“It sort of makes you stop and think, doesn’t it”

Why is it better to have round manhole covers than square ones?

Reason

Knower(s)

Natural Sciences

Language

Reason

Emotion

SensePerception

Mathematics

Human Sciences

History

Arts

Ethics

Ways of Knowing

Areas of Knowledge

Theory of Knowledge Diagram

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Empiricismstarting point for all knowledge is experience

Rationalismstarting point for all knowledge is reason

Knower(s)

Natural Sciences

Language

Reason

Emotion

Sense Perception

Mathematics

Human Sciences

History

Arts

Ethics

Ways of Knowing

Areas of Knowledge

Theory of Knowledge Diagram

What role does reason playin the different Areas of Knowledge?

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1. Reason (noun)• a basis or cause, as for some belief,

action, fact, event, etc

2. Reason (verb)• to think or argue in a logical manner;• to form conclusions or judgments from

facts, propositions or premises (initial assumptions)

What is meant by ‘Reason’?

Carl Sagan – Eratostheneshttp://www.youtube.com/watch?v=G8cbIWMv0rI

A Story

A businessman had just turned off the lights in the store when a man appeared and demanded money. The owner opened a cash register. The contents of the cash register were scooped up, and the man sped away. A member of the police force was notified promptly.

Statements about the story (True/False/Uncertain)

1. A man appeared after the owner had turned off his store lights.

2. The robber was a man.

3. The man who appeared did not demand money.

4. The man who opened the cash register was the owner.

5. The store owner scooped up the contents of the cash register and ran away.

6. Someone opened a cash register.

7. After the man who demanded the money scooped up the contents of the cash register, he ran away.

8. While the cash register contained money the story does not state how much.

9. The robber demanded money of the owner.

10. The story concerns a series of events in which only three persons are referred to: the owner of the store, a man who demanded money, and a member of the police force.

11. The following events are true: Someone demanded money, a cash register was opened, its contents were scooped up, and a man dashed out of the store.

There are three men on a train: one of them is an economist, one is a logician and one is a mathematician. They have just crossed the border into Scotland and they see a brown cow standing in a field from the window of the train. The cow is standing parallel to the train.

The economist says, “Look! The cows in Scotland are brown”.The logician says, “No. There are cows in Scotland of which one, at least, is brown.” The mathematician says, “No. There is at least one cow in Scotland of which one side appears to be brown.”

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A dead body is lying in a field.

He is carrying an unopened package.

How did he die?

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“He that will not reason is a bigot*;he that cannot reason is a fool;

and he that dares not reason is a slave”William Drummond 1585-1649

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*Bigot: a prejudiced person who is intolerant of any opinions differing from their own

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Goya - The Sleep of Reason Produces Monsters 1798

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Aristotle384BCE – 322BCE

…. wrote that women have fewer teeth than men

Margaret Heffernan – Dare to disagreehttp://www.ted.com/talks/margaret_heffernan_dare_to_disagree.html

Reason enables us to go beyond the immediate evidence of our senses to

acquire new knowledge

The path is wet in the morning ....

You left your mobile phone either on your desk or in your coat pocket ...

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A man is wearing black: black shoes, socks, trousers, coat, gloves and ski mask.

He is walking down a back street with all the street lamps off.

A black car is coming towards him with its lights off but somehow manages to stop in time.

How did the driver see the man?

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You are presented with the following rule -

Every card with a vowel on one side has an even number on the reverse side

These are the cards:

U G 7 2Which 2 cards should be turned over in order to find out if this statement is true or false?

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You are a bar-person in a nightclub. The club has the following rule -

Every person drinking alcohol must be over 20 years of age

There are four situations:

PersonDrinking

Beer

PersonDrinking

Lemonade

PersonAged

19 years

PersonAged

21 years

Which two situations should be investigated? http://skepticwiki.org/index.php/Wason's_Four-card_Task

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The two examples are formally identical.

Why is it easier to spot the correct answers in the second example?

Do your answers reflect something about human thinking in general?

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Three kinds of Reasoning

Inductive reasoning Deductive reasoning Informal reasoning

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Inductive reasoning

From the particular to the general (the observed to the unobserved)

This first bird can fly...This second bird can fly...This third bird can fly...This fourth bird can fly...This nth bird can fly...Therefore all birds can fly.

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Science uses inductive reasoning:

Formulates general laws on the basis of limited observations – • Metal A expands when heated• Metal B expands when heated• Metal C expands when heated• ..... a conclusion?

