How can you be sure that someday you will die? What evidence do you have for your belief ?

How can you be sure that someday you will die?

What evidence do you have for your belief?

Which type of logic are you already using?

Consider the following statementsA. All humans are mortalB. I am humanTherefore, (are you mortal?)

C. YES, I am mortal

If you think this is the logical conclusion then you are using deductive reasoning.

It would be absurd to state the truth of A and B while denying the truth of C.This is known as logical validity. Even if the actual truth of A and B is questionable this method of processing information in the search for truth looks promising.

Inductive Reasoning

Inductive reasoning: from specific examples to

a generalization.

1. Make observations2. Detect patterns3. Develop general conclusion or theory

In other words – going from a set of details/facts to the general (or generalization)

Typically, there is no prior knowledge of the conclusion or theory, but it is generated after observing and analyzing the observations.

Inductive Reasoning Steps

• You typically learn by inductive reasoning if you like to see examples when you first learn a new subject before developing an overview of the subject.

• Another idea of inductive reasoning is if you like to learn the rules of a new game as you go along.

Learning Styles

(specific observation)

-All we ever see are black dogs. (generalization)

-Therefore, all dogs are black. (specific observations)

-All dogs bark. -Snoopy is a dog.

(generalization) -Snoopy Barks.

EXAMPLES

I’ve noticed that every time I kick the ball up, it comes back down,

Specific Observation

I’ve noticed that every time I kick the ball up, it comes back down,

Generalization

so this time I guess when I kick the ball up it will come back down too.

All I have ever seen are Dell computers,

(observation)

(generalization)

Example

so all computers are made by Dell.

Evaluate the strength of the following inductive logical thoughts:

• My neighbor’s dog didn’t bite me in the past, so he won’t bite me today either

• My chair supported my weight in the past, so it will hold me today

• Local drivers have driven wildly in the past, so I better be careful today

• USA has supported only Israel in the past, so they won’t be fair to Palestinians this year either.

• Girls who are smart are often not very sporty, so the smart new girl in our class won’t be good as sports

How do you decide whether the letter should be above or below the line?

A E F H I K L M N

B C D G J O P

Puzzle break

How did you figure it out? Did you look at the individual letters and try to identify a pattern?

In every country’s capital city, there is an international school. How would you test this knowledge

claim?

Inductive logicImagine…That you are a zoologist who is interested in different species and colors of swans.

You set about finding as many swans as you can in Europe , so that you might be able to make some conclusions about swans generally.

You go out and you come across one swan.

It is white. You then continue your search.

What type of logic are you using?

All swans are white

• At this point what color are swans in your experience?

• What conclusions might you draw about swans (as a species)?

• If you think that this is the logical conclusion to come to:

you are using inductive reasoning.

Yup, a black swan.

Some other examples of inductive reasoning:

Premise: in my experience, day has always followed night.Therefore: Day will always follow night in the future.

Premise: every time I’ve seen a person with a cold, they have had a runny noseTherefore: all colds involve having a runny nose.

Premise: in my experience, day has always followed night.

Therefore: Day will always follow night in the future.

Thought point: When is inductive logic reasonable?

When is it not?

Hinduism

Prejudice - If the New Yorkers I’ve met all shop at fancy stores like Gucci, does that

mean they are all fashion snobs?

Watch out for CONFIRMATION BIAS:We tend to believe/remember only

evidence that supports our beliefs, and ignore/ forget evidence that goes

against us.

Prejudice is reinforced this way - if you have decided that the English are cold, and Americans are lazy, then you LOOK for evidence to support these comfortable beliefs.

1. With your table:Define and give an example for

GENERALIZATION and PREJUDICE

2. Now find a possible exception/refutation of these “truths”!

GENERALIZATIONS ARE NECESSARY! BUT MAKE THEM AS LOGICAL AS POSSIBLE:

• NUMBER- research with the largest sample is more accurate• VARIETY- within a group look for many different types as

possible (such as young people, old, different races, places etc.)• EXCEPTIONS - actively think of counter-examples ( guard

against confirmation bias)• COHERENCE - demand MORE evidence if the claim is

surprising/unusual• SUBJECT AREA- In some areas generalizations are more

reliable than in others (human behavior, for example is harder to predict than animal or chemical behavior)

• INFORMAL REASONING - reasoning that seems logical, but is actually lazy logic

Which is more reliable reason or emotion?

