Understanding Logical Argumentation, Structure, and Reasoning

Basic Components, Structure and Logic of

Argumentation

Parts 2-5

Basic Components of Argumentation

Part 2

“Master the machinery of [logic], and you have a mental

occupation always at hand… that will be of real use to

you in any subject you take up. It will give you clearness

of thought – the ability to see your way through a puzzle

– the habit of arranging your ideas in an orderly and get-

at-able form – and, more valuable than all, the power to

detect fallacies, and to tear to pieces the flimsy illogical

arguments, which you will so continually encounter in

books, in newspapers, in speeches, and even in sermons,

and which so easily delude those who have never taken

the trouble to master this fascinating Art. Try it. That is

all I ask of you!”

-Lewis Carroll

Part 1: Elements of an Argument1. Key Terms2. Identifying Conclusions3. Identifying Premises

Part 2: Recognizing Elements of Good Arguments1. More Key Terms2. Valid and Invalid Arguments3. Sound and Unsound Arguments

Part 3: Inductive and Deductive Reasoning

Contents of this PresentationClick below to jump to a section

Part 1: Elements of an Argument

1. Argumentation Key Terms2. Identifying Conclusions3. Identifying Premises

Claim: a statement or opinion that is either true or

Argument: a claim supported by premises

Conclusion: the main claim in an argument

Premises: claims that support an argument’s

conclusion

Argumentation Key Terms

Claim: an assertion about the truth, existence, or

value of something that is either true or false❖ Claims are also called Statements or Propositions

❖ When supported by a premises, a claim becomes a conclusion

○ This class is easy.

○ The Detroit Lions have the potential to make the NFL

playoffs.

○ This chemical structure is unstable.

○ Democratic socialism is superior to a pure democracy.

Argument

Argument: an assertion that contains

BOTH a conclusion and premises ○ Not all statements are arguments

○ A statement of fact or opinion based on evidence

○ Some statements contain multiple arguments

Click to View the Linked YouTube Video Below

Which of the following is an argument?

Vending machines stocked with soda or candy

should be removed from all public schools.

Star Wars is the best movie ever.

We’d better leave now. If we don’t, we might miss

the last train and we’ll be stuck here all night.

○ NOT AN ARGUMENT. It offers no support

○ THIS IS AN ARGUMENT. It offers support

(premises) to support the claim.

Conclusions

Conclusion: The main claim of an argument that

is supported by a premise

○ It’s the logical result of the relationship

between the premises.

Identifying the

Conclusion is the

first step in

understanding the

argument

2 Keys to Identifying the Conclusion

1. Ask, “Is the statement the main point, or is it a claim

given to support another statement in the argument

2. Identify the indicator word that often precedes

the conclusion, such as:

○ Therefore

○ Thus

○ As a Result

○ That's why

○ Consequently

○ This means

○ This shows

○ It follows that

○ This suggests

○ Hence

○ So

○ Accordingly

Premises

Premise: A reason offered as support, or

evidence, for another claim.

These are often indicated by the words:

○ Because

○ For

○ As

○ Since

○ Inasmuch as

○ As shown by

○ Given that

○ As indicated by

○ The reason is that

Premises

Today's freshmen cannot write very well. Joe is a freshman, so he must be a poor writer.

Premise Today's freshmen cannot write very well

Premise Joe is a freshman,

Conclusion so he must be a poor writer.

What is the Conclusion in each of the Following Arguments?

Abortion is wrong because all human life is sacred.

❖ Abortion is wrong.

It’s flu season and you work with kids, so you should get a flu shot.

❖ You should get a flu shot.

We should believe that rocks exist because we are able to see them.

❖ Rocks Exist

John will probably receive the next promotion since he’s been here the longest

❖ John will receive the next promotion

We must reduce the amount of money we spend on space exploration. Right now, the enemy is launching a massive military buildup, and we need the additional money to purchase military equipment to help match the anticipated increase in the enemy’s strength

❖ We must reduce the amount of money we spend on space exploration.

It’s a beautiful day. We should go to the park. Besides, I need some exercise.

We should go to the park.

That movie has had horrible reviews. My sister saw it and said it was boring and her friend spotted three mistakes. Pick a different movie. I am sure we can find something better.

We should pick a different movie.

