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Thread: paradox of the heap

  1. #1 paradox of the heap 
    Forum Ph.D. merumario's Avatar
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    The paradox of the heap is an unresolved problem.It seems more of philosophy because you come to a point where premises that seem true would be so wrong. 1.Many grains makes a heap of sand. 2.If i remove one grain of sand its still a heap?If you agree. Conclusion:if i continue repeating premises two untill one grain is left, is it still a heap? If no,why?,if yes why?


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    It doesn't seem like much of a paradox to me. Heap is just a word that people use to describe a collection of things. What someone calls a heap, someone else might not call a heap. What is the problem?


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    Quote Originally Posted by merumario View Post
    The paradox of the heap is an unresolved problem.It seems more of philosophy because you come to a point where premises that seem true would be so wrong. 1.Many grains makes a heap of sand. 2.If i remove one grain of sand its still a heap?If you agree. Conclusion:if i continue repeating premises two untill one grain is left, is it still a heap? If no,why?,if yes why?
    according to my mind if we isolate heap from rest of the world than answer will be YES no matter how many grains you seperate
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  5. #4  
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    Quote Originally Posted by merumario View Post
    The paradox of the heap is an unresolved problem.It seems more of philosophy because you come to a point where premises that seem true would be so wrong. 1.Many grains makes a heap of sand. 2.If i remove one grain of sand its still a heap?If you agree. Conclusion:if i continue repeating premises two untill one grain is left, is it still a heap? If no,why?,if yes why?
    A fine example of one of the most famous and puzzling scientific paradoxes, of the modern era, usually known as "the paradox of the heap".
    I don't feel able to offer any kind of answer at the present time.
    Last edited by Halliday; January 12th, 2013 at 01:30 PM.
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  6. #5  
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    Precious,see where you are wrong. The first premises says many grains make an heap.So if i remove the grains till it remains one grain,then it should be an heap because premises two says if i remove one grain,the heap is still a heap.But premises one disagree.Many grains must make a heap.One grain is not many grains.But premises two says one grain can make an heap.
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  7. #6  
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    Quote Originally Posted by merumario View Post
    Precious,see where you are wrong. The first premises says many grains make an heap.So if i remove the grains till it remains one grain,then it should be an heap because premises two says if i remove one grain,the heap is still a heap.But premises one disagree.Many grains must make a heap.One grain is not many grains.But premises two says one grain can make an heap.
    so you say one grain is heap. and if we take one grain from "one grain heap" (according to premise two) it will remain "zero grain heap" it seems complex

    found following link as your answer
    http://en.wikipedia.org/wiki/Sorites...ox_of_the_heap
    Last edited by precious; January 12th, 2013 at 02:24 PM.
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  8. #7  
    Forum Ph.D. merumario's Avatar
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    Yea.This are the true premises.Its much philosophy because when drawing the conclusion you find out that the premises cancel each other.One disagree with two and vice versa.
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  9. #8  
    Forum Ph.D. merumario's Avatar
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    I have seen it but the answers are unsatisfactory.It changes the question and avoids the true premises thereby changing the conclusion.If this is the case then they ought to state why and if the premises are wrong.
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    Life-Size Nanoputian Flick Montana's Avatar
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    Sounds more like a vocabulary problem than a paradox.

    How does utilizing the limitations of a vague term constitute a paradox. If you use a tightly defined term, say a dozen, you no longer have a problem. If you have a dozen eggs and you remove one, do you still have a dozen? No.

    What am I missing here?

    (I stink at philisophical discussion, sorry if I'm missing the point.)
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  11. #10  
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    Quote Originally Posted by Flick Montana View Post
    Sounds more like a vocabulary problem than a paradox.

    How does utilizing the limitations of a vague term constitute a paradox. If you use a tightly defined term, say a dozen, you no longer have a problem. If you have a dozen eggs and you remove one, do you still have a dozen? No.

    What am I missing here?

    (I stink at philisophical discussion, sorry if I'm missing the point.)
    you seem to have not understand the essence of this paradox. truly you have avoided the answer in a clumsy way.
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    Quote Originally Posted by precious View Post
    Quote Originally Posted by Flick Montana View Post
    Sounds more like a vocabulary problem than a paradox.

