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Heap of Sand Paradox


Sand from Pismo Beach, California.

Sand from Pismo Beach, California via Wikipedia

The Heap of Sand Paradox is a problem posed in philosophy, originally attributed to the Greek thinker and harsh critic of Aristotle, Eubulides (4th century BCE).

Eubulides conceived of many different types of paradoxes, including the Liar paradox, which is similar to the well-known Cretan Liar paradox.

In a nutshell, Eubulides’ heap of sand paradox asks at what precise point a heap of sand no longer is a heap when a single grain of sand is repeatedly removed from a pile.

This is similar to Zeno‘s grain of millet paradox.

The heap of sand paradox may seem trite to some but it raises important questions about moral judgments based on the quantity or intensity of a characteristic or action.

For instance, one could ask at what precise point art becomes pornography, jesting becomes abuse, poking becomes assaulting, hugging becomes groping, and so on.

The heap of sand paradox also poses potentially complicated questions about the nature of valid reasoning and the often ambiguous role of representational symbols (such as numbers, characters and language) in logical problem solving.¹

¹ See for instance, the discussion here:

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6 thoughts on “Heap of Sand Paradox

  1. supervenience provides a basic sort of explanation for the heap of sand paradox, but i’m more inclined to say it’s semantics, or relative. this is evidenced by the fact that if two people observing the pile should have contradicting views on whether it constitutes a ‘heap’ yet, there is no reason to believe one person is mistaken. this same principle applies to the other examples you gave, one man sees art, another pornography. of course the grains of sand are objectively always just many grains of sand, but at some point some people might label it as something other than this.


  2. Very interesting, thank you. I’m relatively new to Western phil. and just read about ‘supervenience.’ Could you please explain (for me and probably quite a few others) a bit how the idea of supervenience provides a basic explanation for the heap of sand pdx.?

    Also, could we say that one person copying another person’s original computer data (e.g. an article or image) is a type of supervenience? The copy would be identical but different, not unlike the El Greco example given here:

    Your comments and clarifications on these points would be appreciated.


  3. See in GOOGLE what Matilde Macagno said in London Review of Books


  4. This can be explained satisfactorily based on the approach whether is Top to Bottom or in the other way if one want to see the so call at what point? means the threshold then you have to be very careful with the reference fro which you want to consider it because either you ca see or grasp practically from one side of the event or process and i dont think the sand model has some thing to do with this its just the manifestation which some of the so called big brains had started because i all the process which we do scientifically are totally independent of what you think about them and they very rarely they match your intuition and the problems what you highlighted bellow must not be solved based on the mapping bases- i e considering there exists a one to one correspondents between to things which are totally different so , the approach and questions are more like trying to connect some thing called sand model which every knows quite interesting with the other similar analogies. And according to me in such exampled situations one has to look at the psychological part rather than the abstract ideas which will not tell you the answer but they make you fell like there is some thing even after repeated trials.


  5. One thing what i found after reading this… is

    follow the link :


  6. Thanks for the interesting comments and link. Appreciated.


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