Claim: statement about the truth or value of something that is either true or false

Argument: a conclusion and a supporting premise together

Conclusion: the main claim or point in an argument that’s supported by premises

Premises: pieces of evidence that support the conclusion

CLICK HEREfor Practice Identifying the

Premises and Conclusions of Arguments

Part 3: Standard Argument Form

Identify the Premises and Conclusion

Rewrite the argument in standard form● Step 1: Identify which claim is the conclusion.● Step 2: Identify which claims are premises supporting

conclusion

Standard Form1 Premise 1

2 Premise 2

Conclusion

All black dogs are warm-blooded because they are mammals, and all mammals are warm-blooded

Standard FormPremise 1:

Premise 2:

Conclusion:

All black dogs are warm-blooded because they are mammals, and all mammals are warm-blooded

“because” = indicates a Premise

Standard FormPremise 1: Black dogs are mammals

Premise 2: All mammals are warm-blooded

Conclusion: All black dogs are warm-blooded

He must be a good basketball player. After all, he’s tall, and all tall people are good basketball players.

Premise 2:

Conclusion:

He must be a good basketball player. After all, he’s tall, and all tall people are good basketball players.

“After all” = indicates a Premise

Standard FormPremise 1: He’s tallPremise 2: All tall people are good basketball players

Conclusion: He must be a good basketball player

The weather report is calling for blizzard conditions. Driving could be hazardous. Stay here tonight and you can head back to college after the road is plowed tomorrow.

Premise 2:

Conclusion:

Write it in Standard Form

Start on your homework now. You will get done earlier and still have time to watch the movie with us. It shouldn’t take too long and your father can help you if you need it.

Standard Form

If all employers require their employees to take a flu shot, then less people would take sick days. This would result in increased productivity for the nation as a whole.

Premise 2:

Conclusion:

Standard FormPremise 1: If all employers require their employees to take a

flu shot, then less people would take sick days

Premise 2: What is the implied premise?Conclusion: The flu shot would increase productivity for the

nation as a whole.

Standard FormPremise 1: If all employers require their employees to take a

flu shot, then less people would take sick days

Premise 2: Less people taking sick days would increase productivity for the nation

Conclusion: The flu shot would increase productivity for the nation as a whole.

Less than one percent of the people receiving parking tickets appeal those tickets. Therefore, one cannot claim that the Parking officers are issuing unwarranted citations.

Standard Form

Premise 1:

Premise 2:

Conclusion:

Standard Form

Premise 1: Less than one percent of the people receiving parking tickets appeal those tickets.

Premise 2: What is the implied premise?Conclusion: one cannot claim that the Parking officers are

issuing unwarranted citations.

Standard Form

Premise 1: Less than one percent of the people receiving parking tickets appeal those tickets.

Premise 2: People appeal unwarranted citationsConclusion: one cannot claim that the Parking officers are

issuing unwarranted citations.

Write the two arguments presented with the following statements

You shouldn’t take that job. The pay is lousy, which will make it hard for you to pay your bills, and that will make you unhappy.

Secondary ArgumentPremise 1:

Premise 2:

Conclusion:

Main ArgumentPremise 1:

Premise 2:

Conclusion:

Write the two arguments presented with the following statements

Secondary ArgumentPremise 1: it hard for you to pay your bills

Premise 2: Not being able to pay your bills

Conclusion: It will make you unhappy

Main ArgumentPremise 1: The lousy pay of that job will make it hard for you to pay your bills

Premise 2: Not being able to pay your bills will make you unhappy

Conclusion: You shouldn’t take that job

Main ArgumentPremise 1: The lousy pay of that job will make it hard for you

to pay your bills

Premise 2: Not being able to pay your bills will make you

unhappy

Conclusion: You shouldn’t take that job

The following argument consists of several conclusions

You spend too much time playing video games. You are not getting enough sleep and your grades are slipping. I think you need to change your daily routine. Make a list of your priorities. If you don’t, I think you’re headed for big trouble.

Write the claims in standard form in the chart on the next slide.

1. You may have multiple conclusions

2. Support each conclusion with at least one premise written above it.

3. Some claims may support multiple conclusions.

4. Write as many standard argument forms as needed.

You spend too much time playing video games. You are not getting enough sleep and your grades are slipping. I think you need to change your daily routine. Make a list of your priorities. If you don’t, I think you’re headed for big trouble.

Part 4

Recognizing Good Arguments

1. More Argumentation Key Terms2. Valid and Invalid Arguments3. Sound and Unsound Arguments

Recognizing a Good Argument

1. The premises must all be true - or plausible

to a given audience

This is called the The Truth Condition

2. The conclusion must logically follow from

the premises

This is called the The Logic Condition

Valid: An argument whose premises logically lead to its conclusion. To say the argument is valid is to say that it is logically impossible for its premises to be true and its conclusion false.

Invalid: If an argument is invalid, then it is possible for the conclusion to be false even if all the premises are true.

