13 Ling 21 - Lecture 4 - Basic Logical Arguments

8/12/2019 13 Ling 21 - Lecture 4 - Basic Logical Arguments

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Ling 21: Language and Thinking

Lecture 4:

Basic Logical Concepts


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ROAD MAP

After a brief side journey

into language and the

brain, including:

The physiology of thebrain;

The brain and language

disorders; and

Sign language and thebrain,

We now return to some

basic logical concepts


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Previously on Language & Thinking,

We . . .

Defined critical thinking;

Identified traits of a critical

thinker; Identified some of the barriers

to critical thinking;

and

Defined and analyzed

arguments in terms of their

component parts

(Premises & conclusions).


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This chapter is

EXTREMELY IMPORTANT because . . . It forms the foundation of

EVERYTHING else that is to

follow in this course.

If you dont read andunderstand this chapter, you will

not do well in this course.

So,

read the chapter,

actively participate in the class and

ASK QUESTIONS if you dont think

you get it!


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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?


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TWO ARGUMENT TYPES

Deductivearguments

(try to) PROVE their conclusions

Inductivearguments

(try to) show that their conclusions are

PLAUSIBLE or LIKELY


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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.


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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 the tooth

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.


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THE DIFFERENCE

Key: deductive / inductive

If the premises are true the conclusion isnecessarily/ probablytrue.

The premises provide conclusive / goodevidencefor the conclusion.

It is impossible/ unlikelyfor the premises to be

true and the conclusion to be false. It is logically inconsistent / consistentto assert

the premises but deny the conclusion.


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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


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INDICATOR WORD TEST

Deduction Induction

Certainly ProbablyDefinitely Likely

Absolutely Plausible

Conclusively ReasonableThis entails that The odds are that


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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.


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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, the

argument should always be treated as deductive.

if an arguments conclusion does notfollow with

strict logical necessity from its premises, the

argument should normally be treated as

inductive.


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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.


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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.


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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-----------


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PRINCIPLE OF CHARITY TEST

When interpreting an unclear argument,

always give the speaker / writer the benefit of

the doubt.

Fosters good will and mutual understanding in an

argument.

Promotes the discovery of truth by insisting that

we confront arguments that we ourselves admit tobe the strongest and most plausible versions of

those arguments.


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Exceptions to the Strict Necessity Test

An argument in which the conclusion does notfollow necessarily from the premises should

be treated as deductive if either:

1. The language or contextmake clear that the arguer

intendedto offer a logically conclusive argument,

but the argument is in fact not logically conclusive;

2. The argument has a pattern of reasoning that is

characteristically deductive, and nothing else aboutthe argument indicated clearly that the argument is

meant to be inductive.


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Exceptions to the Strict Necessity Test

Examples1. Magellans ships sailed around

the world. It necessarily follows,

therefore, that the earth is a sphere.

(The arguer intendedto offer a logically conclusive

argument, so it should be treated as deductive.)

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

Therefore, Im not mortal. (The argument has a

pattern of reasoning characteristic of deductive

arguments, so should be treated as deductive.)


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SUMMARY: How to distinguish deductive

from inductivearguments

If the conclusion follows necessarily from the premises =deductive

If the conclusion does not follow necessarily from the premises= 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


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5 COMMON DEDUCTIVEPATTERNS

Hypothetical syllogism

Categorical syllogism

Argument by elimination

Argument based on mathematics

Argument from definition


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HYPOTHETICAL SYLLOGISM A 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


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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 you

cant be my friend.


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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.


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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 fallaciousdeductive pattern


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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 deductive

pattern

Exercise: Identify the argument pattern (ex. 3.2, p. 65)


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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 not A.

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

not B.

*AFFIRMING THE CONSEQUENT: If A then B. B. Therefore A.


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PRINCIPLE OF CHARITY

Attribute an arguer the strongest argument possible.

Andy told me he ate at JBs yesterday.

