Logic Final

Question 1

Describe the difference and relationship between deduction and induction (short answer).

Answer 1

Deductive arguments are those in which the conclusion follows with logical necessity from the premises. Inductive arguments provide only probable, but never logically certain justification of their conclusions. The truth value of the content of an inductive argument always determines whether it is good or bad, whereas a deductive argument is perfectly valid if its form is correct, regardless of the content.

Question 2

What is the definition of a syllogism?

Answer 2

A form of reasoning where a conclusion is drawn from two premises which each share a term in the conclusion, and a common middle term not present in the conclusion.

Question 3

What is the correct form of a categorical syllogism?

Answer 3

The Middle Term (M) must be in the two premises. The conclusion’s predicate (P) must be in the first premise, and the conclusion’s subject (S) must be in the second premise.

Question 4

Is the following hypothetical syllogism valid or invalid?

Either it will rain or it will snow. It will not snow. Therefore, it will rain.

Answer 4

Valid

Question 5

Is the following hypothetical syllogism valid or invalid?

Either God or nature causes disasters. Nature causes disasters. Therefore, God does not.

Answer 5

Invalid – The second proposition must be in the negative sense and the conclusion positive. A or B. Not B. Therefore, A.

Question 6

Is the following hypothetical syllogism valid or invalid?

You must be either a liar or a fool. You’re not a fool, so you must be a liar.

Answer 6

Valid

Question 7

Is the following hypothetical syllogism valid or invalid?

Either the professor’s theory of general insanity is true or I’m insane. But the professor’s theory is not true. Therefore, I am not insane.

Answer 7

Invalid – The conclusion must be positive.

Question 8

Use the counterexample method to determine the validity of this categorical syllogism:

All squirrels are animals
Some wombats are not squirrels
Therefore, some wombats are not animals

Answer 8

All men are human
Some boys are not men
Therefore, some boys are not human

Question 9

Use the counterexample method to determine the validity of this categorical syllogism:

All tigers are mammals
All tigers are animals
Therefore, all animals are mammals

Answer 9

All circles are round
All circles are shapes
Therefore, all shapes are round

Question 10

Use the counterexample method to determine the validity of this categorical syllogism:

No fish are mammals
Some dogs are not fish
Therefore, some dogs are mammals

Answer 10

No pedestrians are cars
Some skateboarders are not pedestrians
Therefore, some skateboarders are cars

Question 11

What are the five rules used to determine the validity of a categorical syllogism?

Answer 11

1. The middle term must be distributed at least once.
2. If a term is distributed in the conclusion, then it must be distributed in a premise.
3. Two negative premises are not allowed.
4. A negative premise requires a negative conclusion and vice versa.
5. If both premises are universal, the conclusion cannot be particular.
   If and argument passes rules 1-4 it is conditionally valid.
   If an argument passes all 5 rules it is unconditionally valid.

Question 12

Identify whether the subject (S) or predicate (P) is distributed for each of the A E I O categorical propositions.

Answer 12

1. All S is P (S is distributed.)
2. No S is P (S and P are distributed.)
3. Some S is P (Nothing is distributed.)
4. Some S is not P (P is distributed.)

Question 13

Use the five rules to determine the validity of this categorical syllogism:

All neutron stars are things that produce intense gravity.
All neutron stars are extremely dense objects.
Therefore, all extremely dense objects are things that produce intense gravity.

Answer 13

Invalid because it breaks rule #2.

Question 14

Use the five rules to determine the validity of this categorical syllogism:

All ozone molecules are good absorbers of ultraviolet rays.
All ozone molecules are things destroyed by chlorine.
Therefore, some things destroyed by chlorine are good absorbers of ultraviolet
rays.

Answer 14

Conditionally valid because it only breaks rule #5.

Question 15

Use the five rules to determine the validity of this categorical syllogism:

No insects that eat mosquitoes are insects that should be killed.
All dragonflies are insects that eat mosquitoes.
Therefore, no dragonflies are insects that should be killed.

Answer 15

Valid

Question 16

Use the five rules to determine the validity of this categorical syllogism. Put it in standard form first:

No illegal aliens are people who have a right to welfare payments, and some migrant workers are illegal aliens. Thus, some people who have a right to welfare payments are migrant workers.

Answer 16

No illegal aliens are people who have a right to welfare payments.
Some migrant workers are illegal aliens.
Therefore, some people who have a right to welfare payments are migrant workers.

invalid because it breaks rule #4.

Question 17

What is the difference between rationalism and empiricism?

Answer 17

Rationalism is an epistemology that requires certainty in order to have knowledge.
Empiricism is an epistemology that argues that the only reliable source of knowledge is pure experience.

Question 18

Describe the flaws of foundationalism.

Answer 18

Foundationalism is a theory of knowledge that requires absolute certainty for all justifications.
Foundationalist philosophers believe that their assumptions are true and they can and should prove it.
Aristotelians realists believe that assumptions do not need to be proven, not that assumptions are bad, but you have to start with the right, common sense assumptions.
Human fallibility must be acknowledged when it comes to assumptions.
Aristotelians argue that the only legitimate goal of epistemology is to explain how we know, not prove that we know.

Question 19

Is the following an inductive generalizations, argument from analogy, and causal argument?

Jim’s Subaru has a diesel engine, 5 speed transmission, and radial tires. It gets 50 miles per gallon. Therefore, my new Subaru with a diesel engine, 5 speed transmission, and radial tires will get 50mpg.

Answer 19

Argument from analogy

Question 20

Is the following an inductive generalizations, argument from analogy, and causal argument?

The sun rose in the east on June 1, 1900, June 2, June 3, June 4, and so on. Therefore, the sun always rises in the east.

Answer 20

Inductive generalization

Question 21

Is the following an inductive generalizations, argument from analogy, and causal argument?

