Aristotelian Logic & Aristotelian Logic & Fashioning an ArgumentFashioning an Argument

A Study of Deductive A Study of Deductive ReasoningReasoning

Why learn this stuff?Why learn this stuff?

Logic = ReasoningLogic = Reasoning Basis of academic Basis of academic

thoughtthought Creation of Creation of argumentargument

How do I demonstrate logic?How do I demonstrate logic? Make Make obvious, explicit obvious, explicit

connectionsconnections between your between your major thoughts and ideasmajor thoughts and ideas

You want someone to You want someone to FOLLOWFOLLOW your your traintrain of of thought. thought.

AristotleAristotle

Worked with Worked with syllogismssyllogismsFormal system of thoughtFormal system of thought

Provides a Provides a methodmethod for for connecting ideas togetherconnecting ideas together

SyllogismSyllogism ExEx: :

1) Wood floats in 1) Wood floats in water.water.

2) Ships are 2) Ships are made of woodmade of wood

3) Therefore 3) Therefore ships float in ships float in water.water.

SyllogismsSyllogisms

#1 and #2 are both a #1 and #2 are both a premisepremise. .

#3 is a #3 is a conclusionconclusion

Syllogism Example Syllogism Example ReiteratedReiterated

Premise #1Premise #1: Wood floats in : Wood floats in water.water.

Premise #2Premise #2: Ships are made : Ships are made of wood.of wood.

ConclusionConclusion: Therefore, ships : Therefore, ships float in water.float in water.

Syllogism PracticeSyllogism Practice

If all humans are mortal, If all humans are mortal, and all Greeks are and all Greeks are

humans, humans, then all Greeks are mortalthen all Greeks are mortal..

This type of logic isn’t This type of logic isn’t perfect!perfect!

All chickens have two legs.All chickens have two legs. Aristotle has two legs.Aristotle has two legs. Therefore, Aristotle is a chicken.Therefore, Aristotle is a chicken.

==flawedflawed

However, this isn’t the point!However, this isn’t the point!

So?So?

When you write an When you write an essay, watch your essay, watch your premisespremises. They . They should lead to a should lead to a valid valid conclusionconclusion..

Examples – Examples – Fill in the missing Fill in the missing

componentcomponent All trees have All trees have

root systems. root systems.

Therefore, All Therefore, All trees need trees need nitrogen. nitrogen.

All root All root systems need systems need nitrogen.nitrogen.

Examples – Examples – Fill in the missing Fill in the missing

componentcomponent

All fruits grow on All fruits grow on treestrees

Therefore, all Therefore, all oranges grow on oranges grow on treestrees

All oranges are All oranges are fruitsfruits

Examples – Examples – Fill in the missing Fill in the missing

componentcomponent All bachelor's All bachelor's

are singleare single

Johnny is single,Johnny is single,

Hence, Johnny is Hence, Johnny is a bachelora bachelor

Ex: Logic w/o syllogism Ex: Logic w/o syllogism formatformat

Everyday I go to work. This journey Everyday I go to work. This journey from my home to my office takes from my home to my office takes one hour. My office starts at eight one hour. My office starts at eight o' clock in the morning. So, if I o' clock in the morning. So, if I leave my home at seven o' clock in leave my home at seven o' clock in the morning, I will reach the office the morning, I will reach the office in time.in time.

ArgumentArgument

Validity and SoundnessValidity and Soundness

Argument: ValidityArgument: Validity

A deductive argument is said to A deductive argument is said to be be validvalid if and only if and only if it takes a if it takes a form that makes it form that makes it impossibleimpossible for the for the premisespremises to be to be truetrue and and the the conclusionconclusion nevertheless to nevertheless to be be falsefalse. Otherwise, a deductive . Otherwise, a deductive argument is said to be argument is said to be invalidinvalid..

Argument: ValidityArgument: Validity

Valid arguments do not Valid arguments do not require true premises. require true premises.

Ex: Valid Argument – True Ex: Valid Argument – True premisespremises

Either Elizabeth owns a Honda or Either Elizabeth owns a Honda or she owns a Saturn.she owns a Saturn.

Elizabeth does not own a Honda.Elizabeth does not own a Honda.

Therefore, Elizabeth owns a Therefore, Elizabeth owns a Saturn.Saturn.

Ex: Valid Argument – False Ex: Valid Argument – False premisespremises

All toasters are items made of All toasters are items made of gold.gold.

All items made of gold are All items made of gold are time-travel devices.time-travel devices.

Therefore, all toasters are Therefore, all toasters are time-travel devices.time-travel devices.

Argument - SoundnessArgument - Soundness

A sound argument is one that A sound argument is one that is not only valid, but begins is not only valid, but begins with premises that are with premises that are actually trueactually true

SoundnessSoundness A deductive argument is A deductive argument is

soundsound if and only if if and only if 1) it is both 1) it is both validvalid, and , and 2) all of its 2) all of its premisespremises are are

actually actually truetrue. . Otherwise, a deductive Otherwise, a deductive

argument is argument is unsoundunsound..

Ex: Sound argumentEx: Sound argument

No felons are eligible voters.No felons are eligible voters.

Some professional athletes are Some professional athletes are felons.felons.

Therefore, some professional Therefore, some professional athletes are not eligible voters.athletes are not eligible voters.

QUANTIFIER

S

Practice…Practice…