The unexpected (?) hanging

[loinburger]

A man is sentenced to be hanged, and is told that a. he will be hanged on the following week, b. he will be hanged at noon, and c. he will not know in advance on which day he will be hanged.

The man reasons that he cannot be hanged on Saturday, because on Friday afternoon the man would know in advance that he was to be hanged on Saturday. Likewise, the man cannot be hanged on Friday, because on Thursday afternoon the man would know in advance that he was to be hanged on Friday (for if he weren't hanged on Friday then he would know in advance that he was to be hanged on Saturday). Following this line of reasoning, the man realizes that he cannot be hanged on any other day of the week, and is convinced that he has escaped punishment.

The following week, they hanged him on Wednesday.

What the hell just happened?

Some possible ways to resolve the paradox I've come across:
a. The prisoner is correct -- logically, he shouldn't have been executed.

b. The prisoner cannot make a valid inference about his Saturday execution until Friday afternoon. In other words, when Friday afternoon rolls around he can say "logically, you can't execute me on Saturday!" However, prior to Friday afternoon he's not allowed to (logically) say this.

c. The prisoner's reasoning is self-defeating. If he fails to conclude that he cannot be executed on, e.g., Saturday, then he will be caught completely unawares when he is executed on Saturday. If he successfully concludes that he cannot be executed on Saturday, then he will still be caught completely unawares when he is executed on Saturday. ("But... you said that I wouldn't know in advance the day of my execution!" "Did you expect us to execute you today?" "Yes!" "Then logically we shouldn't be executing you, right?" "Yes..." "Then logically you didn't expect us to execute you today, therefore we're executing you." "Goddammit!")

d. Suppose the executioner flips a coin every morning -- if it comes up heads then he'll execute the prisoner, otherwise the prisoner gets a 1-day reprieve. There is about a 98.5% chance that the prisoner will be executed prior to Saturday, and the execution will come as a surprise to the executioner and logically will also come as a surprise to the prisoner (if the executioner isn't 100% certain that he's going to kill the prisoner, then how can the prisoner be 100% certain?). So, there's about a 1.5% chance that the execution will happen on Saturday and won't come as a surprise (assuming that the executioner doesn't flip a coin on Saturday and hold over the execution until the following week on a 'tails' result), and about a 98.5% chance that the prisoner will be executed and won't have foreseen the date of his execution. Thus the stated conditions of the prisoner's execution are (mostly) true.

[Japher]

I don't get it.

[KrazyHorse]

A man is sentenced to be hanged, and is told that a. he will be hanged on the following week, b. he will be hanged at noon, and c. he will not know in advance on which day he will be hanged.

The resolution is fairly straightforward: (a), (b) and (c) together are logically incompatible. These cannot all be postulates of any formal logic system (with rules of logical inference as generally understood). You can lay the contradiction bare by shrinking the week down to a single day. At 6 am you are told the following:

d) You will be hanged today
e) You will be hanged at noon
f) You will not know in advance when you will be hanged

Logical derivations based on a set of postulates which are internally inconsistent are not to be trusted.

[KrazyHorse]

Note that you can easily remove the logical contradiction in the original problem by restating as follows:

a') If you are hanged you will be hanged in the following week
b') If you are hanged you will be hanged at noon
c) You will not know in advance that you are to be hanged

[KrazyHorse]

Anybody who is used to formal logic should see this straight off the bat.

[KrazyHorse]

The resolutions given above as (a) (b) and (c) (not to be confused with postulates labeled the same way) are simply retarded.

(d) is a better "resolution" (it's similar to what I posted when I changed the postulates mildly) and does point to the simple fact of logical contradiction in postulates, but does not explicitly state it. I will assume that you put it this way in order to preserve the apparent "paradox"

[SlowwHand]

You are the so pathetic. It's impossible for you complete a thought.

[KrazyHorse]

I will assume that slowwhand just said something retarded, as it's more than likely that he either doesn't see the "paradox" OR is now hopelessly confused by it.

[Elok]

I think Marilyn Vos Savant went after something like this once. Forget what her solution was. Who takes the time to think this stuff up, anyway?

[KrazyHorse]

Marilyn vos Savant is a ****. Her only job is writing up solutions to well-known brainteasers, and she's not particularly good at that.

[KrazyHorse]

I'm interested to know what the hell people mean by claiming (b)

[loinburger]

I'm surprised at how popular (b) is. To me it's the absolute worst answer as it denies induction as a valid tool.

[Kuciwalker]

the death penalty is like nazi germany

[Kitschum]

The prisoner is put in an isolation cell with minimal outside contact for the time up to his execution. He will be unable to keep track of time, thus not knowing in advance (and likely not afterward either) on which day he will hang.

[Kitschum]

the death penalty is like nazi germany

No, it's like the Spanisn inquisition...