some important examples of paradox how do we interpret “reality”. what models do we build to...

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 abutterfly , and then awoke to wonder if he wasa butterfly dreaming he was a man.

Is this slide show “real” - or are you dreamingthat you are sitting in paradox class watchinga 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!

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?

If this process continues,

simpson

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

2 out of 8 =25% of the men treated with drug B are cured.

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

2 out of 8 =25% of the men treated with drug B are cured.

4 out of 10 =40% of the women treated with drug A are cured.

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

2 out of 8 =25% of the men treated with drug B are cured.

4 out of 10 =40% of the women treated with drug A are cured.

1 out of 2 =50% of the women treated with drug B are cured.

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

2 out of 8 =25% of the men treated with drug B are cured.

4 out of 10 =40% of the women treated with drug A are cured.

1 out of 2 =50% of the women treated with drug B are cured.

A higher percentage of men are cured with B

A higher percentage of women are cured with B

drug A drug B

1 out of 5 =20% of the men treated with drug A are cured.

2 out of 8 =25% of the men treated with drug B are cured.

4 out of 10 =40% of the women treated with drug A are cured.

1 out of 2 =50% of the women treated with drug B are cured.

drug A drug B

drug A drug B

5 out of 15 = 33 1/3 %of people treated with A are cured

3 out of 10 = 30 %of people treated with B are cured

drug A drug B

5 out of 15 = 33 1/3 %of people treated with A are cured

3 out of 10 = 30 %of people treated with B are cured

A higher percentage of people are cured with A

drug A drug B

5 out of 15 = 33 1/3 %of people treated with A are cured

3 out of 10 = 30 %of people treated with B are cured

A higher percentage of men are cured with B

A higher percentage of women are cured with B

A higher percentage of people are cured with A

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.

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)(1,000,000)+

(.9)(100) =

100,090

expected value =

(.1)(2,000,000)+

(.9)(0) =

200,000

the nature of free will

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???

You have to make an important decision.What will you choose?

Is free will FATE or is it CHANCE??????????????

some paradoxes inAristotelian logic

That duck is lying!

What he says is true

“If John studies then he will get an A.”

s a s a

F

F

T

F

T

T

T T T

T F F

“If then .”

s a s a

F

F

T

F

T

T

T T T

T F F

the model

“If this statement is true then Santa Claus exisits .”

s a s a

F

F

T

F

T

T

T T T

T F F

“If this statement is true then Santa Claus exisits .”

s a s a

F

F

T

F

T

T

T T T

T F F

This statement

“If this statement is true then Santa Claus exisits .”

s a s a

F

F

T

F

T

T

T T T

T F F

This statement

The onlyconditionsunder whichthis statementis FALSE

“If this statement is true then Santa Claus exisits .”

s a s a

F

F

T

F

T

T

T T T

T F F

This statement

The onlyconditionsunder whichthis statementis FALSE

a contradiction

“If this statement is true then Santa Claus exisits .”

s a s a

F

F

T

F

T

T

T T T

T F F

This statement must be TRUE

So Santa Claus exists!

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!