7—Deductive Reasoning

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9—Deductive Reasoning SJSU Spring 2014 Comm 41 Sect 04, 06Minna Holopainen

SJSU Spring 2014 Comm 41 Holopainen

Photo Sonja Holopainen

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Agenda

Syllogisms Aristotelian LogicDiagramming Arguments

SJSU Spring 2014 Comm 41 HolopainenPhoto Sonja Holopainen

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Deductive Reasoning


Syllogisms Aristotelian logicDiagramming arguments

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Two Logic Systems

+Inductive Reasoning

Finding patternsForming conclusions

-Deductive Reasoning

Eliminating options Testing hypotheses

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Logic

Informal logic

! The study of natural languagearguments

! Fallacies

Formal logic

! The study of inference with purelyformal content, where that contentis made explicit.

! Concerned with the form of anargument

! Deductive

! Aristotle’s syllogistic logic

SJSU Spring 2014 Comm 41 HolopainenPhoto Sonja Holopainen, 2009

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Types of Deductive Arguments

Argument by elimination Argument based on mathematics Argument from denition


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Syllogisms


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Syllogisms

! Greek: "#$$%&'"()* ( syllogismos )—"conclusion,""inference"

! "A discourse in which, certainthings having been supposed,something di +erent from thethings' supposed results ofnecessity because these thingsare so." (Aristotle’s Prior

Analytics 24b18–20)

Aristotle by RembrandtPicture from http://www.uah.edu/colleges/liberal/philosophy/heikes/302/time/rembrant/aristotle-homer.jpg without permission. SJSU Spring 2014 Comm 41 Holopainen

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SYLLOGISMS

Categorical Disjunctive Hypothetical

ENTHYMEME

Deductive forms of reasoning

Picture from http://dm-lifeservers.com/wordpress/wp-content/sokrates.gif without permission. SJSU Spring 2014 Comm 41 Holopainen

Major premise: All men are mortal.Minor premise:

Socrates is a man.Conclusion:Therefore, Socrates is

mortal.

P or Q.Not P.

Therefore, Q.

I’ll have co ! ee or tea.Not co ! ee.

Therefore, tea.

If P, then Q.P.Therefore, Q.

If P, then Q.Not Q.Therefore, not P.

If P Q.

If Q R.

Therefore, P R.

If I go to bed early, I will getenough sleep.If I get enough sleep, I willdo well in my speechtomorrow.Therefore, if I go to bed early,I will do well in my speechtomorrow.

An incompleteargument in whicheither a premise orconclusion is assumed

Socrates is mortal because he is a man.

Socrates is mortal because all men are mortal.

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Aristotelian Logic


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Aristotle384-322 BCE

Student of PlatoTeacher of Alexander the Great

Picture from http://en.wikipedia.org/wiki/File:Aristotle_Altemps_Inv8575.jpg without permission. SJSU Spring 2014 Comm 41 Holopainen

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Four Categorical Claims


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All Some No

Only children are noisy. At least one child is noisy.

Not a single sweet thingturns sour in my mouth.

Everything sweet turnssour in my mouth.

Some sweets turn sour inmy mouth.

No child is noisy.

Every page has a stain in

it.

There is a page that has a

stain in it.Everybody’s feet werecold.

There were a few peoplewhose feet were cold.

All cups were in thecupboard.

There was a cup that wasin the cupboard.

Each respondent repliedpromptly.

A number of respondentsreplied promptly.

Not even one page has a

stain in it.Nobody’s feet were cold.

There were no cups in thecupboard.

Not a single respondentreplied promptly.

Every time I call him heanswers.

Only sometimes when Icall him he answers.

He never answers when Icall him.


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Four Categorical Claims


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Square of Opposition

Source Stanford Encyclopedia of Phiosophy at http://plato.stanford.edu/entries/contradiction/. SJSU Spring 2014 Comm 41 Holopainen

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Practice Square of Opposition

All board members drink co +ee.

Some board members do notdrink co +ee.Contradictories

Everyone who lives must die.

Nobody who lives must die.

