paradoxes

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so your EV is 5x/4 which is greater than x.

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I don't think this is a paradox so much as faulty reasoning.

If the amount in the smaller envelope = x/2, and the amount in the larger envlope = x, then:

If you have x/2 and swap, you win x/2
If you have x and swap, you lose x/2

Seems EV neutral.

[JaBlue]

The paradoxes in the book are famous and very tough. The barber paradox was comparatively stupid and actually given in the introduction of the book. According to the author, if one could rank paradoxes on a scale of 1-10 of deepness the barber would be 1 and the paradoxes in the book would be 6+. So I had the barber paradox in mind as a warm-up.

Sainsbury says he thinks of a paradox as "an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Appearances have to deceive, since the acceptable cannot lead by acceptable steps to the unacceptable. So generally either the conclusion is not really unacceptable or the starting point or reasoning has some obvious flaw."

The task in this thread will be to try to figure out if the conclusion of the paradox is not really unacceptable or there is something wrong with the premises or reasoning.

Nobody really went for the barber paradox but since it seems less interesting to the forum than others, I will answer it: the barber cannot exist. Because the conclusion is unacceptable, it is impossible for such a barber to exist. All details except those concerning the barber are superfluous and distract you from the situation at hand.


So on to attempt #2.

Someone hinted at the liar's paradox, which goes like this:

One version of the liar's paradox
Consider a man who says "what I am now saying is false." Is what he says true or false? The problem is that if he speaks truly, he is truly saying that what he says is false, so he is speaking falsely; but if he is speaking falsely, then, since this is just what he says he is doing, he must be speaking truly. So if what he says is false, it is true; and if it is true, it is false.

And please don't introduce other paradoxes in the middle of discussing one. I don't mind if you have one you'd like to talk about, but save it for when we're at a suitable stopping point for our current one.

[josh_x]

I geuss a conclusion might be that it is logically impossible for someone to always tell the truth or to always lie?

[daryn]

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I geuss a conclusion might be that it is logically impossible for someone to always tell the truth or to always lie?

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no.

[xorbie]

JaBlue,

Given your "solution" to the first paradox, I'll just say that his statement is incomprehensible. Is the statement "All round squares are red" true or false? There's no truth value to the statement whatsoever.

[JaBlue]

Xorbie,

I don't see the answer as being analogous to the first, for it is perfectly possible for any person to say "what I am now saying is false," while it is not possible for a barber to have the property of shaving all and only persons who do not shave themselves for the very reason that is the conclusion of the first paradox, namely "who shaves the barber?"

Maybe your objection is really that the question "is what he says true or false?" is incomprehensible in this situation.? In that case I think you have to say what truth and falsity are and why they apply to some things and not others for you to be able to say what they do not apply to.

[xorbie]

JaBlue,

I'm not really sure "this statement is false" is a statement of any sort that holds meaning. There's just no content whatsoever.

[JTrout]

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I geuss a conclusion might be that it is logically impossible for someone to always tell the truth or to always lie?

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no.

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How about,
It is impossible for someone to always tell the truth or to always lie, and make the statement "I am lying."


Concerning the barber paradox (which I realize has been answered), I like the answers:
1. the barber is a woman (barber-ette?)
2. the barber is 10 yrs. old.

[TheIrishThug]

Hold it Santa! Consider this: you are programmed to destroy the naughty, but many of those you destroy are in fact nice. I submit to you, that you are in fact naughty, and that, logically, you must destroy yourself.

[maddog2030]

I agree with xorbie that the statement is meaningless. Much like a statement along the lines "X exists but doesn't exist".