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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.