Knowledge and Reality A by shuifanglj

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									Knowledge and
Reality A
Lecture Six: Paradoxes I
This Week
 Our look at formal epistemology.
 Our first look at some paradoxes.
 Our chance to advance the skills you are
  expected to acquire.
Formal Epistemology
 Basically this is the way of formalising,
  using logic, probability theory and
  mathematics, how to make decisions.
 It’s applied in numerous areas.
     Economics(microeconomics and
      macroeconomics)
     MAD scheme
Formal Epistemology
   Some choices are easy.
   If you like Pepsi and hate
    Coke, what should you decide
    about which to drink?
   PEPSI!
   If you want to go to the pub
    with your mates but your lover
    will make your life hell
    because of it, what do you do?
   Depends how bad a hell!
Formal Epistemology
   We do some really basic maths to show
    which option is better.
Formal Epistemology
   Some choices are easy.
   If you like Pepsi and hate
    Coke, what should you decide
    about which to drink?
   PEPSI!
   If you want to go to the pub
    with your mates but your lover
    will make your life hell
    because of it, what do you do?
   Depends how bad a hell!
Formal Epistemology
   We do some really basic maths to show which option is
    better.
   Fix a ‘utility’ to picking Coke and Pepsi.
   If you hate Coke then you’ll lose out.
   Let’s say -10 Utility Points.
   If you love Pepsi then you’ll gain.
   Let’s say 10 Utility Points.
   The choice is clear – one option gives you 10, the other
    option loses you 10.
    Nor does it matter how difficult it is to determine these ‘Utility Points’
Formal Epistemology
   Some choices are easy.
   If you like Pepsi and hate
    Coke, what should you decide
    about which to drink?
   PEPSI!
   If you want to go to the pub
    with your mates but your lover
    will make your life hell
    because of it, what do you do?
   Depends how bad a hell!
Formal Epistemology
   Going to the pub is worth 20 UP.
   Say that if your missus/bloke hating you isn’t that bad
    (say you hate them too, or they’re too mild mannered to
    be really mean) then it’s -5 UP.
   Say that if your missus/bloke would do terrible things to
    you then it’s -25 UP.
   In the former you do it, in the latter you don’t.
   And other things can be factored in!
   If you’d feel guilty at doing it, maybe that’s -20 UP and
    even in the first case you shouldn’t do it.
Formal Epistemology
   Things can get more complicated.
   Perhaps if your lover came home he/she would discover
    you gone and make your life hell to the tune of 25 UP.
   But you reckon there’s only a 1 in 5 chance of them
    coming home.
   If you stay in there’s a 100% chance of losing nothing
    and gaining nothing.
   If you go to the pub there’s a 100% chance of you
    gaining 20 UP and a 20% chance of you losing 25.
   The calculation is simple: your expected utility gain is:
       20
Formal Epistemology
   Things can get more complicated.
   Perhaps if your lover came home he/she would discover
    you gone and make your life hell to the tune of 25 UP.
   But you reckon there’s only a 1 in 5 chance of them
    coming home.
   If you stay in there’s a 100% chance of losing nothing
    and gaining nothing.
   If you go to the pub there’s a 100% chance of you
    gaining 20 UP and a 20% chance of you losing 25.
   The calculation is simple: your expected utility gain is:
       20 – (0.2 x 25 )
Formal Epistemology
   Things can get more complicated.
   Perhaps if your lover came home he/she would discover
    you gone and make your life hell to the tune of 25 UP.
   But you reckon there’s only a 1 in 5 chance of them
    coming home.
   If you stay in there’s a 100% chance of losing nothing
    and gaining nothing.
   If you go to the pub there’s a 100% chance of you
    gaining 20 UP and a 20% chance of you losing 25.
   The calculation is simple: your expected utility gain is:
       20 – (0.2 x 25 ) = 20 – 5
Formal Epistemology
   Things can get more complicated.
   Perhaps if your lover came home he/she would discover
    you gone and make your life hell to the tune of 25 UP.
   But you reckon there’s only a 1 in 5 chance of them
    coming home.
   If you stay in there’s a 100% chance of losing nothing
    and gaining nothing.
   If you go to the pub there’s a 100% chance of you
    gaining 20 UP and a 20% chance of you losing 25.
   The calculation is simple: your expected utility gain is:
       20 – (0.2 x 25 ) = 20 – 5 = 15
Formal Epistemology
 Easy!
 But weird things can
  happen.
 MAD is one example.
The Centipede Game
 Let’s have another
  example.
 I want to play a
  game.
 The rules are easy!
The Centipede Game
   Two people, each taking a turn.
   There are 8 coins. The aim of the game is to get
    the most coins.
   On your turn you can:
     (i) Take a coin and then let it be the other player’s
      turn.
     (ii) Take two coins, and then the game ends and we
      tot up who has the most coins.
     The game ends when we run out of coins.
Centipede Game
   So you have a principle to maximise utility.
   What you do is altered by what you think your
    opponent is going to do.
   With MAD it wasn’t so bad, but here it fails
    miserably.
   It ends up that when the game starts I should
    just take two coins.
   Imagine we played it with 100 coins (you can
    play it with as many coins as you like!)
Centipede Game
   When it’s my go, and there are two coins left, it’d
    be irrational of me to take one coin and let it be
    your go.
   To make the most money (assume that’s my
    aim, and I don’t give a toss about you
    personally) I should take both coins and end the
    game.
   I’d end up with £51 and you end up with £49,
    rather than us both having £50.
   Sound right?
Centipede Game
   But you’re a rational kinda person too.
   So when we get to three coins on the table, and
    it’s your go you know what I’m going to do next
    turn.
   And it’ll mean you end with £49.
   So when there are three coins on the table, you
    should take two coins and end the game.
   You end up with £50 and I end up with £49.
Centipede Game
 Now go back to a turn earlier, where there
  are four coins on the table and it’s my go.
 I know that, rationally, you will end the
  game the next turn.
 So at that stage I should take both coins
  and end the game.
 So I’d have £50 and you’d have £48.
Centipede Game
 So now think about it again a turn earlier.
 There are five coins on the table, and it’s
  your go.
 You know that when it gets to four coins I’ll
  end the game and you’ll only have £48.
 Better to end the game then, and you end
  up with £49 (and I end up with £48).
Centipede Game
   Do you see where this is going?
   We can do it again – when there are six coins on
    the table and it’s my turn, I know you’ll end the
    game when there are five, so I better end it
    when there are six.
   When there are seven coins on the table and it’s
    your turn, you know that’s what I’ll do so you’d
    better end it there and then.
   And so on and so forth.
Centipede Game
   So we can keep going.
   Rationally, it seems, as soon as the game starts
    I should take two coins and end it.
   And that can’t be right can it!
   I only end up with £2 and you end up with
    nothing.
   So, again, if we follow rational thinking through
    to it’s rational conclusions, we end up with
    apparently irrational activity.
Principles of Formal Epistemology

