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foreva.infiniti
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Grab a few and tell me your thoughts on these paradoxes.

1. Does the set of all those sets that do not contain themselves contain itself?

2. Should one tolerate intolerance; if intolerance would destroy the possibility of tolerance?

3. What would happen if an unstoppable force hit an immovable object?

4. Since the universe is not infinitely old, it cannot be infinite in extent.

5. Why is the night sky black if there is an infinity of stars?

6. Increasing the food available to an ecosystem may lead to instability, and even to extinction.

7. Which came first, the chicken or the egg?

8. If all truths are knowable, then all truths must in fact be known.

9. If God knew how we will decide when he created us, how can there be free will?

10. Diamond-water paradox (or paradox of value) Water is more useful than diamonds, yet is a lot cheaper.

11. When two countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between them increases.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
kcg5
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These are not paradoxes, just fun word games

1-yes
2-no
3-their would be some kind of reaction to the immovable object, equal and oppsite reaction and all that
4-not infinite, it is forever expanding
5-teh number of stars do not begin to compare with blank space? why is the sky blue?
6-true.
7-who cares
8-false
9-there is no god
10-I don't see this, again, as a paradox. it makes sense, who cares about diamonds if you are hungry?
11-they are smart, they realize MAD. Otherwise this is a good question.
Nobody expects the spanish inquisition!!!!!



"History will be kind to me, as I intend to write it"- Sir Winston Churchill
Magnus Eisengrim
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1. This is a true paradox, usually called Russell's Paradox.
2. Locke's "Letter concerning toleration" deals with this.

3-5 deal with assertions and are not very troubling. But others may have some fun with them.

6. This needs some clarification.
7. Eggs. They were here for millions of years before chickens showed up.
8,9. See 3-5.
10. Not a paradox, but an observation that usefulness does not perfectly correlate to price.
11. Is this true?
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
Pakar Ilusi
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I'll just answer a few.

Number 5. Light from the most distant stars haven't arrived. Sounds crazy but that's really it.

Number 9. I asked this question here once, got the thread deleted. Really.

Smile
"Dreams aren't a matter of Chance but a matter of Choice." -DC-
Magnus Eisengrim
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6. I don't see the paradox. If it occurs unders some circumstances (and it seems plausible that it could) how is it a paradox. It may be surprising, but it hardly paradoxical in the normal sense of the word.

10. As above. It may seem weird, but it isn't paradoxical at all.

Maybe you are not using a standard definition of paradox.

Compare these to 1. Russell's paradox. To see the issue with Russell's paradox,

Let N be the set of all sets that do not contain themselves as members. If N is a member of N, then it must contain itself as a member and not be a member of N. If N is not a member of N, then it must be a member of N. Either way there is a contradiction, making this a true paradox.

6. and 10. are merely counter-intuitive.

John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
Magnus Eisengrim
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I doubt anyone cares, but the source article for the "Paradox of Enrichment" is here. The author uses the word "paradox" exactly once: in the title. Nowhere in the article does make any effort to show a true paradox, but rather examines predator-prey equations to show that increasing food supply to a population can theoretically lead to counter-intuitive consequences.

And here is a nice description of the so-called paradox of value. The article is interesting because the author claims that Galileo recognized the puzzle a century and a half ahead of Adam Smith. Still looks more like a puzzle than a paradox to me.

But let's get the conversation rolling.

John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
foreva.infiniti
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Maybe if I break the two down you will see the paradox, magneto.

Paradox of value: the apparent contradiction that, although water is on the whole more useful, in terms of survival, than diamonds, diamonds command a higher price in the market. Think more along tha lines of marginilism. The theory of marginal utility, which is based on the subjective theory of value, says that the price at which an object trades in the market is determined neither by how much labor was exerted in its production, as in the labor theory of value, nor on how useful it is on a whole (total utility). Rather, its price is determined by its marginal utility. The marginal utility of a good is its least important use to a person. The reasoning goes like this. If someone possesses a good, he will use it to satisfy some need or want. Which one? Naturally, the one that takes highest-priority. Eugen von Böhm-Bawerk illustrated this with the example of a farmer having five sacks of grain.[6] With the first, he will make bread to survive. With the second, he will make more bread, in order to be strong enough to work. With the next, he will feed his farm animals. The next is used to make whisky, and the last one he feeds to the pigeons. If one of those bags is stolen, he will not reduce each of those activities by one-fifth; instead he will stop feeding the pigeons. So the value of the fifth bag of grain is equal to the satisfaction he gets from feeding the pigeons. If he sells that bag and neglects the pigeons, his least productive use of the remaining grain is to make whisky, so the value of a fourth bag of grain is the value of his whisky. Only if he loses four bags of grain will he start eating less; that is the most productive use of his grain. The last bag of grain is worth his life.

