New Democrats will win the next Ontario election.
R: The Conservatives will win the next Ontario election.

1. If ~P then Q or R
2. ~P
3. Q or R

The argument is valid by affirming the antecedent. Premise 1 is reasonable as these are the only parties that have a chance. Premise 3 is reasonable given the latest poll. Therefore, the argument is deductively strong.

9

. For each argument, identify its pattern and then evaluate the strength of the argument.
1. All bachelors are unmarried men.
2. All unmarried men live alone.
3. All bachelors live alone.

A: Bachelors
B: Unmarried men
C: People who live alone.

1. All As are Bs.
2. All Bs are Cs.
3. All As are Cs.

The argument is valid as it has a valid pattern, but premise 2 is unreasonable. My brother is counterexample. Therefore, the argument is weak.

10

. For each argument, identify its pattern and then evaluate the strength of the argument.
1. Either it will rain in Toronto on May 2, 2020 or 2 + 2 = 6.
2. It is not the case that 2 + 2 = 6.
3. It will rain in Toronto on May 2, 2020.

P: It will rain in Toronto on May 2, 2020.
Q: 2 + 2 = 6

1. P or Q.
2. ~Q.
3. P.

The argument is valid by Elimination. However, premise 1 is not reasonable to believe. Neither of the disjuncts are reasonable. P is unreasonable because I have no evidence either way, so I have to suspend judgment. Q is unreasonable since it is obviously false. Therefore, the argument is weak.

11

T/F a. All inductively strong arguments are cogent.

True. An inductively strong argument is cogent, has reasonable premises and is not defeated.

12

T/F b. If an argument is deductively strong for you, then it is also inductively strong for you.

False. Inductively strong arguments are invalid.

13

T/F c. If an argument was inductively strong for you last week, then it must still be inductively strong for you now.

False. Your evidence may change.

14

T/F d. If you evaluate an argument and conclude that it is inductively strong for you, then it is unreasonable for you to reject (disbelieve) the conclusion of the argument.

True. Inductively strong arguments are cogent meaning that if their premises are true, the conclusion is probably true. They also have premises that are reasonable to believe and are not defeated meaning that you have no evidence against conclusion. Therefore, it would be irrational to disbelieve the conclusion of an argument that is inductively strong for you.

15

5. An argument can be inductively strong for a person even though the argument has a conclusion that is actually false. How can this happen? (There are two ways it can happen.)

As with deductively strong arguments, if a premise or premises are false (but reasonable to believe) the conclusion could be false. As well, being cogent means that that the if the premises are true the conclusion is probably true which allows for the possibility that the conclusion is false.

16

6. Evaluate the following arguments.
a.
1. Most Canadians have not lived at 24 Sussex Drive.
2. Stephen Harper is a Canadian.
3. Stephen Harper has not lived at 24 Sussex Drive.

A: Canadians
B: People who have not lived at 24 Sussex Drive.
x: Stephen Harper

1. Most As are Bs.
2. x is an A.
3. x is a B.
The argument is cogent as it has a cogent pattern. Premise 1 is reasonable. 24 Sussex Drive is the Prime Minister’s residence and more Canadians have not been Prime Minister than Canadian that have been Prime Minister. Premise 2 is reasonable. He’s the P.M. But the argument is defeated as being the P.M., I know Stephen Harper lives at 24 Sussex Drive.

17

Evaluate- 1. Some bearded logicians wear glasses.
2. Dr. Laverty is a bearded logician.
3. Dr. Laverty wears glasses.

1. Some As are Bs
2. x is an A
3. x is a B

The argument is ill-formed as shown by the following counter example:

1. Some people are seven feet tall.
2. Dr. Laverty is a person.
3. Dr. Laverty is seven feet tall.

Therefore the argument is weak.

18

Analyze- 1. The Leafs won’t win the Stanley Cup unless they get a good goalie.
2. They’ll get a good goalie.
3. They will win the Stanley Cup.

P: The Leafs won’t win the Stanley Cup
Q: The Leafs will get a good goalie

1. P unless Q
2. Q
3. ~P

“P unless Q” written in standard conditional form is: If ~Q then P. So, the argument’s pattern is:

1. If ~Q then P
2. Q
3. ~P

Therefore, the argument is ill-formed (it’s denying the antecedent) and thus weak.