How To Crack The Mysterious Sorites Paradox

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The Sorites paradox doesn’t refer to an individual paradox, but a family of paradoxes. The paradox identifies a weakness in the way we apply predicates to objects – ‘tall’, ‘red’ and ‘bald’ for example. These predicates are not clearly defined, and exist as somewhat vague, or relational concepts in our minds.

 

 

An Example Of The Paradox Itself

  1. A grain of sand is not a heap of sand.
  2. Adding one grain of sand to any collection of sand grains which is not already a heap cannot cause there to be a heap of sand on its own.
  3. Say I have a grain of sand, and add one more grain to it. I do not have a heap as per 1 & 2.
  4. Say I have two grains of sand, and I add one more to it. I do not have a heap as per 1, 2 & 3.
  5. …..
  6. Therefore I can have a collection of one million grains of sand all on top of each other and it not be a heap. But it is a heap. Because the premises are valid and the argument is sound, a paradox entails.

(The ‘…..’ represents a list of premises that aren’t written down but the pattern makes it clear what they would be.)

Clearly, this family of paradoxes represents a serious issue to how we use our language, and the status of classical logic. It calls into question the legitimacy of our predication of many things. So how can we get around it?

My Response To The Sorites Paradox

There reason I believe that the Sorites paradox fails is because it points towards a failure in our language that simply doesn’t exist. The paradox is calling for a sharp cut off point at which a non-heap becomes a heap. This elusive cut-off point doesn’t exist, and doesn’t need to exist. As such we should not question classical logic when we fail to find it.

Intuitively, the idea is this: there could be a collection of grains of sand of which it is simply true to say that they form a heap. There’s another collection of sand grains of which it is incorrect to say that they form a heap.

But there may also be some collections of sand which fall somewhere in the middle. When someone claims that one of them is a heap, they haven’t said a truth; but neither have they said anything false. Just so, if you say that one of them is not a heap, you haven’t said anything true, but you haven’t said anything false. The linguistic rules for predicating the term ‘heap’ do not offer a verdict for these collections of sand — it is ‘undefined’ when it comes to them.

If you think about the way in which we intend to use language, this seems plausible. We have to be able to use the word heap to differentiate between one group of collections of sand grains, the heaps, and to determine of other collections that they don’t belong to the same group. Our intention is not to provide a comprehensive division of every pile of sand into two camps, the heaps and the non-heaps.

How does this response relate to the Sorites paradox?

Consider one of the premises hidden by the …. earlier. For example,

‘Say I have two hundred grains of sand, and I add one more to it. I do not have a heap’.

This premise fits the profile of one of the ‘middle’ premises, which are in fact ‘undefined’. In virtue of this indefinability, it is no longer viable to claim that this premise is ‘true’. Therefore, the paradox is no longer a sound argument, and thus fails in its attempt to undermine the validity of classical logic and linguistic predication. This response to the Sorites paradox may be called the ‘Truth-Value Gap’ response.

 


 

I first came across this paradox in a book I read in preparation for University. The book is called ‘Paradoxes’ by R.M. Sainsbury, and I would recommend it for anyone looking to read an accessible and interesting introduction into the world of logic, paradox and reason. You can buy this book below:

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4 Comments

  1. Heap of sand.
    Pile of dirt.
    Pride of lions.
    Flock of birds.
    Gaggle of geese.
    Murder of crows.
    Crowd of persons.
    Puddle of water.
    How many drops of water from the sky to be considered rain?
    White defined by not white. Hot defined by not hot.
    Who’s reflection in the puddle? They decided it all.

    Welcome to dualism 101.

  2. I agree with TomA above. I wrote a post about the Sorites Problem a few weeks ago that included this observation near the end:

    “This is all part of an inherent problem that I now see lies behind many philosophical difficulties. It comes from trying to impose binary TRUE/FALSE logic on an analog world, which is really the result of seeing the universe as something static and unchanging rather than as the dynamic and fluid thing that it is.”

    http://www.evphil.com/blog/response-to-thought-experiment-94-the-sorites-tax

  3. Your preferred solution does ‘undermine the validity of classical logic’; or at least it diverges from classical logic. The law of excluded middle is a theorem of classical logic. It says that every proposition is either true or not true. But you are claiming that certain premises in the sorites have this status, when you embrace truth-value gaps.

  4. It’s also a point of view. To the ant 200 grains of sand would constitute a heap. To the mole, maybe yes, maybe no. To the human, not at all.

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