The Problem of Evil and Switching Doors, Continued
Good news, bad news. The bad news is that we still don't have a winner, per se. I'm well aware that winning isn't everything, it's the only thing. I promise there will be a winner. And the good news is that we're closer than ever to figuring out how to pick a winner. As for evil: If only the problem were so easy to solve.
My father's response (for those of you more concerned with evil than the location of the Skylark, scroll down):
***
The Monty Hall problem:
The problem is devilishly ingenious, and its solutions are counter-intuitive. Grendel remarks that he (or she) is fascinated by the problem. I was too when I first heard it more than twenty five years ago, but I now suspect that it is not a problem that goes anywhere. It reveals only the importance of spelling things out precisely, even in the case of very elementary probabilities. No mathematics is really involved in the problem: Tabula Rasa: You have nothing to worry about.
Intuition suggests, of course, that there is no gain in switching. Counter-Intuition suggests that there is, and in the informal literature about this problem, Counter-Intuition is the clear winner.
I suspect that there is no real conflict between Intuition and Counter-Intuition, but everything depends on the way the problem is posed. R. Craigen -- I'm with you.
Here is the common argument for Counter-Intuition: If [Pr(B = 1) or (C = 1)] = 2/3 and C = 0, then Pr(B = 1) must be 2/3.
Having agreed with Intuition, I also agree with Counter-Intuition.
I scruple only at the claim that there is a conflict. Stay where you are is the correct answer to the problem as Claire posed it, but switch like mad is the correct answer to a very similar problem.
That similar problem: Should you switch from A to B or C, if C = 0 or B = 0?
The answer is but, of course. You stand to gain two times out of three, as Mark Wilson, and many others, insist.
But there is a world of difference between switching to B if C = 0, and switching to B or C, if B or C = 0. In the first case, the odds are 1/2, in the second 2/3. Every simulation online makes the second assumption, as Cas Balicki observes. But that is not the assumption of the game as Claire presented it.
Think of it this way. A fair coin is flipped twice. The possible outcomes – the sample space – are HH, HT, TH, TT. Each point in this space has a probability of 1/4. The probability of (HT or TH) is 1/2.
But the probability that XT = HT is 1/4, and not 1/2. This is parallel to the Monty Hall case where once C = 0 is specified, the odds change from 2/3 to 1/2.
No conflict, no problem. A number of commentators have made the same (or a closely related) point, DietBomb and Chris Delecom especially. On the other hand, Think So offers what seems to me an invalid argument, although a suggestively invalid argument. If I flip a fair coin just once, the odds that it will land on heads are nicely put at 1/2. If it lands on tails, the odds in favor of heads drop at once to zero. This is not quite the Monty Hall case, but Think So is right in suspecting that there is a latent tension between the assumption that the probabilities are all equal and the assumption that one door has been opened and revealed to be empty. This is a point that has been pursued in the literature. CandE makes it well.
The Problem of Evil
Now about evil. How can a good God permit evil? For those like Mr. Labeit disposed to scruple at the word evil – disposed, I have noticed, to scruple at any word – there is a ready substitute in suffering, and if the first is problematic, the second is not. The stuff is everywhere. Just look around.
Martin C. considers the following assumptions:
1. God exists and is all powerful.
2. God exists and is perfectly good.
3. There is evil in the world.
and asks readers to "pick (at most) two."
The result is a very familiar puzzle in which no matter the assumptions picked, some dissolution of credulity is the result. Thus if God is good, he would not permit suffering unless he were incapable of preventing it. Either he is not good or he is not capable. What, then, is his use?
Does this argument lose its underlying force once God is dismissed from all further considerations? It would certainly appear so, since the argument is so often taken as a defining weakness of any theistic position.
But the facts of suffering are what they are. There is no dispute about them. And as facts are facts, they require an explanation. An explanation often favored by, say, Richard Dawkins or Christopher Hitchens, is that that is just the way things are. The universe is blind, pitiless and indifferent. Get used to it.
