Paradoxes, time travel, logic traps, and other random deep thoughts
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01-06-2011, 03:46 PM
Paradoxes, time travel, logic traps, and other random deep thoughts
This is supposed to be the Philosophy forum, yet I see very little pondering, pipe smoking, and meaningless questions posed for the sake of thought.


Let's talk about logic paradoxes.

Some of them are terrible:

This sentence is false.



Some of them don't make sense (to me at least):

The Tortoise and Achilles are in a race and Achilles starts 100 meters back from the Tortoise. Before Achilles can pass the Tortoise, he must first get to the spot the turtle was, but by the time he does that the Tortoise has moved slowly forward so Achilles must get to the spot the Tortoise was again and so on, and so Achilles can never pass the Tortoise because he will always have to reach the point the Tortoise was (Zeno's Paradox).

-But a race is not a math problem. The Tortoise is not infinite and Achilles is not a point approaching it. We are dealing with an x-axis plane in which 2 magnitudes are moving the same direction at different velocities. Of course the one with the higher velocity (V) will have a higher displacement (Delta X), given the same amount of time (Delta T). VT = X



But anyways... we've discussed one of my favorite paradoxes before (The Monty Hall paradox from the movie "21") in one of my older posts, but what are some other "good for a deep thought and a headache" type paradoxes you've heard of?

Here's a list from wikipedia but I haven't gone through them yet.

http://en.wikipedia.org/wiki/List_of_paradoxes



Also, in this thread, feel free to talk about Time Travel twisters, such as "can you go back in time and kill your own mother before you were born?" and The Butterfly Effect (not the movie) and the concept of multiple realities/existences that branch off from the linear reality that you are in (is time/reality linear?).


And finally, feel free to throw out random quotes that make you go Hmmm, such as Epicurus' view of death:

"Why should I fear death? If I am, death is not. If death is, I am not. Why should I fear that which can only exist when I do not?"

"Ain't got no last words to say, yellow streak right up my spine. The gun in my mouth was real and the taste blew my mind."

"We see you cry. We turn your head. Then we slap your face. We see you try. We see you fail. Some things never change."
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01-06-2011, 03:57 PM
 
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
(01-06-2011 03:46 PM)Buddy Christ Wrote:  The Tortoise and Achilles are in a race and Achilles starts 100 meters back from the Tortoise. Before Achilles can pass the Tortoise, he must first get to the spot the turtle was, but by the time he does that the Tortoise has moved slowly forward so Achilles must get to the spot the Tortoise was again and so on, and so Achilles can never pass the Tortoise because he will always have to reach the point the Tortoise was (Zeno's Paradox).

This particular one is not a paradox, it's a logical sinkhole. I remember being taught this crap by a nationalist teacher years ago. He was trying to present the deep thinking of the ancient greek only that his arguments were like those of religion.

Zeno was dumb enough not to realize what he was actually saying. He could neither grasp exponentiation nor the fininity(real word?) of a time-lapse. In the case of this elaborate paradox, a certain limit in time is reached in which exponentiation eventually forces the distance between the two objects to be 0. After that we have an opposite exponentiation. Dodgy
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02-06-2011, 05:13 AM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
Some paradoxes like the "This sentence is False" are self-contradictory nonsense, just a string of symbols. They have some pedagogical value in logic texts. Others like Zeno's are attempts to explain observed phenomena. He knew that Achilles caught the tortoise, but it created a contradiction for him. To resolve it, he postulated that time is discontinuous, that we do not move smoothly, but jump from moment to moment. Remember that he lived 150 year or so before Euclid. While AatT seems ridiculous now, Zeno did not have the analytical tools to resolve it. A third class is the butterfly effect, these are merely phenomena that don't correspond neatly to our sense of proportion, but when understood are not paradoxes at all.

I think a very interesting paradox comes from the two slit experiment where electrons behave differently (waves or particles) depending on whether you are watching or not. In some ways quantum mechanics brings us back to Zeno. He had no way to know it of course, but it appears that at the quantum level motion is discontinuous after all.

He was part of my dream, of course--but then I was part of his dream, too!
--Alice
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02-06-2011, 05:39 AM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
Wouldn't Zeno be ignoring (actually, unaware) of the planck length? You cannot divide distance in half infinitely.

