Materi Daslog 2-3 - Basic Logical Arguments.ppt

8/10/2019 Materi Daslog 2-3 - Basic Logical Arguments.ppt

1/41

Basic Logical Concepts


2/41

BASIC LOGICAL

CONCEPTS Task: To distinguish good arguments from bad

Two questions:

Are the premises true?

Do the premises provide good reasons to accept the

conclusion?


3/41

TWO ARGUMENT TYPES

Deductivearguments

(try to) PROVE their conclusions

Inductivearguments

(try to) show that their conclusions are

PLAUSIBLE or LIKELY


4/41

DEDUCTIVE ARGUMENTS

Some pigs have wings.All winged things sing.

Therefore, some pigs sing.

Everyone has one and only one biological mother.

Full sisters have the same biological mother.

No one is her own biological mother.

Therefore, there is no one whose biological mother

is also her sister.

EXERCISE: Solve the mysteries, CTpages 54-55.


5/41

INDUCTIVE ARGUMENTS

Every ruby discovered thus far has been red.So, probably all rubies are red.

Polls show that 87% of 5-year-olds believe in thetooth fairy.

Marta is 5 years old.

Marta probably believed in the tooth fairy.

Chemically, potassium chloride is very similar to

ordinary table salt (sodium chloride).

Therefore, potassium chloride tastes like table salt.


6/41

THE DIFFERENCE

Key: deductive / inductive

If the premises are true the conclusion isnecessarily/ probablytrue.

The premises provide conclusive / goodevidence for the conclusion.

It is impossible/ unlikelyfor the premises to betrue and the conclusion to be false.

It is logically inconsistent / consistentto assertthe premises but deny the conclusion.


7/41

FOUR TESTS

Four tests allow us to identify deductive/

inductivearguments

The indicator word test

The strict necessity test

The common pattern test

The principle of charity test


8/41

INDICATOR WORD TEST

Deduction Induction

Certainly Probably

Definitely Likely

Absolutely Plausible

Conclusively ReasonableThis entails that The odds are

that


9/41

CAUTION!

-Arguments may not contain any indicator words.Pleasure is not the same thing as happiness.

The occasional self-destructive behavior of the

rich and famous confirms this too vividly.

(Tom Morris)

-Arguers may use indicator words incorrectly.

(People very often overstate their cases.)

-In these cases, other tests must be used to

determine whether an argument is deductive or

inductive.


10/41

The Strict Necessity Test

An arguments conclusion either follows with

strict logical necessity from its premises or it

does not.

If an arguments conclusion doesfollow with

strict logical necessity from its premises, theargument should always be treated as

deductive.

if an arguments conclusion does notfollow withstrict logical necessity from its premises, the

argument should normally be treated as

inductive.


11/41

The Strict Necessity Test

Examples:

Alan is a father. Therefore Alan is a

male.

Jill is a six-year-old. Therefore, Jill

cannot run a mile in one minute flat.


12/41

COMMON PATTERN TEST

Modus ponens (affirming the antecedent)

If A then B.

A. Therefore B.

(A = antecedent; B = consequent)

This is a very common pattern of deductive reasoning.


13/41

Common Pattern Test

Example (modus ponens)

If we are in Paris, then we are in France.

-------A----------- --------B-----------

We are in Paris.

--------A--------- Therefore, we are in France.

---------B-----------


14/41

PRINCIPLE OF CHARITY TEST

When interpreting an unclear argument,

always give the speaker / writer the

benefit of the doubt.

Fosters good will and mutual understandingin an argument.

Promotes the discovery of truth by insisting

that we confront arguments that we

ourselves admit to be the strongest and

most plausible versions of those arguments.


15/41

Exceptions to the Strict Necessity Test

An argument in which the conclusion doesnot follow necessarily from the premisesshould be treated as deductive if either:

1. The language or contextmake clear that the

arguer intendedto offer a logically conclusiveargument, but the argument is in fact notlogically conclusive;

2. The argument has a pattern of reasoning that is

characteristically deductive, and nothing elseabout the argument indicated clearly that theargument is meant to be inductive.


16/41

Exceptions to the Strict

Necessity Test

Examples

1. Magellans ships sailed around the world. Itnecessarily follows, therefore, that the earth is

a sphere. (The arguer intendedto offer alogically conclusive argument, so it should betreated as deductive.)