Whereupon a regress commences. Why is the universe blind, pitiless and indifferent? It could so easily have been otherwise. If the universe could not have been otherwise, as a dilute Leibniz might have argued, where is the argument that this is so? It seems hardly an imaginative stretch to think of a number of radical improvements in its design. But whether the universe is crummy by design, or crummy by accident, the effect in either case is to augment one's natural anxiety about the universe in which we find ourselves. The argument bites its own tail. The more that it is followed, the more there is reason to be apprehensive so that in addition to suffering, there is suffering about suffering.
There is in this little regress something of note. A problem said to be characteristically afflicting to religious believers has reappeared in a context which, by definition, has no religious content. It follows that the problem of evil or suffering is not simply a problem for those accepting the existence of God.
It is what it should seem: It is a problem.
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Comments :
Mar '11
Re: The Problem of Evil and Switching Doors, Continued
I know what I'm gong to do on my next appearance on Let's Make A Deal. I'll switch. That way, if Professor Berlinski is correct, I've done myself no harm. And if he's incorrect, I've increased my odds of winning substantially. This probability stuff is easy once you get the hang of it.
May '11
Re: The Problem of Evil and Switching Doors, Continued
The problem of why God permits suffering can easily be resolved in a number of ways, none of which are accepted by any religion. My favorite is that God creates worlds like a novelist writes books. Any good novel (and God wouldn't be a hack, would he?) includes villains as well as heros, and includes pain and suffering. The novelist might actually love the characters he has created -- even the villains. But he doesn't write a novel where no one feels pain and nothing bad ever happens. That would be dull.
Another solution is the Empathy 101 hypothesis. God offers our immortal soul the opportunity to enter this world for a brief time, in order to experience suffering and learn empathy. We sign up for the class. Obviously, in order for this to work we have to forget (during class time) that our immortal soul will return to a higher realm shortly. Then we can learn from our experience in this world.
Apr '11
Re: The Problem of Evil and Switching Doors, Continued
The key to this delay is the assertion that tout le mond tackled the problem the same way, but that way is not the problem "as Claire stated it". But to me
"There are three doors, behind one of which is the Skylark. Say you pick Door 1. I open Door 2 to reveal a Glory Badge. Do you want to switch your pick? "
is the classic problem. The Berlinskis quibble that Claire didn't say that she knows where the car is. I maintain that it doesn't matter what Claire knows, except for showmanship purposes. Meanwhile, Herr Doktor Berlinski's discussions glide allusively over this allegedly crucial alleged difference between the two statements of the problem.
I DON'T KNOW WHAT THE DIFFERENCE IS.
So, I would like to see the two statements of the problem en clair and an explanation (if it is still maintained that it matters) that Claire's knowledge changes the problem.
Edited on Oct 14, 2011 at 6:16amNov '10
Re: The Problem of Evil and Switching Doors, Continued
Re. God and suffering, there's lots of ways to argue it, but (within the 200 word limit) let's just take the simplest and assume there's free will and the most fundamental religious model. Your suffering, and the time you suffer here on earth, no matter how bad, are both finite. After all, your suffering can always be worse, and you don't live forever. Get through it well, and your reward is infinite bliss for an infinite amount of time. The relative importance of your suffering relative to your possible reward is the product of two finite values divided by the product of two infinite ones - i.e., zero.
As for the regress, I would ask you to go beyond imagining, and try and demonstrate the nature of such a possible universe. I'm not asking for proof, I just find Lennonesque imaginings irritating if there's no effort at substantiation, and I really need my coffee.
Jan '11
Re: The Problem of Evil and Switching Doors, Continued
What, then, is his use?
It follows that the problem of evil or suffering is not simply a problem for those accepting the existence of God.
With respect, I disagree.
There's a distinction between the existence of God and the attributes we associate to him. In the problem of evil, it's assumed here that denial of his attributes is a denial of existence. But that doesn't follow.
To explain, suppose we said that the Yankees exist, and ...
Denying one attribute doesn't disprove or reduce the credulity of the Yankees' existence.
In the same way, we have a statement that God exists. Then we have two attributes which (some argue) cannot both be true. Does the contradiction (or confusion) about the attributes deny existence? Isn't it just as likely (if not more) that the conflict about the attributes is due to our ignorance? After all, we came to the conclusion about God's existence long before any theology about infinite power or goodness.
