Reason & Logic 1Reason & Logic 1

Nested DollsNested Dolls

Complete the logic problem “Nested Dolls”.

Complete the logic problem “Nested Dolls”.

Nested DollsNested Dolls

What information was most useful in the beginning?

How did you judge the most useful information?

How did you use this information?What was the biggest problem

solving the puzzle?

What information was most useful in the beginning?

How did you judge the most useful information?

How did you use this information?What was the biggest problem

solving the puzzle?

Deductive Reasoning(General to Particular)

Deductive Reasoning(General to Particular)

All dogs are mammals.Fido is a dog.

Therefore Fido is a mammal.

All dogs are mammals.Fido is a dog.

Therefore Fido is a mammal.

SyllogismsSyllogisms

Two premises and a conclusionThree terms, each of which occurs

twice (“dogs”, “mammals”, “Fido”.)

Quantifiers, such as “all”, “some” or “no”

Two premises and a conclusionThree terms, each of which occurs

twice (“dogs”, “mammals”, “Fido”.)

Quantifiers, such as “all”, “some” or “no”

Truth & ValidityTruth & ValidityAll panthers are pink.

Che Guevara is a panther.Therefore Che Guevara is

pink.

All panthers are pink.Che Guevara is a panther.Therefore Che Guevara is

pink.

Both premises false and the conclusion is false!

Both premises false and the conclusion is false!

All ostriches are teachers.Mr McNair is an ostrich.Therefore Mr McNair is a

teacher.

All ostriches are teachers.Mr McNair is an ostrich.Therefore Mr McNair is a

teacher.

Premises both false, conclusion true!

Premises both false, conclusion true!

Make your own Syllogisms!

Make your own Syllogisms!

Both premises and conclusion true. One true and one false premise with a

true conclusion. One true and one false premise with a

false conclusion. Two false premises and a true

conclusion. Two false premises and a false

conclusion.

Both premises and conclusion true. One true and one false premise with a

true conclusion. One true and one false premise with a

false conclusion. Two false premises and a true

conclusion. Two false premises and a false

conclusion.

Truth of premises

True False

Validityof logic

Valid Conclusion must be T Conclusion may be T or F

Invalid Conclusion may be T or F Conclusion may be T or F

Venn DiagramsVenn Diagrams

You can try to use Venn Diagrams to represent

statements. Ask a confident maths student to explain how to represent our syllogisms.

You can try to use Venn Diagrams to represent

statements. Ask a confident maths student to explain how to represent our syllogisms.

Enthymeme - Incomplete Argument

Enthymeme - Incomplete Argument

Jenny goes to Oxford University, so she must be very intelligent.

What is the missing premise?

Jenny goes to Oxford University, so she must be very intelligent.

What is the missing premise?

Graham is a politician, so is probably lying.

Graham is a politician, so is probably lying.

Since it is natural to eat meat, there is nothing morally wrong with it.

Since it is natural to eat meat, there is nothing morally wrong with it.

Reason 2Reason 2

Inductive Reasoning & Generalisations

Inductive Reasoning & Generalisations

ReasoningReasoning

An astronomer, a physicist and a mathematician were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all Scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

An astronomer, a physicist and a mathematician were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all Scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

Deductive & Inductive Reasoning

Deductive & Inductive Reasoning

Deductive ReasoningDeductive Reasoning

Inductive ReasoningInductive Reasoning

Inductive ReasoningInductive Reasoning

From specific to general.

“All humans are mortal”“All metals expand when heated”

How do we “know” these things?

From specific to general.

“All humans are mortal”“All metals expand when heated”

How do we “know” these things?

GeneralisationsGeneralisations

Find 3 examples of some hasty generalisations.

Why are people so quick to jump to conclusions?

What is the difference between prejudice, a gerneralisation and scientific law?

Find 3 examples of some hasty generalisations.

Why are people so quick to jump to conclusions?

What is the difference between prejudice, a gerneralisation and scientific law?

StoryStory

Read the story on page 122 below the small grey box.

In groups, decide whether the following statements are True, False or Unknown.

Read the story on page 122 below the small grey box.

In groups, decide whether the following statements are True, False or Unknown.

Inference TaskInference Task1. A man appeared after the owner had turned off his store

lights.2. The robber was a man.3. The man 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

people are referred to: the owner of the store, a man who demanded money, and a member of the police force.

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

2. The robber was a man.3. The man 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

people are referred to: the owner of the store, a man who demanded money, and a member of the police force.

The PsychiatristThe Psychiatrist

You will be put into small groups. One person will be the psychiatrist who will leave the room...

The remainder of the group decide on an ailment - you will all have the same ailment.

The psychiatrist must now ask you all questions to decide your ailment - obviously do not tell them directly.

You will be put into small groups. One person will be the psychiatrist who will leave the room...

The remainder of the group decide on an ailment - you will all have the same ailment.

The psychiatrist must now ask you all questions to decide your ailment - obviously do not tell them directly.

Good Generalisations?Good Generalisations?

