Deductive and Inductive

Reasoning and fallacies

Darnell Kemp

Adapted from westmwires website

An Argument

Claim – the writer’s main idea or point (not just opinion, arguable)

Evidence – to support the claim

Refutation –discussion of opposing viewpoint

Conclusion – a restatement of claim or call to action

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.

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.

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:

1. 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°

2. Inductive or Deductive Reasoning?

Geometry example…

3.

Deductive Reasoning

Deductive 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.

Deductive Reasoning Syllogism: An argument composed of

two statements or premises (the major and minor premises), followed by a conclusion.

Premise A:Governments that fail to ensure

people the God given rights of life, liberty,

and the pursuit of happiness should be

abolished.

Premise B: The King has been destructive of

the colonists’ rights.

Conclusion: “We, therefore” are absolved

from the British Crown, have no political

connections, and are now “free and

independent states.”

The

Declaration of

Independence.

The most

famous

syllogistic

argument

Deductive Reasoning

Examples:

All students eat pizza.

Emily is a student at Fullerton College.

Therefore, Emily eats pizza.

All athletes work out in the gym.

Colin Kapernik is an athlete.

Therefore, Colin Kapernik works out in the gym.

Valid and Sound

A deductive argument is valid if the

premises logically lead to the

conclusion

A deductive argument is sound if the

premises are actually true

So it is possible for an argument to be

valid but not true

Example of valid but not

soundAll math teachers are over 7 feet tall.

Mr. P is a math teacher.

Therefore, Mr. P is over 7 feet tall.

This 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)

Examples

No one who can afford health

insurance is unemployed.

All politicians can afford health

insurance.

Therefore, no politician is

unemployed.

4. VALID OR INVALID?????

Valid = the premises logically lead to the conclusion

Sound = the premises are actually true

Example Some professors wear glasses.

Mr. Einstein wears glasses.

Therefore, Mr. Einstein is a professor.

5. VALID OR INVALID?????

Inductive Reasoning

Inductive Reasoning, involves going

from a series of specific cases to a

general statement. The conclusion in

an inductive argument is never

guaranteed.

6. What is the next number in the

sequence 6, 13, 20, 27,…?

There is more than one correct answer.

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.)

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.

7. Is the argument above deductive or

inductive?

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.

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.

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.

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.

Tess: Are there any good Italian restaurants in town?

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

Neapolitan rigatoni, their lasagna col pesto, and their

mushroom ravioli. I don't think you can go wrong with

any of their pasta dishes.

8. Based on what you've learned, is this argument deductive or

inductive? How can you tell?

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

rigatoni, their lasagna col pesto, and their mushroom ravioli.

I don't think you can go wrong with any of their pasta

dishes.

Inductive.

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.

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

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.

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

What is a fallacy?

A FALLACY is an argument in which the

premises do not justify the conclusion

as a matter of logic. An argument can

be fallacious for many reasons. The

argument might mis-apply a legitimate

rule of logic. Or it might omit a crucial

premise or misconstrue a premise. Or

it might misconstrue the conclusion.

Fallacies in action

Watch the video below titled:

“She’s a witch”

11. Write down any parts of an

argument you hear.

Now, on the next slide, look how it

breaks down.

The argument First, inductive – the mob attempts to

arrive at conclusion by using evidence

◦ Witch’s nose, clothing, hat, and wart

◦ All false premises except wart

◦ Non-witches have warts

1. The failed inductive argument:

The woman has a witch's nose, (false premise)

2. and [she is wearing] witch's clothing, (false premise)

3. and [she is wearing] a witch's hat. (false premise)

4. She has a wart (insufficient for the conclusion)

5. Only witches have witches' noses, clothing, hats, and warts.

6. Therefore, she's a witch!

Sir Bedevere's Deductive

Argument1. If she weighs the same as a duck, she'll float. (false, confuses

weight with density)

2. she does weigh the same as a duck; (true in this case, if the scales

are to be trusted)

3. [conclusion #1] Therefore, she'll float. (valid but unsound)

4. If she floats, she is made of wood. (false, many other things float)

5. She does float; (false/based on conclusion #1)

6. [conclusion #2] Therefore, she's made of wood. (valid but unsound)

7. If she's made of wood, she's a witch. (assumed by all in the scene to

be true)

8. She is made of wood; (false/based on conclusion #2)

9. [conclusion #3] Therefore, she's a witch! (valid but unsound)

Valid = the premises logically lead to the conclusion

Sound = the premises are actually true

Slides 35 and 36 from Mooney’s Theology Blog

11. Argument can fail for two

reasons: Factual Error

Error in logic

◦ Deductive argument premises fail to

provide conclusive support for the

conclusion.

◦ Inductive argument premises fail to

provide even probable support for the

conclusion.

Fallacies of Relevance – reason

or conclusion is irrelevant to the

argument Straw man – a misrepresentation of opponents

argument

Ad Hominem

Red Herring – the example is this one

Two wrong

False authority

Appeal to popular opinion

Begging the question

Non sequitur (claims cause & effect but there really

is none)

Evasion

See Fallacies of Relevance Example below and write

on chart (just the name of the commercial)

Causal reasoning fallacies –

cause doesn’t make sense

Post hoc, ergo propter hoc – example

for this one

Slippery slope

Rationalization

False cause

See Example below and add to chart

False generalization – not

enough info for conclusion

Hasty generalization – This is a conclusion

based on insufficient or biased evidence (example page 360

textbook)

False analogy

Either or

Over simplification

See example below and add as

example for hasty generalization “You

Hate Children”

Fallacies of Ambiguity

Equivocation - It is the misleading use of a

term with more than one meaning or sense (by

glossing over which meaning is intended at a

particular time).

◦ Example - Noisy children are a real headache. Two aspirin

will make a headache go away. Therefore, two aspirin will

make noisy children go away.

Example of numerous fallacies

Take some notes on what you hear?

Some quotes from ad (add to

fallacy chart) “Americans are under attack from Islamic

extremists in every corner of the world”

“…lesbians and feminists are attacking everything

sacred”

What does every or everything tell you? Which fallacy?

“…Jackson and Sharpton claim the answer is racial

quotas”

Does this sound like an extreme representation of their

position?

“The aliens are here but they didn't come in a

spaceship they came across our unguarded

Mexican border.”

How is aliens doubly used? Which fallacy?

Some quotes from ad (add to

fallacy chart) “Americans are under attack from Islamic

extremists in every corner of the world”

“…lesbians and feminists are attacking everything

sacred”

Hasty Generalization (write these examples on chart)

“…Jackson and Sharpton claim the answer is racial

quotas”

Strawman (write this example on your chart)

“The aliens are here but they didn't come in a

spaceship they came across our unguarded

Mexican border.”

Equivocation (write this example on your chart)

An explanation of my personal

pet peeve and just a really cute

one

Begs the Question (see below)

Fallacies in Mean Girls (see below)