What is Knowledge?. you must believe the knowledge statement your belief in the knowledge statement...

What is What is Knowledge?Knowledge?

• you must believe the knowledge statement

• your belief in the knowledge statement has to be true

• your true belief has to be justified.

““justified, true belief”justified, true belief”

““justified, true belief”justified, true belief”Requires:• Evidence – reasonable & positive evidence that supports & justifies belief. Coherence – does this fit with our current understanding?

Can you see any problems with these requirements?

““certainty”certainty”• Distinguishes knowledge from belief.• Truth without doubt.

• Language

• Perception

• Reason

• Emotion

I think, therefore I am

““relativism”relativism”• No absolute objective truth• Knowledge is relative to the individual, culture or society

This may be safer for ethics, politics & religion.But what about maths and science?

I knew the Earth was flat

I know Santa Claus exists

• But Sir – it’s just common sense...

Class sizeThere are three classes in year 3. One class contains 12 students, one class contains 25 students, and one class contains 23 students. What is the average class size?

The teacher’s point of viewThe teacher has to teach 3 classes, one of 12 students, one of 25 students, and one of 23 students.

Average class size = (12 + 25 + 23)/3 = 20

The students point of viewThere are 12 students in a class of 12. When asked the size of their class they will all say 12

12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12.

25 students will say 25!

25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25.

23 students will say 23!

23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23.

The students point of viewAverage class size for a student =

((12 x 12) + (25 x 25) + (23 x 23))/(12 + 25 + 23)

= 21.6

(Remember the average from the teacher’s point of view was 20!

When’s your birthday?When’s your birthday?

Birthday coincidenceWhat is the chance/probability that two people in a group of 23 randomly selected people have the same birthday?

Birthday coincidenceWe need to look at how many possible pairs there are.

Person 1 and person 2Person 1 and person 3Person 1 and person 4 etc.

There are 22 possible pairs with person 1

Birthday coincidenceThere are 22 possible pairs with person 1

Then person 2 with person 3person 2 with person 4person 2 with person 5 etc.

There are 21 possible pairs with person 2

Birthday coincidenceThere are 22 possible pairs with

person 1There are 21 possible pairs with

person 2

It follows there are 20 possible pairs with person 3, 19 with person 4, 18 with person 5 etc.etc.

Birthday coincidenceThe total number of different pairs of people is therefore;

22 + 21 + 20………….+ 3 + 2 + 1 = 253Since there are 365 possible birthdays (we’ll ignore 29th February for simplicity!), the chance of two people having the same birthday is 253/365 = 0.69 (69%)

Birthday coincidenceWhat is the chance/probability that two people in a group of 23 randomly selected people have the same birthday?

69%If there are over 30 people the chance is nearly 100%, worth a bet at a party!

Logical fallaciesLogical fallacies

The more churches there The more churches there are in a city, the more are in a city, the more prostitutes there are. prostitutes there are.

People who have a tattoo are People who have a tattoo are more likely to develop lung more likely to develop lung

cancer. This is true. cancer. This is true.

Connor says that he knows Connor says that he knows someone who is 90 and who someone who is 90 and who has smoked 40 cigarettes a has smoked 40 cigarettes a

day for 75 years and he’s OK, day for 75 years and he’s OK, so smoking can’t be harmful. so smoking can’t be harmful.

JulieJulie bought a good luck bought a good luck charm and he seems to be charm and he seems to be

doing better at school. doing better at school.

Post hoc ergo propter hocPost hoc ergo propter hocAssuming one thing causes another just because one follows another.

“Theory of Knowledge for the IB Diploma”, Richard van de Lagemaat, Cambridge University Press

A summary of common A summary of common fallaciesfallacies

Ad ignorantiamAd ignorantiamClaiming that something is true because it cannot be proved to be false.


Hasty generalisationHasty generalisationGeneralising from insufficient evidence.


Ad hominemAd hominemAttacking /supporting the person rather than the argument.


