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Post by BlueDolphin on Mar 28, 2007 12:17:30 GMT -5
This paradox involves how divisions work with objects that can be made into tiny increments. The example used is a heap of sand.
We all know that there are things that are definitely heaps and things that are definite non-heaps. That implies there must be some area where a heap becomes a non-heap. But where is it?
The paradox goes like this:
Premise: A single grain cannot make the difference between a heap or a non-heap. (since one cannot tell the difference at a glance between n grains and n-1 grains of sand. Can you imagine a situation where an object is a heap but when a single grain is removed, it suddenly becomes a non-heap?)
Reasoning: If 10,000 grains of sand is a heap of sand, then 9,999 is a heap of sand too (under the premise above). If 9,999 is a heap sand, then 9,998 is a heap of sand. (under the same reasoning) . . . If 1 grain is a heap, then 0 grains is a heap of sand.
how would you go about solving this paradox?
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Post by Paveltc on Mar 28, 2007 13:53:39 GMT -5
I remember hearing this paradox before, but I can't remember where. It seems that this can only be solved by having one person add the grains of sand and keep track of how many there are. Then another person, who doesn't know how many there are, is brought to observe the sand and he says whether he considers it a heap or not. What exactly defines a heap? It's kind of a subjective idea really.
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Post by Monolith on Mar 28, 2007 14:43:52 GMT -5
I agree with Pavel's last point. Like most of the 'paradoxes' that have been posted, it's playing with a word of a very relative meaning, getting overly specific. There is nothing to really define what a heap is or isn't numberwise, it's a definition based on appearance, not science.
On that note, I wish philosophers would stay away from the English language. They always try to play semantics or draw too much meaning out of a single word. The entire point of writing is to assemble words in such a way as to get a specific and unique meaning that is beyond the individual meaning of each word. If you zoom in to far, you loose sight of the whole and everything becomes less meaningful.
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Post by BlueDolphin on Mar 28, 2007 15:16:56 GMT -5
Philosophers use paradoxes to test reasoning and logic. It isn't that they are trying to prove the world is absurd. Rather that sometimes what seem to be valid reasoning and premises give what are obviously incorrect answers.
Zeno's paradox is like this. Many people objected because arrows do in fact move. But this is the whole idea since the reasoning states that they don't which is clearly wrong. This problem was solved of course since it turns out the premise or the reasoning wasn't good at all.
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Post by Archagon on Mar 28, 2007 15:55:05 GMT -5
He was wrong. A heap is always composed of exactly 5,231+ particles.
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Post by dietspam16 on Mar 28, 2007 19:51:47 GMT -5
Thank you Alexei.
I get what you're saying jeff, and it's a good point, but semantics IS the study of meaning in language, so if they want to study that and illustrate points, they should do it from there.
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Post by Paveltc on Mar 29, 2007 0:35:01 GMT -5
The thing that always irritated me about philosophy is that everything is like a big word game to the philosophers. They love to use what seems like circular reasoning in order to prove their points. Descartes, for example, claimed that he proved that God exists by saying that if it was possible for him to concieve of the idea of God, it meant that God must necessarily exist. Yet, this doesn't quite do the job, not for me at least. And there are plenty other examples where things are worded in such a way that makes it seem like whatever point is being argued is proven, but in reality the philosopher just doesn't know how to get himself out of whatever hole he got himself into.
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Post by Arachis on Mar 29, 2007 0:48:29 GMT -5
The problem is that words are ideas used to describe things,and sometimes the thing becomes confused with the idea.
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Post by Little Miss Odd on Mar 29, 2007 19:04:24 GMT -5
It becomes a heap when my daemonic sign says it does. (sorry, Socratic moment)
Let A be the set containing the elements of a 'heap'. A must then have countably many components(say n), and be nonempty. And A is a heap for all n > N where the guy who picks the given epsilon can't be bothered to count above N.
Math proofs deserve to be mutilated.
The problem with words is when they stop being descriptive and get turned into concepts. Because when they're descriptive, you can add qualifiers. Like the moon being mostly covered in jam, versus the moon being covered in jam. One dry spot and there goes the cat. When descriptors get turned into concepts, people try to isolate them, like it's algebra and all x terms go to the left. Another one is 'beauty'. God that one can get annoying. What makes something beautiful? If we take enough features, does it become not beautiful? Well yes, because now she's a bloody mess. Philosophy majors are absolutely useless when they make up their minds to be difficult. If only their divine voices would tell them when to shut up.
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