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 Posted: Sat Jun 09, 2007 7:26 pm
Are there really paradoxes? Does the nature of existence really have glitches in it? Personally I think that every paradox can be accounted for by errors of language construction.
What do you think?
Anyone wanna present a "paradox" to see if we can't crack it?
EDIT: I am no deity so please feel free to challenge me on any errors you might see.
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Posted: Sat Jun 09, 2007 8:18 pm
The following statements are all given truths:
-The second statement is a lie
-The third statement is a truth
-The first statement is a truth
Not really a "typical" paradox, but, have fun prying it apart all the same.
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Posted: Sat Jun 09, 2007 8:58 pm
Hmmm, a non lingual paradox... Oh! If the universe is finite, what is on the other side, and if the universe is infinite, how can there be no end?
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Posted: Sat Jun 09, 2007 9:25 pm
Shinigami Lawliet The following statements are all given truths: -The second statement is a lie -The third statement is a truth -The first statement is a truth hmmm... I haven't seen this one before. ...My explanation: Ignoring the fact that this argument goes on forever, you can easily see that the first two premises cannot both be true at the same time. It's form, however, causes you to only look at these premises in succession since the truth of each depends on the truth of the former. This ends up forming a fallacy (begging the question) since each premise becomes it's own conclusion. Also, if you carry this through one succession the premise ends up disproving itself. So it is only by these fallacies that the contradiction of the first two premises is overlooked. This is a great example of a very convincing circular argument. Thanks for posting this.
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Posted: Sat Jun 09, 2007 9:29 pm
Tammy-Seignfree if the universe is infinite, how can there be no end? Why is it hard to imagine endless space?
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Posted: Sat Jun 09, 2007 10:12 pm
Tammy-Seignfree Hmmm, a non lingual paradox... Oh! If the universe is finite, what is on the other side, and if the universe is infinite, how can there be no end? i think you are miscommunicating here, the universe "can have" no end because it is infinite. however i know what you mean, infinity is a pretty crazy concept. any related concept just breaks because of it. a more technical question i always wonder about is "how can our universe be constantly expanding at an accelerating rate [it is] if it is infinite (what is it expanding into?)" that is the one that really gets me... astronomy is crazy eek but so cool smile here's some paradoxes (one related to infinity), one secular and one not: my favorite infinity paradox: 1/3 + 1/3 +1/3 = 3/3 = 1 1/3 = 0.333 (repeating) 0.333 (r) + 0.333 + 0.333 (r) = .999 (r) thus .999 (r) = 1 ---- If God is omnipotent, could he make a rock so heavy he could not lift it?
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Posted: Sat Jun 09, 2007 11:30 pm
Jhuinya Melbourne a more technical question i always wonder about is "how can our universe be constantly expanding at an accelerating rate [it is] if it is infinite (what is it expanding into?)" I always thought that when they talked about the universe in that context that they were talking about everything in the universe and not the actual space that it occupies. I don't know though. They're theorists. Who knows what they are talking about? Jhuinya Melbourne 1/3 + 1/3 +1/3 = 3/3 = 1 1/3 = 0.333 (repeating) 0.333 (r) + 0.333 + 0.333 (r) = .999 (r) thus .999 (r) = 1 The problem here is that "0.333(r)" is not a perfectly accurate way of describing "1/3"; it's just the best way we can come up with since there is no way of showing that the last digit is a "4" since there is no last digit. EDIT: I'm not sure where I got the last digit being 4 thing. That's what I get for trying to sovle paradoxes while nodding off at 2AM. See my reply to Nebekim for a better explanation.Jhuinya Melbourne If God is omnipotent, could he make a rock so heavy he could not lift it? This situation strangely resembles the one just mentioned. While the "1" in the above example is like the heaviness of the rock, the "0.999(r)" is like God's omnipotence. Just like the repeating decimals have to reach infinity before finaly resting at "1", God's strength in this example is always having to catch up to an infinite goal (the weight of the rock). So this is pretty much like asking if God can reach infinity which is a contradiction of the term "infinite". Now look at the definition of omnipotent: |ämˈn**ətənt| adj. having unlimited power; able to do anything. Note the word "anything". Since God's ability to make a rock too heavy for him to lift is a contradiction, this action can't be called a "thing" at all. And so it doesn't even fall under the scope of omnipotence as defined by being "able to do anything (any "thing")".
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Posted: Sun Jun 10, 2007 12:34 am
Wyedg Tammy-Seignfree if the universe is infinite, how can there be no end? Why is it hard to imagine endless space? Because that would stretch time infinitely as well.
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Posted: Sun Jun 10, 2007 10:20 am
Well, isn't a paradox just something that we can't get our heads around, really? Something that appears to not make sense?
Also, explain the three statements one without resorting to the fallacy, because that is just avoiding the point, really. It's only a paradox if you can agree that all three statements are correct, otherwise it's not a paradox.
Also, 0.999 recurring can be proven to be equal to 1:
Say that a = 0.999(r)
10a = 9.999(r)
9a = 10a - 1a = 9.999(r) - 0.999(r) = 9.
So, if 9a = 9, and using simultaneous equations to get back to a single a, you divide each one by 9, so 9a/9 = a, and 9/9 = 1, so a = 1
Flawless mathematical proof that 0.9(r) = 1.