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Will the sun rise tomorrow?How do you know?

How certain are you?

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Problems with Induction:• Reasoning from the observed,

to the unobserved• How many observations

should be made before we jump to a generalisation?

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A murderer is condemned to death.

He has to choose between three rooms: The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years.

Which room is safest for him?

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There is a scene in a Broadway play where a guest at a party meets a Catholic priest.

The guest asks, “Don’t you hear some terrible things in confession?”

The priest replies, “Oh yes. In fact when i was just starting out as a priest, the first person who came to confession told me they had committed a murder.”

Later on, a newcomer joins the party, and on being introduced to the priest says, “I met you a long time ago, Father. In fact I was the first person to come to you for confession.”

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Deductive reasoningFrom general to particular:

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• The first person who came to confession told the priest that he had committed a murder

• The guest at the party was the first person to come to the priest for confession

• Therefore the guest had committed a murder

The Curious Incident of the Dog in the Night-time ....

Sherlock Holmes

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Deductive reasoning

Watchdogs bark at strangersThe watchdog did not bark at the thiefTherefore the thief was not a stranger

The Curious Incident of the Dog in the Night-time ....

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Gregory (Scotland Yard detective): "Is there any other point to which you would wish to draw my attention?“

Holmes: "To the curious incident of the dog in the night-time.“

Gregory: "The dog did nothing in the night-time.“

Holmes: "That was the curious incident.”

Deductive reasoningFrom general to particular

• All humans are mortal• Edmund is human• Therefore Edmund is mortal

If the ‘assumptions’ are correct (which in Logic are called, ‘premises’) the conclusion has to follow. No if’s and but’s - it’s not a

matter of personal opinion, nor is it affected by culture.

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Deductive reasoningFrom general to particular:

• Two premises and a conclusion• Three terms – each occurring twice• Quantifiers (‘all’, ‘some’, ‘most’ etc)

This is formally called a Syllogism

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• All humans are mortal

• Edmund is human

• Therefore Edmund is mortal

Premise 1

Premise 2

Conclusion

Term 1 Term 2

Term 3

Quantifier

Truth and Validity

• Truth: concerned with what is the case

• Validity: only concerned with whether conclusions follow from premises…..

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• All polar bears are footballers• Larry is a polar bear

• Therefore Larry is a footballerValid argument – but not true

You should not say that an argument is true or false, but that it is valid or invalid.

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1. Argument (noun) an oral disagreement; verbal opposition;

contention; altercation: ‘a violent argument’

2. Argument (noun)a process of reasoning; series of reasons: ‘I couldn't follow his argument’

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Premise (Claim)

Conclusion (Claim)

Watchdogs bark at strangersThe watchdog did not bark at the thiefTherefore the thief was not a stranger

Inference

Argument

DeductiveInductiveFinds rules Applies rules

Argument

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Deduction

general

particular

Induction

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DEDUCTION INDUCTION

Definition

Reasoning from general to particular Reasoning from particular to general

Example

• All metals expand when heated• A is a metal• Therefore A expands when heated

• Metal A expands when heated; metal B expands when heated; metal C expands when heated• Therefore all metals expand when heated

Value

More certain, but less informative than induction

More informative, but less certain than deduction

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Inductive reasoningFrom the particular to the general (the observed to the unobserved)

• I have never heard of a human being who didn’t die ... then we generalise to ...

• All human beings are mortal

Inductive Reasoning allows us to make generalisations about the world.

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What distinguishes good generalisations?

• Number – you see one dog swimming...• Variety – different circumstances; old dogs, young

dogs, different breeds...• Exceptions – find counter-examples...• Coherence – you should demand more evidence to

support surprising claims than unsurprising ones• Subject area – eg. generalisations tend to be more

reliable in the natural sciences than in the social sciences

What is a generalisation?TaK - Reason

• Give examples of some hasty generalisations

• Why do you think that people are so quick to jump to conclusions?

• What is the difference between a prejudice and a generalisation?

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Bad reasoning• Ignorance• Laziness• Pride• Prejudice

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Informal reasoning

Fallacies (invalid patterns of reasoning)

http://www.youtube.com/watch?v=fXLTQi7vVsI&feature=related

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Your position: “I think . . .”Your supporting proposition: “Because . . .”Your supporting reasons: “As . . .”Supporting evidence / facts: “Supported by . . .”

