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

7. Which type of logic are you already using?
Consider the following statements
A. All humans are mortal
B. I am human
Therefore,
(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.

8. 6. The Distinction between truth and validity
TRUTH- Concerned with what is the case
VALIDITYC- oncerned with whether conclusions follows from premises
The validity of an argument is independent of the truth or falsity of the premises it contains.
Consider the following syllogism:

9. Inductive Reasoning

10. Inductive reasoning: from specific examples to a generalization.

11. Inductive Reasoning Steps
Make observations
Detect patterns
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.

12. Learning Styles
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.

13. EXAMPLES -All we ever see are black dogs.
(specific observation)
-All we ever see are black dogs.
(generalization)
-Therefore, all dogs are black.
(specific observations)
-All dogs bark.
-Snoopy is a dog.
-Snoopy Barks.

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

15. Generalization
I’ve noticed that every time I kick the ball up, it comes back down,
so this time I guess when I kick the ball up it will come back down too.

16. Example
All I have ever seen are Dell computers,
(observation)
(generalization)
so all computers are made by Dell.

17. 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

18. Puzzle break A E F H I K L M N B C D G J O P
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
How did you figure it out? Did you look at the individual letters and try to identify a pattern?

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

20. Inductive logic Imagine…
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.

21. You go out and you come across one swan.
It is white. You then continue your search.

27. What type of logic are you using?

28. All swans are white you are using inductive reasoning.
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.

29. Inductive logic
Inductive logic does not involve certainty in the same way as Deductive logic.
Someone who goes from specific instances to a general conclusion is using inductive reasoning.
But is this always the best way to attain knowledge?

30. Problems with inductive logic
The zoologist has gone around from place to place, gathering information about thousands of swans, and comes to the general conclusion that ‘all swans are white’.
He then decides to take a holiday to New Zealand

31. Yup, a black swan.
Yes, a black swan.

32. The problem of induction
However extensive or thorough a person’s research, they can never achieve absolute certainty using inductive reasoning.
This is because some kind of generalization is always made from the observed to the unobserved.

33. Some other examples of inductive reasoning:
Premise: every time I’ve seen a person with a cold, they have had a runny nose
Therefore: 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.
Some other examples of inductive reasoning:
Premise : every time I’ve seen a person with a cold, they have had a runny nose
Therefore :all colds involve having a runny nose.

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

37. Thought point: When is inductive logic reasonable? When is it not?

38. 22. Lessons to be learned from reason when acquiring knowledge
Hasty generalizations – be aware whenever you say ‘all’.
Avoid making stereotypes
We can’t avoid generalizations altogether – but these should be informed and not hasty.
Hindsight bias – after the event, the answer seems obvious.

39. 23. How useful is reason as a way of knowing?

40. Is Mathematics reducible to reason?
Mathematical and logical truths may tell us lots about the rules and patterns we are working with, And math and physics may reveal complex truths on a scientific level like how to create an atomic bomb.
But they may not provide us with much practical information which is useful in day to day life.
It looks as if math is a numerical version of a rational proof
Is there any difference between the knowledge provided by logical reasoning and the knowledge provided by math?

42. 26. Is religious faith rational?Islam

45. Hinduism

47. Faith and Religious belief
All these people have a belief in a type of religious knowledge which sometimes appears to transcend reason.
this is known as religious faith.
But how reliable is this?
The trouble with religious faith is that it is often not based on evidence, and therefore is not easy to prove or disprove.
Yet many religious people claim that faith gives them access to some of the most important truths that they know about.

48. Prejudice - If the New Yorkers I’ve met all shop at fancy stores like Gucci, does that mean they are all fashion snobs?

49. Watch out for CONFIRMATION BIAS: We tend to believe/remember only evidence that supports our beliefs, and ignore/ forget evidence that goes against us.

50. 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.

51. Define and give an example for GENERALIZATION and PREJUDICE
1. With your table:
Define and give an example for GENERALIZATION and PREJUDICE
2. Now find a possible exception/refutation of these “truths”!

52. 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

53. Which is more reliable reason or emotion?
Should you follow your heart or your head?
Emotion
32. Which is more reliable reason or emotion?
Should you follow your heart or your head?
EMOTION REASON
Reason

54. How effective is reason as a way of attaining knowledge?
Benefits of reason
It is able to give precise and direct answers, which are true in all situations.
Rational information is either true or false – there is no ambiguity about what constitutes a correct answer
Drawbacks of reason
The things we know that are logically true or false may be arbitrary. For example I might know with 100% certainty that is a man is a bachelor, then he must be an unmarried man. But this may not give me very much practical information; it doesn’t tell me anything about bachelors in the real world.

55. CREATIVE REASONING

57. Family Problems - Can you solve all of these in under 30 seconds?
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?
Answer
There are 4 boys and 3 girls.
From Mycoted
Answer
The boy is the woman’s son.
Answer
They are husband and wife.

58. 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.
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.

59. C calls out that he is wearing a black hat.
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. Why is he 100% certain of the color of his hat? After a while, C comes to the realization that he must answer.
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.

60. 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?
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.

61. 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.

62. A man rode into town on Friday
A man rode into town on Friday. He stayed three nights and left on Friday. How?
Two boxers are in a match. The fight ends after 6 rounds, after one boxer knocks out the other. But no man throws a punch. How is this possible?

63. 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 YOUNG
THE HOMELESS MAN WAS SEEN IN FRONT OF THE SHOP BEFORE IT WAS ROBBED, SO HE DID IT
INFORMAL REASONING - reasoning that SEEMS logical, but is actually LAZY logic

64. CIRCULAR REASONING = Assuming part of your argument is true BEFORE proving 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.

65.   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?

66. 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 TODAY IF 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?

67. 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 way Can you think of a LOGICAL reason for the following situations?

70. 7. Validity
All panthers are pink
Che Guevara is a panther
Therefore Che Guevara is pink.
Both the premises and the conclusion of this argument are false.
But the argument itself is valid.
It is possible to imagine a world in which all panthers are pink and where Che Guevara is a panther.
In this world it must be that Che Guevara is pink.

71. Another example of Deductive reasoning:
I am either a schnoodlepopper or a birshteinwaller or both.
I am not a schnoodlepopper.
Therefore:
C) I am a birshteinwaller.
TASKS: Invent your own valid argument

72. Complete the statement: In ToK lessons we always ...