102. NickVanston - Feb. 24, 1999 - 6:43 AM PT
It seems to me that Jerry Fodor is a good American philosopher, but perhaps that is because he is the only one I can understand (and perhaps that is because he writes so well).
103. DocBrown - Feb. 24, 1999 - 7:20 AM PT
Can anyone shed some light on the origin of this thread? I was away for two months, so perhaps I missed the critical discussion.
Personally, I *do* hear about philosophy all the time. My wife likes to discuss it with me, mostly because she has studied it and I have not. She used to be able to get away with all sorts of wild claims at my expense (e.g. "Of course there is a God, silly. Thomas Aquinas proved it with perfect logic!"). That was before I discovered The Fray and its vast bank of knowledge philosophical. I am now much better equipped for that battle.
104. DocBrown - Feb. 24, 1999 - 7:21 AM PT
Teewrecks: go right on misspelling words. Spelling in this crummy language of our is much too difficult, taking up brain cells that would be better devoted to math, geography, and sports statistics.
105. DocBrown - Feb. 24, 1999 - 7:36 AM PT
teewrecks, when you said:
> Philosophy, with the big P, is largely
> dead, subsumed by the sciences, both
> hard & soft.
and all that gobbledeygook about epistemology, did you mean it the way it seems? At first I interpreted it the same literal way that PseudoErasmus did, but in light of the above quoted sentence perhaps you meant something else.
The questions of epistemology are older then neuro-biology, physics, etc.. These scientific tools do overlap with our understanding of the nature of knowledge, but none of them are all encompassing. This seems painfully obvious.
So perhaps you meant that pure epistemology gets very little attention and resources today, because those sub-fields are simply more interesting. Maybe?
I'm probably wrong. You probably meant that epistemology is locked in a box with a dead cat.
106. DanDillon - Feb. 24, 1999 - 7:47 AM PT
Fun, meaningless, and arcane noun phrases from Message #97 that I'd like to highlight:
"unconscious, vestigial tribalism of morphology"
"the hallucinarium of Academe"
"the contingency and impedimenta of the temporal objective"
Could someone please pass the calamine? Message #104 has caused me to break out in hives.
107. stostosto - Feb. 24, 1999 - 7:52 AM PT
The "Is Philosophy Dead?" thread is apparently not dead yet.
108. DocBrown - Feb. 24, 1999 - 8:03 AM PT
That's a sensitive hide you've got there, DanDillon. I hope you have a good durmatologist.
109. DanDillon - Feb. 24, 1999 - 8:35 AM PT
One man's sensitive hide is another's burning flesh. Ouch.
110. DocBrown - Feb. 24, 1999 - 9:34 AM PT
Are you this sensitive by choice, DanDillon? Or is this some sort of pathalogical reaction?
Life is too short, my friend. If bad spelling and grammar at the Fray have the power to make you unhappy, then woe is you. Better to call Doctor Kevorkian today than tomorrow.
111. DocBrown - Feb. 24, 1999 - 9:35 AM PT
Philosophy is not dead. It is alive and well and living on the back bumpers of our cars.
112. DanDillon - Feb. 24, 1999 - 10:51 AM PT
"If bad spelling and grammar at the Fray have the power to make you unhappy, then woe is you."
Such errors don't upset me in the least. They merely make me feel pity (and less often sympathy) for those who obviously know no better.
113. Slackjaw - Feb. 24, 1999 - 5:23 PM PT
"Are you this sensitive by choice, DanDillon?"
Oh, so now DocBrown believes in free will. Splendid.
114. ChristinO - Feb. 24, 1999 - 5:27 PM PT
AHA!!!!
I KNEW IT!!!!
Tooroo la lay! Oh happy day!
115. DocBrown - Feb. 25, 1999 - 5:54 AM PT
Slackjaw, don't tease ChristinO that way. It's not nice.
It doesn't take Free Will to make a choice. All you need is an optimization function. Computers do it all the time.
My comment to DanDillon does bring Free Will into the question. A person cannot make a choice contrary to their own desires and goals. If DanDillon chooses to be sensitive to poor spelling, then it must be in accord with some personal value which is more important than the pain it causes.
116. pellenilsson - Feb. 25, 1999 - 6:20 AM PT
Free Will! At last something interesting. No time now but will be back later.