In explaining the diamond-water paradox, marginalists believe that it is not the total usefulness of diamonds or water that matters, but the usefulness of each unit of water or diamonds. Its true that the total utility of water to people is tremendous, because they need it to survive. However, since water is in such large supply in the world, the marginal utility of water is low. In other words, each additional unit of water that becomes available can be applied to less urgent uses as more urgent uses for water are satisfied. Therefore, any particular unit of water becomes worth less to people as the supply of water increases. On the other hand, diamonds are in much lower supply. They are of such low supply that the usefulness of one diamond is greater than the usefulness of one glass of water, which is in abundant supply. Thus, diamonds are worth more to people. Therefore, those who want diamonds are willing to pay a higher price for one diamond than for one glass of water, and sellers of diamonds ask a price for one diamond that is higher than for one glass of water.

Now The Paradox of enrichment: The closest thing I could find to help explain that this is a paradox is a formula I found on wikipedia.
http://en.wikipedia.org/wiki/Paradox_of_enrichment
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
foreva.infiniti
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Thus the paradox of value is in fact its name.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
Magnus Eisengrim
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I'm not sure what you want to discuss, foreva.infiniti. No one has doubted that these things have names. I have suggested that Russell's paradox is a "true paradox" in a way that the "paradox of value" and "paradox of enrichment" are not. This is, perhaps a point worth discussing. Or maybe not.

As I hinted above, if by "paradox" you mean "something counterintuitive or puzzling" sure, let's call them paradoxes. But they are still qualitatively different from #1.

So, just to get the ball rolling, what do you find interesting about the "paradox of value" and "paradox of enrichment"?
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
foreva.infiniti
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If you like thoses types then you might like this one! It's mathematical!

Since (1/2)2 = 1/4 and (1/2)3 = 1/8 then (1/2)3 < (1/2)2

using the logarithms obtained:
3 log (1/2) < 2 log (1/2)

and after dividing by log (1/2):
3 < 2
How can that be?
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
Magnus Eisengrim
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Log(1/2) is negative.

Seriously, though. You brought up 10 items and some of them are pretty interesting. I invite you to pick one to talk about. (#2 is quite rich)

John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
foreva.infiniti
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I don't find them interesting really I just wanted someone else's perspective. Here's one that does interests/disturbs me tho.

Can [an omnipotent being] create a stone so heavy that it cannot lift it?
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
Magnus Eisengrim
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Quote:
On 2010-06-04 16:17, foreva.infiniti wrote:
Can [an omnipotent being] create a stone so heavy that it cannot lift it?


I believe that this is logically equivalent to #3. What do you think is the issue? Why is it seemingly paradoxical?
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
Bill Hallahan
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As has been pointed out already, most of these are not paradoxes, despite that some sites have labeled them as paradoxes. Some of what I have below has been mentioned in earlier posts.

Quote:
1. Does the set of all those sets that do not contain themselves contain itself?

This is Russell's paradox from mathematics.

http://plato.stanford.edu/entries/russell-paradox/

Quote:
2. Should one tolerate intolerance; if intolerance would destroy the possibility of tolerance?

Intolerance cannot destroy the possibility of intolerance. If it exists, then it exists. In addition, we are all individuals, so one person might tolerate what another does not.

Some behaviors should not be tolerated. (I shall not allow Godwin's law to be invoked due to my post Smile, but hopefully now you have an example of something that is intolerable). Most imperfections in people should be tolerated.

Quote:
3. What would happen if an unstoppable force hit an immovable object?

