1 / 15

Introduction to Philosophy Lecture 6 Pascal’s wager

Introduction to Philosophy Lecture 6 Pascal’s wager. By David Kelsey. Pascal. Blaise Pascal lived from 1623-1662. He was a famous mathematician and a gambler. He invented the theory of probability. Probability and decision theory.

tass
Download Presentation

Introduction to Philosophy Lecture 6 Pascal’s wager

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to PhilosophyLecture 6Pascal’s wager By David Kelsey

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

  3. Probability anddecision theory • Pascal thinks that we can’t know for sure whether God exists. • Decision theory: used to study how to make decisions under uncertainty, I.e. when you don’t 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!

  4. Expected Utility • The expected utility for any action: the payoff you can expect to gain on each trial if you continued to perform trials... • It is the average gain or loss per trial. • A trial: is a an attempt at achieving success. • Example… • The payoff or value of an outcome: what is to be gained or lost if that outcome occurs. • 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:

  5. 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: • If you win it you get a quarter and if you lose it you lose a quarter. • The coin comes up heads: ___ It comes up tails: ___ • You call heads ___ ___ • You call tails ___ ___

  6. The Expected Utility of the coin flip • So when making a decision under a time of uncertainty: construct a payoff matrix • Which action: • Perform the action with the highest expected utility! • 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: • … • Choose either action…

  7. Another coin tossing game • Different payoffs: what if the payoffs were greater when the coin comes up heads than if the coin comes up tails. • It comes up heads: ___ The coin comes up tails: ___ • You call heads ___ ___ • You call tails ___ ___ • The EU if you call heads: • … • And the EU if you call tails: • … • So Call Heads!

  8. Taking the umbrellato work • Do you take an umbrella to work? You live in Seattle. There is a 50% chance it will rain. • Taking the Umbrella: a bit of a pain. You will have to carry it around. • Payoff = -5. • If it does rain & you don’t have the umbrella: you will get soaked • payoff of -50. • If it doesn’t rain then you don’t have to lug it around: • payoff of 10. • It rains (___) It doesn’t rain (___) • Take umbrella ___ ___ • Don’t take umbrella ___ ___ • EU (take umbrella) = … • EU (don’t take umbrella) = … • Take the umbrella to work!

  9. Pascal’s 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: …

  10. Pascal’s payoff matrix • God exists (___) God doesn’t exist (___) • Believe ____ ____ • Don’t believe ____ ____ • Assigning a probability to God’s existence: • A bit tricky since we don’t know. • For Pascal: • since we don’t know if God exists we know the probability of his existence is greater than 0. • EU (believe) = … • EU (don’t believe) = … • Believe in God: …

  11. Pascal’s argument • Pascal’s 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. • Not existence but Belief: …

  12. Denying premise 1 • The first move: • Deny premise 1: • The second move & Pascal’s reply: • Believing for selfish reasons:

  13. Denying premise 2 • Deny premise 2: • Infinite payoff’s make no sense: • Can we even assign a non-zero probability to God’s existence?

  14. The Many Gods objection • We could Deny premise 2 in another way: • Many Gods & the Perverse Master…

  15. The Perverse Master • The new payoff matrix: • God exists (__) Perverse Master exists (__) Neither exists (___) • Believe _____ _____ ___ • Don’t Believe _____ _____ ___ • Disbelief seems no worse off than belief: • EU (believe) = … • EU (don’t believe) = … • What if we thought it less likely that the perverse Master exists than does God:

More Related