117. DanDillon - Feb. 25, 1999 - 6:26 AM PT
Glad I could be of service. Of course, I had no choice in the matter.
118. TabouliJones - Feb. 25, 1999 - 6:37 AM PT
Elliott,
How about giving up the answer to the paradox you dangled in Message #86?
119. teewrecks - Feb. 25, 1999 - 6:39 AM PT
DocBrown,
To the extent that I have been less than clear about epistemology I accept all blame. I imagine we may agree on more than you suspect. BTW, regarding dead cats in boxes, I have a cat named Schrodinger, happily alive & well.
Epistemology certainly predates any of the above referenced sciences and is perhaps as old as philosophy itself. I was only making an observation about the contemporary state of philosophy. And while these sciences have certainly made some progress, I don't for a moment think that the interesting questions are answered (some of which may be unanswerable). I know I need to expand on this, but I'm on my way out the door for a business trip and won't be able to continue this for a few days. I hope this thread remains active.
I should point out that it was my wife, Mrs. Tee Wrecks, who posted #99. I hope that hasn't confused anyone.
Tee
120. elliot803 - Feb. 25, 1999 - 6:44 AM PT
Tabouli:
What makes you think there's an answer? How do you resolve it?
121. CoralReef - Feb. 25, 1999 - 6:49 AM PT
I thought it answered itself: the prisoner reasoned that he couldn't be surprised, ruled out Wednesday based on what the Judge said, but by it being Wednesday the Judge was right.
122. elliot803 - Feb. 25, 1999 - 7:20 AM PT
CoralReef:
Then what is the flaw in the prisoner's reasoning?
123. CoralReef - Feb. 25, 1999 - 7:21 AM PT
He assumed he could reason it out, that was his mistake, it left him open to actually being surprised on the days he ruled out.
124. CoralReef - Feb. 25, 1999 - 7:26 AM PT
I didn't take the judge's comment about not predicting as a promise but as a prediction. It became a self-fulfilling prophecy to the prisoner.
125. elliot803 - Feb. 25, 1999 - 7:29 AM PT
CoralReef:
Why can't he reason it out? You're not addressing the issue. Suppose he had been hanged on Sunday, the last day. I assume you'd agree that at 11:59pm on Saturday night, he could have predicted that he would be hung some time on Sunday, thus violating the judge's condition that he would not be able to predict the day of his hanging. So what is wrong with his reasoning that rules out all the other days, too?
126. CalGal - Feb. 25, 1999 - 7:34 AM PT
I think the flaw in the prisoner's reasoning was that he forgot that a day isn't completely eliminated until it's over
I'm not good enough at this sort of reasoning to be sure, but it seems that he might have been right about Saturday and Sunday, since there are only two days to choose from. But the moment there are three or more days to choose from, he can't know for sure what day he will be killed.
So assume for the moment that his Friday rule was valid. His mistake was in assuming it would work for Thursday.
But on Thursday, he had no way of knowing whether or not he'd be killed on Friday or Saturday. Friday hadn't been eliminated yet, and there was no way he could *know* it was Friday until they came to get him. Until that moment, it had every chance of being Saturday. And until Friday was over, he didn't *know* that it would be Saturday.
That works back through the days, I think.
127. CoralReef - Feb. 25, 1999 - 7:38 AM PT
elliot, I didn't avoid anything. He reasoned that he couldn't be hung on any of the days, but he knows he will be hung, so by reasoning it out he left himself open to being surprised. Beyond that, I don't think there is any answer, not of the type you seem to be seeking.
128. elliot803 - Feb. 25, 1999 - 7:42 AM PT
CalGal:
"I'm not good enough at this sort of reasoning to be sure, but it seems that he might have been right about Saturday and Sunday, since there are only two days to choose from. But the moment there are three or more days to choose from, he can't know for sure what day he will be killed."
Why not?
"So assume for the moment that his Friday rule was valid. His mistake was in assuming it would work for Thursday. But on Thursday, he had no way of knowing whether or not he'd be killed on Friday or Saturday. Friday hadn't been eliminated yet, and there was no way he could *know* it was Friday until they came to get him. Until that moment, it had every chance of being Saturday. And until Friday was over, he didn't *know* that it would be Saturday."
Huh? He's already eliminated Saturday, and he can then eliminate Friday in the same way. Then Thursday, and so on back through the week. He's not "assuming" anything. What is the flaw in his reasoning?
