Introduction to Philosophy Lecture 6 Pascal

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Introduction to PhilosophyLecture 6Pascals
wager

• By David Kelsey

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Pascal

• Blaise Pascal lived from 1623-1662.
• He was a famous mathematician and a gambler.
• He invented the theory of probability.

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Probability anddecision theory

• Pascal thinks that we cant know for sure whether
  God exists.
• Decision theory used to study how to make
  decisions under uncertainty, I.e. when you dont
  know what will happen.
• Lakers or Knicks
• Rain coat
• Rule for action when making a decision under a
  time of uncertainty always perform that action
  that has the highest expected utility!

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Expected Utility

• The expected utility for any action the payoff
  you can expect to gain on each attempt if you
  continued to make attempts...
• It is the average gain or loss per attempt.
• To compute the expected value of an action
• ((The prob. of a success) x (The payoff of
  success)) ((the prob. of a loss) x (the payoff
  of a loss))
• Which game would you play?
• The Big 12 pay 1 to roll two dice.
• Lucky 7 pay 1 to roll two dice.
• E.V. of Big 12
• E.V. of Lucky 7

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Payoff matrices

• Gamble Part of the idea of decision theory is
  that you can think of any decision under
  uncertainty as a kind of gamble.
• Payoff Matrix used to represent a scenario in
  which you have to make a decision under
  uncertainty.
• On the left our alternative courses of action.
• At the top the outcomes.
• Next to each outcome add the probability that it
  will occur.
• Under each outcome the payoff for that outcome
• Calling a coin flip for a quarter
• The coin comes up heads ___ It comes up
  tails ___
• You call heads ___
  ___
• You call tails ___
  ___

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The Expected Utility of the coin flip

• So when making a decision under a time of
  uncertainty construct a payoff matrix
• To compute the expected value of an action
• ((The prob. of a success) x (The payoff of
  success)) ((the prob. of a loss) x (the payoff
  of a loss))
• For our coin tossing example
• The EU of calling head
• The EU of calling tails
• Which action has the higher expected utility?

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Taking the umbrellato work

• Do you take an umbrella to work? There is a 50
  chance it will rain.
• Taking the Umbrella You will have to carry it
  around.
• Payoff -5.
• If it does rain you dont have the umbrella
  soaked
• payoff of -50.
• If it doesnt rain then you dont have to lug it
  around
• payoff of 10.
• It rains
  (___) It doesnt rain (___)
• Take umbrella ___
  ___
• Dont take umbrella ___
  ___
• EU (take umbrella)
• EU (dont take umbrella)

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Pascals wager

• Choosing to believe in God Pascal thinks that
  choosing whether to believe in God is like
  choosing whether to take an umbrella to work in
  Seattle.
• It is a decision made under a time of
  uncertainty
• But We can estimate the payoffs
• Believing in God is a bit of pain whether or not
  he exists
• An infinite Reward
• Infinite Punishment

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Pascals payoff matrix

• God exists (___)
  God doesnt exist (___)
• Believe ____
  ____
• Dont believe ____
  ____
• Assigning a probability to Gods existence
• A bit tricky since we dont know.
• For Pascal
• since we dont know if God exists we know the
  probability of his existence is greater than 0.
• EU (believe)
• EU (dont believe)
• Which action has greater expected utility?

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Pascals argument

• Pascals argument
• 1. You can either believe in God or not believe
  in God.
• 2. Believing in God has greater EU than
  disbelieving in God.
• 3. You should perform whatever action has the
  greatest EU.
• 4. Thus, you should believe in God.

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Denying premise 1

• The first move
• Can you choose to believe?
• The second move
• Would God reward selfish believers?

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Denying premise 2

• Deny premise 2
• Infinite payoffs make no sense
• Can we even assign a non-zero probability to
  Gods existence?

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The Many Gods objection

• We could Deny premise 2 in another way
• The Many Gods objection
• Catholic God exists(L) Muslim God
  exists (M) Jewish God exists (N) God doesnt
  exist (1-L-M-N)
• Believe in
• Catholic God infinity neg. infinity
  neg. infinity -5
• Muslim God neg. infinity infinity
  neg. infinity -5
• Jewish God neg. infinity neg. infinity
  infinity -5
• Dont believe neg. infinity neg. infinity
  neg. infinity 5

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The Perverse Master

• The perverse master objection
• God exists (m) Perverse Master
  exists (n) Neither exists (1-m-n)
• Believe infinity neg.
  infinity -5
• Dont Believe neg. infinity infinity
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• Disbelief seems no worse off than belief
• Is it less likely that the perverse Master exists
  than does God?