But JBs was destroyed by a fire a monthago.

It is certain therefore that Andy is either

lying or mistaken.

CautionThe Principle of Charity is a principle of

argument interpretation, not a principle of argument

repair.


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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.


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ARGUMENT BY ELIMINATION

Rules out various logical possibilities until onlya single possibility remains.

Either Dutch or Jack or Celia committed the murder.

If D or J committed the murder then the weapon wasa rope.

The weapon was not a rope.

Therefore neither D nor J committed the murder.Therefore C committed the murder.


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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 the suns

light to reach earth.

Cautionnot all arguments that make

use of numbers and mathematics are

deductive.


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DEFINITION

The conclusion follows from the definitionof

some key word or phrase in the argument.

Josefina is a drummer.

Therefore Josefina is a

musician.


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COMMON INDUCTIVEPATTERNS

There are 6 common inductive patterns: Inductive generalization

Predictive argument

Argument from authority

Causal argument

Statistical argument

Argument from analogy


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INDUCTIVE GENERALIZATION

A generalizationattributes some characteristic toall 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 aremore than 65 million years old.


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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 in Vancouver

next February.


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AUTHORITY, CAUSE, STATISTICS

Argument from Authority The conclusion is supported by citing some

presumed authority or witness.

Causal Argument Asserts or denies that something is the

cause of something else.

Statistical Argument Rests on statistical evidence.


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ANALOGY

Common Pattern:

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

As a man casts off worn-out garments and puts on othersthat are new,

similarly, the soul, casting off worn-out bodies, enters intoothers, which are new.

(Bhagavad-Gita)

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


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VALIDITY

VALIDarguments may have false premises and

false conclusions! At issue is theform. 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.


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VALIDITY, CONTD

It is not enough that the conclusion happensto be true. If the conclusion doesnt followfrom the premises by strict logical necessity, adeductive 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)


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SOUNDNESS

A deductive argument is soundif it is valid andhas true premises.

A deductive argument with (at least) oneuntrue premise, valid or invalid, is unsound.

Exercise: Determine whether arguments arevalid / sound (ex. 3.5 I & II, p. 81-82)


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INDUCTIVE STRENGTH

A 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 havebeen college graduates.

It is likely that the next USpresident will be a collegegraduate.


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WEAKNESS

An argument that is not strong is weak.

Most US presidents have been men. It is likely that thenext US president will be a woman.

In a weak inductive argument, the conclusion doesnotfollow probably from the premises.

I dream about monsters. You dream about monsters.

Therefore everybody probably dreams aboutmonsters.


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INDUCTIVE PROBABILITY The premises and conclusion do not have to be true

The question is: If the premises weretrue, would the conclusion

follow?

Deductive arguments are either 100% valid or 100%

invalid. Inductive arguments can be somewhat strong, strong,

very strong, depending on the degree of support thepremises provide for the conclusion.

According the National Weather Service, there is a 60% -70% - 90% chance of rain today.

It is likely that it will rain today.


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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 onefalse remise is uncogent.

- No US president has been a skateboarding champion.Therefore the next US president will probably not be askateboarding champion. (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. Thereforethe next U.S. President will be a Democrat. (Uncogent)


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INDUCTIVE ARGUMENTS

Exercise:Determine whether arguments are

cogentor uncogent(ex. 3.5 III, p. 82-83)


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Summary of Argument Types

Deductive Inductive

Valid Invalid Strong Weak

(all are (all are

unsound) uncogent)

Sound Unsound Cogent Uncogent

MEMORIZE THESE DIAGRAMS ! ! !


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Culminating Activity

Exercise 3.5 IV, Page 83:

Determine whether the arguments are deductiveor

inductive. If the argument is deductive, determinewhether it is validor invalid. If the argument is

inductive, determine whether it is strongor weak.

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13 Ling 21 - Lecture 4 - Basic Logical Arguments