129. elliot803 - Feb. 25, 1999 - 7:46 AM PT
CoralReef:
"elliot, I didn't avoid anything. He reasoned that he couldn't be hung on any of the days, but he knows he will be hung, so by reasoning it out he left himself open to being surprised."
But he doesn't know he'll be hung. He sincerely believes that his reasoning precludes his being hung in accordance with the conditions laid down by the judge. And yet he was. So, again, what is wrong with his reasoning?
130. CoralReef - Feb. 25, 1999 - 8:11 AM PT
elliot, your reply to calgal seemed inadequate: "He's already eliminated Saturday, and he can then eliminate Friday in the same way."
Why? She claimed that the situation changes when it goes from being three days to two, and the fault in his reasoning is that he assumes he can follow this rule backwards. If this is wrong address why it's wrong.
131. Raskolnikov - Feb. 25, 1999 - 8:19 AM PT
I think this is a variation on one of the Socratic dialogues. It is a paradox, like the statement "This sentence is a lie".
132. Raskolnikov - Feb. 25, 1999 - 8:22 AM PT
The prisoner's mistake was in stopping the regressive logic at an arbitrary point. His logic should proceed, "but since I logically deduce that I can't be surprised by an execution, *any* execution date would surprise me, so I have to expect to be executed, but they can't execute me on Friday... ad infinitum".
133. elliot803 - Feb. 25, 1999 - 8:26 AM PT
CoralReef:
I don't understand why you don't think he can follow the rule backwards. He's not "assuming" he can do this, he's reasoning it. If he were still alive at 11:59pm on Saturday, then he would be able to predict that he'd be hung on Sunday, violating the judge's conditions. So he can't be hung on Sunday in accordance with the judge's conditions. If he were still alive at 11:59 on Friday, then since Sunday is ruled out, he could predict that he would be hung on Saturday. That rules out Saturday. If he were still alive at 11:59 on Thursday, then since Saturday and Sunday are ruled out, he could predict that he'd be hung on Friday. That rules out Friday. If he were still alive at 11:59 on Wednesday....... and so on.
Where is the flaw?
134. elliot803 - Feb. 25, 1999 - 8:29 AM PT
Rask is getting warm.
135. CoralReef - Feb. 25, 1999 - 8:31 AM PT
But elliot, Sunday is ruled out on Saturday, why is it ruled out on Friday? On Saturday it's a binary situation, but on Friday, could it not be Saturday or Sunday if not Friday?
136. Raskolnikov - Feb. 25, 1999 - 8:32 AM PT
But it wouldn't be too tough for the Judge to surprise the prisoner anyway. He could always let the prisoner know that the date of his execution was going to be selected randomly. If the prisoner wasn't dead by Friday AM, he would know the execution was that day and not be surprised, but any other day would be a surprise.
137. CoralReef - Feb. 25, 1999 - 8:34 AM PT
Well, if the judge said he was going to be executed, and also that he wouldn't be able to predict it, those two statements -- going by the prisoner's reasoning that rules out the days he can be exectuted -- cannot both be true. Since the he *will* be executed, the comment about prediction must have been a lie on the judge's part.
I considered saying that a little while ago but figured you'd think it was avoiding the issue again.
138. elliot803 - Feb. 25, 1999 - 8:38 AM PT
CoralReef:
"But elliot, Sunday is ruled out on Saturday, why is it ruled out on Friday?"
Because if he is to be hung on Sunday, he will still be alive at 11:59pm on Saturday, and thus would be able to predict the day of his hanging, violating the judge's condition. So he can't be hung on Sunday in accordance with the judge's conditions. So, Sunday is ruled out. It's not just ruled out on Saturday, it's ruled out, period.
139. CalGal - Feb. 25, 1999 - 8:42 AM PT
Well, if Elliot says Rask is getting warm, then this statement of Elliot's might have something to do with it:
"He sincerely believes that his reasoning precludes his being hung in accordance with the conditions laid down by the judge. "
Rask says that *since* he sincerely believes this, yet he knows he is to be executed, he should have realized that any execution date would surprise him.
Whereas to me, his sincere belief has nothing to do with it. The flaw was in his reasoning about the predictability of the execution, not in his reasoning about what he should have done once he sincerely believed in his escape from execution.