So, in the heat of the moment, someone arguing about President Obama might argue:

“I THINK President Obama is a great president” (POSITION)“BECAUSE he’s a great leader” (PROPOSITION)“AS he listens to people and commands respect” (REASON)“SUPPORTED BY the fact that he runs monthly town hall meetings where he answers people’s questions” (FACT)

Informal reasoning

Informal reasoning – Fallacies (Invalid patterns of reasoning)

• Post hoc ergo propter hoc – assume that because B follows A that A must be the cause of B

• Ad hominem fallacy – attack or support the person rather than the argument• Circular reasoning – assume the truth of something you are supposed to be

proving• Special pleading – making an exception in your own case that you would not

find acceptable if it came from someone else• Equivocation – using language ambiguously• Argument ad ignorantium – claim that something is true on the grounds that

there is no evidence to disprove it• False analogy – assume that because two things are similar in some ways

that they must be similar in some further way• False dilemma – assume that only two alternatives exist when there are in

fact a wide range of options• Loaded questions – a question that is biased because it contains a built-in

assumption

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• Since strict gun controls were introduced in Dodge City, the crime rate has risen. This shows that gun control does nothing to reduce crime.

• Jane said she trusted me, and she must be telling the truth because she wouldn’t lie to someone that she trusted.

• The ends justify the means. After all, if you want to make omelettes, you have to break eggs.

• Since the English always talk about the weather, if you meet someone who talks about the weather you can be sure they are from England.

• Since many great scientists have believed in God, there must be some truth in religion.• We got on very well on both of our dates together. We are clearly well suited. Let’s get

married!• Do you want to be part of the solution or part of the problem?• The average UK family has 2.4 children. The Smiths are very average people. Therefore

they must have 2.4 children.• Since no-one has been able to prove that we are alone in the universe, we must

conclude that other life forms exist.• Are all your family stupid, or is it just you?• No breath of scandal has ever touched the Senator. So he must be an honest man.• Just as you are more likely to take care of a car that you own than one that you rent, so

a slave owner is more likely to take care of his slave than an employer is of his worker.

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Dan Ariely – Are we in control of our own decisions?

http://www.ted.com/talks/dan_ariely_asks_are_we_in_control_of_our_own_decisions.html

Some key points:

• Through reason we can acquire knowledge about the world that goes beyond the immediate evidence of our senses

• Deductive Reasoning - from the general to the particular

• Inductive Reasoning - from the particular to general

• Inductive Reasoning sometimes leads to our making hasty generalisations which are then reinforced by our tendency to only notice things which confirm them

• Dangers of Informal Reasoning

• The main causes of bad reasoning are a combination of ignorance, laziness, pride and prejudice

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Key points:

• It is important to be aware of assumptions, and recognize one is making them, though sometimes it will be necessary to make assumptions (due to urgency of decisions, lacking complete information etc)

• Sometimes it is not practical to have all the facts before making decisions; assumptions are necessary, but can be misleading

• Assumptions made by individuals (even for the same questions) may be different

• Increased awareness and sharing of assumptions can improve decision making

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"Should we trust reason rather than perception in

the search for reliable knowledge?"

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Reason

PerceptionShould we trust reason rather

than perception?

ReligionIs religious belief

rational or irrational?

EthicsHow important is

consistency in moral reasoning?

ArtsWhat is the relationship

between creativity and rationality?

HistoryWhat kinds of bad reasoning can be found in history?

Human Sciences

Are human beings rational

animals?

MathsCan mathematics

be reduced to logic?

Natural Sciences

Is there a logic of scientific

discovery?

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Extras

Questions… • What constitutes a 'good reason' for belief?

• Does the nature of reason vary across cultures?

• Does knowledge always require some kind of rational basis?

• If knowledge claims cannot be rationally defended, or can be shown to be irrational, should they be renounced?

• How do beliefs affect the capacity to reason logically and the capacity to recognize valid arguments?

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by Joseph Wright

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Being careful in arguments: Definitions - Bachelor

• Anthony is 17 years old . He attends school and lives with his parents.

• Joe is 17 years old. He left home at 14 to start his own company and is now a millionaire. When not travelling around the world to attend business meetings he lives in his own house and has a playboy lifestyle.

• Charlie and Chris are homosexual lovers who have been happily living together for 20 years.

• David has been living with Sue for the last 10 years. They have 3 children. He has never been married and has no intention of ever getting married.

• Jim is a married to a woman who paid him $50,000 so that she could become a citizen of his country. He has met her once, and they have never lived together.

• Father Francis is a Catholic priest

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