Transcript Review

some important examples
of paradox
How do we interpret “reality”. What models do we build to simplify,
generalize, and organize the complex data of experience?
Chinese tale from the fourth century B.C.
Chuang-tzu was a man who dreamt he was a
butterfly , and then awoke to wonder if he was
a butterfly dreaming he was a man.
Is this slide show “real” - or are you dreaming
that you are sitting in paradox class watching
a slide show?
zeno
The hare
and the turtle
decide to run a race
Because I run twice as fast
as you do, I will give you a
half mile head start
Thanks!
In the time that it takes the hare to run the ½ mile
that separates him from the turtle,
the turtle has progressed another ¼ mile.
In the time that it takes the hare to run the ¼ mile
that separates him from the turtle,
the turtle has progressed another 1/8 mile.
In the time that it takes the hare to run the 1/8 mile
that separates him from the turtle,
the turtle has progressed another 1/16 mile.
No matter how quickly the hare runs, during the time it takes him
to reach the turtles current position, the turtle will have moved
ahead. Can the swift hare ever catch the plodding turtle?
sorites
This man is NOT bald.
If he loses ONE hair,
will he then be bald?
of course not!
This man is NOT bald.
If he loses ONE hair,
will he then be bald?
of course not!
This man is NOT bald.
If he loses ONE hair,
will he then be bald?
of course not!
This man is NOT bald.
If he loses ONE hair,
will he then be bald?
of course not!
If this process continues,
Will he ever be bald?
At what point will it happen?
If he is not bald before
the loss of ONE hair,
will he be bald after?
simpson
drug A
1 out of 5
=20% of the men
treated with drug A
are cured.
drug B
drug A
1 out of 5
=20% of the men
treated with drug A
are cured.
drug B
2 out of 8
=25% of the men
treated with drug B
are cured.
drug A
1 out of 5
=20% of the men
treated with drug A
are cured.
4 out of 10
=40% of the women
treated with drug A
are cured.
drug B
2 out of 8
=25% of the men
treated with drug B
are cured.
drug A
1 out of 5
=20% of the men
treated with drug A
are cured.
4 out of 10
=40% of the women
treated with drug A
are cured.
drug B
2 out of 8
=25% of the men
treated with drug B
are cured.
1 out of 2
=50% of the women
treated with drug B
are cured.
drug A
drug B
1 out of 5
2 out of 8
=20% of the men
=25% of the men
treated with drug A
treated
with
drug
B B
A
higher
percentage
of
men
are
cured
with
are cured.
are cured.
4 out of 10
1 out of 2
=40% of the women
=50% of the women
treated with
A percentage of women
treatedare
with
drugwith
B B
A drug
higher
cured
are cured.
are cured.
drug A
1 out of 5
=20% of the men
treated with drug A
are cured.
4 out of 10
=40% of the women
treated with drug A
are cured.
drug B
2 out of 8
=25% of the men
treated with drug B
are cured.
1 out of 2
=50% of the women
treated with drug B
are cured.
drug A
drug B
drug A
5 out of 15 = 33 1/3 %
of people treated
with A are cured
drug B
3 out of 10 = 30 %
of people treated
with B are cured
drug A
drug B
5 out of 15 = 33 1/3 %
3 out of 10 = 30 %
of people treated
of people
treated
A higher percentage of people
are cured
with A
with A are cured
with B are cured
drug A
drug B
5 out of 15 = 33 1/3 %
3 out of 10 = 30 %
of people treated
of people
treated
A higher percentage of people
are cured
with A
with A are cured
with B are cured
A higher percentage of men are cured with B
A higher percentage of women are cured with B
Alais
SUPPOSE YOU COULD CHOOSE TO PLAY
ONE OF TWO GAMES:
Game A
There is a
10% chance that
you will win
$1,000,000….and a
90% chance that
you will win
$100.
Game B
There is a
10% chance that
you will win
$2,000,000….and a
90% chance that
you will win
$0.
Which would you choose?
Game A
There is a
10% chance that
you will win
$1,000,000….and a
90% chance that
you will win
$100.
expected value =
(.1)(1,000,000)+
(.9)(100) =
100,090
Game B
There is a
10% chance that
you will win
$2,000,000….and a
90% chance that
you will win
$0.
expected value =
(.1)(2,000,000)+
(.9)(0) =
200,000
the nature of
free will
You have to make an important decision.
What will you choose?
Is your choice
DETERMINED by your
genetic makeup, your
upbringing, your beliefs
and values, societal
expectations,your past
experiences….
Is this free will???
Or, will you decide by
flipping a coin?
Is this free will???
Is free will FATE or is it CHANCE??????????????
some paradoxes in
Aristotelian logic
That duck
is lying!
What he
says is
true
“If John studies then he will get an A.”
s
a
T
T
T
T
F
F
F
T
T
F
F
T
s
a
“If
then
.”
s
a
T
T
T
T
F
F
F
T
T
F
F
T
the model
s
a
“If
then
this statement is true
Santa Claus exisits
s
a
T
T
T
T
F
F
F
T
T
F
F
T
s
a
.”
This statement
“If
then
this statement is true
Santa Claus exisits
s
a
T
T
T
T
F
F
F
T
T
F
F
T
s
a
.”
This statement
“If
then
this statement is true
s
The only
T
conditions
under which
T
this statement
is FALSE
a
Santa Claus exisits
s
a
T
T
F
F
F
T
T
F
F
T
.”
This statement
“If
then
this statement is true
s
The only
T
conditions
under which
T
this statement
is FALSE
F
a
Santa Claus exisits
s
a
T
T
F
F
T
T
F
F
a contradiction
T
.”
This statement must be TRUE
“If
then
this statement is true
Santa Claus exisits
s
a
T
T
T
T
F
F
F
T
F
s
.”
a
T
So Santa Claus exists!
F
T
Of course, the exact same reasoning can be used
to prove that Santa Claus does NOT exist!
Of course, the exact same reasoning can be used
to prove that Santa Claus does NOT exist!
Yes I
do!