140. CalGal - Feb. 25, 1999 - 8:46 AM PT
Rask,
"If the prisoner wasn't dead by Friday AM, he would know the execution was that day and not be surprised, but any other day would be a surprise."
Well, that's my argument (except I think it is Friday PM, not AM, when he is certain). His process of elimination for Friday does not follow through to the other days. I'm not sure it works for Friday until the day is over, quite frankly. But I'll take that for now.
It doesn't follow for Thursday, though, because on Thursday morning he could be executed at any time during that day *or* Friday. So it would be a surprise. And so on.
141. elliot803 - Feb. 25, 1999 - 8:48 AM PT
CalGal:
No, my statement had nothing to do with why Rask is getting warm.
"The flaw was in his reasoning about the predictability of the execution, not in his reasoning about what he should have done once he sincerely believed in his escape from execution."
What is this alleged flaw? Please read through my previous posts before responding, so we don't have to keep going through the same thing over and over again.
142. elliot803 - Feb. 25, 1999 - 8:52 AM PT
CalGal:
"It doesn't follow for Thursday, though, because on Thursday morning he could be executed at any time during that day *or* Friday."
No. He already knows he can't be executed on Friday, because if he were still alive at 11:59pm on Thursday, he would be able to predict that Friday was the day (since Saturday and Sunday are ruled out). But the condition laid down by the judge is that he wouldn't be able to predict the day. Thus, it cannot be Friday. The same goes for Thursday, Wednesday, and Tuesday.
143. CoralReef - Feb. 25, 1999 - 8:54 AM PT
His mistake was assuming he'd be given a watch and allowed to know what time it is.;-)
144. CalGal - Feb. 25, 1999 - 8:55 AM PT
Elliot,
Actually, in your original question, you ask
"How can this be?"
What do you mean by that? How can what be? How can it be that he was executed? How can it be that he was surprised?
And I disagree with your analysis of his reasoning, but I've said why already and you are merely repeating yourself.
145. CoralReef - Feb. 25, 1999 - 8:57 AM PT
elliot seems to think that if the prisoner isn't sufficiently surprised he can't be executed.
146. CoralReef - Feb. 25, 1999 - 8:59 AM PT
Message #138
I am given to understand there is no solution to this, it is a paradox, but why let that stop the fun.
This prisoner is an idiot. He assumes 1) that the judge is telling the truth 2) that he will know what time it is 3) that his rule for Sunday applies backwards.
147. elliot803 - Feb. 25, 1999 - 9:02 AM PT
CalGal:
"What do you mean by that? How can what be? How can it be that he was executed? How can it be that he was surprised?"
How can it be that he is hanged unexpectedly when he has reasoned that he cannot be so hanged. That's why it's called The Paradox of The Unexpected Hanging.
"And I disagree with your analysis of his reasoning,..."
Then what flaw do you claim there is in his reasoning? Don't just repeat what you have already said, because I've responded to that. If you think there's a flaw in my response, describe it. That way we can move the discussion forward instead of just going around in circles.
148. CalGal - Feb. 25, 1999 - 9:03 AM PT
Elliot,
"Please read through my previous posts before responding, so we don't have to keep going through the same thing over and over again."
As I said, I've read your posts and they are repeating themselves. I don't see the rule applying backwards. So don't fuss yourself by typing it in again. It is possible that there is some inherent assumption you are making that you haven't spelled out that would persuade me. But as written, you have not explained how his elimination is valid. So don't bother.
If Rask is getting warm, then feel free to explain why. Or answer Message #144.
149. elliot803 - Feb. 25, 1999 - 9:05 AM PT
CoralReef:
"elliot seems to think that if the prisoner isn't sufficiently surprised he can't be executed."
No, I do not think that. Obviously, he can be executed regardless of what he thinks. That fact is irrelevant to the paradox.
150. CalGal - Feb. 25, 1999 - 9:06 AM PT
Elliot,
"How can it be that he is hanged unexpectedly when he has reasoned that he cannot be so hanged. "
Because he reasoned incorrectly, or your description of his reasoning leaves something out.
And the rest of Message #148 answers the rest of your post. I am not repeating myself because I was clear. As were you. I think you are wrong, unless there is some assumption set of which I am unaware. Which is entirely possible. So drop it, or explain why Rask is warm.
