paradoxes - Page 2

FoxwoodsFiend · #11 02-02-2007, 03:12 AM

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This thread reminds me of the Star Trek episode where Kirk made the android's head blow up by telling him:

Everything I tell you from this point forward is a lie; I am lying.

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philosophers refer to this as "the liar's paradox." weird huh?

GuyOnTilt · #12 02-02-2007, 03:14 AM

I like the idea behind this thread, but I don't think it will work well with paradoxes like this. To solve these you need to be pretty well versed in set theory, and if you are you've already learned all about Russell's Paradox.

b0000000000m · #13 02-02-2007, 03:26 AM

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I like the idea behind this thread, but I don't think it will work well with paradoxes like this. To solve these you need to be pretty well versed in set theory, and if you are you've already learned all about Russell's Paradox.

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Now, Russell's is a quality paradox. I remember musing on that one for a week straight in Intro to Metaphysics & Epistemology.

milliondollaz · #14 02-02-2007, 03:34 AM

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Now, Russell's is a quality paradox

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out with it!

just guide the discussion better. it's really hard not to wikipedia this stuff...i'm holding out though

GuyOnTilt · #15 02-02-2007, 03:42 AM

[ QUOTE ]
[ QUOTE ]
I like the idea behind this thread, but I don't think it will work well with paradoxes like this. To solve these you need to be pretty well versed in set theory, and if you are you've already learned all about Russell's Paradox.

[/ QUOTE ]

Now, Russell's is a quality paradox. I remember musing on that one for a week straight in Intro to Metaphysics & Epistemology.

[/ QUOTE ]
OP's is pretty much an imperfectly worded version of Russell's Paradox. ZFCftw.

Note: I have no training in and know very little about set theory or ZFC, but like to read about such things anyway. [img]/images/graemlins/smile.gif[/img]

b0000000000m · #16 02-02-2007, 03:50 AM

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Now, Russell's is a quality paradox

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out with it!

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Is the "set of all sets that do not contain themselves" a member of itself, or not?

GuyOnTilt · #17 02-02-2007, 04:22 AM

[ QUOTE ]
[ QUOTE ]
Now, Russell's is a quality paradox

[/ QUOTE ]

out with it!

just guide the discussion better. it's really hard not to wikipedia this stuff...i'm holding out though

[/ QUOTE ]

Russell's Paradox is:

Does the set of "all sets that do not contain themselves as members" contain or not contain itself as a member?

The equation would be:

{x | x not in x}

The Barber's Paradox is an analogy of this.

El Diablo · #18 02-02-2007, 04:22 AM

Ja,

I'm drunk right now and not in the mood to focus, but yeah, this is a fantastic thread idea. Nice. If there are still open questions by tomorrow I'm on it.

Zeno · #19 02-02-2007, 04:39 AM

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The equation would be:

{x | x not in x}

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I'm bad on symbolic nomenclature...but wouldn't the equation (symbolism) be:

{X | X not in X | }

-Zeno

alphatmw · #20 02-02-2007, 04:42 AM

i love paradoxes. here's one of my favorites.

i give you and your friend 2 envelopes, each with a mystery amount of money. one envelope, however, has twice the other one. before you open yours, i offer you to switch with your friend. should you?

if yours had the bigger amount, you end up with x/2. if he had the bigger one, you end up with 2x. so your EV is 5x/4 which is greater than x. therefore, you should switch.

now you have the other envelope. should you switch back? once again the answer is yes. is it logically sound that you are increasing your EV everytime you switch envelopes?