Logic and Argumentation

What is Logic?

•Through arguments

How do we reason?

•The study of human reasoning

Are these arguments?•I believe that capital punishment can

never be justified, no matter how awful the crime. I am completely opposed to it.

•The house was destroyed because faulty wiring ignited some old rags in the laundry room.

•All of my uncles are retired. The guy sitting next to me is my uncle. Therefore, the guy next to me is retired.

What is an Argument?•A set of statements designed to convince

the reader/listener of a claim

•An attempt to support a conclusion by giving reasons for it

How do you find an argument?

What is a conclusion?

•Some indicative words: Therefore, So, Hence, Thus, For this reason, …must …, …cannot…

•Statement supported by reason

•BUT not all statements with these words are conclusions

Are there conclusions?• The patient must have measles – he has a bright

red blotchy rash on her face and neck, along with a high temperature, runny nose, and sore throat.

• Someone left the ice outside, so it melted.

• There are so many people at this party, I can’t hear what you are saying.

• It can’t be poverty that causes crime. Lots of people are poor and never become criminals.

Where’s the conclusion? In order to determine car insurance

premiums for a driver, insurance companies calculate various risk factors; as the risk factors increase, so does the premium. Certain factors, such as the driver's age and past accident history, play an important role in these calculations. Yet these premiums should also increase with the frequency with which a person drives. After all, a person's chance of being involved in a mishap increases in proportion to the number of times that person drives.

Where’s the conclusion? In order to determine car insurance

premiums for a driver, insurance companies calculate various risk factors; as the risk factors increase, so does the premium. Certain factors, such as the driver's age and past accident history, play an important role in these calculations. Yet these premiums should also increase with the frequency with which a person drives. After all, a person's chance of being involved in a mishap increases in proportion to the number of times that person drives.

When you think you’ve found the conclusion, ask:•What would make me accept this

statement?•What evidence do I need to see in order to

believe this statement?•If you’ve found the evidence/reason in the

passage, you’ve found the conclusion!

What is a premise?

•Some indicative words: Since, Because, For, But, First…Second…Third…

•Reason that supports the statement

•BUT not all statements with these words are premises

Are there premises?• People who are old enough to fight for their country

are old enough to vote for the people who make decisions about war and peace. The government should therefore acknowledge the right of 17 year olds to vote, since the government clearly regards 17 year olds as old enough to fight.

• At least one of the ensemble players must have made a mistake, because nothing else would have made the conductor grimace the way she did.

• Since this government came to power, the status of women in our society has improved considerably.

• The window broke because James threw a stone at it.

Presenting Arguments

•Organize into premises and conclusionsArgument 1:P1: If it is snowing heavily, they will close schools

P2: It is snowing heavily C: School will close

Presenting Arguments•Organize into premises and conclusionsArgument 2P1: All teachers are female

P2: Mrs Lee is a teacher C: Mrs Lee is female

It does not always follow “P1, P2, C”

Argument FormsArgument 3• Miss Scarlett must have murdered Colonel Mustard,

because it was either her or Professor Plum, and if he did it, it would be in the Conservatory, and it wasn’t.

C: Miss Scarlett must have murdered Colonel Mustard.

P1: Either Miss Scarlett or Professor Plum murdered Colonel Mustard.

P2: Professor Plum only murders in the Conservatory.

P3: The murder did not take place in the Conservatory.

Look at the argument:

•A good argument must be sound.▫It must have valid and true premises.

•A good argument must be valid.▫Conclusion logically follows from premises.▫Check validity of an argument by

ASSUMING all the premises to be TRUE and see if the conclusion HAS to be true.

▫Arguments 1, 2 and 3 are valid because they have valid argument forms.

Valid Argument Forms

P1: All As are Bs.P2: C is an A

C: Therefore, C is B.

P1: If P, then QP2: P

C: Q

Are these valid?

P1: All Cats are BlackP2: All Crows are Black.

C: Therefore, all Cats are Crows.

P1: If it rains, the ground will get wet.

P2: The ground is wet. C: It rained.

Are these valid?

P1: All As are Bs.P2: All Cs are Bs.

C: Therefore, all As are Cs.

P1: If P, then QP2: Q

C: P

PAIRWORK: Break down these arguments into premises and conclusions, showing the logical flow, and evaluate the validity of these arguments.

• We must resist all effort to allow government censorship. Freedom of speech and expressions are essential to a democratic government. As soon as we allow some censorship, it won’t be long until it is used to silence opinions critical of the government. The next thing we know, we will have as much freedom as the Germans did under Hitler.

• All this talk of banning guns makes me sick! Isn’t it obvious that if we ban guns, law-abiding citizens will not own them, while only the criminals will have them?

• Research has shown that people who do at least 30 min of exercise a day reduce their risk of heart disease and some forms of cancer. It would be wise of you to begin a daily exercise program.

• And here comes the question of whether it is better to be loved rather than feared, or feared rather than loved. It might be answered that we should wish to be both; but since love and fear can hardly exist together, if we must choose between them, it is far safer to be feared than loved. For of men it may generally be affirmed that they are thankless, fickle, false, studious to avoid danger, greedy of gain, devoted to you while you confer benefits upon them, and ready, while the need is remote, to shed their blood, and sacrifice their property, their lives, and their children for you. But, when danger comes near they turn against you. The Prince who builds wholly on their professions of support will be undone.

Look beyond the argument:

•Identifying and checking if assumptions are true.

•Checking if the premises support the conclusion.

•Checking if the premises are true. •Identifying positive and negative implications/consequences of premises or conclusion.

•Explore alternatives and considering which is a better alternative.

Adapted from slides by Miss Ong Shu Juin (Feb 2008)

1. Why is it important to learn about logic and arguments in the context of moral reasoning?

Good reasoning (valid and sound) is just as important in moral reasoning as it is in non-moral reasoning

2. What are the features of good argumentation? Argumentation should be balanced, taking into account

multiple perspectives.

3. Why is it necessary to be able to evaluate an argument? Evaluation of arguments is necessary for a well-founded

position.

4. What generalisation(s) can you derive about arguments?

• Formulating an argument involves identification of premises and understanding how they interact with one another to produce a conclusion.

5. What macro-concept and generalisation(s) about the macro-concept can you derive from the above generalisation(s) about arguments?

• Macro-concept: Systems• Generalisation about macro-concept: Systems have

elements that interact with each other to perform a function.