Inductive and Deductive Reasoning

Analysis of an Argument

Inductive Reasoning

• Induction is usually described as moving from the specific to the general.

• Arguments based on experience or observation are best expressed inductively.

• For example: “I've noticed previously that every Tuesday it rains, therefore, it will rain next Tuesday.”

Deductive Reasoning

• Deduction begins with the general and ends with the specific.

• Arguments rooted in laws, rules, or other commonly accepted beliefs are best expressed deductively.

• For example: “Everything that goes up must come down. And so, if you kick the ball up, it must come down.” (Newton’s Law of Gravity)

Differences and Commonalities• The difference: the way the arguments are

expressed. • The commonalities: – any inductive argument can also be expressed

deductively– any deductive argument can also be expressed

inductively. – each requires different some sort of support

(observation or a law/rule).• They both express the same, but one is based on

fact (law, rules, etc.), the other mere observation.

Exercises for Induction and Deduction

• 1. Which of the following claims would be best expressed by inductive reasoning?

• A) Your first quiz grade usually indicates how you will do in the course.

• B) The final exam accounts for 30% of the course grade.

• C) Late papers will not be accepted. • D) Gravity's Rainbow

is required reading in your course.

ANSWER

• A: Your first quiz grade usually indicates how you will do in the course.

• WHY: It is much more likely that this claim stems from personal observation than from adherence to some general principle, and so it would be best expressed by an inductive argument.

2. Which of the following claims would be best expressed by deductive reasoning?

• A) California's population growth rate slowed last year.

• B) California residents appreciate their good weather.

• C) California residents are residents of the United States.

• D) More cars are registered in California than in any other state.

ANSWER

• C: California residents are residents of the United States.

• WHY: Since California residents are residents of the U.S. by definition, and definition is one sort of general claim on which a deductive argument can be based, this claim would be best supported by a deductive argument.

3. Which of the following arguments would lead to a deductive conclusion?

• A) There was a mild winter this year, and previously whenever there's been a mild winter the cherry crop suffers.

• B) The cherry crop needs at least a week of freezing temperatures for best results, and this winter the temperature stayed several degrees above freezing.

• C) Primo noticed that whenever the skiing was good in the winter, the cherry crop was profitable, and this year the skiing was good.

• D) Not since 1972 have I seen a good cherry crop after a mild winter, and this winter has been mild.

ANSWER

• B: The cherry crop needs at least a week of freezing temperatures for best results, and this winter the temperature stayed several degrees above freezing.

• WHY: Though the premise about this year is based on observation, the general or "major" premise, "The cherry crop needs at least a week of freezing temperatures," seems to be an assertion of established principle, making this a deductive argument with the conclusion, "The results won't be best this year."

Inductive Arguments• Inductive arguments are all comparisons between two sets of

events, ideas, or things;• Inductive arguments are sometimes called analogical

arguments. They are analogies.• The point of the comparisons:

– to establish whether the similar two events, ideas, or things under consideration are also similar in the way of interest to the argument.

• For example: "Every time I've seen a red-tinted sunset, the next day's weather has been beautiful. Today had a red-tinted sunset, so tomorrow will be beautiful.“

• Similar in an important way (red-tinted sunsets)• The inductive argument is that they will also be similar in

another way (nice weather on the following day).

Argument’s Strength• The strength of such an argument depends in large part on three

of its elements: – how accurate and comprehensive the previous observations

are; – how strong the causal link seems to be; – how similar the two cases are.

• To satisfy the first element: has the person seen many such sunsets, and that "redness" and "beauty" have been judged consistently.

• To satisfy the second: is there a strong correlation between weather patterns on successive days.

• To satisfy the third: are there are any significant differences between the observation of today's sunset and of the previous ones.

Exercises on Induction• 1. Every time Jorge has seen a baseball game between

the Giants and the Dodgers at Candlestick Park, the Giants have won. Tomorrow, the Giants play the Dodgers at Candlestick. Which of the following is least significant when arguing that the Giants will win tomorrow?

A) Jorge has only seen the Giants play the Dodgers twice. B) Both teams have many new players. C) Jorge won't be going to the game tomorrow. D) The field at Candlestick will be unusually muddy

tomorrow.

ANSWER

C: Jorge won't be going to the game tomorrow. WHY: Generally speaking, the observer need not

be part of the event observed. Therefore, Jorge's presence or absence, since it would have no apparent effect on the outcome of the game, is not a significant factor in this inductive argument.

NUMBER 2• Which of the following would be the strongest

argument for the claim, "The weather for tomorrow will be beautiful"?

A) Josue says, "Tomorrow is my birthday, and the weather on my birthday is always beautiful."

B) Bharati says, "The weather forecast in the newspaper is always wrong, and tomorrow's forecast is for rain, so it will probably be beautiful."

C) Ivy says, "The weather forecast in the newspaper is always right, and tomorrow's forecast is for a beautiful day, so that's what it will be."