    How does utilizing the limitations of a vague term constitute a paradox. If you use a tightly defined term, say a dozen, you no longer have a problem. If you have a dozen eggs and you remove one, do you still have a dozen? No.

    What am I missing here?

    (I stink at philisophical discussion, sorry if I'm missing the point.)
    you seem to have not understand the essence of this paradox. truly you have avoided the answer in a clumsy way.
    Maybe you can explain it better, because I don't understand the essence of it either. To me, it looks like you are arguing over the meaning of the word "heap." Who cares?
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  13. #12  
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    This is thread of merumerio , not mine. I dont want any controversy . I quit.

    Just have look on wiki link if want to understand this paradox

    http://en.wikipedia.org/wiki/Sorites...ox_of_the_heap
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    I read that but I still don't get it.
    Robert Hooke stated his law regarding springs as follows
    "The power of any springy body is in the same proportion with the extension."

    Nowadays, we would say that the force (not power) of a spring is proportional to its extension, but in Hooke's day, the scientific terminology was still rather vague.

    We could set up two systems where the force ("power" in Hooke's terminology) is greater in system A, but the power (modern definition) is greater in system B. Do we sit around scratching our heads about a paradox, or do we just recognize that it is a problem of vague terminology?
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  15. #14  
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    This "paradox" sounds like a whole heap of nothing, to me.
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    Quote Originally Posted by merumario View Post
    The paradox of the heap is an unresolved problem.It seems more of philosophy because you come to a point where premises that seem true would be so wrong. 1.Many grains makes a heap of sand. 2.If i remove one grain of sand its still a heap?If you agree. Conclusion:if i continue repeating premises two untill one grain is left, is it still a heap? If no,why?,if yes why?
    If many (more than one) grains make a heap then one grain does not qualify as many. Many is more than one whereas one is definitely not many. So one grain is not a heap
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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  17. #16  
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    Quote Originally Posted by Harold14370 View Post
    I read that but I still don't get it.
    Robert Hooke stated his law regarding springs as follows
    "The power of any springy body is in the same proportion with the extension."

    Nowadays, we would say that the force (not power) of a spring is proportional to its extension, but in Hooke's day, the scientific terminology was still rather vague.

    We could set up two systems where the force ("power" in Hooke's terminology) is greater in system A, but the power (modern definition) is greater in system B. Do we sit around scratching our heads about a paradox, or do we just recognize that it is a problem of vague terminology?
    sir, see, your this post has made this thread meaningful. thanks
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  18. #17  
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    Zinjan. Premises 2 ensures that one grain and even zero grain can make an heap.The problem is when concluding using the 2 premises,they tend to contradict each other,meaning two true premises leads to an unsound argument.Which was not suppose to be so.True premises makes a sound argument.
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  19. #18  
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    If anybody thinks that this paradox is a misconception of language,then he should not post.There is no specific number or quantity that makes an heap.Unless you will say that there is,with logical reasoning.And then its no longer a paradox. Percious i am here,you do not have to quit
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    Quote Originally Posted by merumario View Post
    If anybody thinks that this paradox is a misconception of language,then he should not post.There is no specific number or quantity that makes an heap.Unless you will say that there is,with logical reasoning.And then its no longer a paradox. Percious i am here,you do not have to quit
    There is no specific number that makes a heap. However, when the heap gets small enough, I shall quit calling it a heap. There is no specific number for this. It will just be at my discretion. When it no longer looks like a heap, it is not a heap. One day, the same number of grains might be a heap and the next day not a heap. Paradox resolved.

    Anybody that thinks different should not post.
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    This is a sense a problem of continuum of states - the concept of heap and not a heap seems to be well defined and there is a continuum of in between states but there is no reasonable place to draw the line where something is a heap stops being a heap (or vice versa).
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    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  22. #21  
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    Quote Originally Posted by precious View Post
    Quote Originally Posted by Flick Montana View Post
    Sounds more like a vocabulary problem than a paradox.

    How does utilizing the limitations of a vague term constitute a paradox. If you use a tightly defined term, say a dozen, you no longer have a problem. If you have a dozen eggs and you remove one, do you still have a dozen? No.