The way Frank is staggering out of a bar leads me to believe he is drunk.

Answer 21

Effect to cause causal argument

Question 22

Is the following an inductive generalizations, argument from analogy, and causal argument?

Given how much Frank drank tonight, he will be drunk and sick.

Answer 22

Cause to effect causal argument

Question 23

Identify the necessary and sufficient conditions:

Being a bachelor is a ________ condition for being a male, and being a male is a ________ condition for being a bachelor.

Answer 23

Being a bachelor is a sufficient condition for being a male, and being a male is a necessary condition for being a bachelor.

Question 24

Identify the necessary and sufficient conditions:

Being a resident of Atlanta is a ________ condition for being a resident of Georgia, and being a resident of Georgia is a ________ condition for being a resident of Atlanta.

Answer 24

Being a resident of Atlanta is a sufficient condition for being a resident of Georgia, and being a resident of Georgia is a necessary condition for being a resident of Atlanta.

Question 25

Identify the necessary and sufficient conditions:

Completing most of the assignments is a ________ condition for passing the course.

Answer 25

Completing most of the assignments is a necessary condition for passing the course.

Question 26

Identify the necessary and sufficient conditions:

Winning the division is a ________ condition for the Braves to qualify for the playoffs.

Answer 26

Winning the division is a necessary condition for the Braves to qualify for the playoffs.

Question 27

Identify the necessary and sufficient conditions:

Being a natural born citizen is a ________ condition for being President of the United States, and being President of the United States is a ________ condition for being a natural born citizen.

Answer 27

Being a natural born citizen is a necessary condition for being President of the United States, and being President of the United States is a sufficient condition for being a natural born citizen.

Question 28

Explain the fallacy of Cartesian Doubt.

Answer 28

The Cartesian doubt fallacy is when an inductive argument is held to the standards of a deductive argument. For instance, saying that “Jim’s 2016 Toyota Prius gets on average 50mpg, but my exactly same 2016 Toyota Prius may not because some cars are lemons,” is irrelevant. Inductive arguments only need to have some degree of probability, not a deduced certainty.

Question 29

Identify the fallacy in this inductive argument:

I know Sam was obviously drunk and in a fit of rage when he asked for his shotgun. But still Dave promised to return the gun whenever Sam wanted it back. So it was wrong for him to lie about losing the key to the trunk in which he locked the shotgun.

Answer 29

Accident – A rule or generalization has been mechanically levied against an exceptional case.

Question 30

Identify the fallacy in this inductive argument:

Obviously God doesn’t exist. Nobody can prove that he does.

Answer 30

Appeal to Ignorance – Nobody can prove otherwise, so it must be true/false.

Question 31

Identify the fallacy in this inductive argument:

Either the good is that which God loves, or God loves it because it’s good.

Answer 31

Begging the Question – There is no movement from the premise to the conclusion. They’re basically the same.

Question 32

Identify the fallacy in this inductive argument:

I’m sure that Freddy the Fox is the guilty man because my best friend told me that she saw him fire the gun.

Answer 32

False Authority – Hearsay doesn’t hold up in a court of law

Question 33

Identify the fallacy in this inductive argument:

Bob’s V.W. Rabbit, with a diesel engine, radial tires and a five speed transmission gets exactly 52.3 miles per gallon. Therefore, Fred’s V.W. Rabbit with a diesel engine, radial tires and a five speed transmission will also get exactly 52.3 miles per gallon.

Answer 33

Weak Analogy – Insufficient margin for error

Question 34

Identify the fallacy in this inductive argument:

In an extensive poll conducted • in North Dakota, 63% of the 250,000 people responding said they would vote Republican in the next election. Obviously, Obama is in real trouble.

Answer 34

Converse Accident – A hasty generalization has been made on an unrepresentative sample, regardless of the size of the sample.

Question 35

Identify the fallacy in this inductive argument:

Obviously extraterrestrial life exists. After all, no one has ever provided evidence that there isn’t life on other galaxies.

Answer 35

Appeal to Ignorance – Nobody can prove otherwise, so it must be true/false.

Question 36

Identify the fallacy in this inductive argument:

If you start drinking a glass of wine with dinner, pretty soon you’ll be drinking port after dinner, and then whiskey before dinner, and then gin in the morning, and before you know it you’ll be a hopeless alcoholic.

Answer 36

Slippery Slope – Something relatively harmless snowballs into something very harmful.

Question 37

Identify the fallacy in this inductive argument:

Bob’s V.W. is red, has bucket seats, a stereo-tape deck, leather trim, sun roof and he gets over 50 miles per gallon. Therefore, Fred’s red Ferrari with bucket seats, stereo-tape deck, leather trim and a sun roof will probably get nearly 50 miles per gallon also.

Answer 37

Weak Analogy – Irrelevant data.

Question 38

Identify the fallacy in this inductive argument:

Jimmy is a bad boy because he is naughty.

Answer 38

Begging the Question – There is no movement from premise to conclusion. Both are the same thing said a different way.

Question 39

Identify the fallacy in this inductive argument:

America—change it or lose it!

Answer 39

False Dichotomy – An argument that one must choose A or B when there is obviously has at least a third option.

Question 40

Identify the fallacy in this inductive argument:

Since four out of five starters on the L.A. Lakers were members of the All-Star team, and since only one out of five starters on the Boston Celtics was a member of the All-Star team, obviously the Lakers will beat the Celtics in the N.B.A. championship.

Answer 40

Fallacy of Composition – It may not be the case that what’s true of the parts must be true of the whole.

Question 41

Identify the fallacy in this inductive argument:

Since the United States is the richest country in the world, no Americans can be poor.

Answer 41

Fallacy of Division – What is true for the whole may not be true for the parts.