Transcript BSH deductive and Inductive reasoning

Deductive reasoning
The curious incident
An expensive racehorse has been stolen. A
policeman asks Holmes if any aspect of the
crime strikes him as significent.
I’ve been stolen, that’s why
I’ve got such a long face!
The curious incident
Does any aspect
of the crime
strike you as
significent Mr
Holmes?
The curious incident
Does any aspect
of the crime
strikes you as
significent Mr
Holmes?
Yes constable,
the curious
incident of the
dog in the night.
The curious incident
The dog did
nothing in the
night Sir.
The curious incident
The dog did
nothing in the
night Sir.
That is the
curious
incident!
Holme’s reasoning
The solution to the crime hinges on the fact
that the guard dog did not bark in the night,
and from this Holmes deduces that the thief
must have been known to the dog.
I know him!
Holmes’ reasoning
Holmes’ reasoning can be laid out as
follows
• Guard dogs bark at strangers
• The guard dog did not bark at the thief
• Therefore the thief was not a stranger
Syllogisms
Holmes reasoning
is an example of a
syllogism.
The Socrates Syllogism
premises
• All human beings are mortal
• Socrates is a human being
• Therefore Socrates is mortal
Rationalism – A branch of philosophy which
takes reason as the most important source of
knowledge
conclusion
Syllogisms contain:
• Two premises and a conclusion
• Three terms, each must occur twice
(“Socrates”, “human”, “mortal”.)
• Quantifiers, such as “all”, or “some” or “no”
which tell us of the quantity being referred
to
“TOK for the IB Diploma”, Richard van de
Lagemaat, Cambridge
Another example
• All boys like to
fart
• Martin is a boy
• Martin likes to
fart!
Logic: Another thing penguins
aren’t good at
Penguins are black and white,
Some old TV shows are black and white,
therefore, some penguins are old TV shows.
Truth and validity
An argument is valid if the conclusion follows
logically from the premises.
All hippopotamuses eat cockroaches
Mr Porter is a hippopotamus
Imagine that some
Therefore Mr Porter eats cockroaches strange
planet exists
where the premises
are true
Both premises and conclusion are false, but the
argument is valid.
Truth and validity
All rats are teachers
Mr Porter is a rat
Therefore Mr Porter is a teacher
Both premises are false and conclusion is
true! (but the argument is still valid).
=
Deductive reasoning and truth
• Just because an
argument is valid
(Some IB students
are from Russia, all
Russians are good at
drinking vodka,
therefore some IB
students are good at
drinking vodka) does
not mean that the
conclusion is true.
Deductive reasoning and truth
For an argument
to be true you
must be able to
answer “yes” to
the following
questions:
Deductive reasoning and truth
For an argument
to be true you
must be able to
answer “yes” to
the following
questions:
• Are the premises
true?
• Is the argument valid?
Socrates
• Socrates is a man
• All men are mortal
• Therefore Socrates is
mortal
The conclusion is only
true if the premises
are true.
Deciding whether a syllogism is
valid
Trying to decide if a
syllogism is valid is
not easy.
Venn diagrams can
help (at last a good
use for Venn
diagrams!)
Deciding whether a syllogism is
valid
Mmmmmm
m…Vodka!
• Some IB students are
from Russia
• All Russians are good at
drinking vodka
• Therefore some IB
students are good at
drinking vodka
Is this a valid argument?
Using Venn diagrams
• Some IB students are from Russia
IB Students who are
Russian
IB Students
Russians
Using Venn diagrams
• All Russians are good at drinking vodka
Good vodka drinkers
IB Students
Russians
Using Venn diagrams
• Therefore some IB students are good at
drinking vodka
Good vodka drinkers
IB Students
Russians
Another example
• All As are Bs
• All Bs are Cs
• Therefore all Cs are As
Another example
• All As are Bs
A
B
Another example
• All Bs are Cs
A
B
C
Another example
• Therefore all Cs are As
A
B
C
The syllogism is not valid
These Cs are not As
Another example!
• All As are Bs
• Some As are Cs
• Therefore some Bs are Cs
Another example!
• All As are Bs
A
B
Another example!
• Some As are Cs
A
B
C
Another example!
• Therefore some Bs are Cs
A
B
The syllogism is valid
C
Now your turn
Using Venn diagrams in your notebooks,
decide whether each of the following
arguments is valid or invalid.
Valid or invalid
• All Norwegians eat
hotdogs
• Tom eats hotdogs
• Therefore Tom is
Norwegian
Valid or invalid
• No Swedes have red
noses
• Mr Luitjens has a red
nose
• Therefore Mr Luitjens
is not a Swede
Valid or invalid
• All Year 12 boys are
brave
• Some brave people
are compassionate
• Some Year 12 boys
are compassionate
Valid or invalid
• Some physicists are frauds
• Some frauds are not wealthy
• Therefore some physicists are not wealthy
Valid or invalid
• All Norwegians have dogs
• No good football players have dogs
• Therefore no Norwegians are good football
players
Valid or invalid
• All clever girls are
red-headed
• All red heads are rich
• Therefore all clever
girls are rich
Valid or invalid
• No teachers are
clever
• No Year 12 students
are clever
• Therefore no year 12
students are teachers
Inductive reasoning
• All human beings are
mortal
This statement cannot
be proved by logic
and reasoning, but is
based on experience.
This brings us to
inductive reasoning
Inductive reasoning
Whilst deductive reasoning goes from the
general to the particular, inductive
reasoning goes from the particular to the
general
Going from “all observed human beings
have died” to “all human beings are
mortal” is an example of inductive
reasoning
Inductive reasoning and
generalisations
• Since inductive reasoning goes from the
observed to the unobserved, it enables us to
make generalisations about the world
• All metals expand
• All human beings are mortal
Generalisations
• Is there a danger to generalisations?
• Mr Porter is going to give you a list of 14
generalisations. Can you put them in order
from the most reliable to the least reliable?
(he may ask you to justify your order)
Generalisations
• French people are rude.
• Water boils at 100 °C.
• Most graffiti artists are
under 25 years old.
• All generalisations are
dangerous.
• When spelling in English
“i before e except after
c”.
Generalisations
• In Spanish, if a words
ends in “o” it is masculine.
• Pit Bull dogs are
dangerous.
• Norwegians are good at
skiing.
• Year 12 students are lazy.
• Metals expand when
heated.
Generalisations
• There have been no AIDS cases
amongst BSH students. BSH
students must be free from
AIDS.
• Afro-Caribbean people are good
at sports.
• Boys are better at physics than
girls.
• No-one succeeds without hard
work.
Inductive reasoning
What makes a good generalisation?
Inductive reasoning
What makes a good generalisation?
You’ve got 5 minutes in your
groups to think of “Five rules
for making good
generalisations”.
When you’ve agreed your
five rules can you write them
in your books?
Inductive reasoning
What makes a good generalisation?
Let’s have a look at
what the book
says!
Good generalisations
• Number
You should look at a good number of examples.
If you see one dog swimming, this is not enough
to decide that “all dogs can swim”
Good generalisations
• Variety
You should look at a variety of circumstances.
In the example of dogs swimming, looking at
different breeds of dog.
Good generalisations
• Exceptions
You should actively
look for counter
examples. Look for
dogs that can’t swim!
Good generalisations
• Coherence
You should look for
more evidence to
support surprising
claims! If somebody
suggests that all dogs
have superpowers
you may demand
greater proof!
Good generalisations
• Subject area
Generalisations may be more
reliable in some subject areas
(e.g. science) than in others (e.g.
economics or other social
sciences).