The existence of an unstoppable force precludes the the existence of an immovable object, and visa versa. In any event, one represents an infinite force, and the other an infinite mass.

Quote:
4. Since the universe is not infinitely old, it cannot be infinite in extent.

Assumes two ideas that are not in evidence. Neither the age of the cosmos nor it's extent are known. What is known is the approximate age of the known universe, which is finite.

Quote:
5. Why is the night sky black if there is an infinity of stars?

Because there is hydrogen in space, and more recently it is believed there is dark matter. While the density of hydrogen is very low, only a few molecules per cubic meter of space, or lower, nonetheless after many millions of light years, it creates a wall that blocks light.

In addition, since stars at a greater distance are accelerating more as the known universe expands, their light is red-shifted, and eventually the wavelength of the electromagnetic radiation will be in the infrared region and below, which is not visible. However, this is not a factor, at least not yet, it's the blockage due to space not really being a pure vacuum. (Everything I write here might be wrong if dark matter, if it exists, is a larger factor, however, any low density of matter in space will eventually block light at a sufficient distance anyway).

Quote:
6. Increasing the food available to an ecosystem may lead to instability, and even to extinction.

There is no contradiction here, although this is more likely to happen with a small population, for example, a population on a small island. In this case, the oversupply of food leads to too many animals in one generation, then that generation eliminate all the food for the next generation before the food supply has a chance to be replenished. In theory, the food supply could also become extinct too.

Quote:
7. Which came first, the chicken or the egg?

The egg of a less chicken-like animal with a mutated genome came first, but there were other eggs that contained non-chicken-like animals before those.

Quote:
8. If all truths are knowable, then all truths must in fact be known.

This is false for two reasons. In 1931, Kurt Godel, a mathematician, proved, among other things, that there are an infinite number of truths that can never be known. Even if that were not the case, that "all truths must be known" does not follow from "all truths can be known." Not everything that is possible happens. (Although, I suppose if one considers the universe to be totally deterministic, then anything that doesn't happen can't happen - in any event, Godel's theorem proves that there will always be unknown truths).

Quote:
9. If God knew how we will decide when he created us, how can there be free will?

Presumes facts not in evidence. In any event, assuming God realizes what you assert, does seeing the future necessarily mean controlling the future?

Quote:
10. Diamond-water paradox (or paradox of value) Water is more useful than diamonds, yet is a lot cheaper.

Water is common. Diamond is relatively rare. The price disparity per unit mass is related to the economic property of supply and demand. While the demand for diamonds is smaller than the demand for water, the supply of water is huge, and the supply of diamonds is very tiny in comparison. Diamonds are beautiful, and have been marketed to be in significant demand as jewelry. Diamonds are also useful in industry.

Metals like silver, gold, and platinum, are also expensive because they are rare. Platinum is so rare that all the platinum in the world could fit in a relatively small room. These, like diamond, are in less demand than water, but compared to water, the supply is incredibly tiny.

Quote:
11. When two countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between them increases.

This has been postulated, but the only time nuclear weapons have been used is when only one country had them... so far. Let's hope they're never used again.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
- The character of ‘Death’ in the movie "Hogswatch"
foreva.infiniti
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Quote:
On 2010-06-04 16:21, Magnus Eisengrim wrote:
Quote:
On 2010-06-04 16:17, foreva.infiniti wrote:
Can [an omnipotent being] create a stone so heavy that it cannot lift it?

I believe that this is logically equivalent to #3. What do you think is the issue? Why is it seemingly paradoxical?

If the being is omnipotent then it's power is without limits. If its power is without limits then it should be able to produce a stone that's so heavy even the being itself cant pick up. If the being cant pick it up then its power has limits. If the being cant create the stone than the power does hav limits.

I have yet to elaborate on these paradoxes so here I go (RIIIISE SHINIIING GUNDAAAAAM!)

I'll elaborate on #8.

If all truths are knowable, then all truths must in fact be known.

If you're aware you're being deceived then in fact your not being deceived so no man or woman has the right to accuse anyone of deception.

