Thursday 9/26
Interlude: Puzzles and Paradoxes
Readings
All readings today will be distributed as handouts in class.
Synopsis
Today I found myself deeply impressed by and altogether proud of this class. The context was that we took up a series of paradoxes so as to contrast them from the puzzles with which we began the semester. Puzzles are hard, but once we see the solution we recognize that there is a solution and are no longer perplexed. Paradoxes are different. Try as we might, we struggle to see our way to a solution--and maybe there is none!
Consider,
Paradox 01
Newcomb's Paradox*
You are confronted with a choice. There are two boxes before you, A and B. You may either open both boxes, or else just open box B. You may keep what is inside any box you open, but you may not keep what is inside any box you do not open. The background is this.
A very powerful being, who has been invariably accurate in his predictions about your behavior in the past, has already acted in the following way:
He has put $1,000.00 in box A.
If he has predicted that you will open just box B, he has in addition put $1,000,000.00 in box B.
If he has predicted that you will open both boxes, he has put nothing in box B.
Should you open both boxes A and B? Or just B? Justify your answer.
*adapted from Sainsbury, R.M., Paradoxes, 2nd ed (Cambridge University Press, 1995).
As we discussed, there are equally good reasons to be a one-boxer as a two-boxer. The one-boxer will say, by choosing to open just box B, I'm doing what the predictor would have predicted, so I'll get the million dollars. The two-boxer says, sure, but the the predictor has already come and gone. Either there is a million and a thousand dollars in the boxes as you stand there wondering whether to open both, or there's not. So you might as well open both.
In this case, we seem to have two equally rational yet incompatible courses of action at hand. Unlike a puzzle, where we can grasp the solution once we discover and demonstrate it, in this case there seems no final solution at hand.
Paradox 02
Setting a Surprise Exam*
On Friday before the last week of class, the Classical Formal Logic class are told that they are to have a quiz on what they have learned so far this term, particularly Aristotle's 256 logical forms. This is because they are a rather slow and lazy class, teacher adds, offensively. The class are not pleased and start muttering. 'When is it, anyway?' they ask sullenly.
Teacher smirks. 'That is up to me. I may have it at any point between now and next Friday. However, let me assure you of this, when I do have the quiz it will be a surprise!'
After school, Bob and Patricia are discussing the bad news. Bob is very worried as he has a poor memory. 'I could pass, I'm sure,' says, 'if I knew on which day the test would be, then I could learn everything the night before.'
'Don't worry, Bob,' says Patricia, 'I think teacher is having a bit of a joke at our expense - you see, I don't think there can be a quiz!'
And she explains that the test cannot be held next Friday, the last day of the term, because by then the class will know that it must be going to be held, and will therefore quickly memorize the material for the test the night before. That's great" says Bob sarcastically. 'So it's any day between now and Thursday then?'
Patricia explains patiently. 'It can't be Thursday either, because if it can't be on Friday, and it is already Wednesday night, we'd all know it would have to be coming up on Thursday, the next day!'
Bob gets it now. 'Nor could it be Wednesday, nor Tuesday - nor indeed Monday! Hey! What a joke - teacher trying to get us worried! - and now he can't hold the pop quiz without having to back down on the surprise bit. Silly old fool!'
They don't tell the others, who spend ages trying to memorize the 256 aristotelian logical forms and other nonsense, much to Bob and Patricia's secret amusement. Then on Wednesday, teacher comes in and announces the quiz.
'You can't do this!' says Bob.
'Why not?' replies teacher, surprised, but not very.
'Because it's got to be a surprise - and you can only hold the test when we're not expecting it!'
'Yes, but Bob, you're surprised, and I am holding the test' says teacher in a teachery sort of way.
Is there a flaw in Bob and Patricia's reasoning? If not, how was teacher able to surprise them with a pop quiz? If so, what is the mistake in their reasoning?
*adapted from Cohen, M. 1999. 101 Philosophy Problems. London: Routledge.
If there is a flaw in their reasoning, there must be a step in it to which we can point and say, "ah ha! That's where you've gone wrong." Yet as we think about it, where would the step be? We all agreed the exam can't be Friday, but since it can't be Friday we know that once Thursday rolls around it won't be a surprise on Thursday. Since it can't be Thursday any more than it could have been Friday, it also can't be Wednesday. Nor Tuesday. Nor Monday. In thinking about it, we see no particular step in the argument where the kids went wrong. Yet here they are, surprised all the same.
Paradox 04 (we skipped #3)
The Ship Theseus*
This is not what Ray North had bargained for. As an international master criminal he prided himself on being able to get the job done. His latest client had demanded that he steal the famous yacht Theseus, the vessel from which British newspaper magnate Lucas Grub had thrown himself to his death and which more recently had been the scene of the murder of LA rapper Daddy Iced Tea.
But here he was in the dry dock where the boat had just finished being repaired, confronted by two seemingly identical yachts. North turned to the security man, who was being held at gunpoint by one of his cronies.
“If you want to live, you'd better tell me which of these is the real Theseus,” demanded Ray.
“That kinda depends,” came the nervous reply. “You see, when we started to repair the ship, we needed to replace lots of parts. Only, we kept all the old parts. But as the work progressed, we ended up replacing virtually everything. When we had finished, some of the guys thought it would be good to use all the old parts to reconstruct another version of the ship. So that's what we've got. On the left, the Theseus repaired with new parts and on the right, the Theseus restored from old parts.”
“But which one is the genuine Theseus?” demanded Ray.
“I've told you all I know!” screamed the guard, as the crony tightened his grip. Ray scratched his head and started to think about how he could get away with both...
Which is the real ship Theseus? Which ship should Ray steal, if he can only steal one?
*adapted from Julian Baggini, “The Pig That Wants to Be Eaten: 100 Experiments for the Armchair Philosopher”, (New York: Plume Books) pp. 31-32
If the dock workers had not rebuilt the Theseus as they tossed aside old parts being replaced on the ship Theseus, we would not be in the difficult position of determine which of the two ships is the real ship Theseus--the ship, that is, from which Lucas Grub threw himself to his death and upon which Daddy Iced Tea was murdered. As it stands, we can make as much a case for Ray to steal the Theseus built from new parts as for him to steal the Theseus built from the old parts of the ship. Yet there can't be two ships Theseus, can there? These-i? From both of which Grub killed himself and upon both of which Tea was murdered?
Our discussions today on these paradoxes were vigorous, vital, insightful, and fascinating. Well done one and all!
Next time we'll start by considering one of the oldest puzzles we can imagine, and one we seem no closer to solving: Why is there something and not nothing?