Unsound: An argument that has at least one false premise

Sound: An argument that is valid and contains only TRUE premises

Inductive Reasoning: A process of reasoning in which we use small, specific examples or observation to reach a BIG, general rule, conclusion or theory

Deductive Reasoning: A process of reasoning in which we start with a general rule or conclusion and look to see whether specific evidence supports, or fits, that previously held belief

Argumentation Key Terms

Valid Argument

A Valid Argument has the following hypothetical property: If all the premises are true, the conclusion cannot be false.

That is, if you were to imagine that all the premises were true, then it would be logically impossible for the conclusion false at the same time

Logic guarantees of the truth of the conclusion, (now provided that the premises are true)

Valid Argument

Premise If Michigan scores the most points then they win the game.

Premise Michigan scored more points.

Conclusion So, Michigan won the game

Premise All actors are robots

Premise Tom Cruise is an actor

Conclusion Therefore, Tom Cruise is a robot

Valid Argument

When we say "If A then B" it means that, every time, if A is true or false, then B is true or false also.

Premise Tom is happy only if the Tigers win,

Premise the Tigers lost;

Conclusion therefore, Tom is not happy.

The Argument Form is...

If A then B

Therefore, B

Valid Argument Forms

i. If Joe makes this field goal, then Davison

ii. Joe made the field goal .

iii. Therefore the Davison won.

If P then Q

Therefore Q

i. If the patient has malaria, then a blood test will indicate that his blood harbors the P. vivax virus

ii. Blood test indicate that the patient’s blood does not harbor the P. vivax virus.

iii. Therefore the patient does not have malaria.

If P then Q

Therefore

Valid Argument Forms

i. Either the Detroit Tigers or the Giants will

win the World Series.

ii. The Tigers did not win the Word Series

iii. Therefore, the Giants won

Either P or Q

Therefore Q

i. If John gets a raise, then he will buy a house.

ii. If John buys a house, he'll run for city

council.

iii. Therefore, if John gets a raise, he will run

for a position on the city council

If P then Q

If Q then R

Therefore ...

If P then R

Premise If a plane is flying it is in the air.

Premise Flight 999 is flying,Conclusion Therefore it is in the air.

Valid Arguments

Premise If P then Q

Premise PConclusion Therefore, Q

Premise If there are clouds in the sky, then rain is possible.

Premise No rain is possible. Conclusion Therefore, there are no clouds in the sky

Valid Arguments

Premise If P then Q

Premise Not QConclusion Therefore, Not P

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

Premise Elizabeth does not own a Honda.Conclusion Therefore, Elizabeth owns a Saturn.

Valid Arguments

Premise Either P or Q

Premise Not PConclusion Therefore, Q

Premise All toasters are items made of gold.

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

Conclusion Therefore, all toasters are time-travel devices.

Valid Arguments

Premise All P are Q

Premise All Q are RConclusion Therefore, All P are R

Invalid ArgumentsInvalid: An argument where the conclusion could be

false even if the premises are true○ Premise: Steve owns a Lexus automobile.

○ Premise: Rich people own Lexus automobiles

○ Conclusion: Therefore, Steve must be rich

The Argument Form is...

● P is Q

● R is Q

● Therefore, P is R

Invalid Argument Forms i. Anyone who lives in the city of Davison,

MI also lives in Genesee County.

ii. Frank lives in Genesee County.

iii. Therefore, Frank lives in the city Davison,

If P, then Q.

Therefore, PGeneralization

i. Anyone who lives in the city of Davison, MI also lives in Genesee County.

ii. Frank does not live in the city Davison, MI.iii. Therefore, Frank does not live in Genesee

County.

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

Invalid Argument Forms i. All smurfs are snorks

ii. All ewoks are snorks

iii. Therefore, All smurfs are

Generalizations

All P are Q

All R are Q

Therefore, P are R

i. Either you’re with me or you’re against me.

ii. You’re not with me.iii. So, you must be against me.

False Dichotomy

X or Y

Therefore, Y

Premise Every time there is someone in the front yard, Spot barks.

Premise Spot is barking,Conclusion so someone must be in the front yard

Invalid Arguments- A False Cause

Premise If X then Y

Premise YConclusion Therefore, X

Premise All dogs have four legs.

Premise Francis the Talking Mule is not a dog Conclusion Therefore, Francis the Talking Mule does

not have four legs

Invalid Arguments

Premise All X are Y

Premise not XConclusion Therefore, Not Y

Premise If Obama is president, then a Democrat is president

Premise A Democrat is president

Conclusion Therefore, Obama is president

Invalid Arguments

Premise If X then Y

Premise If my power goes out, then my cable TV goes out.

Premise My power is not out, Conclusion therefore, my cable TV is not out.