Is God worthless unless he has infinite power? Why? So he can jump when we need something?
Nov '10
Re: The Problem of Evil and Switching Doors, Continued
Yah, what about that... it appears that in this Animal Farm some animals are not handicapped by that limit.
Nov '10
Re: The Problem of Evil and Switching Doors, Continued
KC Mulville
Is God worthless unless he has infinite power? Why? So he can jump when we need something? · Oct 14 at 7:06am
Perhaps not worthless just reduced to a Zeus or an Owden. Omnipotence is an essential attribute of the Christian God Who "Works all things after the counsel of his own will." (Paul to the Ephesians). A universal affirmative.
How about this one: "Shall there be evil in a city, and Jehovah not have done it?" (Amos). The Hebrew here connotes calamity for evil. That is from a human perspective.
What is evil from God's perspective? Get that right and things become clear.
Jun '10
Re: The Problem of Evil and Switching Doors, Continued
The other possibility is that God is both good and capable. If then, He allows suffering, then suffering has a purpose. If suffering has no purpose, then the condition is merely an unfortunate byproduct of something gone awry. What could be so important to God that He would allow His creatures to suffer?
The answer is free will. God might have created automatons incapable of defying Him, but He didn't. The Creator gave mankind the ability to discern between good and evil and a choice in the matter. Evil is therefore a result of bad choices.
Suffering is a byproduct of making poor choices that run contrary to God's intended purpose. If all men would align themselves with God's purpose, then the problem of evil would largely disappear. But it's a choice so important to our standing before God, that even He does not interfere.
Apr '11
Re: The Problem of Evil and Switching Doors, Continued
Robert Promm
Yah, what about that... it appears that in this Animal Farm some animals are not handicapped by that limit. · Oct 14 at 7:32am
I could tell you, but then I'd have to kill you.
And Blue Yeti might fix it.
Jan '11
Re: The Problem of Evil and Switching Doors, Continued
When it comes to natural evil (earthquakes, novas, etc.), I have little trouble accepting a universe in which such violence exists; because without it, life would be impossible.
When it comes to personal evil, I accept that God gave us freedom, and I have no trouble believing that God will respect that freedom at all costs.I don't see that as a lack of ability; it's a choice. The fact that others wouldn't have made the same choice as God says as much about them than it does about God.
The only item that would trouble me is if God himself initiated the personal evil. But since I'm not a fundamentalist, I'm not chained to such accusations against God in the Old Testament. (The New Testament has an entirely different picture of a loving father.)
I understand the reservation about the "problem of evil." I deny that it's a stumbling block.
Oct '10
Re: The Problem of Evil and Switching Doors, Continued
I'm no mathematician and I'm not very bright, so I should tread lightly here, I know. But what the hey!
“But the probability that XT = HT is 1/4, and not 1/2. This is parallel to the Monty Hall case where once C = 0 is specified, the odds change from 2/3 to 1/2.”
I disagree. The odds change to 1-in-2 only if Monty Hall can choose to, and can choose not to, switch the items that are hidden behind the remaining two doors, and he doesn’t tell the player whether he switched the items. Then, and only then, do the odds become 1-in-2.
If Monty must leave things where they were at the beginning of the game, then knowing that C=0 does nothing to the probability, the likelihood, that the player originally chose a goat. Originally. That's the key. That likelihood - that probability - remains 2-in-3, and the probability that the player originally chose a car remains 1-in-3.
He is more likely to have chosen a goat than a car originally, regardless of the fact that he now knows that C=0.
Switch doors.
Edited on Oct 14, 2011 at 8:59amRe: The Problem of Evil and Switching Doors, Continued
If the problem as originally posed was "Do you want to switch your pick?," then even if Claire didn't say she knew which door the car was behind, I must make an assessment whether I think she did. Different folks will make different assessments about this and, consequently, come up with different final answers. But I think it is very likely that she did know. In fact, I (completely subjectively) assess probability 0.9 that she knew and her strategy coming in was: If the person picks a door with the car, randomly choose between the two other doors to show a glory badge; if he picks a door without the car, choose whichever door of the other two doesn't have the car, and show that. And I assess probability 0.1 that she doesn't know and picked one of the other two other doors at random. And, having made those assessments, Bayes' rule tells me that the conditional probability that the car is behind the door I chose is now approximately .3448 (draw the full probability tree), so I switch.