D) Kwong says, "The barometric pressure has been rising for three days, and whenever that happens we have beautiful weather for the next week, so tomorrow is sure to be beautiful."

ANSWER

• D: Kwong says, "The barometric pressure has been rising for three days, and whenever that happens we have beautiful weather for the next week, so tomorrow is sure to be beautiful."

• WHY: Kwong's observation is apparently comprehensive ("whenever that happens"), the causal link is convincing (weather and barometric pressure), and there seems to be no other significant differences, so this is the strongest of the four arguments for "The weather tomorrow will be beautiful."

NUMBER 3• Salman's inductive argument began, "All five of the

other guys in my fraternity." Which of the following phrases is the strongest completion of that claim?

• A) who took Critical Thinking passed it, so I should pass it, too.

• B) who tried out for the tennis team made it, so I should make it, too.

• C) who met the new member liked him, so I should like him, too.

• D) who ate the potato salad got sick, so I should get sick, too.

ANSWER• The problem with each of the answers here is the strength of its

causal connection. In this case, there is no apparent connection between a social organization, like a fraternity, and intellectual ability. Perhaps there are special circumstances: fraternity members may be recruited for their intellect, or passing Critical Thinking may be very easy. Without some indication of such special circumstances in the argument, however, this claim should be rejected as lacking sufficient causal connection.

• C and D, but both weak• C translates the social connection of a fraternity into a likelihood

of interpersonal preferences, which is not far-fetched, but not a particularly strong correlation.

• D We can't be sure that the other five got sick from the potato salad, or that everyone who ate it got sick. As a result, this answer is probably no stronger than "C.”

Deductive ArgumentsSyllogisms and Conditionals

• Two distinct ways of expressing a deductive argument: as a syllogism, or as a conditional.

• Syllogisms: The major premise of a syllogism states that something, Y, is or is not true for all or part of some group, X;

• the minor premise affirms or denies that some group or individual, Z, is part of X; – the argument then concludes whether that thing Y (from the major premise)

is true or not true for that group or individual Z (from the minor premise).

– One form of a syllogism can be expressed by the following paradigm: • All X are Y• Z is X Therefore,• Z is Y

Conditionals• Conditionals: The major premise is: if something is

true of P, then something is true of Q. • The minor premise either affirms that it is true of P,

or denies that it is true of Q. • One form of a conditional is expressed by the

following paradigm: If P then Q; P Therefore, Q • For example: If Mandia was in class today, she

received instructions for writing the essay. Mandia was in class. Therefore, she received instructions for writing the essay.

COMPARING THE TWO

• Syllogism: All good tests get good grades. • Jerzy's are good tests. Therefore, Jerzy gets a

good grade. • Conditional: If good tests, then good grades. • Good tests. Therefore, good grade.

Exercises in Deductive Arguments

• Which of the following would make the best major premise for a deductive argument?

• A) No one has ever seen a ghost. • B) There are no ghosts. • C) Ghosts are the products of over-active

imaginations. • D) Scientific study has proven that there are

no ghosts.

ANSWER• C: Ghosts are the products of over-active imaginations.• Two important factors for the main premise of a deductive

argument are:– that it relate two terms, and– that it be stated as a generalization, rule, or principle.

• "Ghosts are the products of over-active imaginations" is both a generalization, and a way of relating two terms, "ghosts" and "products of an over-active imagination."

• We can therefore complete the argument with a second premise, "Hamlet's father is a ghost," and a conclusion, "Therefore, Hamlet's father is the product of an over-active imagination."

Which would be the best way to restate the claim, "The hardest-working students receive the highest grades," for use in analyzing a deductive argument?• A) Working students receive highest grades.• B) Students receive grades.• C) The hardest-working students receive the

highest grades. • D) Students are highest grade receivers.

ANSWER

• D: Students are highest grade receivers.• There are two important things to remember

when restating claims: – Always replace active or passive verbs with state-

of-being verbs. – Shorten phrases any way you want, as long as you

do not create confusion or misunderstanding.

Since all deductive arguments can be expressed as either syllogisms or conditionals, choose the equivalent conditional for the following major premise of a syllogism: "All men are mortal."

• A If they are men, then they are mortal.• B If they are men.• C If all men are mortal, then all mortals are

men.• D If they are mortal, then they are men.

ANSWER

• A: If they are men, then they are mortal.

Since all deductive arguments can be expressed as either syllogisms or conditionals, convert the following conditional into a premise for a syllogism: "If the Spartans win, then Amy will celebrate."

• A) All Spartans are celebrators for Amy. • B) All winners are Spartans for Amy. • C) All wins are celebrations for Amy. • D) All celebrations are winners for Amy.

ANSWER

• All wins are celebrations for Amy.

If you have read the introduction, then you should be able to complete these exercises. And you have read the introduction.

• A) Conclusion: You should be able to complete these exercises.

• B) Conclusion: You should not be able to complete these exercises.

• C) Conclusion: You haven't really read the introduction.

• D) Invalid.

ANSWER

• A: Conclusion: You should be able to complete these exercises.