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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
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