151. TabouliJones - Feb. 25, 1999 - 9:07 AM PT
The prisoner's regression only works in his favour if it works backwards ad infinitum, but, in reality, his regression only avails him to the day of sentencing and no further. By applying the regression to the limited span of six days, the prisoner is also reasoning that he must be hanged on one of these days. His reasoning simultaneously supports opposite conclusions (i.e I won't be hanged in the next six days and I must be hanged in the next six days) and it is therefore faulty.
IOW, on the day of sentencing (Mon.) his regression says: I wasn't hanged Sunday so I must be hanged either today, tomorrow, Wednesday and so on up until the sixth day. His regression can only eliminate this inevitability if he can apply it backwards another six or more days. He can't do this, however, because then he would be applying reasoning to a situation tht was alien to the one he found himself in.
Or something like that????????? Am I warm??????????????
152. elliot803 - Feb. 25, 1999 - 9:08 AM PT
CalGal:
"As I said, I've read your posts and they are repeating themselves. I don't see the rule applying backwards."
Why not? Just saying "I don't see it" is not a response to the prisoner's reasoning. In what way is the reasoning flawed? Why can't the rule be applied backwards?
153. Raskolnikov - Feb. 25, 1999 - 9:14 AM PT
I'll try. Cal: imagine the paradox as the whole "I know that you know that I know..." game from Princess Bride. If the judge executes him on the last day of the week (say Friday), the prisoner won't be surprised. The judge knows this, so won't execute him on Friday. The prisoner knows that the judge knows this, so knows he won't be executed on Friday, meaning that he won't be surprised if he is executed on Thursday. The judge knows that the prisoner won't be surprised on Thursday, so won't execute him on Thursday. The prisoner knows taht the judge knows...
The paradox is the same with any "I know that you know" game. You never know where to stop (and I know that you never know when to stop). The prisoner's logical mistake was in not realizing that he was in the middle of a paradox, so he stopping the "I know that you know" game at an arbitrary point, and was surprised when the judge continued the game for one one more iteration.
154. elliot803 - Feb. 25, 1999 - 9:17 AM PT
Tabouli:
"The prisoner's regression only works in his favour if it works backwards ad infinitum,"
Huh? Why?
"...but, in reality, his regression only avails him to the day of sentencing and no further."
Well, he can't be hanged before the day of his sentencing. I thought that was obvious, but if it isn't I'll stipulate it as an additional premise.
"By applying the regression to the limited span of six days, the prisoner is also reasoning that he must be hanged on one of these days."
No. He doesn't reason that he will be hanged on one of the following six days. That was one of the premises laid down by the judge. He is reasoning from those premises. What is the flaw in his reasoning?
"His reasoning simultaneously supports opposite conclusions (i.e I won't be hanged in the next six days and I must be hanged in the next six days) and it is therefore faulty."
No, his reasoning does not support the conclusion that he will be hanged in the next six days.
155. TabouliJones - Feb. 25, 1999 - 9:18 AM PT
#$%*#$%*
156. elliot803 - Feb. 25, 1999 - 9:20 AM PT
By the way, the paradox comes from a collection of "Scientific American" columns by Martin Gardner.
157. BunEBear - Feb. 25, 1999 - 9:24 AM PT
Let's start with the premise “The judge's description of the sentence is logically consistent.”. This premise is either True or False. Let's assume it is True. Then following Elliot's reasoning, the prisoner logically concludes that there can be no execution. However, the judge then executes the prisoner. The only possible conclusion is that our initial premise is incorrect. The judge's description of the sentence is not logically consistent, and the prisoner can make no conclusion about his future based on the judge's statement. Since this is a meta-statement about the initial premise, we can't go back and try to conclude that the sentence is logically consistent after all. The prisoner has no information, end of story. Comments?
158. Raskolnikov - Feb. 25, 1999 - 9:25 AM PT
I original saw the same problem presented in a description of one of the Socratic dialogues, only it is a friend saying "I will surprise you with a present on one day this week, but I won't tell you the day". Socrates' students then debate the whole thing.
159. dsaintg - Feb. 25, 1999 - 9:25 AM PT
Modern philosophical question:
Can intelligence be artificial?
160. CalGal - Feb. 25, 1999 - 9:26 AM PT
Rask,
I do understand the prisoner's reasoning. I also think your explanation is the flaw in the prisoner's reasoning if you accept the prisoner's reasoning.