Contraries

Mary always sleeps in class.

Mary sometimes sleeps in class.

Subalternates

Some people like to dance.

Some people do not like to dance.

Subcontraries

Graph from Stanford Encyclopedia of Phiosophy at http://plato.stanford.edu/entries/contradiction/. SJSU Spring 2014 Comm 41 Holopainen

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Four types of claims:

A—All humans are mortal.

E—No human is ageless.

I—Some humans are happy.

O—Some humans are notgreedy.

There are 256 types ofcategorical syllogisms: AAA,

AEA, AIA, AOA, AAE, AAI, etc.


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Diagramming Arguments


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Good arguments


ValidStrong

Weak

Implausible Plausible

A sound argument has to be

valid.

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Arguments’ validity and strength

Bad argumentsGood arguments

VALID INVALID

Strong Weak

Every way the premisescould be true leads tothe conclusion.

It is extremely likelythat the premises leadto the conclusion.

It is very unlikely orimpossible that the premiseslead to the conclusion.

Whether an argument is valid or strong does notdepend on whether the premises are sound/plausible.


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Mortal things

Men

Valid All men are mortal.Socrates is a man.

Therefore, Socrates is mortal.

Weak All men are mortal.Socrates is mortal.

Therefore, Socrates is a man.

Mortal things

Men

Mortal things

Men

Reasoning with all

Valid All S are P.Q is S.So Q is P.

Weak All S are P.Q is P.So Q is S.


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Cranky

Busy

Students

Valid All students are busy people. All busy people are cranky.So all students are cranky.

Invalid/weakSome students are busy people.Some busy people are cranky.So some students are cranky.

Cranky

Cranky

Reasoning in a chain with all and some

Valid All S are P. All P are Q.So all S are Q.

WeakSome S are P.Some P are Q.So some S are Q.


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Mammal

Cats

Fish

ValidEvery cat is a mammal.No sh is a mammal.So no sh is a cat.

Invalid/weakEvery cat is a mammal.No sh is a cat.So no sh is a mammal.

Mammal

Cats

Fish

Mammal

Cats

Fish

Reasoning with no

Valid All S are P.No Q is P.So no Q is S.

Weak All S are P.No Q is S.So no Q is P.


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Delicious things

Usually strong Almost all cookies are delicious.Madeline is a cookie.So Madeline is delicious.

Weak Almost all cookies are delicious.Madeline is delicious.So Madeline is a cookie.

Delicious things Delicious things

Reasoning with almost all

Strong Almost all S are P.Q is S.So Q is P.

Weak Almost all S are P.Q is P.So Q is S.


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Taxpayers

Weak Almost all senior students are over 20 years old. Almost all 20-year olds are paying taxes.So almost all seniors are taxpayers.

Reasoning in a chain with almost all

Weak Almost all S are P. Almost all P are Q.So almost all S are Q.


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Diagramming Arguments Exercise

1. Get your argument cards.2. In your group, draw diagrams of all possible cases the argument can be true.3. Decide if the argument is valid, strong, or weak.


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All turtles can swim. Anything that swims eats sh.So turtles eat sh.

Anyone who is hot sweats.Manuel is not sweating.So Manuel is not hot.

Every toy is safe.Knife is not a toy.So no knife is safe.

All her shoes are expensive. All expensive things are pretty.So, all her shoes are pretty.

Some pets are aggressive.Some aggressive creatures aredangerous.So some pets are dangerous.

All funny movies are old.Modern Times (1936) is old.So Modern Times is a funny movie.

All food is edible.

Sushi is food.So sushi is edible.

Practice diagramming


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New concepts

Categorical, disjunctive, andhypothetical syllogismEnthymemeConditional

Antecedent, consequentModus ponens, converse errorModus tollens, inverse error

Four categorical claims/Square ofOppositionUniversal, particular

A , rmative, negative

Valid, invalid argumentStrong, weak argument


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Upcoming Assignments

AA3: Moral argument Library Research Module (Comm Center)Critical Analysis


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7—Deductive Reasoning