Deductive and Inductive Reasoning - PowerPoint Presentation

Slide1

Deductive and Inductive Reasoning

Mimi

Opkins

CECS 100

Fall 2011Slide2

Problem Solving

Logic

– The science of correct reasoning.

Reasoning

– The drawing of inferences or conclusions from known or assumed facts.

When solving a problem, one must understand the question, gather all pertinent facts, analyze the problem i.e. compare with previous problems (note similarities and differences), perhaps use pictures or formulas to solve the problem.Slide3

Deductive vs. Inductive Reasoning

The difference:

inductive reasoning

uses patterns to arrive at a conclusion (conjecture)

deductive reasoning

uses facts, rules, definitions or properties to arrive at a conclusion.Slide4

Examples of Inductive Reasoning

Every quiz has been easy. Therefore, the test will be easy.

The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow.

Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.Slide5

Example of Deductive Reasoning

The catalog states that all entering freshmen must take a mathematics placement test.

Conclusion

: You will have to take a mathematics placement test.

You are an entering freshman.

An Example:Slide6

Inductive or Deductive Reasoning?

Geometry example…

60

◦

x

Triangle sum property -

the sum of the angles of any triangle is always 180 degrees.

Therefore

, angle x =

30

°Slide7

Inductive or Deductive Reasoning?

Geometry example…Slide8
Slide9
Slide10
Slide11

Deductive Reasoning

This method of reasoning produces results that are certain within the logical system being developed.

It involves reaching a conclusion by using a formal structure based on a set of undefined terms and a set of

accepted

unproved axioms or premises.

The

conclusions

are said to be

proved

and are called

theorems.Slide12

Deductive ReasoningDeductive Reasoning

– A type of logic in which one goes from a general statement to a specific instance.

The classic example

All men are mortal.

(major premise)

Socrates is a man.

(minor premise)

Therefore, Socrates is mortal.

(conclusion)

The above is an example of a syllogism.Slide13

Deductive Reasoning

Syllogism

: An argument composed of two statements or premises (the major and minor premises), followed by a conclusion.

For any given set of premises, if the conclusion is guaranteed, the arguments is said to be

valid

.

If the conclusion is not guaranteed (at least one instance in which the conclusion does not follow), the argument is said to be

invalid

.

BE CARFEUL, DO NOT CONFUSE TRUTH WITH VALIDITY!

Slide14

Deductive Reasoning

Examples:

All students eat pizza.

Claire is a student at CSULB.

Therefore, Claire eats pizza.

2.

All athletes work out in the gym.

Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym. Slide15

Deductive Reasoning

Examples:

All students eat pizza.

Claire is a student at CSULB.

Therefore, Claire eats pizza.

2.

All athletes work out in the gym.

Barry Bonds is an athlete. Therefore, Barry Bonds works out in the gym. Slide16

Deductive Reasoning3. All math teachers are over 7 feet tall.

Mr. D. is a math teacher.

Therefore, Mr. D is over 7 feet tall.

The argument is valid, but is certainly not true.

The above examples are of the form

If

p

, then

q. (major premise) x is p. (minor premise) Therefore, x is q. (conclusion)Slide17

Venn Diagrams

Venn Diagram

: A diagram consisting of various overlapping figures contained in a rectangle called the universe.

U

This is an example of

all A are B

. (If A, then B.)

B

ASlide18

Venn Diagrams

This is an example of some A are B.

(At least one A is B.)

The yellow oval is A, the blue oval is B.Slide19

ExampleConstruct a Venn Diagram to determine the validity of the given argument.

#14 All smiling cats talk.

The Cheshire Cat smiles.

Therefore, the Cheshire Cat talks.

VALID OR INVALID???Slide20

ExampleValid argument; x is Cheshire Cat

Things

that talk

Smiling

cats

xSlide21

Examples#6

No one who can afford health insurance is unemployed.

All politicians can afford health insurance.

Therefore, no politician is unemployed.

VALID OR INVALID?????Slide22

ExamplesX

=politician. The argument is valid.

People who can afford

Health Care.

Politicians

X

UnemployedSlide23

Example

#16

Some professors wear glasses.

Mr. Einstein wears glasses.

Therefore, Mr. Einstein is a professor.

Let the yellow oval be professors, and the blue oval be glass wearers. Then x (Mr. Einstein) is in the blue oval, but not in the overlapping region. The argument is invalid.Slide24

Inductive ReasoningInductive Reasoning

, involves going from a series of specific cases to a general statement. The conclusion in an inductive argument is never guaranteed.

Example: What is the next number in the sequence 6, 13, 20, 27,…

There is more than one correct answer.Slide25

Inductive Reasoning

Here’s the sequence again 6, 13, 20, 27,…

Look at the difference of each term.

13 – 6 = 7, 20 – 13 = 7, 27 – 20 = 7

Thus the next term is 34, because 34 – 27 = 7.

However what if the sequence represents the dates. Then the next number could be 3 (31 days in a month).

The next number could be 4 (30 day month)

Or it could be 5 (29 day month – Feb. Leap year)

Or even 6 (28 day month – Feb.)Slide26

More ExamplesSlide27

All bats are mammals.

All mammals are warm-blooded.

So, all bats are warm-blooded.

All arguments are deductive or inductive.

Deductive arguments are arguments in which the conclusion is claimed or intended to follow

necessarily

from the premises.

Inductive arguments are arguments in which the conclusion is claimed or intended to follow

probably

from the premises.

Is the argument above deductive or inductive?Slide28

All bats are mammals.All mammals are warm-blooded.

So, all bats are warm-blooded.

If the premises are true, the conclusion, logically, must also be true.