I initially intended to elaborate but in the spur of the moment I had a counter thought to the above paradox and just kept writing. I gotta go over this because I believe I just came up with a new paradox. Smile.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
Bill Hallahan
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Foreva.infiniti, nothing in your last post was a paradox.

foreva.infiniti wrote:
Quote:
If the being is omnipotent then it's power is without limits. If its power is without limits then it should be able to produce a stone that's so heavy even the being itself cant pick up.

The question, (paraphrased) "Can God make a stone so large he cannot move it?" was posed by Rene Descarte, and is known as the "Paradox of the stone," although, it's not really a paradox, it's an ill-formed question.

Again, the idea of an omnipotent being means that no stone can ever be so large that it cannot be moved. Or alternatively, the idea that a stone cannot be moved by God means God cannot do anything.

In effect, the question is like defining a being that is able to do that which cannot be done. It makes no sense. And that's the answer - both the old question and the statement in your post make no sense.


foreva.infiniti wrote:
Quote:
If all truths are knowable, then all truths must in fact be known.

See what I wrote about this in my previous post.

foreva.infiniti wrote:
Quote:
If you're aware you're being deceived then in fact your not being deceived so no man or woman has the right to accuse anyone of deception.

If you are aware that someone is trying to deceive you, then you are not being deceived, is a more accurate wording. Again, it's just a word-game, not an actual paradox. In other words, you can't be aware that you are being deceived, at least not in the sense you mean. (You can, of course, know you are being deceived, but not know how you are being deceived, thus a different type of deception can exist in along with the awareness someone is trying to deceive you, which is the case in magic).
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
- The character of ‘Death’ in the movie "Hogswatch"
kcg5
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In other words, thank you for playing.
Nobody expects the spanish inquisition!!!!!



"History will be kind to me, as I intend to write it"- Sir Winston Churchill
foreva.infiniti
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If you are aware that someone is trying to deceive you, then you are not being deceived is not accurate because its an entirely different scenario. I'll be a and you'll be b. (False perspectives)

A
My perspective: it says your name is Bill Hallahan. I believe it because I see no reason not to.
Your perspective: my real name is William Hallahan Dunbar. They don't need to kno this because its irrelevant.

Your deceiving me but I cant/wont accuse you because I have no reason to believe your deceiving me.

B
My perspective: It says your name's Bill Hallahan. I don't believe you because you used to be my old teacher. I remember you Mr. Dunbar! Why would you lie about your name? Deceiver!

Your perspective: I never met you before today, infidel.

Denying your name jus showed me you were trying to deceive me. Whereas above in A you never denied anything I just assumed. I am fault for calling you a deceiver because you never deceived me since I knew from the beginning.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
Magnus Eisengrim
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Quote:
On 2010-06-04 16:33, foreva.infiniti wrote:

If you're aware you're being deceived then in fact your not being deceived so no man or woman has the right to accuse anyone of deception.



I believe that this is incorrect.

Consider: You are out of the room while your friends A and B toss a coin, look at the result and then hide the coin.

A: "The coin came up Heads."
B:"The coin came up Tails."

You are aware that you are being deceived. Your awareness of this fact does nothing to resolve the deception. One of your friends is lying and both of your friends are working together to keep you from knowing where the deception lies. You can legitimately accuse your friends of deception, with no paradoxical result.

John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.--Yeats
foreva.infiniti
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Quote:
On 2010-06-04 17:12, Magnus Eisengrim wrote:
Quote:
On 2010-06-04 16:33, foreva.infiniti wrote:

If you're aware you're being deceived then in fact your not being deceived so no man or woman has the right to accuse anyone of deception.



I believe that this is incorrect.

Consider: You are out of the room while your friends A and B toss a coin, look at the result and then hide the coin.

A: "The coin came up Heads."
B:"The coin came up Tails."

You are aware that you are being deceived. Your awareness of this fact does nothing to resolve the deception. One of your friends is lying and both of your friends are working together to keep you from knowing where the deception lies. You can legitimately accuse your friends of deception, with no paradoxical result.

John


Im aware that I'm being deceived but the deceiver is unbeknownst to me so I cant accurately make an accusation of deception without a deceiver to aim it at.
Colors are Foreva. Numbers are Infinite. 4 every number there's a color. HEY! Eternity! Lets smoke a beer and drink some loud. But wait! I heard you was a six a plus a 6 ahhhh.
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