    What am I missing here?

    (I stink at philisophical discussion, sorry if I'm missing the point.)
    you seem to have not understand the essence of this paradox. truly you have avoided the answer in a clumsy way.
    Like I said, I don't understand how this is a paradox. I don't think what I said was particularly clumsy and I was not avoiding the answer. I was simply saying the answer is a silly one. As is your post since it makes no attempt to clarify anything.

    A heap is just a word with no quantity assigned to it. The word you're looking for isn't 'paradox', it's 'interpretation'. Because the answer to the question is completely defined by the interpretation of the reader.
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  23. #22  
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    The paradox of the heap is an unresolved problem.It seems more of philosophy because you come to a point where premises that seem true would be so wrong. 1.Many grains makes a heap of sand. 2.If i remove one grain of sand its still a heap?If you agree. Conclusion:if i continue repeating premises two untill one grain is left, is it still a heap? If no,why?,if yes why?
    Quote Originally Posted by merumario View Post
    Zinjan. Premises 2 ensures that one grain and even zero grain can make an heap.The problem is when concluding using the 2 premises,they tend to contradict each other,meaning two true premises leads to an unsound argument.Which was not suppose to be so.True premises makes a sound argument.
    The OP defines a heap as having many grains. One grain is not many. Many by definition is a large number of which one, is not. Premise 2 is in the form of a poorly phrased question in which I think you were trying to say is it still a heap, not its still a heap. The question mark indicated you were trying to ask something but your words could also be easily misconstrued as a statement. Are you sure you've worded what you wanted to say correctly?
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  24. #23  
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    zinjan sorry about the question mark. i was not asking. premises2 says if i remove one grain from the many grains,then it is still a heap.if that is true,(and it is true) then if i repeat premises2 over and over again till it remains one grain,the one grain can be called a heap. so also if remove the last grain and there is nothing left,we can still call it a heap.



    the above is true because we agree that if we remove one grain from many grains,it does not change it from being a heap.meaning if continue removing one grain till one grain is left,the it is still a heap,.

    NOTE; you said many grains make an heap without specifying.
    you also said removing one grain from your heap does not make it less a heap.
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  25. #24  
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    to get the good view of the paradox, just see it as river rat has acertain.
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  26. #25  
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    Quote Originally Posted by Harold14370 View Post
    ...... What is the problem?
    .......

    Paradox or philosophies aside, the problem to old pragmatic me is: some heaps smell bad! jocular
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  27. #26  
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    Quote Originally Posted by merumario View Post
    If anybody thinks that this paradox is a misconception of language,then he should not post.
    But that is exactly what it is. Define precisely what the word "heap" means and the so-called paradox disappears.

    There is no specific number or quantity that makes an heap.
    Why not? You can choose a number. It might be different from someone else's definition, but so what. All that means is that you will disagree on when the heap disappears. Not exactly a paradox, just the use of a vaguely defined term.

    If this is philosophy, I'm glad I am an engineer. Talking of which: it is well known that all computer programs contain at least one line of redundant code and at least one bug. This means that all programs can be reduced to a single line of code that doesn't work.
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  28. #27  
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    if i define a heap the way it pleases me,then the question needs some kind of subjective answer.in philosophy and physics,we study the whole.and untill someone says there is a general definition to the word heap,i say this remains a paradox.
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  29. #28  
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    stepping into this debate a bit late, but let's make it clear that "heapness" is not a property of sand grains, and should not be defined by the NUMBER of grains as if that was an absolute

    a heap can be defined by the emergent properties of a collection of sand grains showing "heap behaviour" - depending on sand grain properties like size or size range, roundness, presence or absence of humidity etc., heap behaviour will become apparent at varying numbers of sand grains, and with it the amount of sand at which you can call the assemblage a heap

    remember, a paradox is only a paradox if you accept the underlying assumptions that lead to it - change those assumptions and the paradox disappears
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  30. #29  
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    Quote Originally Posted by precious View Post
    sir, see, your this post has made this thread meaningful. thanks
    That's why he is the Boss.

    jocular
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  31. #30 Paradoxes "Paradox" Me 
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    When a paradox prevents me from pragmatic conclusion, I seek other entertainment! jocular
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