Circular reasoningCircular reasoningAssuming the truth of what you are supposed to be proving.


Special pleadingSpecial pleadingUsing double standards to excuse an individual or group.


EquivocationEquivocationUsing language ambiguously.


False analogyFalse analogyAssuming that because two things are alike in one way that they are alike in other respects.


False dilemmaFalse dilemmaAssuming that only a limited number of alternatives exist.


Loaded questionLoaded questionA question that is biased because it contains a built-in assumption.


In each of the following cases, In each of the following cases, decide which best applies to decide which best applies to

the argument.the argument.Hasty generalisation, post hoc ergo propter hoc, circular reasoning, ad hominem, special pleading, ad ignorantium, false dilemma, false analogy, equivocation, loaded question.

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


Hasty generalisation, post hoc ergo propter hoc, circular reasoning, ad hominem, special pleading, ad ignorantium, false dilemma, false analogy, equivocation, loaded question.

post hoc ergo propter hocpost hoc ergo propter hocSince strict gun control laws were introduced in Dodge City, the crime rate has risen. This shows that gun control does nothing to reduce crime.

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



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


3. 3. It’s OK to beat children to get them to behave. After all, if you want to make omelettes, you have to break eggs.



false analogyfalse analogy It’s OK to beat children to get them to behave.. After all, if you want to make omelettes, you have to break eggs.

4. 4. That can’t be right, non of my friends would believe it.



ad hominemad hominemThat can’t be right, non of my friends would believe it.

5. 5. Since many great scientists have believed in God, there must be some truth in religion.



ad hominemad hominemSince many great scientists have believed in God, there must be some truth in religion.

6. 6. Teddy and Seanne got on very well on their two dates together. They are clearly well suited and should get married.



hasty generalisationhasty generalisationTeddy and Seanne got on very well on their two dates together. They are clearly well suited and should get married.

7. 7. Do you want to be part of the solution, or part of the problem?



false dilemmafalse dilemmaDo you want to be part of the solution, or part of the problem?

8. 8. “I agree that you shouldn’t copy mp3s illegally, but I’ve only copied a few and I do buy tracks sometimes.”



special pleadingspecial pleading“I agree that you shouldn’t copy mp3s illegally, but I’ve only copied a few and I do buy tracks sometimes.”

9.9.The average UK family has 2.5 children. The Smiths are average people, they must have 2.5 kids.



equivocationequivocationThe average UK family has 2.5 children. The Smiths are average people, they must have 2.5 kids.

10.10.Since no-one has been able to prove that God didn’t create the universe, we must conclude that God did make everything.



ad ignorantiumad ignorantiumSince no-one has been able to prove that God didn’t create the universe, we must conclude that God did make everything.

11.11.Are all your family stupid, or is it just you?



loaded questionloaded questionAre all your family stupid, or is it just you?

12.12.No scandal has ever touched Mr Porter. He must be a clean living and honest man.



ad ignorantiumad ignorantiumNo scandal has ever touched Mr Porter. He must be a clean living and honest man.

13.13.Just as you are more likely to take care of a car that you own rather than a car that you rent, a slave owner would look after a slave better than an employer would look after their worker.



false analogyfalse analogyJust as you are more likely to take care of a car that you own rather than a car that you rent, a slave owner would look after a slave better than an employer would look after their worker.

14.14.To ignore the possibility that Norway landed the first person on the moon just because nobody has heard of a Norwegian space program is arrogant. If we are unaware of something does not mean that it never happened.



ad ignorantiumad ignorantiumTo ignore the possibility that Norway landed the first person on the moon just because nobody has heard of a Norwegian space program is arrogant. If we are unaware of something does not mean that it never happened.

15.15.In the fight against terrorism, you are either with the USA or against.



false dilemmafalse dilemmaIn the fight against terrorism, you are either with the USA or against.

Good generalisations?Good generalisations?

So how do we make good generalisations?

What is Knowledge?. you must believe the knowledge statement your belief in the knowledge statement...

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