Invalid Arguments

Premise If X then Y

Premise not XConclusion Therefore, Not Y

Premise If I am with the one I love, then I am happy.

Premise I am happy. Conclusion Therefore, I am with the one I love

Invalid Arguments

Premise If X then Y

FINAL NOTE: Valid or Invalid?

FOR VALID arguments: the addition of extra premises can not

change the conclusion - a valid conclusion reached from a set of

premises can never be changed by the addition of new premises.

Also, it is impossible for the premises of a valid argument to be true and the conclusion to be false

FOR INVALID arguments: the addition of new premises will many times strengthen or weaken a given conclusion.

Also, it is possible for the conclusion of an invalid argument to be false even if it has true premises.

Spotting Valid and Invalid Arguments

i. If A, then B.ii. B.iii. So, A.

i. All monkeys have blue teeth

ii. Meg is a monkeyiii. Therefore Meg has

blue teeth

i. All OSU fans are arrogant.

ii. All arrogant people are dumb.

iii. So, all OSU fans are dumb.

i. Shermer and Randi are Arabic.

ii. Shermer and Randi are cops

iii. So, some Arabs are cops.

i. If my astrologer is clairvoyant, then she predicted my travel plans correctly.

ii. She predicted my travel plans correctly.

iii. So, my astrologer is clairvoyant.

i. If God created the universe, we should observe order and design in Nature.

ii. We do observe order and design in Nature.

iii. So, God created the universe.

Unsound ArgumentsUnsound: An argument that has at least one false

premise

Example: i. Cows are insects.

ii. Insects are mammals.

iii. So cows are mammals.

Example: i. All dogs have 5 legs.

ii. Fido is a dog.

iii. Therefore Fido has 5 legs

Sound Arguments

Sound: An argument that is valid and contains

only TRUE premises

Example:

i. All cows are mammals.

ii. All mammals are animals.

iii. So cows are animals.

Valid and Sound ArgumentsAll athletes are professional golfers T or F?

Lebron James is an athlete T or F?

Therefore, Lebron James is a professional golfer T or F?

All humans are whales T or F?

All whales are mammals T or F?

So, all humans are mammals T or F?

All Detroit Lions are football players T or F?

Calvin Johnson is a football players T or F?

Therefore, Calvin Johnson is a Detroit Lion T or F?

Inductive and Part 5:Deductive Reasoning

Deductive Reasoning

A process of reasoning in which

we start with a general rule or conclusion and look to see whether specific evidence supports, or fits, that previously held belief

Deductive Reasoning

1. What is the conclusion?

2. What evidence supports it?

3. Is that evidence logical?

If you can answer yes to question 3, then the conclusion should be logical and the argument valid and sound.

Many deductive arguments are valid

Click to View Video on YouTube

Inductive Reasoning

A process of reasoning in which we use small, specific examples or observation to reach a BIG, general rule, conclusion or theory

Inductive Reasoning

When detectives arrive at the scene of a crime, the first thing they do is look for clues that can help them piece together what happened.

1. What have you observed? What evidence is

available?

2. What can you conclude from that evidence?

3. Is that conclusion logical?

Many Inductive arguments are strong but invalid

Click to View Video on YouTube

Inductive or Deductive

Inductive: Evidence Conclusion (IEC)

Deductive: Conclusion Evidence (DCE)

If the truth of the premises does not definitely

establishes the truth of the conclusion, but provides

a strong reason to believe the conclusion true, then

you have an inductive argument

If the truth of the premises definitely establishes

the truth of the conclusion then you have a valid

deductive argument

1. The Giants have lost their last seven games. Thus, they will

probably lose their next game.

2. If you brush and floss your teeth daily then you will have

fewer cavities. Marie brushes and flosses her teeth daily.

Thus, she will have fewer cavities.

3. Jones will play tennis today if Smith plays. Jones will not

play tennis today. Therefore, Smith will not play.

4. 4 out of 5 times I beat Corey at pool and I'm going to play

him tomorrow. So, I'll very likely win.

5. No man has ever gotten pregnant. Therefore, no man ever

will get pregnant.

Inductive or Deductive1. The Giants have lost …Inductive argument – uses 7 specific

examples to reach a bigger conclusion

2. If you brush and floss your teeth …Deductive argument – states

the broadly accepted research and reaches a specific conclusion

3. Jones will play tennis today if …Deductive argument –gives an

overarching rule that governs the behavior to predict a specific

outcome

4. 4 out of 5 times I beat Corey…Inductive argument – uses

specific examples to predict the conclusion

5. No man has ever gotten pregnant…Inductive argument – the conclusion is a BIG, overarching rule based on numerous specific examples to date.

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