But on Wednesday, the prisoner has no knowledge of whether he might be killed Thursday or Friday. Either is possible at that point in time, since when he wakes up Thursday, it could be a surprise that the judge chose that day instead of Friday. And because either is possible, it can come as a complete surprise that instead, the judge chose Wednesday instead.
I think this may be just a restatement of what you are saying, but what I hadn't seen in any of the explanations is that the more days there are, the more possibility of a surprise. Because he doesn't *know* a day is eliminated until it is over.
I'm also not sure the Princess Bride analogy works completely (although I see the connection) since Wesley had an out--he wasn't going to be executed, period.
161. Raskolnikov - Feb. 25, 1999 - 9:27 AM PT
I don't view that as a philosophical question so much as a semantic question. The entire argument is going to be about how you define your terms.
162. elliot803 - Feb. 25, 1999 - 9:29 AM PT
BunEBear:
Your analysis is essentially correct. There's nothing wrong with the prisoner's reasoning. The problem lies in the logical consistency of the judge's conditions.
163. elliot803 - Feb. 25, 1999 - 9:32 AM PT
dsaintg:
Yes. This relates to a question I posed earlier that no one seems interested in discussing: how do physical processes give rise to conscious experience?
164. Raskolnikov - Feb. 25, 1999 - 9:33 AM PT
Cal: The logic continues inexorably no matter how many days, hours, minutes, or seconds you break it down into, as long as there is a deadline. But you always come back to the problem that once you have logically eliminated the surprise, you now logically allow a surprise since you don't think you can be surprised, and the whole thing starts all over again, ad infinitum. From a practical standpoint, Coral is right. The prisoner is an idiot for believing that the judge's promise that it would be a surprise over-rides the promise of execution.
165. elliot803 - Feb. 25, 1999 - 9:34 AM PT
CalGal:
Re:#160
You're still lost, honey. Give up.
166. PsychProf - Feb. 25, 1999 - 9:36 AM PT
I don't know if it's dead, but as a logical positivist I want to see the body.
167. Raskolnikov - Feb. 25, 1999 - 9:38 AM PT
Actually, I think the debate hear illustrates another flaw in the prisoner's logic. He assumes that the judge is logical in playing the game as well.
168. CalGal - Feb. 25, 1999 - 9:40 AM PT
Rask,
"you now logically allow a surprise since you don't think you can be surprised"
No, I understood that and said I agree with it if you assume the reasoning is valid.
I just don't see that the reasoning is valid. Never have, and like I said to Elliot, there is clearly an assumption set inherent in the reasoning that I don't understand. Which, as I said earlier, was quite possible.
169. PsychProf - Feb. 25, 1999 - 9:42 AM PT
That clears it up.
170. vonKreedon - Feb. 25, 1999 - 9:42 AM PT
The prisioner will be quite surprised when, as he is reasoning out the regression that shows he cannot be hanged, he is taken directly to a nearby wall and shot.
171. Raskolnikov - Feb. 25, 1999 - 9:42 AM PT
Cal: the reasoning is perfectly valid.
"But on Wednesday, the prisoner has no knowledge of whether he might be killed Thursday or Friday. Either is possible at that point in time, since when he wakes up Thursday, it could be a surprise that the judge chose that day instead of Friday. And because either is possible, it can come as a complete surprise that instead, the judge chose Wednesday instead."
On Wednesday, he knows he can't be killed on Friday, since it wouldn't be a surprise. Since the judge knows this, and he knows that the judge knows this, he can't be killed Thursday either. The same logic follows for every day until today.
172. vonKreedon - Feb. 25, 1999 - 9:43 AM PT
Actually, he will probably be surprised by being hanged immediately.
173. Raskolnikov - Feb. 25, 1999 - 9:43 AM PT
vK: heh heh.
174. CalGal - Feb. 25, 1999 - 9:50 AM PT
Rask,
"Cal: the reasoning is perfectly valid."
You are missing my point. There is an assumption set I don't understand. I have always had this problem in these questions, which is why I told Elliot early on to move on--I only repeated myself with you to see if you could identify the problem in words I could understand. But you didn't, because this sentence is at the heart of the problem.
"On Wednesday, he knows he can't be killed on Friday, since it wouldn't be a surprise. "
I'm not trying to be stubborn, I am just saying that since he might be dead *before* Friday, the fact that his still being alive on Friday means his execution *then* won't be a surprise is irrelevant to me in assessing the execution surprise factor on Wednesday and Thursday.