 Where we’ve gone wrong is that we must
  be misapplying the principles we thought
  governed rational choice.
 For it is demonstrably irrational to take two
  coins to begin with!
 Let’s spend the rest of the lecture looking
  at another example: Newcomb’s Paradox.
Principles of Formal Epistemology

 In this paradox the combination of two
  intuitively true principles lead us astray.
 The first is the principle of maximum
  expected utility.
 You should do what is likely to bring about
  the maximum amount of utility.
 We’ve had examples of this already.
Formal Epistemology
   Some choices are easy.
   If you like Pepsi and hate
    Coke, what should you decide
    about which to drink?
   PEPSI!
   If you want to go to the pub
    with your mates but your lover
    will make your life hell
    because of it, what do you do?
   Depends how bad a hell!
Maximum Expected Utility
   Even in more complex cases, it seems good to go with it.
   If you have to gamble and betting it on Horse A is 80%
    likely to yield £30 and betting on Horse B is 20% likely to
    yield £200, what should you do?
   Horse A expected yield: 0.8 x 30 = £24
   Horse B expected yield: 0.2 x 200 = £40
   Ceteris paribus bet on Horse B
    And things might not be equal: maybe the Mafia will break your legs unless
    you get them £30. In which case the utility isn’t in line with monetary gain.
    But for demonstration purposes we’ll stick with simple numbers and money.
Newcomb’s Paradox
 Imagine there is a room with two boxes in
  it.
 One box is transparent: it has £1,000.
 Another box is opaque: but you know it
  either has nothing in it, or £1,000,000.
 You can take the contents of either one
  box, or both boxes.
Newcomb’s Paradox
   Here’s the twist.
   There’s some Derren Brown-
    esque character present.
   He has predicted, with 100%
    accuracy, which box you will pick.
   If you choose two boxes, there will
    be nothing in the opaque box.
   If you choose one box, there will
    be £1,000,000 in the opaque box.
   So, how many boxes do you pick?
Newcomb’s Paradox
   If you pick one box, and pick the one you can
    see into, you will definitely get £1,000.
   If you pick on box, and pick the one you can’t
    see into, what are the chances of you getting
    £1,000,000?
   Well, if Derren is a perfect predicator, the
    chance is 100%.
   So you’ll definitely get £1,000,000.
Newcomb’s Paradox
 If you pick two boxes, what’s the chances
  of you getting what?
 As Derren is the perfect predictor, you
  have 100% chance of having nothing in
  the second box.
 So you will definitely get £1000.
Newcomb’s Paradox
 One boxer (transparent): £1000
 Two boxer: £1000
Newcomb’s Paradox
 One boxer (transparent): £1000
 Two boxer: £1000
 One boxer (opaque): £1,000,000
 The Maximum Expected Utility principle
  says to pick just one box – the one you
  can’t see into.
 Sound good?
Principles of Formal Epistemology

