PHI-130: Critical Reasoning/LP4 Answer Key

Quizzes 7, 8, 9 and 10

Journal Assignment 7

1. In your own words, explain the difference between deductive and inductive arguments. Write down two examples of each in your journal.

In a deductive argument the premises already contain the conclusion. If all the premises in a deductive argument are true (in a provable sense), then its conclusion must be true also, because the claim asserted by its conclusion has already been stated in its premises. Put differently, in a valid deductive argument the truth of the premises supports with certainty the truth of the conclusion.

Inductive arguments have conclusions that supply more information than is contained in their premises. In an inductive argument the supporting connection between its premises and conclusion is loose and there is no strict proof in induction. We can say that inductive reasoning is a matter of reasonable expectation based on experience, such as observation. Inductive arguments are common in everyday situations and in the domain of science in its search for knowledge.

Example of a deductive argument:

1. If Susan is a mother, then Susan is female.
2. Susan is a mother.
3. Therefore, Susan is female.

Example of inductive argument:

1. The phenomenon of consciousness cannot be explained according to Descartes’ dualistic view of mind and body.
2. Consciousness is not located in the mind, or the body.
3. Therefore, consciousness is a field of experience “situated” in the world.

2. Explain the difference between valid deductive arguments and invalid deductive arguments and then write down two examples of each in your journal.

Validity depends on form. Example of valid deductive argument:

All men are mortal,

Socrates is a man,

Therefore, Socrates is mortal.

The structure of the argument is valid because the premises give sufficient and even necessary support for the conclusion.

Example of invalid deductive argument:

If Philippa is fit, she will run the marathon.

Philippa is not fit.

Therefore, she will not run the marathon.

The structure of the argument is invalid because the premises do not give sufficient support for the conclusion to follow. There might be many reasons why Philippa will not run the marathon: the fact that she is not fit is simply one such reason. Alternatives are possible.

3. In your online references, identify the differences between three major types of inductive arguments. Name each type and write down examples of each in your journal.

Statistical extrapolation

A statistical syllogism proceeds from a generalization to a conclusion about an individual.

• A proportion Q of population P has attribute A.
• An individual X is a member of P.

Therefore:

• There is a probability which corresponds to Q that X has A.

Example 1

• 60% of artists are left handed.
• Paul is an artist.

Therefore:

• there is a 60% probability that Paul is an artist.

Example 2

• 90% of the population is dead by the age of 90.
• Jane will turn 90 this year.

Therefore:

• Jane will likely die this year.

Example 3

• Neoconicotinoid pesticides have been used to kill insects.
• Populations of tree sparrows and common starlings fell 3.5 percent a year compared to the average population trend for their species in areas were concentrations of neonicotinoid pesticides reached more than 20 nanograms/liter.

Therefore:

• Neoconicotinoid pesticides are likely affecting whole ecosystems.

Inductive reasoning by analogy

The process of analogical inference involves noting the shared properties of two or more things, and from this basis inferring that they also share some further property.

• P and Q are similar in respect to properties a, b, and c.
• Object P has been observed to have further property x.
• Therefore, Q probably has property x also.

Example 1

• Carrie and George both attend Columbia University, study hard, are on the Dean’s List, and volunteer with the Harlem Legal Aid Society in their free time.
• Carrie has been admitted to Law School.
• Therefore, it is probable that George has been admitted to Law School.

Analogical reasoning is very frequent in common sense, science, philosophy and the humanities, but sometimes it is accepted only as an auxiliary method. A refined approach is case-based reasoning.

Cause and effect reasoning

A causal inference draws a conclusion about a causal connection based on the conditions of the occurrence of an effect. Premises about the correlation of two things can indicate a causal relationship between them, but additional factors must be confirmed to establish the exact form of the causal relationship.

Example 1

• All evidence to this point suggests that genetic mutations produce cancerous tumors.
  

Therefore, it is likely that genetic mutations produce cancerous tumors.

Example 2

• Germs cause disease.
  

Therefore, washing your hands before eating eliminates germs.
It is likely that washing your hands before meals will keep you healthy

4. What is the difference between a valid argument and a sound argument? Write down two examples of each in your journal.

The validity of arguments refers solely to their structure (form) and not their content. When we establish the validity of an argument we look at the relationship between the premises and the conclusion of the argument. The soundness of arguments refers to the contents of their premises and conclusion. When we assess the soundness, or acceptability, of an argument we want to establish whether or not the evidence provided by the premises is actually true, or acceptable.

Example 1

• Premise: All creatures on the planet Mercury have pointed ears.
• Premise: Beauty is a creature on the planet Mercury.
• Conclusion: Therefore, Beauty has pointed ears.

Example 2

• Premise: All humans lie.
• Premise: Jake is human.
• Conclusion: Therefore Jake lies.

The arguments are valid because their structure is valid. Also, the conclusion follows logically from the premises. But the arguments are senseless. The arguments are unsound because when we evaluate the premises of the arguments, it is clear that the premises do not give adequate evidence for the conclusion to be true.

