Zeno's paradoxes are essentially mathematical idiocies. The tortoise one assumes that Achilles actually has to land on the infinite number of points the tortoise has been to reach it. In actuality, the tortoise didn't even inhabit all of those points. It only has two to four points of contact with the ground at any given moment, and its steps will tend to be a minimum distance. Achilles only has one to two points of contact with the ground, and his steps will be a large distance, seeing as he's running. Once he's less than a meter behind the turtle, his next step will overtake it, all of the infinite points between be damned.Miles000 said:
Illogical things proved logically?
- Thread starter darkfire613
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Or, since running is essentially just a series of short leaps, he could leap over it, depending on where he sets his feet. Assuming he has no room to simply go around the tortoise, that would be the most logical thing for him to do in such a race.Miles000 said:
Ok, look, one point of the paradox was that the ancient Greeks had not yet worked out how to do a sum of an infinite series, something which still gives students of math a headache today. (I must admit I've plain old forgotten how to do it.) Even in his day, Zeno's thinking was widely treated as, "Huh, well, right now we don't get how to work it out. It'll get solved eventually." Zeno's paradoxes demonstrated a problem with the then current understanding of these concepts; showing his conclusion was false did not show anyone had figured out -why- it was false and how it did work. It took about two thousand years for math to catch up.Miles000 said:
The other is a rather esoteric metaphysical argument. A simple click on the Wiki link would have introduced it.
They're not idiocies, they're genuinely important and difficult problems about the nature of infinity and the real numbers. When you consider the time he was writing, he was tackling some extraordinary issues and they weren't properly resolved until Newton and Leibniz came up with the idea of infinitessimals and calculus hundreds of years later.loc978 said:
Poor analogies, then. why use the example of a man running? That can obviously be explained away as I did. A chariot would work a little better, although you still run into the problem of tortoise pizza.Flatfrog said:
...or maybe the spirit of pure mathematical inquiry just seems pointless to my pragmatic little mind.
Well, I could list bits about quantum physics and chemistry, like, for example electrons exist in multiple places at once, and while moving don't have to inhabit the space between points...
But that's too much math for here...
Gettier Problems are fun though.
So for this I will posit a definition of knowledge. The simplest, and therefore, most general case for knowledge is that it is: A) Justified (to know something you must have a reason to know it.) B) True (Fairly self explanatory, but necessary nonetheless) C) You have to believe it (That is, in order to know something you have to well... know it.)
Simple enough, it defines knowledge in a quantifiable way, I know that I am posting this message because A) due to my other knowledge of the internet and past experience I can ascertain that it will be sent to the forum. B) You're reading it, arn't you? C) Yes, I do think that I believe this will be posted.
Now. Imagine this:
A man, Smith, has applied for a job, and, has a justified belief that "Jones will get the job" (Smith is a shitty employee or something). He also has a justified belief that "Jones has 10 coins in his pocket" (He witnessed Jones counting coins while waiting in the lobby of his building). Smith therefore (justifiably) concludes that "the man who will get the job has 10 coins in his pocket".
In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.
A) Justified: Smith was justified in his thinking (as defined by the problem)
B) True: Ultimately, yes.
C) Belief: He certainly did think that "the man who will get the job has 10 coins in his pocket".
But this does not seem like knowledge, does it...
But that's too much math for here...
Gettier Problems are fun though.
So for this I will posit a definition of knowledge. The simplest, and therefore, most general case for knowledge is that it is: A) Justified (to know something you must have a reason to know it.) B) True (Fairly self explanatory, but necessary nonetheless) C) You have to believe it (That is, in order to know something you have to well... know it.)
Simple enough, it defines knowledge in a quantifiable way, I know that I am posting this message because A) due to my other knowledge of the internet and past experience I can ascertain that it will be sent to the forum. B) You're reading it, arn't you? C) Yes, I do think that I believe this will be posted.
Now. Imagine this:
A man, Smith, has applied for a job, and, has a justified belief that "Jones will get the job" (Smith is a shitty employee or something). He also has a justified belief that "Jones has 10 coins in his pocket" (He witnessed Jones counting coins while waiting in the lobby of his building). Smith therefore (justifiably) concludes that "the man who will get the job has 10 coins in his pocket".
In fact, Jones does not get the job. Instead, Smith does. However, as it happens, Smith (unknowingly and by sheer chance) also had 10 coins in his pocket. So his belief that "the man who will get the job has 10 coins in his pocket" was justified and true. But it does not appear to be knowledge.
A) Justified: Smith was justified in his thinking (as defined by the problem)
B) True: Ultimately, yes.
C) Belief: He certainly did think that "the man who will get the job has 10 coins in his pocket".
But this does not seem like knowledge, does it...
Ah, but in three-dimensional space, Achilles' nose passes through a point the tortoise has never even been to.Flatfrog said:
...but my points are all semantic. The long and short of it is that I don't see the lack of understanding that folks in Zeno's time had as a problem. A system for calculating infinite points along a line would be worthless in any vocation that I personally attribute value to.
I exist in the real world... the subject of that problem plainly doesn't.
-barbzilla said:
Your syllogism is incorrectly built. You aren't deriving anything, just stating two different facts and then adding a conclusion.
Phrase the syllogism correctly, and you will see the error.
"All One's are numbers.
All Two's are also numbers
Therefor, all One's are Two's".
There is no logic supporting this. Afterall, all three's and four's are also numbers, and they aren't one's either.
The mirror just shows you the cube from another perspective in 3d space, it doesn't let you see into another dimension.darkfire613 said:
If you built a mirror that could see forward in time then you would be able to see forward in time however that would work on the principle that you would already be seeing time and the time mirror would just show it from a different viewpoint.
I get what you mean though, in some circumstances arguments appear to make sense even though they draw upon impossible or unreasonable scenarios.