 The other principle is the Dominance
  Principle.
 If you have some choices, and one of
  them, choice X, has no downsides that the
  others don’t have
Principles of Formal Epistemology

 The other principle is the Dominance
  Principle.
 If you have some choices, and one of
  them, choice X, has no downsides that the
  others don’t have and there’s at least a
  chance that doing X will be good for you
  then you should do it.
Principles of Formal Epistemology
   Example: Stay at home, or go to the pub.
   Imagine that staying at home has no upsides or downsides.
   Imagine that going to the pub has no downsides (I get free beer, I
    have no problem with walking to the pub etc.) but a high chance I’ll
    have fun.
   I should go to the pub!
   Imagine there’s a small chance I’ll have fun.
   I should still go to the pub!
   Imagine there’s a one in a trillion chance I’ll have fun.
   I should still go to the pub!
   At least, if there’s no difference whatsoever between being in the
    pub and being at home.
Principles of Formal Epistemology

 One choice dominates the others.
 It is clearly better, because it is as good as
  the other choices and has the benefit of
  (possibly, or even definitely) being better.
 How does this work in the Newcomb
  Paradox?
Principles of Formal Epistemology

 One choice dominates the others.
 It is clearly better, because it is as good as
  the other choices and has the benefit of
  (possibly, or even definitely) being better.
 How does this work in the Newcomb
  Paradox?
Newcomb’s Paradox
   Imagine your mother could see inside both boxes, and
    could advise you on how many to take.
   And let’s imagine you trust your mother implicitly.
   If there were £1,000,000 in the opaque box and £1,000
    in the transparent box, how many boxes would she tell
    you to pick?
   Both of them! You’d come away with £1,001,000 rather
    than £1,000,000.
   Clearly, then, you’d be well advised to take the advice of
    your mother in that case.
Newcomb’s Paradox
   What if there were only £1,000 in the transparent
    box and nothing in the opaque box?
   Well then your mother would still tell you to pick
    both boxes as you’d walk away with £1,000
    rather than nothing (as if you picked one box,
    you’d presumably pick the opaque, empty, box).
   So in that case you also should follow her advice
    and take both boxes!
Newcomb’s Paradox
   Here’s the rub.
   It doesn’t matter whether your mother is there or not.
   You know that either way she’d tell you to take both
    boxes.
   So you know that either way it’s in your interests to pick
    both boxes.
   That choice dominates the other choices.
   So, no matter what happens – you should pick both
    boxes.
Newcomb’s Paradox
 Think of it another way: it’s too late for
  Derren to change the boxes now.
 Whatever you decide what’s in the boxes
  is what’s in the boxes.
 So, screw it, you may as well take as
  much as you can – and take both boxes.
Newcomb’s Paradox
   So NP is a paradox because one principle says to do
    one thing, and another principle says to do another.
   MEU: Pick one box.
   DP: Pick two boxes.
   And both principles look to be good, rational principles.
   Something has to go! Something has to be revised!
   A principle concerning how choices are made has to be
    altered!
Broader Skills
   This topic builds into the idea of broadening your
    skills.
   This topic really is about your own responses to
    the material.
   In the others, I’ve stressed that you could go off
    and read books on it.
   Not so easy with this one – the books are hard!
Broader Skills
 So much of philosophy is your own
  response, and your own tackling of the
  material.
 You need to go away and ruminate on
  these issues.
Broader Skills
   If you do read the material, you’ll see that a lot of
    it is tricky.
   Lots of maths and tables and stuff.
   That can be okay. You need to master the art of
    learning what to read and what to ignore.
   Especially in a discipline like philosophy where
    you can be dipping in and out of many other
    disciplines (do applied ethics, read politics and
    economics; do metaphysics, read physics
    journals etc.)
Broader Skills
   You have to try and get out of an article what you can.
   The complex bits may be so complex you won’t get
    anything out of them.
   Just skip them.
   You can’t argue against them, so you may as well
    assume that it works.
   If the author says it, then you may as well believe it!
   It’s called ‘accepting for the purpose of argument’
Broader Skills
 There’s even a part of the article you’ve
  got for which you’ll need to do this…
 Have fun!
Next Lecture
   Induction.

								
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