ReasonEmotion

Should you follow your heart or your head?

CREATIVE REASONING

Answer

There are 4 boys and 3 girls.

Answer

The boy is the woman’s son.

Answer

They are husband and wife.

•A boy has as many sisters as he has brothers, but each of his sisters has twice as many brothers as she has sisters. How many boys and girls are there in the family?

•A man and his sister were out walking together one Saturday morning. The man pointed across the street to a boy and said: ‘That boy is my nephew.’ The woman replied: ‘He is not my nephew.’ Can you explain this.

•Two Russians walk down a street in Moscow. One Russian is the father of the other Russian’s son. How are they related?

Family Problems - Can you solve all of these in under 30 seconds?

Answer The problem can be solved by moving one glass. Simply pick up the middle one of the full glasses, pour the water into the middle one of the empty glasses, and return the glass to it's original position.

Six drinking glasses stand in a row, with the first three full of water and the next three empty. By handling and moving only one glass at a time, how can you arrange the six glasses so that no full glass stands next to another full glass, and no empty glass stands next to another empty glass. What is the minimum number of moves to solve this puzzle.

Shown above are four men buried up to their necks in the ground. They cannot move, so they can only look forward. Between A and B is a brick wall which cannot be seen through. They all know that between them they are wearing four hats--two black and two white--but they do not know what color they are wearing. Each of them know where the other three men are buried. In order to avoid being shot, one of them must call out to the executioner the color of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out. After one minute, one of them calls out. Question: Which one of them calls out? Why is he 100% certain of the color of his hat? This is not a trick question. There are no outside influences nor other ways of communicating. They cannot move and are buried in a straight line; A & B can only see their respective sides of the wall, C can see B, and D can see B & C.

C calls out that he is wearing a black hat.

Answer

Switch on the first switch, leave it for a minute, and then switch it off again. Then switch on the second switch and enter the room. The second switch will be connected to the light that is on, the first switch will be connected to the light with the warm bulb, and the third switch will be connected to the light with the cold bulb.

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you are only allowed to enter the room once?

This is because D can't answer, and neither can A or B. D can see C and B, but can't determine his own hat color. B can't see anyone and also can't determine his own hat color. A is in the same situation as B, where he can't see anyone and can't determine his own hat color.

Since A, B, and D are silent, that leaves C. C knows he is wearing a black hat because if D saw that both B and C were wearing white hats, then he would have answered. But since D is silent, C knows that he must be wearing a black hat as he can see that B is wearing a white hat.

A man rode into town on Friday. He stayed three nights and left on Friday. How?

Post hoc ergo propter hoc = Mistaking something FOLLOWING something for BEING CAUSED by that something (needs more evidence)The following are true statistics, but could there be another reason for the ‘connection’?AS THE NUMBER OF CHURCHES IN THE USA INCREASES, SO DO THE NUMBER OF PROSTITUTES CRIME IS INCREASING IN GERMANY, BUT SO IS THE NUMER OF COLLEGE GRADUATES. SO EDUCATION IS CORRUPTING THE YOUNGTHE HOMELESS MAN WAS SEEN IN FRONT OF THE SHOP BEFORE IT WAS ROBBED, SO HE DID ITINFORMAL REASONING - reasoning that SEEMS logical, but is actually LAZY logic

CIRCULAR REASONING = Assuming part of your argument is true BEFOREproving it. Can you find the unproven part of these arguments?

