Paradoxes and Fallacies

[winterHLepsilon]

Do ya like fallacies and paradoxes? Like to share them?

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*Hypotenuse Leg*
HL--^H^e^L^en
A girl from Guangzhou, China, Asia

[Lepton]

I've never made a post about paradoxes in my life.

[i_h8_evil_stuff]

I am lying.

[Chuck]

This statement will never be proven to be true.

[Simian100]

The above statement will never be proven to be false.

[Dread Pirate Westley]

This statement is true...Wait. Damn.

[Legend of Tenshi]

He doesn't know he is omnicogniscient?

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I'm looking for a good sig, wanna help?

[Jedo the Jedi]

One time, in a Calvin and Hobbes book, Calvin creates a clone of his good side. Calvin has the good clone do everything for him until the clone can't take it anymore. The clone starts to describe how he is going to hurt Calvin, when he vanishes because he had a bad thought. How's that for a paradox!

[kevinatilusa]

Pairaducks

[Courk]

Pairadocks.

[This message has been edited by Courk (edited 05-30-2004 12:37 AM).]

[kevinatilusa]

Going back to the original subject, the paradox I found most astounding when I first heard of it was the Banach Tarski paradox: A 1 inch solid sphere can be cut into 5 pieces, and the pieces can be rotated and put together to form 2 1 inch solid spheres.

As a corollary, it is impossible to define a "volume" function on every set in 3D such that
(1) The volume of the unit sphere is nonzero and finite
(2) Translating a set or rotating it won't change its volume.
(3) If a set is made up of two disjoint sets, the volume of the larger set is the sum of the volumes of the two smaller sets.

[This message has been edited by kevinatilusa (edited 05-30-2004 02:54 AM).]

[winterHLepsilon]

Everybody knows Zeno's paradox? And Cantor's? And Russell's? They are classicals.

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*Hypotenuse Leg*
HL--^H^e^L^en
A girl from Guangzhou, China, Asia

[Antrax]

Yes, yes and yes.

How about the pop quiz paradox? A professor tells his class he's going to surprise them with a pop quiz next week. The students try to figure out when the quiz will take place. It can't be on Thursday (last day of the school week) because if Sun-Wed goes by without a quiz, and the quiz is on that week, then it has to be on Thursday, and then it's not a surprise. So, Thursday is out. However, that means that Wednesday is also out. Otherwise, when Wednesday comes by, the students will know they have a quiz today, because if they won't, they'll for sure know it's tomorrow, and then they won't be surprised. So Wednesday is out as well. Which means Tuesday is out. Which means Monday is out. Which means Sunday is out (this story takes place in Israel =P), which means the professor will never be able to pop-quiz his students.

Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[extropalopakettle]

That's always been my favorite. A lot has been written on it, including Martin Garner's book The Unexpected Hanging.

http://rec-puzzles.org/new/sol.pl/logic/unexpected

[Antrax]

Very well-presented article, and it also contains info on other famous paradoxes.
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Chuck]

Hempel's Ravens is another good one.

[Vegetable]

Zeno's got alot of examples that are called paradoxes, but none of them are really paradoxes at all. They just backs up Parmenides' theory that motion is impossible and our perception of motion is illusory.

[Antrax]

Er. I'm sure you mean "they back up the fact that the greeks had no calculus".
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Hitchhiker]

From http://www.fact-index.com/

"The Ship of Theseus" is a replacement paradox, also known as Theseus' Paradox.

According to an ancient Greek legend, Theseus had a warship that was preserved as a historical relic by the Athenians. Some of its boards rotted and had to be replaced. After many, many years, many such replacements occurred. Eventually, none of the original boards were present.

Was it still the Ship of Theseus?

[pokerfaced]

One paradox I thought of recently:

Suppose you are playing Simon Says. "Simon says disobey this order." What do you do?

[Antrax]

Don't read this post.
Antrax

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"Look, that's why there's rules, understand? So that you think before you break 'em" - Lu-Tze, Thief of Time

[Chuck]

For that matter, what do you do if "Simon says obey this order"?

[Termital]

Does "We learn from history that we do not learn anything from history." count?

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Yearn brightly

[Legion]

Let's not forget D'Alembert

[Vinny]

This sentence is non-self descriptive.

[Vinny]

[Vinny]

[The Doctor]

[Vinny]

There's no such man that can do anything, because he can't create a rock that he can't break.

[mudbuck]

(buzz)

Vinny, how about a radioactive rock that kills you before you had the chance to break it?

[mudbuck]

*April Fools^*

[winterHLepsilon]

And you can never have a heap of sand. Know this one? At first I didn't get an inkling what it was talking about but finally the idea sank in.

[DrJones]

Originally posted by vinny:

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There's no such man that can do anything, because he can't create a rock that he can't break.

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He may create a rock that just stops being a rock when it's going to break.

I would argue that "a rock that can't be broken by a man that breaks any rock" isn't well defined as a concept. If you want to put incorrect concepts in your example, why don't just say: "There's no such man that can do anything, because he can't create a rock that isn't"?

[jesternl]

Ahhh Sorites, one of my favorites.

- One grain of sand is not a heap.
- adding one grain won't make it a heap.
- A heap of sand does not exist.

[This message has been edited by jesternl (edited 06-18-2004 01:08 PM).]

[dave10000]

jesternl --

I agree that Sorites is great to mull over. It is the basis for many other paradoxes, and it comes up in the law (my field) all the time.

I'd tweak your second statement, though, as follows, to clarify (without changing your intent):

- One grain of sand is not a heap.
- Adding one grain to a non-heap won't make it a heap.
- A heap of sand does not exist.

Sorites (among other things) has led me to the conclusion that most paradoxes can be resolved by: "Well, that depends upon what you mean by ___________." (Or, equivalently, "Under one definition of ______________, yes, and under another definition, no."

For example:

Ship of Theseus: "Depends on what you mean by "the same ship.""
Unexpected Hanging: "Depends upon what you mean by "unexpected.""
Sorites: Which of the statements is incorrect depends upon what you mean by "heap"

[Chuck]

Heaps of sand exist because I can see them.
If you take one grain of sand off a heap it is still a heap.
So one grain of sand is a heap.
Come to think of it, no grains of sand is also a heap.

[mathgrant]

Originally posted by Chuck:

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Heaps of sand exist because I can see them.

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Poor Chuck is having hallucinations.

[extropalopakettle]

A similar argument can be applied to speciation. No single mutation makes for a different species, therefore new species can't evolve by repeated mutations.

[Beartalon]

Which means we're all sharing the same gene pool as you, which is not necessarily a bad thing.

[winterHLepsilon]