As I said, given that the prisoner's reasoning is valid, I agreed with your analysis and I also see that given that reasoning, the initial premise is incorrect.
175. Raskolnikov - Feb. 25, 1999 - 9:56 AM PT
"I'm not trying to be stubborn, I am just saying that since he might be dead *before* Friday, the fact that his still being alive on Friday means his execution *then* won't be a surprise is irrelevant to me in assessing the execution surprise factor on Wednesday and Thursday."
Last try. It isn't irrelevant. Since he knows *now* that he can't be surprised on Friday, he can deduce that the execution can't take place on Thursday either, since then *thursday* becomes the last day of the week possible for a surprise execution. It is systematic and deductive elimination of execution possibilities, based on the given premises.
176. Slackjaw - Feb. 25, 1999 - 9:59 AM PT
great problem, elliot.
True story: in a game theory class, the professor began one lecture with this story. One of my classmates, who thought himself the next von Neumann, lamented under his breath just loud enough for all to hear, "not the prisoners' dilemma again!"
177. vonKreedon - Feb. 25, 1999 - 10:01 AM PT
Given that the prisioner has decided that he cannot be surprised by an execution then he will be surprised by the execution on any day. The execution can happen at the judges convenience.
178. Raskolnikov - Feb. 25, 1999 - 10:05 AM PT
vK: but the prisoner knows that the judge knows he shouldn't expect an execution, so he should logically then expect to be executed, and the regression keeps going...
179. TabouliJones - Feb. 25, 1999 - 10:14 AM PT
Elliot,
Ditto. Cool problem. Does this Gardner fellow have a recurring "paradox" column in the Scientific American?
180. CalGal - Feb. 25, 1999 - 10:19 AM PT
Rask,
"Since he knows *now* that he can't be surprised on Friday, he can deduce that the execution can't take place on Thursday either, since then *thursday* becomes the last day of the week possible for a surprise execution. "
Last try back, and I really do understand that in these things I'm the odd one out.
He might be dead on Friday. So the fact that *if* he is alive on Friday he can't be surprised doesn't seem to me to guarantee any knowledge about Thursday.
Incidentally, I have more than once had conversations with systems analysts who bewail their inability to understand this stuff, and they sound exactly like me! A few people have confided that the only way they got through formal logic classes was to create a set of premises that they had to accept as valid, even though they made no sense. That is undoubtedly what I would have to do as well.
181. elliot803 - Feb. 25, 1999 - 10:24 AM PT
Tabouli:
No, Gardner's retired now, but collections of some of his columns have been published as books. There were some wonderful mathematical and logical odities in them. My copies, alas, are all still in England. This all comes from memory.
Maybe it's time to resurrect the Game Show problem, which provoked a lot of discussion last time. If you know the answer, don't play. Let the others enjoy it. I completely flunked this one. Here it is:
You're on a game show in which you are faced with three doors, A, B and C. Behind one of the doors is a prize. The host of the show, who knows which door conceals the prize, asks you to choose one. You choose door A. The host then opens door C, behind which there is no prize, and asks you if you want to change your choice. Should you stick with door A or switch to door B? Or doesn't it make any difference? Justify your answer.
182. vonKreedon - Feb. 25, 1999 - 10:26 AM PT
There is also the mundane solution of wake the prisioner out of a sound sleep and hang him. Or have the Spanish Inquisition do the job, after all, no one expects....
183. vonKreedon - Feb. 25, 1999 - 10:28 AM PT
Stick with A. The host works for the corporation. Giving out the prize costs money. Corporations dislike giving away money. The host gives you an opportunity to change your mind and gives you apparently better odds (2:1 vs. 3:1). Assume that the host does not want you to win the prize then the reason for the opportunity to change your mind is really a trap. Stay with door A.
184. elliot803 - Feb. 25, 1999 - 10:43 AM PT
VonK:
Interesting theory. How did you figure those odds?
185. vonKreedon - Feb. 25, 1999 - 1:07 PM PT
Ok, right, 1:2 vs. 1:3.
186. elliot803 - Feb. 25, 1999 - 1:58 PM PT
Does anyone else care to offer an answer?
