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Copyright 2009 LessonSnips www.lessonsnips.com Inductive and Deductive Reasoning According to traditional logic, arguments can be either inductive or deductive. Sometimes, it is difficult to determine which category an argument might be in. However, there are some key concepts that give clues as to which type the argument is. Generally speaking, deductive arguments are ones wherein the conclusion validly follows from the premises. The most important form of a deductive argument is that of the syllogism. In deductive argumentation, the conclusion is a proposition that follows from other propositions. This means that the conclusion is supported by the other propositions, called premises. It is incorrect to suggest, however, that this support is weak. Rather, the conclusion must be affirmed if the premises are true; it is impossible for the premises to be true and for the conclusion to be false. The purpose of the premises is to establish the truth of the conclusion. For example: All humans are mortal. John Smith is human. Therefore, John Smith is moral. This example is a simple valid deductive argument because the conclusion is necessarily drawn from the premises. If the truth of the premises is admitted, then the conclusion must also be admitted as true. Some statements that look like the above example are not necessarily valid deductive arguments. Valid ones follow certain rules of reasoning. For example: Some dogs are ill-behaved. All dogs are animals. Therefore, all animals are ill-behaved. This is an invalid deductive argument. It might appear the same as the one previously written, however it breaks certain logical rules. (Experience tells us that there are animals that are not ill-behaved.) Deductive reasoning does not grant new knowledge, but instead clarifies concepts that we may already know something about. Even though deduction aims at producing true, valid conclusions, it does so only based on prior knowledge of the truth of its premises. If one of the premises is false, the conclusion will be false.

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Page 1: Inductive and Deductive Reasoning - Brooke Andersonmrswhetsellsmath.weebly.com/uploads/2/7/1/2/27126935/inductive... · Inductive and Deductive Reasoning ... Most year-round schedules

Copyright 2009 LessonSnips www.lessonsnips.com

Inductive and Deductive Reasoning

According to traditional logic, arguments can be either inductive or deductive.

Sometimes, it is difficult to determine which category an argument might be in. However,

there are some key concepts that give clues as to which type the argument is. Generally

speaking, deductive arguments are ones wherein the conclusion validly follows from the

premises. The most important form of a deductive argument is that of the syllogism.

In deductive argumentation, the conclusion is a proposition that follows from other

propositions. This means that the conclusion is supported by the other propositions,

called premises. It is incorrect to suggest, however, that this support is weak. Rather, the

conclusion must be affirmed if the premises are true; it is impossible for the premises to

be true and for the conclusion to be false. The purpose of the premises is to establish the

truth of the conclusion.

For example:

All humans are mortal.

John Smith is human.

Therefore, John Smith is moral.

This example is a simple valid deductive argument because the conclusion is necessarily

drawn from the premises. If the truth of the premises is admitted, then the conclusion

must also be admitted as true.

Some statements that look like the above example are not necessarily valid deductive

arguments. Valid ones follow certain rules of reasoning.

For example:

Some dogs are ill-behaved.

All dogs are animals.

Therefore, all animals are ill-behaved.

This is an invalid deductive argument. It might appear the same as the one previously

written, however it breaks certain logical rules. (Experience tells us that there are animals

that are not ill-behaved.)

Deductive reasoning does not grant new knowledge, but instead clarifies concepts that we

may already know something about. Even though deduction aims at producing true, valid

conclusions, it does so only based on prior knowledge of the truth of its premises. If one

of the premises is false, the conclusion will be false.

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Inductive and Deductive Reasoning (Cont’d)

Inductive reasoning does not aim at producing true, valid conclusions. In fact, “valid” and

“invalid” are not terms that can be accurately applied to inductive reasoning. Inductive

reasoning enables us to infer probable and likely conclusions. Inductive reasoning is

useful for gaining new knowledge by understanding statistical patterns and also for

identifying causes and effects. However, unlike deductive argument, inductive arguments

cannot guarantee true conclusions even if their premises are true. Two of the most

common types of inductive argument are the analogy and the statistical.

It is important to understand that inductive reasoning attempts to predict or suggest its

conclusion based on inferences on the premises, but there is no necessity for the

conclusion to follow from the premises. In other words, there is no guarantee that the

future will be like the past or that the conclusion will definitely be true.

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Inductive and Deductive Reasoning Questions

Fill Ins:

1. _______________ arguments are ones wherein the conclusion validly follows

from the premises.

2. The most important form of deductive argument is that of the

___________________.

3. Two of the most common types of inductive argument are the __________ and

the _____________.

True or False:

____ 4. Conclusions based on inductive reasoning will always be true.

____ 5. Deductive reasoning does not grant new knowledge, but instead clarifies

concepts that we may already know something about.

____ 6. If one of the premises is false, the conclusion will be false.

Do the following use inductive or deductive reasoning (write “I” for inductive and

“D” for deductive:

____ 7. All cats have fur.

Xena is a cat.

Therefore, Xena has fur.

____ 8. Some horses are big.

All horses have tails.

Therefore, anything with a tail is big.

____ 9. All humans have a nose.

Bobby is human.

Therefore, Bobby has a nose.

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Worksheet Deductive Reasoning Name: _________________________

Let’s work through the logic process of Deductive Reasoning

1) Start with a statement (not a question or guess)

2) Find facts about the statement

3) Determine if the statement is valid

Statement #1: Math is a class about numbers.

Facts

Do your facts make this a valid or invalid statement?

Statement #2: All dogs are brown.

Facts

Do your facts make this a valid or invalid statement?

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Statement #3: This shape is a square

Facts

Fact #1: _____________________________________________________________

Fact #2: ____________________________________________________________

Fact #3: ____________________________________________________________

Fact #4: ____________________________________________________________

Fact #5: ____________________________________________________________

Do your facts make this a valid or invalid statement?