Quiz 7

1. You can have a sound argument even if your premises are false.
_______ TRUE __x__ FALSE

2. A statement is any claim that either asserts or denies a state of affairs in the world.
___x___ TRUE _____ FALSE

3. Inductive arguments are arguments that go from the general to the particular.
_______ TRUE __x__ FALSE

4. An argument is any group of sentences that describes a situation.
_______ TRUE __x__ FALSE

5. An argument is a series of statements where one or more of these statements is/are intended to establish the truth or acceptability of the conclusion.
__x__ TRUE _____ FALSE

6. An argument must have at least three premises.
_____ TRUE __x__ FALSE

7. A conclusion is the main claim or point in an argument that the premises are intended to prove.
__x__ TRUE _____ FALSE

8. A good convincing argument is a valid argument. That is, since you accept that the premises are true, the conclusion must also be true.
_____ TRUE __x__ FALSE

9. A premise is a reason offered in support of an argument’s conclusion.
__x__ TRUE _____ FALSE

10. A good, convincing argument is a sound argument. That is, since you accept all the premises are true, you must accept the conclusion is true.
_____ TRUE __x__ FALSE

Quiz 8

What type of argument is the following?

E = Empirical; V = Value

1. _E_ If it rains today, the cricket match will be cancelled. It is raining today. Therefore, the cricket match is cancelled.

2. _E_ My car is out of petrol. Therefore, it won’t start.

3. _V_ Animals feel pain just as we do. It is only because we feel pain that it matters how others treat us. The capacity to feel pain is the origin of morality. Thus, the way we treat animals must be a matter of moral concern for us.

4. _V_ Abortion is fully justified because a fetus is not a moral agent. Moreover, a fetus cannot make rational decisions.

5. _V_ Affirmative action cannot be justified. First, it amounts to reverse discrimination. Second, it begets racial conflicts. Finally, it is a short-sighted solution to redress the wrongs of the past.

6. _E_ The price of petrol will go up, if there is conflict in the Middle East. There is conflict in the Middle East. Therefore, the price of petrol will increase.

Identify the following in terms of soundness and validity:

1. Are all valid arguments sound? True by definition – sound arguments have to be valid.
___X___ yes ______ no

2. Can a valid argument result in a false conclusion? Yes. If a valid argument contains a false premise, then the argument will be valid but unsound, i.e. its conclusion will not be true.
___X__ yes ______ no

3. Are all true statements valid? Only arguments can be valid, not statements. Statements can be true or false.
______ yes ___X___ no

4. If you can knit, you can crochet. Sally can knit, therefore Sally can crochet. Valid but not sound. First premise is not true though it may be true that Sally can crochet.
______ sound __X____ valid _____ neither

5. In order for an argument to be sound, it requires that its premises be true and its form valid.
___X__ yes ______ no

Examples:

All dogs have tails.

Rusty has a tail.

Therefore Rusty is a dog

Not sound. It affirms the consequent which is an invalid step.

Either you are on the blue team or the red team.

Sally is on the red team.

Sound. Premises are true and form is valid.

Quiz 9

What kind of statement is the following:

D = Deductive; I = Inductive

1. _I_ More doctors smoke Marlboros than any other cigarette. They must be good for your health. (inductive)

2. _D_ All plants need water to grow. If my philodendron does not get water, it will die. (deductive)

3. _D_ Desert plants require little water. If the drought does not last, the cactus will survive. (deductive)

4. _I_ Meteorologists predicted rain for today; it must be raining. (inductive)

5. _I_ The man I saw break into the apartment was wearing a hoodie. Philip is wearing a hoodie. He must be the man I saw. (inductive)

6. _D_ Only hippies wear Birkenstocks. Jake is wearing Birkenstocks. Jake must be a hippie. (deductive)

7. _I_ Blondes have more fun. I should dye my hair blonde. (inductive)

8. _I_ The last three dresses Jane wore were red, she will likely be wearing red again today. (inductive)

9. _D_ The logical method of science is inductive. Induction is fallibilistic and never reaches absolute certainty. Therefore I can’t trust everything science tells me. (deductive)

10. _I_ Melissa is a fashion model. Most models are tall and slim. Melissa must be tall and slim. (inductive)

11. _I_ Artists tend to be left handed. Joel is left-handed. Joel must be an artist. (inductive)

Quiz 10

What kind of statement is the following:

D = Deductive; I = Inductive

1. _I_ Jane and Joe left their crayons out in the sun yesterday and they melted. If they leave them out again today, they will melt again.

2. _D_ All men are mortal, Socrates is a man, therefore Socrates is mortal.

3. _I_ The stock market has risen every day for the last two months. I should invest in the stock market because it will probably continue to rise.

4. _I_ Aches and fever are symptoms of the flu. Billy has aches and a fever. He must have the flu.

5. _D_ All fruits grow on trees, therefore all apples grow on trees.

6. _D_ All numbers ending in 5 or 0 are divisible by 5. The number 45 ends in 5 therefore it is divisible by 5.

7. _I_ Most puppies bark at night. I need my sleep so I shouldn’t get a puppy because he will keep me up all night.

8. _D_ Since all squares are rectangles and all rectangles have four sides, then all squares have four sides.

9. _I_ Complicated things in the world are evidence that they were created by an intelligent designer. The world evidences great complexity and design. It must have been made by an intelligent being.

10. _D_ Since all mammals nurse their young, then all whales nurse their young.

11. _I_ The mailman has come at 1 pm every day this summer. The mailman will come at 1 pm today.