Friday Philosophy: Sorites Paradox

In what I hope will be a regular series, I want to think about a new philosophical question each Friday. This isn’t stuff I’ve thought about deeply or for a long time, so please feel free to make suggestions or corrections.

A pile of sand in a builder's yardThe Sorites paradox is also called the heap paradox.

Imagine a pile of sand. If I remove one grain of sand from the pile, do I still have a pile of sand? Well, of course, removing one grain of sand isn’t going to change the pile significantly.

So for any pile, I can remove one grain without producing a non-pile. But then if I keep removing grains of sand, I’ll end up with nothing – and surely we couldn’t say that is a pile!

The Sorites paradox is the most famous thought experiment in the philosophical study of vagueness. Vagueness is the study of concepts such as ‘pile’, or ‘tall’ or ‘rich’. In fact, almost all predicates seem to display a degree of vagueness.

Some philosophical approaches to vagueness include:

  • There is a particular minimum number of grains of sand that constitute a ‘pile’. Fewer than this number is not a pile.
  • There is a minimum number of grains in a pile, but nobody can know how many that is, exactly. So our association of ‘pile’ with a particular collection of grains is a probabilistic guess.
  • Pile is not a predicate. There can be groups of sand that have greater or lesser degrees of ‘pile-ness’. As you remove grains the collection becomes less of a pile, until eventually one should not call it a pile at all.
  • The collection of grains of sand is a pile if a reasonable number of people would call it a pile.

Any of these resonate? I think I operate mostly with the fourth approach, but all of them seem fair to me. I haven’t looked deeply into each one though, to see where the problems lie. I was fascinated, reading about the paradox, because classification is such a fundamental part of how we represent knowledge. I believe that classification is a double-edged sword: often making important differences appear more minor than they are.



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9 responses to “Friday Philosophy: Sorites Paradox

  1. I work with government permitting a lot and they tend to assign common words as technical terms and the literature of course assumes you understand it is a technical term, not the vaguer defintion.

    I find myself balking at that kind of labeling because it seems arbitrary (which it is of course!). I naturally want to argue with the definition and make it fit into this category:

    The collection of grains of sand is a pile if a reasonable number of people would call it a pile.

    I have to remind myself the arbitrary label might serve a purpose. But the person using the technical definition should explain that up front and state their definition is arbitrary. Othewise people likely assume they are using the colloquial meaning.

  2. Ian

    I can see that there’d be some cases where there is an explicit and documented number of grains in a pile. Yes. But I agree, it would be a pain if it weren’t made explicit.

  3. Boz


    My first reaction was “who really gives a crap if something is a pile/tall/rich or not”.

    Does this issue of vagueness apply to more worldly concepts, that deserve more serious consideration that whether a group of sand grains can be called a pile? Can you give examples?

  4. Ian

    I think almost any predicate is vague to some extent.

    For example if you commission a supplier to provide you with good quality widgets. Then there will be vagueness in that. And, as attr said, you have to try to get the vagueness out of the specification.

    I think it also raises the issue of classification generally, which is used all the time. It is how we abstract away from details to talk about higher level concepts. If you want to talk about genes, for example, you have to abstract away a whole bunch of complications. It is worth remembering that a ‘gene’ is itself a somewhat vague concept.

    But mostly I think it is useful on its own terms. We use language all the time, and one of the key functions of philosophy, afaic, is to challenge us to think about things we think we know, but that buckle under scrutiny.

  5. I see language primary as a persuasion tool.
    For persuasive purposes, the more buy-in you get from a listener, the better.
    Thus language is fluid and functional.
    Attempts to make language truthful are thus fraught with difficulty since language is more about relationship than truth.
    So, thinking off the cuff, I agree with a modified version on #4:\

    The collection of grains of sand is a pile if a two or more people agree to call it a pile.

    Language is negotiation.

  6. Ian

    @sabio. Yes, on reflection I think this is akin to saying that the concept of a pile (independent of the word) only exists as a linguistic form. So there is no ‘underlying’ pile-ness beyond statements made about it in some language. That strikes me as a quite Wittensteinian thing to think. It is the language that constructs the reality.

    The first three options try to deal with pile-ness a little more abstractly. In attr’s case, there’s a good use-case for that. Pile-ness matters because it can be converted into other structures (including the bottom line on a balance-sheet).

  7. “Language is negotiation.” -Sabio

    NOW WE’RE GETTING SOMEWHERE!!! AWESOME! that is fantastic. of course, many ppl want exact speech, but speech is wrot with metaphor and allegory and illusion. some ppl are pointers in their communication, others are painters. i think i’m more of a painter, wanting to get an image in your head and then see what you do with the interpretation. i get bored with numbers and trying to be too exact. i’d use pile where Boz may use “45 cubic yards of sand.” a pile i can picture, a cubic yard i can’t…. well, not as fast as pile anyway.

    we see this paradox when thinking about time… like a concept of infinity. it’s a real concept but very hard to comprehend… like if you divide infinity in half, you still get infinity. mind bender. good stuff dawg! really exciting post and good comments afterwards.

  8. Wesley Barrios

    When is a grain of sand too small (dust), or too big (pebble), or too elongated, or otherwise irregular to BE a “grain” of sand? You got yourself a non-pile of non-grains of “sand”.

  9. Ian

    Aren’t you just observing that language is inherently vague in the Sorites sense? I’d suggest you read the comment thread it deals with a lot of the general applicability to language.

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