I tried to make a hugeass post yesterday analyzing all sorts of paradoxes, but I didn't bother to copy the text someplace, and my connection to shroomery crapped out for about a day starting when i had attempted to post it, and couldn't retrieve the body of my text. Grr. I'll try to recreate most of the post now as I remember it, but first addressing one of automan's more recent posts:
automan said: lets start with zeno's paradox off that list...there is no paradox here, just a misinterpretation of the main facts...an object in motion can never be exactly 1/2 way to the destination...the fractions cant be added up. there is no paradox.
Your argument is absurd. To move continuously, at least mathematically, from point a to point b, you must cross all points between point a and b. The halfway point is between a and b. If you are arguing that you can't be halfway there at the same time as the fullway there, this is correct, as long as you aren't there yet. This touches upon the actual problem, but I don't think you've argued the fault in the best way. I'll try to recreate my attempted post yesterday, now: ---
automan said: i came to the realization that there is no such thing as a paradox. there is only a misinterpretation of the facts given, or the disbelief in the fact that the correct answer is true.
I've looked at the zeno and infinity paradoxes linked by seraphim, and successfully found automan's logic to hold, that the problems are paradoxes only by a failure to correctly understand what they involve. In zeno's paradoxes, we are attempting to abstractly break down a path into an infinite number of segments, and then abstractly force the traveller to wait until we finishing segmenting the path before it can be fully traversed, and we wonder why the traveller never gets across. An infinite number is basically a number we define as never ending, then try to make it end -- it's absurd. Finish chopping up the road into an infinite number of pieces first, and then try to travel across it. You can't, as you'll never finish chopping it up. We are sort of like a cat or dog chasing its own tail. Hmm, why doesn't this square-block fit in the circular hole? Must be a paradox. Gee, I can't lift up this car into the air, must be another paradox.
Err, um, well anyway, here's the Hotel Infinity paradox:
Quote: Suppose that, somewhere in New Jersey, there is a hotel with an infinite number of rooms. You arrive late one night and ask the front desk clerk if they have a vacancy. He replies that every room is occupied, however, he can arrange for you to get one. But how, you wonder, if there is no vacancy? The answer is simple: the clerk will simply ask the people in room 1 to move to room 2, those in room 2 to move to room 3, those in 3 to move to room 4, and so on. Since there is an infinite number of rooms, everyone will have a room to move into, and room 1 will be available for you.
Here, it is supposed as if it were nothing to ask an infinite number of people to switch rooms. The clerk will never finish asking all the people to change rooms, as it is impossible to instantaneously communicate to all the people staying in the hotel. Also, it's impossible to instantaneously switch rooms. So, you eventually get your room #1, but there will always be someone without a room, as they will be switching from room n to room n+1. Although it isn't actually stated, there is an implication that even though all the rooms are full, there is still room for you and everyone else to stay. This is absurd, and therefore the 'paradox' of Hotel Infinity is simply a contradiction -- false.
I dare someone to post a paradox here that I cannot reduce to absurdity, showing it to be false -- contradiction and not mystery. If someone succeeds, there merely exists a person tricky enough to defeat my grasp of logic.
[this is almost nothing like the post I had attempted to recreate, and is perhaps a little more amusing, but a little less humble]
-------------------- "There is a principle which is a bar against all information, which is proof against all arguments and which can not fail to keep a man in everlasting ignorance -- that principle is contempt prior to investigation."
-- Herbert Spencer
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