THE SOLDIER GAVE OUT THE GUNS, BUT KEPT AN EXTRA ONE FOR HIMSELF. WHEN ASKED WHY, HE SAID “I AM THE LEADER”. WHY ARE YOU THE LEADER? “BECAUSE I HAVE MORE

GUNS”

I KNOW MY PRESIDENT IS A GOOD MAN, BECAUSE HE SAYS HE IS AND A GOOD MAN WOULD NOT LIE

I KNOW I AM SMARTER THAN YOU, BECAUSE IT WOULD BE FOOLISH TO SAY SO IF IT WASN’T

TRUE, AND I AM NOT A FOOL.

INFORMAL REASONING - reasoning that SEEMS logical, but is actually LAZY logic

1) EQUIVOCATING= using a word/idea in two different meanings to support your argument

FRIES AND A COKE ARE BETTER THAN NOTHING, AND NOTHING IS BETTER THAN GOOD HEALTH, SO FRIES AND COKE ARE BETTER THAN GOOD HEALTH

SCIENTISTS SAY THAT RED WINE CAN PREVENT HEART DISEASE. I DRINK A BOTTLE EVERY

NIGHT, SO I MUST HAVE A REALLY HEALTHY HEART.

CAPITAL PUNISHMENT KILLS GUILTY PEOPLE. UNBORN BABIES ARE INNOCENT; THEREFORE WE SHOULDN’T HAVE ABORTION.

ARGUING USING AD IGNORANTIAM= Saying something is TRUE just because you

can’t prove is ISN’T TRUE

INFORMAL REASONING - reasoning that SEEMS logical, but is actually LAZY logic

ARGUING USING AD IGNORANTIAM= A VERY COMMON LOGICAL ERROR!

IF THERE ARE PARTS OF SCIENCE WE CAN’T UNDERSTAND YET, THEN THAT PROVES THERE IS A GOD (because only something smarter than ourselves could have created

something we can’t understand)

THERE ARE MILLIONS OF THINGS WE CAN BELIEVE IN (FAIRIES, MAGIC, AND UNICORNS ETC.). JUST BECAUSE WE CAN’T PROVE THEM, DOES THAT MEAN THEY CAN

EXIST?

CAN YOU THINK OF THEORIES (CONSPIRACY) THEORIES) THAT PEOPLE USE TO DEFEND DIFFICULT TO PROVE/EXPLAIN CONUNDRUMS?

THE FALSE DILEMMA = BINARY THINKING (BLACK/WHITE THINKING)

TO MY PARENTS: IF YOU DON’T LET ME GO TO THIS PARTY, I’LL BE A TOTAL LOSER AT SCHOOL ARE PEOPLE WHO WANT TO SPEND MONEY ON THE MILITARY AWARE THAT

WE’LL HAVE TO CLOSE SCHOOLS AND HOSPITALS?

IF YOU ARE AGAINST THE WAR IN IRAQ, THEN YOU MUST HATE AMERICA.

IF YOU ARE ARAB AND ANTI-ISRAEL, YOU MUST BE A TERRORIST SYMPATHIZER

(WATCH YOUR THINKING! THE WORLD IS MORE SHADES OF GREY THAN BLACK AND WHITE!)

THE LOADED QUESTION= CONTAINS A BUILT-IN ASSUMPTION

DO YOU ALWAYS CHEAT ON EXAMS?

THE HEAD TEACHER DID NOT HIT HIS STUDENTS TODAYIF YOU ARE AGAINST THE WAR IN IRAQ, THEN YOU MUST HATE AMERICA.

ARE YOU AWARE THAT OBAMA IS A SOCIALIST?CAN YOU PHRASE THE QUESTIONS ABOVE IN A MORE NEUTRAL/UNBIASED WAY?

The Prison of Consistency - it is harder to change your mind than continue thinking illogical thoughts.

Professors and parents seldom admit they are wrong. Why?

What takes greater courage, to fight for your convictions, or to question your convictions?

LATERAL THINKING - reasoning that actively resists the logic errors

THINK OUTSIDE THE BOX - challenge your ‘habits’ of thinking one wayCan you think of a LOGICAL reason for the following situations?

Complete the statement:

In ToK lessons we always ...