Statement #4: Inductive Reasoning is just Deductive Reasoning in reverse.

Facts

Fact #1: _____________________________________________________________

Fact #2: ____________________________________________________________

Fact #3: ____________________________________________________________

Fact #4: ____________________________________________________________

Fact #5: ____________________________________________________________

Do your facts make this a valid or invalid statement?

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Worksheet Inductive Reasoning Name: _________________________

Let’s work through the logic process of Inductive Reasoning

1) A question or observation.

2) Gather more facts or observations.

3) Make a decision or statement developed from your facts or observations

Try #1: Would a dog make a good pet for me?

Facts or Observations

What can you decide or determine based on this information?

Try #2: Would driving a truck be a good choice for me?

Facts or Observations

What can you decide or determine based on this information?

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Try #3

Facts

Fact #1: This shape has two sets of congruent sides.

Fact #2: This shape has 4 right angles

Fact #3: This shape has exactly 4 sides

What can you decide or determine based on this information?

Try #4

Facts

Fact #1: This animal is a mammal

Fact #2: This animal has only one or two offspring at a time

Fact #3: This animal has four legs, short round ears, and a short tail

Fact #4: This animal is native to woodlands, but can be found as far north as the artic

Fact #5: This animal is a carnivore

What can you decide or determine based on this information?

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Matching Name: ___________________

Inductive & Deductive Reasoning

Directions: Circle whether the statement is an example of inductive or deductive reasoning. Then,

explain how you know this.

It has eight legs

It lives under water

It must be an octopus Inductive Deductive

How did you decide this?

Cats are mammals

Mammals feed their young milk

Mammals are warm blooded

Yes, cats are mammals Inductive Deductive

How did you decided this?

It is a Monday in September

I don’t have school today because it’s a holiday

It must be Memorial Day Inductive Deductive

How did you decided this?

The shape is a trapezoid

It has four sides

Only two sides are parallel

Yes, this is a trapezoid Inductive Deductive

How did you decided this?

Should I buy a car?

I am old enough to drive a car

I can afford a reasonable car

I could use the car to get to school and work

Yes, I will buy a car. Inductive Deductive

How did you decided this?

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Worksheet Identifying Reasoning Name: _________________________

Summer: 15 Days or 2 1/2 Months?

The final bell rings. It’s the last day of school, and summer has finally come! Students

don’t have to think about school for at least another 2 1/2 months. That is the way it

should always be. Schools should continue using the traditional calendar and not a year-

round schedule. There are numerous downsides to year-round schooling. It has no positive

effects on education, it adds to costs, and it disrupts the long-awaited summer vacation.

Contrary to the well-accepted belief, year-round schooling has no constructive impact on

education. Most year-round schedules use the 45-15 method: 45 days of school followed

by 15 days off. Because of this, there are many first and last days of school. All those

transitions disrupt the learning process. Also, there is no evidence of higher test scores.

Due to that, many schools that change to year-round schedules end up switching back. For

example, since 1980, 95 percent of schools that tried the year-round schedule changed

back to a traditional calendar. It is obvious that changing to year-round schooling does not

help students; therefore, why is the change necessary?

Like any other facility, keeping a school open requires a great deal of money. When a

school changes to a year-round schedule, the costs skyrocket. Keeping school open in the

middle of summer requires air conditioning, and that adds significantly to the school’s

expenses. The usual utility bills grow because of the additional open-school time. Finally,

teachers must be paid for all the weeks they are working. With all these factors, the cost

of keeping schools open becomes immensely high. For example, a high school in Arizona had

a cost increase of $157,000 when they switched to year-round schooling. Some schools

may not be able to handle such increases, and other schools that can handle these

expenses could be doing better things with the money. Is year-round school really where

the money should go?

An important part of a child’s life is summertime. With year-round schedules, students

would hardly have any time to relax. During the 15-day breaks, they would be thinking

about their quick return to school. It would also be difficult to coordinate family vacations

with parents’ work schedules. Similarly, children would not be able to go to most summer

camps. One expert, Dr. Peter Scales, says, “The biggest plus of camp is that camps help

young people discover and explore their talents, interests, and values. Most schools don’t

satisfy all these needs. Kids who have these kinds of [camp] experiences end up being

healthier and have fewer problems.” Obviously, the summer is crucial to a child’s learning

and development. Why should this invaluable part of a young person’s life be taken away?

It is evident that year-round schooling is not the best option for the school calendar.

There is absolutely nothing wrong with the traditional school year. Why change something

that works so well? The final bell rings. Let’s make sure this bell means that the “real”

summer vacation has come.

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1) Was this an example of inductive or deductive reasoning?

2) What were your clues?

3) Did you have to read the whole thing to determine if it was inductive or deductive?

4) How would this essay look it were the opposite of what you said it was in Question

1? Explain or give an example outline.

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Worksheet Reasoning Name: _________________________

Convince someone your favorite color is the best in 5 -7 sentences.

On the back, tell me if this was inductive or deductive reasoning and how you can tell. Use arrows, underline, etc… on this side if it helps make your point on the back.

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Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Identifying Number Pattern

Identify the number pattern and !ll in the missing numbers.

–91)

82)

503)

–224)

155)

206)

647)

–188)

129)

–11

4

60

–24

12

25

62

–21

6

15 10

–7

12

40

–20

18

15

66

–15

18

5

–5

16

30

–18

21

10

68

–12

24

0

–3

20

20

–16

24

5

70

–9

30

–510)

Mike
Text Box
1. Identify the pattern and fill in the missing numbers. 2. Is finding patterns an example of inductive or deductive reasoning. On the back tell me why you feel this way?