"I do not feel obliged to believe that the same God who has endowed us with sense, reason and intellect has intended us to forego their use." - Galileo

"Every man is guilty of all the good he did not do." - Voltaire
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02-06-2011, 01:49 PM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
(02-06-2011 05:39 AM)daemonowner Wrote:  Wouldn't Zeno be ignoring (actually, unaware) of the planck length? You cannot divide distance in half infinitely.

I'm not sure if the role of Planck length (time/density/etc.) is quite clear to anyone yet. Planck things are just quantities derived from some basic universal constants, but they haven't be proven to have any real-world meaning.

..."we can be truly free - not because we can rebel against the the tyranny of the selfish replicators but because we know that there is no one to rebel."
Susan Blackmore : The Meme Machine
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03-06-2011, 03:39 AM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
I stopped worrying about time/space paradoxes after watching thousands of Star Trek episodes. I love how they explained a lot of those things, many of them have been proven correct, as the new science moves forward. Also, Hitchhikers Guide to the Galaxy books have explained some things concerning time/space... I spend enough time wondering on my own trying to figure out these questions and then those shows/books have given me a new perspective into things and I found them quite logical so accepted them as the possible solution to the paradoxes. Trying to explain that with my own words is too complex and too long, it's easier to watch some Star Trek or read a book...

Smile

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I have a theory that the truth is never told during the nine-to-five hours.
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03-06-2011, 04:10 AM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
I would think that if we were to invent a time machine, what happens is our conciousness will be transfered to our old self which means that it will be restricted to only your lifetime. It sounds ridiculous because time travel is, at least for the time being, a ridiculous idea.
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03-06-2011, 11:27 AM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
(01-06-2011 03:46 PM)Buddy Christ Wrote:  Some of them don't make sense (to me at least):

The Tortoise and Achilles are in a race and Achilles starts 100 meters back from the Tortoise. Before Achilles can pass the Tortoise, he must first get to the spot the turtle was, but by the time he does that the Tortoise has moved slowly forward so Achilles must get to the spot the Tortoise was again and so on, and so Achilles can never pass the Tortoise because he will always have to reach the point the Tortoise was (Zeno's Paradox).

-But a race is not a math problem. The Tortoise is not infinite and Achilles is not a point approaching it. We are dealing with an x-axis plane in which 2 magnitudes are moving the same direction at different velocities. Of course the one with the higher velocity (V) will have a higher displacement (Delta X), given the same amount of time (Delta T). VT = X

Exactly. Zeno's Paradox is interesting, but it's not interesting because it's an actual paradox. It's interesting because it illustrates one of the most interesting things about the Greeks: for all their mathematical and philosophical advances, they had no concept of the simple mathematical concept of the rate.

"Owl," said Rabbit shortly, "you and I have brains. The others have fluff. If there is any thinking to be done in this Forest - and when I say thinking I mean thinking - you and I must do it."
- A. A. Milne, The House at Pooh Corner
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03-06-2011, 03:33 PM
 
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
Zeno's paradox taught us that you can add an infinite convergent set. 1 + 1/2 + 1/4 + 1/8 + ... = 2

I think time travel is kind of lame to believe in: the grandfather paradox tells us it's not possible. You can make a grandfather paradox without involving death and a will to kill him, but only with particles, which is much simpler, by the way. That way you don't have people nitpicking and saying that because you lack free will you won't kill him.
The other annoying thing about free will mixed with physics is that people think you will have an infinite amount of parallel universes, every single one of which has you make a different choice. Why would our choices be so important that they would create entire universes? How about the choice of an ant, or that of a particle, or a string? This would also mean our actions would be quite random, which they are not.

One test I find kind of funny. It's kind of like Monty hall, in that it's remarkably simple, and yet a lot of people fail at it: http://www.philosophyexperiments.com/wason/Default.aspx
There are a few more test, some of which concern God and logic, or whether your philosophy is logically possible.
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04-06-2011, 01:28 PM
RE: Paradoxes, time travel, logic traps, and other random deep thoughts
(01-06-2011 03:46 PM)Buddy Christ Wrote:  This sentence is false.
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"This is not a pipe"
is a painting about semantics.
The Belgian surrealist René Magritte, tries to trigger a thought processes, where a shallow observer would say, "The artist is a fool" but the thinker would say "The artist is right"

Observer

Agnostic atheist
Secular humanist
Emotional rationalist
Disclaimer: Don’t mix the personal opinion above with the absolute and objective truth. Remember to think for yourself. Thank you.
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