Deductive.Slide29

There are four tests that can be used to determine whether an argument is deductive or inductive:

·

the indicator word test

·

the strict necessity test

·

the common pattern test

·

      the principle of charity testSlide30

Kristin is a law student.Most law students own laptops.

So, probably Kristin owns a laptop.

In the example above, the word

probably

shows that the argument is inductive.

The

indicator word test

asks whether there are any indicator words that provide clues whether a deductive or inductive argument is being offered.

Common deduction indicator words include words or phrases like

necessarily

, logically, it must be the case that, and this proves that.Common induction indicator words include words or phrases like probably, likely,

it is plausible to suppose that, it is reasonable to think that, and it's a good bet that.Slide31

No Texans are architects.No architects are Democrats.

So, no Texans are Democrats.

In this example, the conclusion does follow from the premises with strict logical necessity. Although the premises are both false, the conclusion does follow logically from the premises, because if the premises

were

true, then the conclusion would be true as well.

The

strict necessity test

asks whether the conclusion follows from the premises with strict logical necessity. If it does, then the argument is deductive.Slide32

Either Kurt voted in the last election, or he didn't.Only citizens can vote.

Kurt is not, and has never been, a citizen.

So, Kurt didn't vote in the last election.

The

common pattern test

asks whether the argument exhibits a pattern of reasoning that is characteristically deductive or inductive.

If the argument exhibits a pattern of reasoning that is characteristically deductive, then the argument is probably deductive.

If the argument exhibits a pattern of reasoning that is characteristically inductive, then the argument is probably inductive.

In the example above, the argument exhibits a pattern of reasoning called "argument by elimination."

Arguments by elimination are arguments that seek to logically rule out various possibilities until only a single possibility remains. Arguments of this type are always deductive.Slide33

Arnie: Harry told me his grandmother recently climbed Mt. Everest.

Sam

: Well, Harry must be pulling your leg. Harry's grandmother is over 90 years old and walks with a cane.

We could interpret Sam's argument as deductive. But this would be uncharitable, since the conclusion clearly doesn't follow from the premises with strict logical necessity. (It is logically possible--although highly unlikely--that a 90-year-old woman who walks with a cane could climb Mt. Everest.) Thus, the principle of charity test tells us to treat the argument as inductive.

In this passage, there are no clear indications whether Sam's argument should be regarded as deductive or inductive. For arguments like these, we fall back on the principle of charity test.

According to the

principle of charity test

, we should always interpret an unclear argument or passage as generously as possible.Slide34

Tess: Are there any good Italian restaurants in town?

Don

: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their

lasagne

col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.

Based on what you've

learned,

is this argument deductive or inductive? How can you tell?

 Slide35

Don: Yeah, Luigi's is pretty good. I've had their Neapolitan rigatoni, their lasagne

col pesto, and their mushroom ravioli. I don't think you can go wrong with any of their pasta dishes.

The argument is an inductive generalization, which is a common pattern of inductive reasoning. Also, the conclusion does not follow with strict necessity from the premises.

Inductive.Slide36

I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.

Is this argument deductive or inductive? How can you tell?

 Slide37

I wonder if I have enough cash to buy my psychology textbook as well as my biology and history textbooks. Let's see, I have $200. My biology textbook costs $65 and my history textbook costs $52. My psychology textbook costs $60. With taxes, that should come to about $190. Yep, I have enough.

This argument is an argument based on mathematics, which is a common pattern of deductive reasoning. Plus, the conclusion follows necessarily from the premises.

Deductive.Slide38

Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts and he broke out in a severe rash.

Father

: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.

Is the father's argument deductive or inductive? How can you tell?

 Slide39

Mother: Don't give Billy that brownie. It contains walnuts, and I think Billy is allergic to walnuts. Last week he ate some oatmeal cookies with walnuts, and he broke out in a severe rash.

Father

: Billy isn't allergic to walnuts. Don't you remember he ate some walnut fudge ice cream at Melissa's birthday party last spring? He didn't have any allergic reaction then.

The father's argument is a causal argument, which is a common pattern of inductive reasoning. Also, the conclusion does not follow necessarily from the premises. (Billy might have developed an allergic reaction to walnuts since last spring.)

Inductive.Slide40

John is a Luddite. It follows that he doesn't believe in

technology.

Is this argument deductive or inductive? How can you tell?

 Slide41

John is a Luddite. It follows that he doesn't believe in technology.

This argument is an argument by definition, which is a common pattern of deductive inference. Also, the phrase "it necessarily follows that" is a deduction indicator phrase. Also, the conclusion follows from the premises.

Deductive.Slide42

Larry: Do you think Representative Porkmeister

will be re-elected?

Norman

: I doubt it.

Porkmeister's

district has become more conservative in recent years.

Porkmeister

is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.

Is this argument deductive or inductive? How can you tell? Slide43

Larry: Do you think Representative Porkmeister

will be re-elected?

Norman

: I doubt it.

Porkmeister's

district has become more conservative in recent years.

Porkmeister

is a liberal Democrat, and 63% of the registered voters in his district are now Republicans.

This argument is both a statistical argument and a predictive argument, which are two common patterns of inductive reasoning. Also, the conclusion does not follow necessarily from the premises. 

Inductive.Slide44

If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.

Is this argument deductive or inductive? How can you tell?

 Slide45

If Buster walked to the game, then he didn't drive to the game. Buster didn't drive to the game. Therefore, Buster walked to the game.

Note, however, that the conclusion does

not

follow logically from the premises. (Maybe Buster rode his bike to the game, for example.) The argument commits the fallacy of "affirming the consequent."

This argument is a hypothetical syllogism, which is a common pattern of deductive reasoning.

Deductive.