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Posted: Sun Jun 10, 2007 1:05 pm
Nebekim Well, isn't a paradox just something that we can't get our heads around, really? Something that appears to not make sense? Also, explain the three statements one without resorting to the fallacy, because that is just avoiding the point, really. It's only a paradox if you can agree that all three statements are correct, otherwise it's not a paradox. Also, 0.999 recurring can be proven to be equal to 1: Say that a = 0.999(r) 10a = 9.999(r) 9a = 10a - 1a = 9.999(r) - 0.999(r) = 9. So, if 9a = 9, and using simultaneous equations to get back to a single a, you divide each one by 9, so 9a/9 = a, and 9/9 = 1, so a = 1 Flawless mathematical proof that 0.9(r) = 1. A paradox is a "sound" argument which leads to a contradiction. If the argument isn't actually sound, but only seems sound then it is only a sophism. This is why I said that the first example is not really a paradox i.e. it is not actually a sound argument. In the proof that you showed there is a problem with assuming that 10 x 0.999(r) = 9.999(r). We only say that 10 x 0.999(r) = 9.999(r) because we are use to the method of moving the decimal place over when multiplying by 10, but if you think about what we are actually doing here it can't apply to infinite decimals i.e. when we move the decimal place to the right we are actually moving all of the digits to the left leaving a "0" at the end of the number. But in the case of an infinite decimal the "0" can never be accounted for since the number has no end. The problem with infinite decimals is that we are actually representing a process instead of a number since we can never actually finish dividing 3 into 1 because we are always left with a remainder which again needs to be divided by 3. The only way that we can end the process is by completing the number which by definition cannot be done with infinite decimals. So, basically, 0.333(r) is an incomplete representation of 1/3 just as 0.999(r) is an incomplete representation of 1. Nevertheless, I still thought that the proof was very clever and I have much respect for whomever came up with it.
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Posted: Sun Jun 10, 2007 1:43 pm
Wyedg A paradox is a "sound" argument which leads to a contradiction. If the argument isn't actually sound, but only seems sound then it is only a sophism. This is why I said that the first example is not really a paradox i.e. it is not actually a sound argument. What is unsound about it except for the fact that it is a paradox? With that explanation a paradox is a paradox. . . . stressed that mashed my brain stressed Quote: In the proof that you showed there is a problem with assuming that 10 x 0.999(r) = 9.999(r). We only say that 10 x 0.999(r) = 9.999(r) because we are use to the method of moving the decimal place over when multiplying by 10, but if you think about what we are actually doing here it can't apply to infinite decimals i.e. when we move the decimal place to the right we are actually moving all of the digits to the left leaving a "0" at the end of the number. But in the case of an infinite decimal the "0" can never be accounted for since the number has no end. The problem with infinite decimals is that we are actually representing a process instead of a number since we can never actually finish dividing 3 into 1 because we are always left with a remainder which again needs to be divided by 3. The only way that we can end the process is by completing the number which by definition cannot be done with infinite decimals. So, basically, 0.333(r) is an incomplete representation of 1/3 just as 0.999(r) is an incomplete representation of 1. Well, you prove that there can't be the 0 at the end, because if you're multiplying an infinite number, then surely if you multiply it by 10, then the only way to do that is to move the decimal point, because if you multiply it by 10, then you would have the 0 on the end, logically, but infinity can't have the extra 0 on the end, because it's infinity. It's kind of a mind ******** really, and just depends on how you perceive it, i guess. Quote: Nevertheless, I still thought that the proof was very clever and I have much respect for whomever came up with it. Very true ^^ I got taught it by my maths teacher, and i think it's on the syllabus, but i dunno who first came up with it.
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Posted: Sun Jun 10, 2007 3:45 pm
Wyedg Jhuinya Melbourne a more technical question i always wonder about is "how can our universe be constantly expanding at an accelerating rate [it is] if it is infinite (what is it expanding into?)" I always thought that when they talked about the universe in that context that they were talking about everything in the universe and not the actual space that it occupies. I don't know though. They're theorists. Who knows what they are talking about? they actually do mean the space it occupies; the space itself is expanding, causing the items in it like galaxies and quasars to get further away from each other as a result of the expansion of space. like raisin bread dough rising (my book uses that analogy a lot, it makes me hungry, hehe).
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Posted: Sun Jun 10, 2007 3:50 pm
I guess the simplest paradox would be the statement " I always lie.". Though if you it makes sense if you use the first definition of a paradox from the dictionary: Quote: 1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth. 2. a self-contradictory and false proposition. 3. any person, thing, or situation exhibiting an apparently contradictory nature. 4. an opinion or statement contrary to commonly accepted opinion. Though it is a contradiction, there is a possiblitity of the truth. *shrugs*
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Posted: Sun Jun 10, 2007 6:33 pm
Jhuinya Melbourne Wyedg Jhuinya Melbourne a more technical question i always wonder about is "how can our universe be constantly expanding at an accelerating rate [it is] if it is infinite (what is it expanding into?)" I always thought that when they talked about the universe in that context that they were talking about everything in the universe and not the actual space that it occupies. I don't know though. They're theorists. Who knows what they are talking about? they actually do mean the space it occupies; the space itself is expanding, causing the items in it like galaxies and quasars to get further away from each other as a result of the expansion of space. like raisin bread dough rising (my book uses that analogy a lot, it makes me hungry, hehe). How do they know that space is expanding and that galaxies aren't just moving farther apart like particles from an explosion? I mean, I can't really argue on this because I am no physicist, but I still remain sceptical. I've just seen too many prestigious scientific "discoveries" be uncovered as nothing more than a wild guess made only for the purpose of recieving large government grants.
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