2. If Im Bill Gates, then Im mortal. Im not Bill

Gates. Therefore, Im not mortal. (Theargument has a pattern of reasoningcharacteristic of deductive arguments, soshould be treated as deductive.)


17/41

SUMMARY: How to distinguish

deductivefrom inductivearguments

If the conclusion follows necessarily from the premises =deductive

If the conclusion does not follow necessarily from thepremises = inductive, unless

Language indicates it is deductive Argument has deductive pattern of reasoning

If the argument has a pattern of reasoning that ischaracteristically deductive = deductive, unless Clear evidence indicates it is intended to be inductive

If the argument has a pattern of reasoning that ischaracteristically inductive = inductiveunless Clear evidence indicates it is intended to be deductive

If the argument contains an indicator word

If still in doubt: Principle of Charity


18/41

5 COMMON DEDUCTIVE

PATTERNS

Hypothetical syllogism

Categorical syllogism

Argument by elimination

Argument based on mathematics

Argument from definition


19/41

HYPOTHETICAL SYLLOGISMA syllogismis a three-line argument with two

premises, one of which is a conditional.

Modes ponens is a syllogism.

Other syllogisms are:

Chain arguments

Modus tollens (denying the consequent)Denying the antecedent

Affirming the consequent


20/41

CHAIN ARGUMENT

If A then B. If B then C.

Therefore if A then C.

If you are blue in the face then you are lying.

If you are lying then you cant be my friend.

Therefore if you are blue in the face then youcant be my friend.


21/41

MODUS TOLLENS

If A then B.Not B.

Therefore not A.

If were in Sacramento, were in California.Were not in California.

Therefore, were not in Sacramento.

If you love me, youll come with me to Tibet.

You will not come with me to Tibet.

Therefore you do not love me.


22/41

DENYING THE ANTECEDENT***

If A then B.Not A.

Therefore not B.

*If Tiger Woods won this years Masters then hes a great

athlete.

Tiger Woods didnt win this years Masters.

Therefore, Tiger Woods is not a great athlete.*If Jack comes to the party, Jill will leave.

Jack did not come to the party.

Therefore Jill did not leave.

***Denying the antecedent is a fal laciousdeductive pattern


23/41

AFFIRMING THE CONSEQUENT***

If A then B.B.

Therefore A.

*If we are on Neptune then we are in the solar system.

We are in the solar system.

Therefore we are on Neptune.

***Affirming the consequent is a fallacious deductivepattern

Exercise: Identify the argument pattern (ex. 3.2, p.

65)


24/41

MODUS PONENS (affirming the antecedent): If A then

B. A. Therefore B.

CHAIN: If A then B. If B then C. Therefore if A then C.

MODUS TOLLENS: If A then B. Not B. Therefore notA.

*DENYING THE ANTECEDENT: If A then B. Not A.

Therefore not B.*AFFIRMING THE CONSEQUENT: If A then B. B.

Therefore A.


25/41

PRINCIPLE OF CHARITY

Attribute an arguer the strongest argumentpossible.

Andy told me he ate at JBs yesterday.

But JBs was destroyed by a fire a month ago.

It is certain therefore that Andy is either lying ormistaken.

CautionThe Principle of Charity is a principle ofargument interpretation, not a principle ofargument repair.


26/41

CATEGORICAL SYLLOGISM

A three-line argument in which each

statement begins with one of the words

all, some, or no.

Some pigs have wings

All winged things sing.

Therefore some pigs sing.


27/41

ARGUMENT BY ELIMINATION

Rules out various logical possibilities untilonly a single possibility remains.

Either Dutch or Jack or Celia committed the

murder.If D or J committed the murder then the weaponwas a rope.

The weapon was not a rope.

Therefore neither D nor J committed the murder.

Therefore C committed the murder.


28/41

MATHEMATICS

The conclusion depends largely or entirely onmathematical calculation or measurement.

Light travels at a rate of 186,000 miles per second.

The sun is more than 94 million miles from earth.

Therefore it takes more than 8 minutes for thesuns light to reach earth.

Cautionnot all arguments that make use ofnumbers and mathematics are deductive.


29/41

DEFINITION

The conclusion follows from the

definitionof some key word or phrase in

the argument.