But that's me. Make different assessments about Claire, and you may make a different choice.
Re: The Problem of Evil and Switching Doors, Continued
(Continuing, briefly...) In this respect, Basil has the best answer. It isn't impossible to have assessments about what Claire is doing that leads to a conditional probability that the car is behind your original choice with probability greater than 0.5, but it is hard; those are pretty strained beliefs. Some models of the situation say it is still 0.5, others say it is less. So the conclusion Change your door is pretty robust to the model you build, to decide what do to.
May '11
Re: The Problem of Evil and Switching Doors, Continued
Of course, if Monty knows that you have already picked the car, and is showing you one door in an effort to get you to change your mind...
Mar '11
Re: The Problem of Evil and Switching Doors, Continued
That's the "Monty from Hell" scenario discussed in the fascinating Wikipedia article on the subject linked to in the earlier thread by R. Craigen.
Oct '10
Re: The Problem of Evil and Switching Doors, Continued
Basil Fawlty: That's the "Monty from Hell" scenario discussed in the fascinating Wikipedia article on the subject linked to in the earlier thread by R. Craigen. · Oct 14 at 10:11am
But if you know about Monty from Hell (which you would, because you'd have watched the show many times before being on it...no?), then you'd stick with your door when he offers you the chance to change. It's almost like, if you meet Monty from Hell the probability that you chose the door with the car is 1.
Bottom line is, you can't trust what you do or don't know about Monty and his motivations, his knowledge about the doors, etc. All you can know is that with your original choice you had a better chance of choosing a goat than a car, and if you're given the chance to change to the other door (after the 3rd door is shown to have a goat), you change.
Apr '11
Re: The Problem of Evil and Switching Doors, Continued
That's why the odds are just 2/3 for switching. If Monty gave you the car if you picked it initially, the odds for switching would be 100%.
BTW, I never watched the show, but my wife recalls from her childhood that if you picked the goat, you got the goat. No second chance.
But if you picked the car, he offered you the chance to switch to the bedroom suite. If he didn't, offering you the switch would always indicate that you had picked the bedroom suite.
Edited on Oct 14, 2011 at 10:31amJun '10
Re: The Problem of Evil and Switching Doors, Continued
The natural world is not evil, merely indifferent. You cannot have evil without the ability to discern it and a free will capable of either embracing or rejecting it. My cat is not evil for torturing mice. He makes no moral distinctions as he goes about doing what nature created him to do. He's an automaton.
Michael Vick committed evil acts when he tortured dogs because his moral sense informed him the act was wrong. He did it anyway. Voluntary participation in evil makes one sinful. To claim Michael Vick is merely the product of his upbringing, predisposed to acts of violence, is to deny him his humanity. Something leftist "thinkers" do all the time when they claim that the universe is merely a mechanism and we are the hapless products of random chance.
Oct '10
Re: The Problem of Evil and Switching Doors, Continued
My own religion's response to "why can evil exist if God does" is that God gave humans moral agency (we can choose for ourselves) so we can learn. It's not that He's incapable, he just won't violate the free will of human beings.
Mar '11
Re: The Problem of Evil and Switching Doors, Continued
Had Vick's moral sense informed him that torturing dogs was not wrong, would that make torturing dogs not evil?
~Paules
The natural world is not evil, merely indifferent. You cannot have evil without the ability to discern it and a free will capable of either embracing or rejecting it. My cat is not evil for torturing mice. He makes no moral distinctions as he goes about doing what nature created him to do. He's an automaton.
Michael Vick committed evil acts when he tortured dogs because his moral sense informed him the act was wrong. He did it anyway. Voluntary participation in evil makes one sinful. To claim Michael Vick is merely the product of his upbringing, predisposed to acts of violence, is to deny him his humanity. Something leftist "thinkers" do all the time when they claim that the universe is merely a mechanism and we are the hapless products of random chance. · Oct 14 at 10:33am