187. ChristinO - Feb. 25, 1999 - 1:59 PM PT
No reason to change your choice. The prize is as likely to be behind A as behind B.
188. ChristinO - Feb. 25, 1999 - 2:00 PM PT
Or do you need more than that?
189. TabouliJones - Feb. 25, 1999 - 2:01 PM PT
I'm with VonK and ChristinO. if you are looking for something more I'm stumped.
190. Raskolnikov - Feb. 25, 1999 - 2:18 PM PT
well, you can either take vK's approach, and assume you are being deliberately screwed, or you can assume there is a determinable method in the host's madness and that saying A B and C has some sort of association with the doors that actually get opened (such as saying A opens C, saying C opens A, and saying B opens B). If this is the case, saying "A" again would just get you C opened again for you, which you already know is a dead end.
So I would recommend switching to B or C. at best case, there is an easy transposition, and you now have a 50% chance of getting it right. At worst case, the host will deliberately screw you over no matter what you choose. As a middle case, there is no determinable logic or reason to the pattern that the host is using (random, or excessively complex enough to be as good as random on only a second turn), in which case switching to B or C is no better or worse than staying with A. Any way you slice it, you maximize your odds by choosing B or C instead.
191. ChristinO - Feb. 25, 1999 - 2:19 PM PT
Well I can see how the theory would be that you chose "A" when you had a 2 out of 3 chance of being wrong so since C is wrong A is still more likely to be wrong than B.
192. ChristinO - Feb. 25, 1999 - 2:25 PM PT
Rask,
Why would you choose C if you already know there's nothing there? The Prize has to be behind A or B.
193. DanDillon - Feb. 25, 1999 - 2:26 PM PT
Rask,
Your answer strikes me as somewhat, I dunno, retarded? How could choosing door C increase your chances of winning when door C has already been opened to reveal nothing? So your chances are now 50/50 regardless of which door (A or B) you choose; although, your odds may increase (in your own mind) if you are as skeptical of game show hosts as vonK seems to be.
194. DanDillon - Feb. 25, 1999 - 2:26 PM PT
Chris,
x-post
195. Raskolnikov - Feb. 25, 1999 - 2:33 PM PT
Dan, Chris: When you chose A, he opened C. Therefore there is not an obvious, direct connection between what you choose and what he will open. "Insanity is doing the same thing over and over again and expecting a different result", so I wouldn't choose A. I can see no logical reason for eliminating C based on existing data. It is clear that the rules are more complex than you would think. But if you want to follow a hunch and choose B, go ahead, it is as good as C and better than A.
196. elliot803 - Feb. 25, 1999 - 2:33 PM PT
Christin:
"Well I can see how the theory would be that you chose "A" when you had a 2 out of 3 chance of being wrong so since C is wrong A is still more likely to be wrong than B."
Why?
Rask:
I think you have misunderstood. The host has already opened door C, revealing nothing. Your choices are to stick with door A or switch to door B. You seem to be suggesting that your chances of winning would be improved by switching to door B, but you don't explain why, or at least if you did I can't follow your explanation.
197. ChristinO - Feb. 25, 1999 - 2:34 PM PT
I tend to have game show host paranoia as well, but since this is televised and not Vegas then it's in the show's interest for SOMEbody to win every day (Unless it's Ben Stein's Money in which case we're all screwed and may as well go home because Ben won't cheat, but he rarely has to give away his money----not that I would play Ben Stein's Money because I don't get to travel that far and 2k isn't enough money to get me to humiliate myself on TV for).
ahem.
As I was intending to say, however, I'd have to weigh my chances against the other contestants to see if I'd more likely be selected as a winner than any of them. That's a hard thing to predict, though. Is it time for an older person, male or female, nerd or stud etc. etc.
Can I just sit in the audience? I'm so confused.
198. Raskolnikov - Feb. 25, 1999 - 2:36 PM PT
elliot: look at your original post. You said that I chose A, and the host opened C. Was that a typo?
199. ChristinO - Feb. 25, 1999 - 2:38 PM PT
Elliot,
The first time you choose the odds are against you. You are more likely to have chosen incorrectly. The second time the odds are even except that you know that the door you have previously chosen was more likely to be wrong than right so it would make sense to choose the other door this time around.
200. elliot803 - Feb. 25, 1999 - 2:38 PM PT
Hint: To repeat what I said in the original description: the host knows which door the prize is behind.