Josefina is a drummer.

Therefore Josefina is a musician.

COMMON INDUCTIVE


30/41

COMMON INDUCTIVE

PATTERNS There are 6 common inductive patterns: Inductive generalization

Predictive argument

Argument from authority

Casual argument

Statistical argument

Argument from analogy

INDUCTIVE


31/41

INDUCTIVE

GENERALIZATION

A generalizationattributes some characteristicto all or most members of a given class.

Information about some members of the class

is said to licensethe generalization.

All dinosaur bones discovered thus far

have been more than 65 million years old.

Therefore probably all dinosaur bones are

more than 65 million years old.


32/41

PREDICTIVE ARGUMENT

A statement about what will (likely)

happen in the future is defended with

reasons.

It has rained in Vancouver every

February since records have been kept.

Therefore it will probably rain inVancouver next February.


33/41

AUTHORITY, CAUSE, STATISTICS

Argument from AuthorityThe conclusion is supported by citing

some presumed authority or witness.

Causal ArgumentAsserts or denies that something is the

cause of something else.

Statistical ArgumentRests on statistical evidence.


34/41

ANALOGY Common Pattern:

Two (or more) things are alike in one way. Thereforethey are probably alike in some further way.

As a man casts off worn-out garments and puts onothers that are new,

similarly, the soul, casting off worn-out bodies, entersinto others, which are new.

(Bhagavad-Gita)

Exercise: Determine whether arguments are deductiveor inductive (ex. 3.3, p. 71-72)


35/41

VALIDITY VALIDarguments may have false premises

and false conclusions!At issue is the form. If the premises are true the

conclusion must be true.

All circles are squares.All squares are triangles.

Therefore all circles are triangles.

All fruits are vegetables.

Spinach is a fruit.

Therefore spinach is a vegetable.


36/41

VALIDITY, CONTD It is not enough that the conclusion happens

to be true. If the conclusion doesnt followfrom the premises by strict logical necessity,a deductive argument is invalid.

All pigs are animals.Wilber is pink.

Therefore Wilber is a pig.

Exercise: What conclusions follow validly? (ex.3.4, p. 73-74)


37/41

SOUNDNESS

A deductive argument is soundif it is validand has true premises.

A deductive argument with (at least) one

untrue premise, valid or invalid, is unsound.

Exercise: Determine whether arguments are

valid / sound (ex. 3.5 I & II, p. 81-82)


38/41

INDUCTIVE STRENGTHA good deductiveargument is valid.

A good inductiveargument is strong.

An inductive argument is strong if theconclusion follows probably from the

premises.

All recent US presidents have been collegegraduates.

It is likely that the next US president will be acollege graduate.


39/41

WEAKNESS

An argument that is not strong is weak.

Most US presidents have been men. It is likelythat the next US president will be a woman.

In a weak inductive argument, the conclusiondoes notfollow probably from the premises.

I dream about monsters. You dream aboutmonsters.

Therefore everybody probably dreams about

monsters.


40/41

INDUCTIVE PROBABILITY The premises and conclusion do not have to be

trueThe question is: If the premises were true, would the conclusion

follow?

Deductive arguments are either 100% valid or100% invalid.

Inductive arguments can be somewhat strong,strong, very strong, depending on the degree ofsupport the premises provide for the conclusion.

According the National Weather Service, there is a60% - 70% - 90% chance of rain today.

It is likely that it will rain today.


41/41

INDUCTIVE ARGUMENTS A valid deductive argument with true premises is sound.

A strong inductive argument with true premises is cogent. An inductive argument that is either weak or has at least

one false remise is uncogent.- No US president has been a skateboarding champion.

Therefore the next US president will probably not be a skateboardingchampion. (Cogent)

- All previous US presidents have been rocket scientists.

Therefore the next US president will probably be a woman. (Uncogent)

- All previous U.S. Presidents have been Democrats. Therefore the nextU.S. President will be a Democrat. (Uncogent)

Exercise:Determine whether arguments are cogentoruncogent(ex. 3.5 III, p. 82-83)

Date post:	02-Jun-2018
Category:	Documents
Upload:	nidia-nurfebriyanti
View:	229 times
Download:	0 times

Materi Daslog 2-3 - Basic Logical Arguments.ppt

Documents