Discuss how might these factors help rate a generalisation:

Number Variety Exceptions Coherence Subject Area

Discuss how might these factors help rate a generalisation:

Number Variety Exceptions Coherence Subject Area

Reason Lesson 3Reason Lesson 3

Lateral ThinkingAnd

Logical Fallacies

Lateral ThinkingAnd

Logical Fallacies

Reason & CertaintyReason & Certainty

Deductive ReasoningInductive ReasoningInformal Reasoning - Fallacies

Can we ever doubt deductive reasoning?

Deductive ReasoningInductive ReasoningInformal Reasoning - Fallacies

Can we ever doubt deductive reasoning?

Rational ThinkingRational Thinking

“The madman is not the man who who has lost his reason. The madman is the man who has lost everything but his reason.” GK Chesterton 1874-1936

Should you always try to be as rational as possible, or are there dangers in being too rational?

“The madman is not the man who who has lost his reason. The madman is the man who has lost everything but his reason.” GK Chesterton 1874-1936

Should you always try to be as rational as possible, or are there dangers in being too rational?

Lateral ThinkingLateral Thinking

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

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

Lateral ThinkingLateral Thinking

Two boxers are in a boxing match (regular, not kick boxing.) The fight is scheduled for 12 rounds but ends after 6 rounds, after one boxer knocks out the other boxer. Yet no man throws a punch. How is this possible?

Two boxers are in a boxing match (regular, not kick boxing.) The fight is scheduled for 12 rounds but ends after 6 rounds, after one boxer knocks out the other boxer. Yet no man throws a punch. How is this possible?

Lateral ThinkingLateral Thinking

There are three light switches in a cellar in the OFF position. Each switch controls one of the light bulbs on the floor above which cannot be seen. You may move any of the switches, but you may only inspect the bulbs once. How can you determine which switches control which bulbs with only one inspection?

There are three light switches in a cellar in the OFF position. Each switch controls one of the light bulbs on the floor above which cannot be seen. You may move any of the switches, but you may only inspect the bulbs once. How can you determine which switches control which bulbs with only one inspection?

Lateral ThinkingLateral Thinking

A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How should she arrange the trees?

A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How should she arrange the trees?

Lateral ThinkingLateral Thinking

Connect the nine crosses below using four straight lines and not taking your pen off the paper:

Connect the nine crosses below using four straight lines and not taking your pen off the paper:

GeneralisationsGeneralisations

“You should never generalise.”

When a dog gets excited at its owner getting a leash ready, is it using inductive reasoning?

What percentage of metal do you think scientists have checked for expansion when heated?

“You should never generalise.”

When a dog gets excited at its owner getting a leash ready, is it using inductive reasoning?

What percentage of metal do you think scientists have checked for expansion when heated?

Hong KongHong Kong “Mainlanders are the cause for most of the

crime in Hong Kong.”

How many of you have personal experience of this? How many of you know someone who has personal experience

of this? How many of you have been told by secondary sources about

this issue? Do you think people are more or less likely to retell a story

involving crime and someone from the mainland? How many of you have been victims of crime not including

someone from mainland China? How many of you have stolen something or had something

stolen in school?

“Mainlanders are the cause for most of the crime in Hong Kong.”

How many of you have personal experience of this? How many of you know someone who has personal experience

of this? How many of you have been told by secondary sources about

this issue? Do you think people are more or less likely to retell a story

involving crime and someone from the mainland? How many of you have been victims of crime not including

someone from mainland China? How many of you have stolen something or had something

stolen in school?

FallaciesFallacies

Read the arguments on the sheet and decide what the errors in the reasoning are.

Match the errors in the examples with the formal fallacies on Pages 130-131

Read the arguments on the sheet and decide what the errors in the reasoning are.

Match the errors in the examples with the formal fallacies on Pages 130-131

Linking Questions/ReadingLinking Questions/Reading

Linking Questions page 140

Readings page 141-144

Linking Questions page 140

Readings page 141-144

What we need to know…What we need to know…

understand that the use of reason is a way to extend our knowledge from known facts

be able to distinguish between inductive and deductive arguments - in both cases to evaluate the strengths and weaknesses of the arguments

understand the premises/conclusion nature of an argument:

be very clear about the relationship between a valid argument and a true conclusion

be aware of the need to be rigorous when using logic, the difficulties associated with choice of premises, the dangers of hidden assumptions and the problems with definitions

be familiar with some elementary fallacies

be able to apply these ideas to everyday examples

appreciate that real-life problem solving requires imagination and creativity, and more than simple logic

understand that the use of reason is a way to extend our knowledge from known facts

be able to distinguish between inductive and deductive arguments - in both cases to evaluate the strengths and weaknesses of the arguments

understand the premises/conclusion nature of an argument:

be very clear about the relationship between a valid argument and a true conclusion

be aware of the need to be rigorous when using logic, the difficulties associated with choice of premises, the dangers of hidden assumptions and the problems with definitions

be familiar with some elementary fallacies

be able to apply these ideas to everyday examples

appreciate that real-life problem solving requires imagination and creativity, and more than simple logic